281 ideas
| 8349 | The best way to do ontology is to make sense of our normal talk [Davidson] |
| Full Idea: I do not know any better way of showing what there is than looking at the assumptions needed to make sense of our normal talk. | |
| From: Donald Davidson (Causal Relations [1967], §4) | |
| A reaction: Davidson was a pupil of Quine. This I take to be the last flowering of twentieth century linguistic philosophy. The ontology we deduce from talk in a children's playground might be very bizarre, but we are unlikely to endorse it. 'Honest, it's true!' |
| 8868 | Objective truth arises from interpersonal communication [Davidson] |
| Full Idea: The source of the concept of objective truth is interpersonal communication. | |
| From: Donald Davidson (Three Varieties of Knowledge [1991], p.209) | |
| A reaction: This is a distinctively Davidsonian idea, arising out of Wittgenstein's Private Language Argument. We could go a step further, and just say that 'objectivity is a social concept'. Davidson more or less pleads guilty to pragmatism in this essay. |
| 3969 | There are no ultimate standards of rationality, since we only assess others by our own standard [Davidson] |
| Full Idea: It makes no sense to speak of comparing or agreeing on ultimate standards of rationality, since it is our own standards in each case to which we must turn in interpreting others. This is not a failure of objectivity, but where 'questions come to an end'. | |
| From: Donald Davidson (Davidson on himself [1994], p.232) | |
| A reaction: This seems wrong, given the commitment to truth and charity in interpretation. He could have said the same about perception, but I doubt if he would. |
| 3972 | Truth and objectivity depend on a community of speakers to interpret what they mean [Davidson] |
| Full Idea: The basis on which the concepts of truth and objectivity depend for application is a community of understanding, agreement among speakers on how each is to be understood. | |
| From: Donald Davidson (Davidson on himself [1994], p.233) | |
| A reaction: Obviously all understanding is, in practice, an interpretation by a community, but that isn't what 'truth' means. We mean 'true independently of any community'. |
| 18137 | Impredicative definitions are wrong, because they change the set that is being defined? [Bostock] |
| Full Idea: Poincaré suggested that what is wrong with an impredicative definition is that it allows the set defined to alter its composition as more sets are added to the theory. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) |
| 6396 | A sentence is held true because of a combination of meaning and belief [Davidson] |
| Full Idea: A sentence is held true because of two factors: what the holder takes the sentence to mean, and what he believes. | |
| From: Donald Davidson (Thought and Talk [1975], p.20) | |
| A reaction: A key question is whether a belief (e.g. an imagistic one, or one held by an animal) could be true, even though no sentence is involved. Linguistic philosophers tend to avoid this question, or assume the answer is 'no'. |
| 23295 | Truth cannot be reduced to anything simpler [Davidson] |
| Full Idea: We cannot hope to underpin the concept of truth with something more transparent or easier to grasp. | |
| From: Donald Davidson (The Folly of Trying to Define Truth [1999], p.21) | |
| A reaction: I suppose precise accounts of correspondence or coherence are offered as replacements for truth, but neither of those ever seem to be possible. I agree with accepting truth as a primitive. |
| 19160 | A comprehensive theory of truth probably includes a theory of predication [Davidson] |
| Full Idea: Theories of truth and theories of predication are closely related: it seems probable that any comprehensive theory of truth will include a theory of predication. | |
| From: Donald Davidson (Truth and Predication [2005], 6) | |
| A reaction: Davidson defends the view that it is this way round. It is tempting to label them both as 'primitive'. Davidson distinguishes a 'theory' about truth from a 'definition'. |
| 23284 | Plato's Forms confused truth with the most eminent truths, so only Truth itself is completely true [Davidson] |
| Full Idea: Plato's conflation of abstract universals with entities of supreme value reinforced the confusion of truth with the most eminent truths. …The only perfect exemplar of a Form is the Form itself, …and only truth itself is completely true. | |
| From: Donald Davidson (Truth Rehabilitated [1997], p.3) | |
| A reaction: Even non-subscribers to Plato often talk as if there were some grand thing called the Truth with a capital T, quite often used in a religious context. Truth is the hallmark of successful (non-fanciful) thought. |
| 23286 | Truth can't be a goal, because we can neither recognise it nor confim it [Davidson] |
| Full Idea: Since it is neither visible as a target, nor recognisable when achieved, there is no point in calling truth a goal. We should only aim at increasing confidence in our beliefs, by collecting further evidence or checking our calculations. | |
| From: Donald Davidson (Truth Rehabilitated [1997], P.6) | |
| A reaction: This is mainly aimed at pragmatists, but Davidson obviously subscribes (as do I) to their fallibilist view of knowledge. |
| 19151 | Antirealism about truth prevents its use as an intersubjective standard [Davidson] |
| Full Idea: Antirealism, with its limitations of truth to what can be ascertained, deprives truth of its role as an intersubjective standard. | |
| From: Donald Davidson (Truth and Predication [2005], 2) | |
| A reaction: I like this, because it lifts truth out of individual minds. I take truth to be an ideal - a simple one with little content, which is thus fairly uncontroversial. Truth is the main general purpose of thinking. |
| 23291 | Without truth, both language and thought are impossible [Davidson] |
| Full Idea: Without a grasp of the concept of truth, not only language, but thought itself, is impossible. | |
| From: Donald Davidson (Truth Rehabilitated [1997], p.16) | |
| A reaction: Davidson never mentions animals, but I like this idea because it points to importance of truth for animals as well. I say that truth is relevant to any mind that makes judgements - and quite small animals (e.g. ants and spiders) make judgements. |
| 8188 | Davidson takes truth to attach to individual sentences [Davidson, by Dummett] |
| Full Idea: Davidson, by contrast to Frege, has taken truth as attaching to linguistic items, that is, to actual or hypothetical token sentences. | |
| From: report of Donald Davidson (True to the Facts [1969]) by Michael Dummett - Truth and the Past 1 | |
| A reaction: My personal notion of truth is potentially applicable to animals, so this doesn't appeal to me. I am happy to think of animals as believing simple propositions that never get as far as language, and being right or wrong about them. |
| 19144 | 'Epistemic' truth depends what rational creatures can verify [Davidson] |
| Full Idea: The 'epistemic' view of truth asserts an essential tie to epistemology, and introduces a dependence of truth on what can somehow be verified by finite rational creatures. | |
| From: Donald Davidson (Truth and Predication [2005], 2) | |
| A reaction: This view, which seems to be widely held, strikes me as an elementary confusion. I take truth to be fully successful belief. If you say belief can never be fully successful, then we can't know the truth - but that doesn't destroy the concept of truth. |
| 19044 | Saying truths fit experience adds nothing to truth; nothing makes sentences true [Davidson] |
| Full Idea: The notion of fitting the totality of experience ...adds nothing intelligible to the simple concept of being true. ....Nothing, ...no thing, makes sentences and theories true: not experience, not surface irritations, not the world. | |
| From: Donald Davidson (The Very Idea of a Conceptual Scheme [1974], p.11), quoted by Willard Quine - On the Very Idea of a Third Dogma p.39 | |
| A reaction: If you don't have a concept of what normally makes a sentence true, I don't see how you go about distinguishing what is true from what is false. You can't just examine the sentence to see if it has the 'primitive' property of truth. Holism is involved.... |
| 23292 | Correspondence can't be defined, but it shows how truth depends on the world [Davidson] |
| Full Idea: Correspondence, while it is empty as a definition, does capture the thought that truth depends on how the world is. | |
| From: Donald Davidson (Truth Rehabilitated [1997], p.16) | |
| A reaction: Just don't try to give a precise account of the correspondence between two things (thoughts and facts) which are so utterly different in character. |
| 18702 | Names, descriptions and predicates refer to things; without that, language and thought are baffling [Davidson] |
| Full Idea: The simple thesis that names and descriptions often refer to things, and that predicates often have an extension in the world of things, is obvious, and essential to the most elementary appreciation of both language and the thoughts we express. | |
| From: Donald Davidson (Replies to Critics [1998], p.323) | |
| A reaction: In 1983 Davidson had been a rare modern champion of the coherence theory of truth, but this is his clearest later renunciation of that view (and quite right too). |
| 18902 | Correspondence theories can't tell you what truths correspond to [Davidson] |
| Full Idea: The real objection to correspondence theories is that such theories fail to provide entities to which truth vehicles (as statements, sentence, or utterances) can be said to correspond. | |
| From: Donald Davidson (The Structure and Content of Truth [1990], p.304), quoted by Fred Sommers - Intellectual Autobiography Notes 23 | |
| A reaction: This is the remark which provoked Sommers to come out with Idea 18901, which strikes me as rather profound. |
| 23298 | Neither Aristotle nor Tarski introduce the facts needed for a correspondence theory [Davidson] |
| Full Idea: Neither Aristotle's formula nor Tarski's truth definitions are sympathetic to the correspondence theory, because they don't introduce entities like facts or states of affairs for sentences to correspond. | |
| From: Donald Davidson (The Folly of Trying to Define Truth [1999], p.25) | |
| A reaction: This seems convincing, although it is often claimed that both theories offer a sort of correspondence. |
| 19148 | There is nothing interesting or instructive for truths to correspond to [Davidson] |
| Full Idea: The real objection to the correspondence theory of truth is that there is nothing interesting or instructive to which true sentences correspond. (C.I. Lewis challenged defenders to locate the fact or part of reality to which a truth corresponded). | |
| From: Donald Davidson (Truth and Predication [2005], 2) | |
| A reaction: Davidson defended a correspondence view in 'True to the Facts'. Davidson evidently also thinks the same objection applies to claims about truthmakers. If you say 'gold is shiny', the gold is very dispersed, but it is still there. |
| 19166 | The Slingshot assumes substitutions give logical equivalence, and thus identical correspondence [Davidson] |
| Full Idea: The Slingshot argument (of Frege, Church and Gödel) assumes that if two sentences are logically equivalent, they correspond to the same thing, and what a sentence corresponds to is not changed if a singular term is replaced by a coreferring term. | |
| From: Donald Davidson (Truth and Predication [2005], 6) | |
| A reaction: This obviously won't work for 'Oedipus thinks he ought to marry Jocasta'. Sentences correspond, I presume, to what they are about, which is often a matter of emphasis or phrasing. Hence the Slingshot sounds like nonsense to me. |
| 19167 | Two sentences can be rephrased by equivalent substitutions to correspond to the same thing [Davidson] |
| Full Idea: Slingshot: 'Scott is the author of Waverley' and 'The number of counties in Utah is twenty-nine' can be rephrased by substitution so that they are both about the number twenty-nine, and are thus correspond to the same thing. | |
| From: Donald Davidson (Truth and Predication [2005], 6) | |
| A reaction: [my paraphrase of Davidson's quote from Church 1956:24] These sentences clearly do not correspond to the same thing, so something has gone wrong with the idea that logically equivalent sentences have identical correspondents. |
| 19081 | Coherence with a set of propositions suggests we can know the proposition corresponds [Davidson, by Donnellan] |
| Full Idea: Davidson argues that the coherence of a set of propositions with a set of beliefs is a good indication that the proposition corresponds to objective facts and that we can know that propositions correspond. | |
| From: report of Donald Davidson (Coherence Theory of Truth and Knowledge [1983]) by Keith Donnellan - Putting Humpty Dumpty Together Again §2.2 | |
| A reaction: Young calls this an 'epistemological route to coherentism'. Davidson is sometimes cited as a fan of the coherence theory of truth, but this just seems to accept Russell's point that coherence is a good test for truth. |
| 19150 | Coherence truth says a consistent set of sentences is true - which ties truth to belief [Davidson] |
| Full Idea: A pure coherence theory of truth says that all sentences in a consistent set of sentences are true. ...I class this with epistemic views, because it ties truth directly to what is believed. | |
| From: Donald Davidson (Truth and Predication [2005], 2) | |
| A reaction: [He cites Neurath] I would have thought that coherence is rather more than mere consistency. Truths which have nothing whatever in common can be consistent with one another. [but see his p.43 n14] |
| 19145 | We can explain truth in terms of satisfaction - but also explain satisfaction in terms of truth [Davidson] |
| Full Idea: Truth is easily defined in terms of satisfaction (as Tarski showed), but, alternatively, satisfaction can be taken to be whatever relation yields a correct account of truth. | |
| From: Donald Davidson (Truth and Predication [2005], 2) | |
| A reaction: Davidson is assessing which is the prior 'primitive' concept, and he votes for truth. A perennial problem in philosophy, and very hard to find reasons for a preference. The axiomatic approach grows from taking truth as primitive. Axioms for satisfaction? |
| 19146 | Satisfaction is a sort of reference, so maybe we can define truth in terms of reference? [Davidson] |
| Full Idea: That the truth of sentences is defined by appeal to the semantic properties of words suggests that, if we could give an account of the semantic properties of words (essentially, of reference or satisfaction), we would understand the concept of truth. | |
| From: Donald Davidson (Truth and Predication [2005], 2) | |
| A reaction: If you thought that words were prior to sentences, this might be the route to go. Davidson gives priority to sentences, and so prefers to work from the other end, which treats truth as primitive, and then defines reference and meaning. |
| 19174 | Axioms spell out sentence satisfaction. With no free variables, all sequences satisfy the truths [Davidson] |
| Full Idea: Axioms specify how each unstructured predicate is satisfied by a particular sequence. Then recursive axioms characterise complex sentences built from simpler ones. Closed sentences have no free variables, so true sentences are satisfied by all sequences. | |
| From: Donald Davidson (Truth and Predication [2005], 7) | |
| A reaction: I take 'all sequences' to mean all combinations of objects in the domain. Thus nothing in domain contradicts the satisfied sentences. Hence Tarski's truth is said to be 'true in a model', where the whole system vouches for the sentence. |
| 23288 | When Tarski defines truth for different languages, how do we know it is a single concept? [Davidson] |
| Full Idea: We have to wonder how we know that it is some single concept which Tarski indicates how to define for each of a number of well-behaved languages. | |
| From: Donald Davidson (Truth Rehabilitated [1997], P.11) | |
| A reaction: Davidson says that Tarski makes the assumption that it is a single concept, but fails to demonstrate the fact. This resembles Frege's Julius Caesar problem - of how you know whether your number definition has defined a number. |
| 23297 | The language to define truth needs a finite vocabulary, to make the definition finite [Davidson] |
| Full Idea: If the definition of the truth predicate is to be finite (Tarski insisted on this), the definition must take advantage of the fact that sentences, though potentially infinite in number, are constructed from a finite vocabulary. | |
| From: Donald Davidson (The Folly of Trying to Define Truth [1999], p.23) | |
| A reaction: Not sure whether this is in the object language or the meta-language, though I guess the former. |
| 19136 | Many say that Tarski's definitions fail to connect truth to meaning [Davidson] |
| Full Idea: It is complained that Tarski's definitions do not establish the connection between truth and meaning that many philosophers hold to be essential. | |
| From: Donald Davidson (Truth and Predication [2005], 1) | |
| A reaction: This, of course, was Davidson's big mission - to build on Tarski's theory a view of truth which dovetailed it with theories of meaning and reference. |
| 19139 | Tarski does not tell us what his various truth predicates have in common [Davidson] |
| Full Idea: There is no indication in Tarski's formal work of what it is that his various truth predicates have in common, and this is part of the content of the concept. | |
| From: Donald Davidson (Truth and Predication [2005], 1) | |
| A reaction: This seems like a good question to raise. If I list all the 'red' things, I can still ask what qualifies them to all appear on the same list. |
| 19147 | Truth is the basic concept, because Convention-T is agreed to fix the truths of a language [Davidson] |
| Full Idea: The key role of Convention-T in determining that truth, as characterised by the theory, has the same extension as the intuitive concept of truth makes it seem that it is truth rather than reference that is the basic primitive. | |
| From: Donald Davidson (Truth and Predication [2005], 2) | |
| A reaction: The key strength of Tarski's account is that it specifies the extension of 'true' for a given language (as expressed in a richer meta-language). |
| 19172 | To define a class of true sentences is to stipulate a possible language [Davidson] |
| Full Idea: When we enquire whether a truth definition defines the class of true sentences in a particular language, we are thinking of the truth definition as stipulating a possible language. | |
| From: Donald Davidson (Truth and Predication [2005], 7) | |
| A reaction: Thus I might say "Nij wonk yang" is true if and only if snow is white, and make my first step towards a new language. An interesting way of looking at Tarski's project. |
| 23296 | We can elucidate indefinable truth, but showing its relation to other concepts [Davidson] |
| Full Idea: We can still say revealing things about truth, by relating it to other concepts like belief, desire, cause and action. | |
| From: Donald Davidson (The Folly of Trying to Define Truth [1999], p.21) | |
| A reaction: The trickiest concept to link it to is meaning. I think Davidson's view points to the Axiomatic account of truth, which flourished soon after Davidson wrote this. We can give rules for the correct use of 'true'. |
| 19153 | Truth is basic and clear, so don't try to replace it with something simpler [Davidson] |
| Full Idea: Truth is one of the clearest and most basic concepts we have, so it is fruitless to dream of eliminating it in favor of something simpler or more fundamental. | |
| From: Donald Davidson (Truth and Predication [2005], 3) | |
| A reaction: For redundancy theorists, I suppose, truth would be eliminated in favour of 'assertion'. Replacing it with 'satisfaction' doesn't seem very illuminating. Davidson would say 'reference' is more tricky and elusive than truth. |
| 19170 | Tarski is not a disquotationalist, because you can assign truth to a sentence you can't quote [Davidson] |
| Full Idea: It is clearly a mistake to call Tarski a disquotationalist. ...We say of a sentence not at hand (such as 'You gave the right answer to this question last night, but I can't remember what you said') that it is true or false. | |
| From: Donald Davidson (Truth and Predication [2005], 7) |
| 23287 | Disquotation only accounts for truth if the metalanguage contains the object language [Davidson] |
| Full Idea: Disquotation cannot pretend to give a complete account of the concept of truth, since it works only in the special case where the metalanguage contains the object language. Neither can contain their own truth predicate. | |
| From: Donald Davidson (Truth Rehabilitated [1997], p.10) | |
| A reaction: Presumably more sophisticated and complete accounts would need a further account of translation between languages - which explains Quine's interest in that topic. […see this essay, p.12] |
| 13439 | Venn Diagrams map three predicates into eight compartments, then look for the conclusion [Bostock] |
| Full Idea: Venn Diagrams are a traditional method to test validity of syllogisms. There are three interlocking circles, one for each predicate, thus dividing the universe into eight possible basic elementary quantifications. Is the conclusion in a compartment? | |
| From: David Bostock (Intermediate Logic [1997], 3.8) |
| 13422 | 'Conjunctive Normal Form' is ensuring that no disjunction has a conjunction within its scope [Bostock] |
| Full Idea: 'Conjunctive Normal Form' (CNF) is rearranging the occurrences of ∧ and ∨ so that no disjunction sign has any conjunction in its scope. This is achieved by applying two of the distribution laws. | |
| From: David Bostock (Intermediate Logic [1997], 2.6) |
| 13421 | 'Disjunctive Normal Form' is ensuring that no conjunction has a disjunction within its scope [Bostock] |
| Full Idea: 'Disjunctive Normal Form' (DNF) is rearranging the occurrences of ∧ and ∨ so that no conjunction sign has any disjunction in its scope. This is achieved by applying two of the distribution laws. | |
| From: David Bostock (Intermediate Logic [1997], 2.6) |
| 13355 | 'Disjunction' says that Γ,φ∨ψ|= iff Γ,φ|= and Γ,ψ|= [Bostock] |
| Full Idea: The Principle of Disjunction says that Γ,φ∨ψ |= iff Γ,φ |= and Γ,ψ |=. | |
| From: David Bostock (Intermediate Logic [1997], 2.5.G) | |
| A reaction: That is, a disjunction leads to a contradiction if they each separately lead to contradictions. |
| 13356 | The 'conditional' is that Γ|=φ→ψ iff Γ,φ|=ψ [Bostock] |
| Full Idea: The Conditional Principle says that Γ |= φ→ψ iff Γ,φ |= ψ. With the addition of negation, this implies φ,φ→ψ |= ψ, which is 'modus ponens'. | |
| From: David Bostock (Intermediate Logic [1997], 2.5.H) | |
| A reaction: [Second half is in Ex. 2.5.4] |
| 13350 | 'Assumptions' says that a formula entails itself (φ|=φ) [Bostock] |
| Full Idea: The Principle of Assumptions says that any formula entails itself, i.e. φ |= φ. The principle depends just upon the fact that no interpretation assigns both T and F to the same formula. | |
| From: David Bostock (Intermediate Logic [1997], 2.5.A) | |
| A reaction: Thus one can introduce φ |= φ into any proof, and then use it to build more complex sequents needed to attain a particular target formula. Bostock's principle is more general than anything in Lemmon. |
| 13351 | 'Thinning' allows that if premisses entail a conclusion, then adding further premisses makes no difference [Bostock] |
| Full Idea: The Principle of Thinning says that if a set of premisses entails a conclusion, then adding further premisses will still entail the conclusion. It is 'thinning' because it makes a weaker claim. If γ|=φ then γ,ψ|= φ. | |
| From: David Bostock (Intermediate Logic [1997], 2.5.B) | |
| A reaction: It is also called 'premise-packing'. It is the characteristic of a 'monotonic' logic - where once something is proved, it stays proved, whatever else is introduced. |
| 13352 | 'Cutting' allows that if x is proved, and adding y then proves z, you can go straight to z [Bostock] |
| Full Idea: The Principle of Cutting is the general point that entailment is transitive, extending this to cover entailments with more than one premiss. Thus if γ |= φ and φ,Δ |= ψ then γ,Δ |= ψ. Here φ has been 'cut out'. | |
| From: David Bostock (Intermediate Logic [1997], 2.5.C) | |
| A reaction: It might be called the Principle of Shortcutting, since you can get straight to the last conclusion, eliminating the intermediate step. |
| 13353 | 'Negation' says that Γ,¬φ|= iff Γ|=φ [Bostock] |
| Full Idea: The Principle of Negation says that Γ,¬φ |= iff Γ |= φ. We also say that φ,¬φ |=, and hence by 'thinning on the right' that φ,¬φ |= ψ, which is 'ex falso quodlibet'. | |
| From: David Bostock (Intermediate Logic [1997], 2.5.E) | |
| A reaction: That is, roughly, if the formula gives consistency, the negation gives contradiction. 'Ex falso' says that anything will follow from a contradiction. |
| 13354 | 'Conjunction' says that Γ|=φ∧ψ iff Γ|=φ and Γ|=ψ [Bostock] |
| Full Idea: The Principle of Conjunction says that Γ |= φ∧ψ iff Γ |= φ and Γ |= ψ. This implies φ,ψ |= φ∧ψ, which is ∧-introduction. It is also implies ∧-elimination. | |
| From: David Bostock (Intermediate Logic [1997], 2.5.F) | |
| A reaction: [Second half is Ex. 2.5.3] That is, if they are entailed separately, they are entailed as a unit. It is a moot point whether these principles are theorems of propositional logic, or derivation rules. |
| 13610 | A logic with ¬ and → needs three axiom-schemas and one rule as foundation [Bostock] |
| Full Idea: For ¬,→ Schemas: (A1) |-φ→(ψ→φ), (A2) |-(φ→(ψ→ξ)) → ((φ→ψ)→(φ→ξ)), (A3) |-(¬φ→¬ψ) → (ψ→φ), Rule:DET:|-φ,|-φ→ψ then |-ψ | |
| From: David Bostock (Intermediate Logic [1997], 5.2) | |
| A reaction: A1 says everything implies a truth, A2 is conditional proof, and A3 is contraposition. DET is modus ponens. This is Bostock's compact near-minimal axiom system for proposition logic. He adds two axioms and another rule for predicate logic. |
| 18122 | Classical interdefinitions of logical constants and quantifiers is impossible in intuitionism [Bostock] |
| Full Idea: None of the classical ways of defining one logical constant in terms of others is available in intuitionist logic (and this includes the two quantifiers). | |
| From: David Bostock (Philosophy of Mathematics [2009], 7.2) |
| 13846 | A 'free' logic can have empty names, and a 'universally free' logic can have empty domains [Bostock] |
| Full Idea: A 'free' logic is one in which names are permitted to be empty. A 'universally free' logic is one in which the domain of an interpretation may also be empty. | |
| From: David Bostock (Intermediate Logic [1997], 8.6) |
| 18114 | There is no single agreed structure for set theory [Bostock] |
| Full Idea: There is so far no agreed set of axioms for set theory which is categorical, i.e. which does pick just one structure. | |
| From: David Bostock (Philosophy of Mathematics [2009], 6.4) | |
| A reaction: This contrasts with Peano Arithmetic, which is categorical in its second-order version. |
| 18107 | A 'proper class' cannot be a member of anything [Bostock] |
| Full Idea: A 'proper class' cannot be a member of anything, neither of a set nor of another proper class. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.4) |
| 18115 | We could add axioms to make sets either as small or as large as possible [Bostock] |
| Full Idea: We could add the axiom that all sets are constructible (V = L), making the universe of sets as small as possible, or add the axiom that there is a supercompact cardinal (SC), making the universe as large as we no know how to. | |
| From: David Bostock (Philosophy of Mathematics [2009], 6.4) | |
| A reaction: Bostock says most mathematicians reject the first option, and are undecided about the second option. |
| 18139 | The Axiom of Choice relies on reference to sets that we are unable to describe [Bostock] |
| Full Idea: The usual accounts of ZF are not restricted to subsets that we can describe, and that is what justifies the axiom of choice. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.4 n36) | |
| A reaction: This contrasts interestingly with predicativism, which says we can only discuss things which we can describe or define. Something like verificationism hovers in the background. |
| 18105 | Replacement enforces a 'limitation of size' test for the existence of sets [Bostock] |
| Full Idea: The Axiom of Replacement (or the Axiom of Subsets, 'Aussonderung', Fraenkel 1922) in effect enforces the idea that 'limitation of size' is a crucial factor when deciding whether a proposed set or does not not exist. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.4) |
| 18108 | First-order logic is not decidable: there is no test of whether any formula is valid [Bostock] |
| Full Idea: First-order logic is not decidable. That is, there is no test which can be applied to any arbitrary formula of that logic and which will tell one whether the formula is or is not valid (as proved by Church in 1936). | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.5) |
| 18109 | The completeness of first-order logic implies its compactness [Bostock] |
| Full Idea: From the fact that the usual rules for first-level logic are complete (as proved by Gödel 1930), it follows that this logic is 'compact'. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.5) | |
| A reaction: The point is that the completeness requires finite proofs. |
| 13545 | Elementary logic cannot distinguish clearly between the finite and the infinite [Bostock] |
| Full Idea: In very general terms, we cannot express the distinction between what is finite and what is infinite without moving essentially beyond the resources available in elementary logic. | |
| From: David Bostock (Intermediate Logic [1997], 4.8) | |
| A reaction: This observation concludes a discussion of Compactness in logic. |
| 13346 | Truth is the basic notion in classical logic [Bostock] |
| Full Idea: The most fundamental notion in classical logic is that of truth. | |
| From: David Bostock (Intermediate Logic [1997], 1.1) | |
| A reaction: The opening sentence of his book. Hence the first half of the book is about semantics, and only the second half deals with proof. Compare Idea 10282. The thought seems to be that you could leave out truth, but that makes logic pointless. |
| 13822 | Fictional characters wreck elementary logic, as they have contradictions and no excluded middle [Bostock] |
| Full Idea: Discourse about fictional characters leads to a breakdown of elementary logic. We accept P or ¬P if the relevant story says so, but P∨¬P will not be true if the relevant story says nothing either way, and P∧¬P is true if the story is inconsistent. | |
| From: David Bostock (Intermediate Logic [1997], 8.5) | |
| A reaction: I really like this. Does one need to invent a completely new logic for fictional characters? Or must their logic be intuitionist, or paraconsistent, or both? |
| 13623 | The syntactic turnstile |- φ means 'there is a proof of φ' or 'φ is a theorem' [Bostock] |
| Full Idea: The syntactic turnstile |- φ means 'There is a proof of φ' (in the system currently being considered). Another way of saying the same thing is 'φ is a theorem'. | |
| From: David Bostock (Intermediate Logic [1997], 5.1) |
| 13349 | Γ|=φ is 'entails'; Γ|= is 'is inconsistent'; |=φ is 'valid' [Bostock] |
| Full Idea: If we write Γ |= φ, with one formula to the right, then the turnstile abbreviates 'entails'. For a sequent of the form Γ |= it can be read as 'is inconsistent'. For |= φ we read it as 'valid'. | |
| From: David Bostock (Intermediate Logic [1997], 1.3) |
| 13347 | Validity is a conclusion following for premises, even if there is no proof [Bostock] |
| Full Idea: The classical definition of validity counts an argument as valid if and only if the conclusion does in fact follow from the premises, whether or not the argument contains any demonstration of this fact. | |
| From: David Bostock (Intermediate Logic [1997], 1.2) | |
| A reaction: Hence validity is given by |= rather than by |-. A common example is 'it is red so it is coloured', which seems true but beyond proof. In the absence of formal proof, you wonder whether validity is merely a psychological notion. |
| 13348 | It seems more natural to express |= as 'therefore', rather than 'entails' [Bostock] |
| Full Idea: In practice we avoid quotation marks and explicitly set-theoretic notation that explaining |= as 'entails' appears to demand. Hence it seems more natural to explain |= as simply representing the word 'therefore'. | |
| From: David Bostock (Intermediate Logic [1997], 1.3) | |
| A reaction: Not sure I quite understand that, but I have trained myself to say 'therefore' for the generic use of |=. In other consequences it seems better to read it as 'semantic consequence', to distinguish it from |-. |
| 13614 | MPP: 'If Γ|=φ and Γ|=φ→ψ then Γ|=ψ' (omit Γs for Detachment) [Bostock] |
| Full Idea: The Rule of Detachment is a version of Modus Ponens, and says 'If |=φ and |=φ→ψ then |=ψ'. This has no assumptions. Modus Ponens is the more general rule that 'If Γ|=φ and Γ|=φ→ψ then Γ|=ψ'. | |
| From: David Bostock (Intermediate Logic [1997], 5.3) | |
| A reaction: Modus Ponens is actually designed for use in proof based on assumptions (which isn't always the case). In Detachment the formulae are just valid, without dependence on assumptions to support them. |
| 13617 | MPP is a converse of Deduction: If Γ |- φ→ψ then Γ,φ|-ψ [Bostock] |
| Full Idea: Modus Ponens is equivalent to the converse of the Deduction Theorem, namely 'If Γ |- φ→ψ then Γ,φ|-ψ'. | |
| From: David Bostock (Intermediate Logic [1997], 5.3) | |
| A reaction: See 13615 for details of the Deduction Theorem. See 13614 for Modus Ponens. |
| 13799 | The sign '=' is a two-place predicate expressing that 'a is the same thing as b' (a=b) [Bostock] |
| Full Idea: We shall use 'a=b' as short for 'a is the same thing as b'. The sign '=' thus expresses a particular two-place predicate. Officially we will use 'I' as the identity predicate, so that 'Iab' is as formula, but we normally 'abbreviate' this to 'a=b'. | |
| From: David Bostock (Intermediate Logic [1997], 8.1) |
| 13800 | |= α=α and α=β |= φ(α/ξ ↔ φ(β/ξ) fix identity [Bostock] |
| Full Idea: We usually take these two principles together as the basic principles of identity: |= α=α and α=β |= φ(α/ξ) ↔ φ(β/ξ). The second (with scant regard for history) is known as Leibniz's Law. | |
| From: David Bostock (Intermediate Logic [1997], 8.1) |
| 13803 | If we are to express that there at least two things, we need identity [Bostock] |
| Full Idea: To say that there is at least one thing x such that Fx we need only use an existential quantifier, but to say that there are at least two things we need identity as well. | |
| From: David Bostock (Intermediate Logic [1997], 8.1) | |
| A reaction: The only clear account I've found of why logic may need to be 'with identity'. Without it, you can only reason about one thing or all things. Presumably plural quantification no longer requires '='? |
| 7332 | There is a huge range of sentences of which we do not know the logical form [Davidson] |
| Full Idea: We do not know the logical form of sentences about counterfactuals, probabilities, causal relations, belief, perception, intention, purposeful action, imperatives, optatives, or interrogatives, or the role of adverbs, adjectives or mass terms. | |
| From: Donald Davidson (Truth and Meaning [1967], p.35) | |
| A reaction: [compressed] This is the famous 'Davidson programme', where teams of philosophers work out the logical forms for this lot, thus unravelling the logic of the world. If they are beavering away, some sort of overview should have emerged by now... |
| 13357 | Truth-functors are usually held to be defined by their truth-tables [Bostock] |
| Full Idea: The usual view of the meaning of truth-functors is that each is defined by its own truth-table, independently of any other truth-functor. | |
| From: David Bostock (Intermediate Logic [1997], 2.7) |
| 13812 | A 'zero-place' function just has a single value, so it is a name [Bostock] |
| Full Idea: We can talk of a 'zero-place' function, which is a new-fangled name for a familiar item; it just has a single value, and so it has the same role as a name. | |
| From: David Bostock (Intermediate Logic [1997], 8.2) |
| 13811 | A 'total' function ranges over the whole domain, a 'partial' function over appropriate inputs [Bostock] |
| Full Idea: Usually we allow that a function is defined for arguments of a suitable kind (a 'partial' function), but we can say that each function has one value for any object whatever, from the whole domain that our quantifiers range over (a 'total' function). | |
| From: David Bostock (Intermediate Logic [1997], 8.2) | |
| A reaction: He points out (p.338) that 'the father of..' is a functional expression, but it wouldn't normally take stones as input, so seems to be a partial function. But then it doesn't even take all male humans either. It only takes fathers! |
| 13360 | In logic, a name is just any expression which refers to a particular single object [Bostock] |
| Full Idea: The important thing about a name, for logical purposes, is that it is used to make a singular reference to a particular object; ..we say that any expression too may be counted as a name, for our purposes, it it too performs the same job. | |
| From: David Bostock (Intermediate Logic [1997], 3.1) | |
| A reaction: He cites definite descriptions as the most notoriously difficult case, in deciding whether or not they function as names. I takes it as pretty obvious that sometimes they do and sometimes they don't (in ordinary usage). |
| 13361 | An expression is only a name if it succeeds in referring to a real object [Bostock] |
| Full Idea: An expression is not counted as a name unless it succeeds in referring to an object, i.e. unless there really is an object to which it refers. | |
| From: David Bostock (Intermediate Logic [1997], 3.1) | |
| A reaction: His 'i.e.' makes the existence condition sound sufficient, but in ordinary language you don't succeed in referring to 'that man over there' just because he exists. In modal contexts we presumably refer to hypothetical objects (pace Lewis). |
| 13813 | Definite descriptions don't always pick out one thing, as in denials of existence, or errors [Bostock] |
| Full Idea: It is natural to suppose one only uses a definite description when one believes it describes only one thing, but exceptions are 'there is no such thing as the greatest prime number', or saying something false where the reference doesn't occur. | |
| From: David Bostock (Intermediate Logic [1997], 8.3) |
| 13814 | Definite desciptions resemble names, but can't actually be names, if they don't always refer [Bostock] |
| Full Idea: Although a definite description looks like a complex name, and in many ways behaves like a name, still it cannot be a name if names must always refer to objects. Russell gave the first proposal for handling such expressions. | |
| From: David Bostock (Intermediate Logic [1997], 8.3) | |
| A reaction: I take the simple solution to be a pragmatic one, as roughly shown by Donnellan, that sometimes they are used exactly like names, and sometimes as something else. The same phrase can have both roles. Confusing for logicians. Tough. |
| 13816 | Because of scope problems, definite descriptions are best treated as quantifiers [Bostock] |
| Full Idea: Because of the scope problem, it now seems better to 'parse' definition descriptions not as names but as quantifiers. 'The' is to be treated in the same category as acknowledged quantifiers like 'all' and 'some'. We write Ix - 'for the x such that..'. | |
| From: David Bostock (Intermediate Logic [1997], 8.3) | |
| A reaction: This seems intuitively rather good, since quantification in normal speech is much more sophisticated than the crude quantification of classical logic. But the fact is that they often function as names (but see Idea 13817). |
| 13817 | Definite descriptions are usually treated like names, and are just like them if they uniquely refer [Bostock] |
| Full Idea: In practice, definite descriptions are for the most part treated as names, since this is by far the most convenient notation (even though they have scope). ..When a description is uniquely satisfied then it does behave like a name. | |
| From: David Bostock (Intermediate Logic [1997], 8.3) | |
| A reaction: Apparent names themselves have problems when they wander away from uniquely picking out one thing, as in 'John Doe'. |
| 13848 | We are only obliged to treat definite descriptions as non-names if only the former have scope [Bostock] |
| Full Idea: If it is really true that definite descriptions have scopes whereas names do not, then Russell must be right to claim that definite descriptions are not names. If, however, this is not true, then it does no harm to treat descriptions as complex names. | |
| From: David Bostock (Intermediate Logic [1997], 8.8) |
| 13815 | Names do not have scope problems (e.g. in placing negation), but Russell's account does have that problem [Bostock] |
| Full Idea: In orthodox logic names are not regarded as having scope (for example, in where a negation is placed), whereas on Russell's theory definite descriptions certainly do. Russell had his own way of dealing with this. | |
| From: David Bostock (Intermediate Logic [1997], 8.3) |
| 13438 | 'Prenex normal form' is all quantifiers at the beginning, out of the scope of truth-functors [Bostock] |
| Full Idea: A formula is said to be in 'prenex normal form' (PNF) iff all its quantifiers occur in a block at the beginning, so that no quantifier is in the scope of any truth-functor. | |
| From: David Bostock (Intermediate Logic [1997], 3.7) | |
| A reaction: Bostock provides six equivalences which can be applied to manouevre any formula into prenex normal form. He proves that every formula can be arranged in PNF. |
| 18914 | Davidson controversially proposed to quantify over events [Davidson, by Engelbretsen] |
| Full Idea: An alternative, and still controversial, extension of first-order logic is due to Donald Davidson, who allows for quantification over events. | |
| From: report of Donald Davidson (The Individuation of Events [1969]) by George Engelbretsen - Trees, Terms and Truth 3 | |
| A reaction: I'm suddenly thinking this is quite an attractive proposal. We need to quantify over facts, or states of affairs, or events, or some such thing, to talk about the world properly. Objects, predicates and sets/parts is too sparse. I like facts. |
| 13818 | If we allow empty domains, we must allow empty names [Bostock] |
| Full Idea: We can show that if empty domains are permitted, then empty names must be permitted too. | |
| From: David Bostock (Intermediate Logic [1997], 8.4) |
| 18123 | Substitutional quantification is just standard if all objects in the domain have a name [Bostock] |
| Full Idea: Substitutional quantification and quantification understood in the usual 'ontological' way will coincide when every object in the (ontological) domain has a name. | |
| From: David Bostock (Philosophy of Mathematics [2009], 7.3 n23) |
| 13801 | An 'informal proof' is in no particular system, and uses obvious steps and some ordinary English [Bostock] |
| Full Idea: An 'informal proof' is not in any particular proof system. One may use any rule of proof that is 'sufficiently obvious', and there is quite a lot of ordinary English in the proof, explaining what is going on at each step. | |
| From: David Bostock (Intermediate Logic [1997], 8.1) |
| 13619 | Quantification adds two axiom-schemas and a new rule [Bostock] |
| Full Idea: New axiom-schemas for quantifiers: (A4) |-∀ξφ → φ(α/ξ), (A5) |-∀ξ(ψ→φ) → (ψ→∀ξφ), plus the rule GEN: If |-φ the |-∀ξφ(ξ/α). | |
| From: David Bostock (Intermediate Logic [1997], 5.6) | |
| A reaction: This follows on from Idea 13610, where he laid out his three axioms and one rule for propositional (truth-functional) logic. This Idea plus 13610 make Bostock's proposed axiomatisation of first-order logic. |
| 13622 | Axiom systems from Frege, Russell, Church, Lukasiewicz, Tarski, Nicod, Kleene, Quine... [Bostock] |
| Full Idea: Notably axiomatisations of first-order logic are by Frege (1879), Russell and Whitehead (1910), Church (1956), Lukasiewicz and Tarski (1930), Lukasiewicz (1936), Nicod (1917), Kleene (1952) and Quine (1951). Also Bostock (1997). | |
| From: David Bostock (Intermediate Logic [1997], 5.8) | |
| A reaction: My summary, from Bostock's appendix 5.8, which gives details of all of these nine systems. This nicely illustrates the status and nature of axiom systems, which have lost the absolute status they seemed to have in Euclid. |
| 13615 | 'Conditonalised' inferences point to the Deduction Theorem: If Γ,φ|-ψ then Γ|-φ→ψ [Bostock] |
| Full Idea: If a group of formulae prove a conclusion, we can 'conditionalize' this into a chain of separate inferences, which leads to the Deduction Theorem (or Conditional Proof), that 'If Γ,φ|-ψ then Γ|-φ→ψ'. | |
| From: David Bostock (Intermediate Logic [1997], 5.3) | |
| A reaction: This is the rule CP (Conditional Proof) which can be found in the rules for propositional logic I transcribed from Lemmon's book. |
| 13616 | The Deduction Theorem greatly simplifies the search for proof [Bostock] |
| Full Idea: Use of the Deduction Theorem greatly simplifies the search for proof (or more strictly, the task of showing that there is a proof). | |
| From: David Bostock (Intermediate Logic [1997], 5.3) | |
| A reaction: See 13615 for details of the Deduction Theorem. Bostock is referring to axiomatic proof, where it can be quite hard to decide which axioms are relevant. The Deduction Theorem enables the making of assumptions. |
| 13620 | Proof by Assumptions can always be reduced to Proof by Axioms, using the Deduction Theorem [Bostock] |
| Full Idea: By repeated transformations using the Deduction Theorem, any proof from assumptions can be transformed into a fully conditionalized proof, which is then an axiomatic proof. | |
| From: David Bostock (Intermediate Logic [1997], 5.6) | |
| A reaction: Since proof using assumptions is perhaps the most standard proof system (e.g. used in Lemmon, for many years the standard book at Oxford University), the Deduction Theorem is crucial for giving it solid foundations. |
| 13621 | The Deduction Theorem and Reductio can 'discharge' assumptions - they aren't needed for the new truth [Bostock] |
| Full Idea: Like the Deduction Theorem, one form of Reductio ad Absurdum (If Γ,φ|-[absurdity] then Γ|-¬φ) 'discharges' an assumption. Assume φ and obtain a contradiction, then we know ¬&phi, without assuming φ. | |
| From: David Bostock (Intermediate Logic [1997], 5.7) | |
| A reaction: Thus proofs from assumption either arrive at conditional truths, or at truths that are true irrespective of what was initially assumed. |
| 13753 | Natural deduction takes proof from assumptions (with its rules) as basic, and axioms play no part [Bostock] |
| Full Idea: Natural deduction takes the notion of proof from assumptions as a basic notion, ...so it will use rules for use in proofs from assumptions, and axioms (as traditionally understood) will have no role to play. | |
| From: David Bostock (Intermediate Logic [1997], 6.1) | |
| A reaction: The main rules are those for introduction and elimination of truth functors. |
| 13755 | Excluded middle is an introduction rule for negation, and ex falso quodlibet will eliminate it [Bostock] |
| Full Idea: Many books take RAA (reductio) and DNE (double neg) as the natural deduction introduction- and elimination-rules for negation, but RAA is not a natural introduction rule. I prefer TND (tertium) and EFQ (ex falso) for ¬-introduction and -elimination. | |
| From: David Bostock (Intermediate Logic [1997], 6.2) |
| 13758 | In natural deduction we work from the premisses and the conclusion, hoping to meet in the middle [Bostock] |
| Full Idea: When looking for a proof of a sequent, the best we can do in natural deduction is to work simultaneously in both directions, forward from the premisses, and back from the conclusion, and hope they will meet in the middle. | |
| From: David Bostock (Intermediate Logic [1997], 6.5) |
| 13754 | Natural deduction rules for → are the Deduction Theorem (→I) and Modus Ponens (→E) [Bostock] |
| Full Idea: Natural deduction adopts for → as rules the Deduction Theorem and Modus Ponens, here called →I and →E. If ψ follows φ in the proof, we can write φ→ψ (→I). φ and φ→ψ permit ψ (→E). | |
| From: David Bostock (Intermediate Logic [1997], 6.2) | |
| A reaction: Natural deduction has this neat and appealing way of formally introducing or eliminating each connective, so that you know where you are, and you know what each one means. |
| 18120 | The Deduction Theorem is what licenses a system of natural deduction [Bostock] |
| Full Idea: The Deduction Theorem is what licenses a system of 'natural deduction' in the first place. | |
| From: David Bostock (Philosophy of Mathematics [2009], 7.2) |
| 13756 | A tree proof becomes too broad if its only rule is Modus Ponens [Bostock] |
| Full Idea: When the only rule of inference is Modus Ponens, the branches of a tree proof soon spread too wide for comfort. | |
| From: David Bostock (Intermediate Logic [1997], 6.4) |
| 13757 | Unlike natural deduction, semantic tableaux have recipes for proving things [Bostock] |
| Full Idea: With semantic tableaux there are recipes for proof-construction that we can operate, whereas with natural deduction there are not. | |
| From: David Bostock (Intermediate Logic [1997], 6.5) |
| 13762 | Tableau rules are all elimination rules, gradually shortening formulae [Bostock] |
| Full Idea: In their original setting, all the tableau rules are elimination rules, allowing us to replace a longer formula by its shorter components. | |
| From: David Bostock (Intermediate Logic [1997], 7.3) |
| 13611 | Tableau proofs use reduction - seeking an impossible consequence from an assumption [Bostock] |
| Full Idea: A tableau proof is a proof by reduction ad absurdum. One begins with an assumption, and one develops the consequences of that assumption, seeking to derive an impossible consequence. | |
| From: David Bostock (Intermediate Logic [1997], 4.1) |
| 13612 | Non-branching rules add lines, and branching rules need a split; a branch with a contradiction is 'closed' [Bostock] |
| Full Idea: Rules for semantic tableaus are of two kinds - non-branching rules and branching rules. The first allow the addition of further lines, and the second requires splitting the branch. A branch which assigns contradictory values to a formula is 'closed'. | |
| From: David Bostock (Intermediate Logic [1997], 4.1) | |
| A reaction: [compressed] Thus 'and' stays on one branch, asserting both formulae, but 'or' splits, checking first one and then the other. A proof succeeds when all the branches are closed, showing that the initial assumption leads only to contradictions. |
| 13613 | A completed open branch gives an interpretation which verifies those formulae [Bostock] |
| Full Idea: An open branch in a completed tableau will always yield an interpretation that verifies every formula on the branch. | |
| From: David Bostock (Intermediate Logic [1997], 4.7) | |
| A reaction: In other words the open branch shows a model which seems to work (on the available information). Similarly a closed branch gives a model which won't work - a counterexample. |
| 13761 | In a tableau proof no sequence is established until the final branch is closed; hypotheses are explored [Bostock] |
| Full Idea: In a tableau system no sequent is established until the final step of the proof, when the last branch closes, and until then we are simply exploring a hypothesis. | |
| From: David Bostock (Intermediate Logic [1997], 7.3) | |
| A reaction: This compares sharply with a sequence calculus, where every single step is a conclusive proof of something. So use tableaux for exploring proofs, and then sequence calculi for writing them up? |
| 13760 | A sequent calculus is good for comparing proof systems [Bostock] |
| Full Idea: A sequent calculus is a useful tool for comparing two systems that at first look utterly different (such as natural deduction and semantic tableaux). | |
| From: David Bostock (Intermediate Logic [1997], 7.2) |
| 13759 | Each line of a sequent calculus is a conclusion of previous lines, each one explicitly recorded [Bostock] |
| Full Idea: A sequent calculus keeps an explicit record of just what sequent is established at each point in a proof. Every line is itself the sequent proved at that point. It is not a linear sequence or array of formulae, but a matching array of whole sequents. | |
| From: David Bostock (Intermediate Logic [1997], 7.1) |
| 13364 | Interpretation by assigning objects to names, or assigning them to variables first [Bostock, by PG] |
| Full Idea: There are two approaches to an 'interpretation' of a logic: the first method assigns objects to names, and then defines connectives and quantifiers, focusing on truth; the second assigns objects to variables, then variables to names, using satisfaction. | |
| From: report of David Bostock (Intermediate Logic [1997], 3.4) by PG - Db (lexicon) | |
| A reaction: [a summary of nine elusive pages in Bostock] He says he prefers the first method, but the second method is more popular because it handles open formulas, by treating free variables as if they were names. |
| 19140 | 'Satisfaction' is a generalised form of reference [Davidson] |
| Full Idea: We can think of 'satisfaction' as a generalised form of reference. | |
| From: Donald Davidson (Truth and Predication [2005], 2) | |
| A reaction: Just the sort of simple point we novices need from the great minds, to help us see what is going on. One day someone is going to explain Tarski's account of truth in plain English, but probably not in my lifetime. |
| 13821 | Extensionality is built into ordinary logic semantics; names have objects, predicates have sets of objects [Bostock] |
| Full Idea: Extensionality is built into the semantics of ordinary logic. When a name-letter is interpreted as denoting something, we just provide the object denoted. All that we provide for a one-place predicate-letter is the set of objects that it is true of.. | |
| From: David Bostock (Intermediate Logic [1997]) | |
| A reaction: Could we keep the syntax of ordinary logic, and provide a wildly different semantics, much closer to real life? We could give up these dreadful 'objects' that Frege lumbered us with. Logic for processes, etc. |
| 13362 | If an object has two names, truth is undisturbed if the names are swapped; this is Extensionality [Bostock] |
| Full Idea: If two names refer to the same object, then in any proposition which contains either of them the other may be substituted in its place, and the truth-value of the proposition of the proposition will be unaltered. This is the Principle of Extensionality. | |
| From: David Bostock (Intermediate Logic [1997], 3.1) | |
| A reaction: He acknowledges that ordinary language is full of counterexamples, such as 'he doesn't know the Morning Star and the Evening Star are the same body' (when he presumably knows that the Morning Star is the Morning Star). This is logic. Like maths. |
| 13541 | For 'negation-consistent', there is never |-(S)φ and |-(S)¬φ [Bostock] |
| Full Idea: Any system of proof S is said to be 'negation-consistent' iff there is no formula such that |-(S)φ and |-(S)¬φ. | |
| From: David Bostock (Intermediate Logic [1997], 4.5) | |
| A reaction: Compare Idea 13542. This version seems to be a 'strong' version, as it demands a higher standard than 'absolute consistency'. Both halves of the condition would have to be established. |
| 13540 | A set of formulae is 'inconsistent' when there is no interpretation which can make them all true [Bostock] |
| Full Idea: 'Γ |=' means 'Γ is a set of closed formulae, and there is no (standard) interpretation in which all of the formulae in Γ are true'. We abbreviate this last to 'Γ is inconsistent'. | |
| From: David Bostock (Intermediate Logic [1997], 4.5) | |
| A reaction: This is a semantic approach to inconsistency, in terms of truth, as opposed to saying that we cannot prove both p and ¬p. I take this to be closer to the true concept, since you need never have heard of 'proof' to understand 'inconsistent'. |
| 13542 | A proof-system is 'absolutely consistent' iff we don't have |-(S)φ for every formula [Bostock] |
| Full Idea: Any system of proof S is said to be 'absolutely consistent' iff it is not the case that for every formula we have |-(S)φ. | |
| From: David Bostock (Intermediate Logic [1997], 4.5) | |
| A reaction: Bostock notes that a sound system will be both 'negation-consistent' (Idea 13541) and absolutely consistent. 'Tonk' systems can be shown to be unsound because the two come apart. |
| 13544 | Inconsistency or entailment just from functors and quantifiers is finitely based, if compact [Bostock] |
| Full Idea: Being 'compact' means that if we have an inconsistency or an entailment which holds just because of the truth-functors and quantifiers involved, then it is always due to a finite number of the propositions in question. | |
| From: David Bostock (Intermediate Logic [1997], 4.8) | |
| A reaction: Bostock says this is surprising, given the examples 'a is not a parent of a parent of b...' etc, where an infinity seems to establish 'a is not an ancestor of b'. The point, though, is that this truth doesn't just depend on truth-functors and quantifiers. |
| 13618 | Compactness means an infinity of sequents on the left will add nothing new [Bostock] |
| Full Idea: The logic of truth-functions is compact, which means that sequents with infinitely many formulae on the left introduce nothing new. Hence we can confine our attention to finite sequents. | |
| From: David Bostock (Intermediate Logic [1997], 5.5) | |
| A reaction: This makes it clear why compactness is a limitation in logic. If you want the logic to be unlimited in scope, it isn't; it only proves things from finite numbers of sequents. This makes it easier to prove completeness for the system. |
| 18125 | Berry's Paradox considers the meaning of 'The least number not named by this name' [Bostock] |
| Full Idea: Berry's Paradox can be put in this form, by considering the alleged name 'The least number not named by this name'. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.1) |
| 18101 | Each addition changes the ordinality but not the cardinality, prior to aleph-1 [Bostock] |
| Full Idea: If you add to the ordinals you produce many different ordinals, each measuring the length of the sequence of ordinals less than it. They each have cardinality aleph-0. The cardinality eventually increases, but we can't say where this break comes. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.5) |
| 18100 | ω + 1 is a new ordinal, but its cardinality is unchanged [Bostock] |
| Full Idea: If we add ω onto the end of 0,1,2,3,4..., it then has a different length, of ω+1. It has a different ordinal (since it can't be matched with its first part), but the same cardinal (since adding 1 makes no difference). | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.5) | |
| A reaction: [compressed] The ordinals and cardinals coincide up to ω, but this is the point at which they come apart. |
| 18102 | A cardinal is the earliest ordinal that has that number of predecessors [Bostock] |
| Full Idea: It is the usual procedure these days to identify a cardinal number with the earliest ordinal number that has that number of predecessors. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.5) | |
| A reaction: This sounds circular, since you need to know the cardinal in order to decide which ordinal is the one you want, but, hey, what do I know? |
| 18106 | Aleph-1 is the first ordinal that exceeds aleph-0 [Bostock] |
| Full Idea: The cardinal aleph-1 is identified with the first ordinal to have more than aleph-0 members, and so on. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.4) | |
| A reaction: That is, the succeeding infinite ordinals all have the same cardinal number of members (aleph-0), until the new total is triggered (at the number of the reals). This is Continuum Hypothesis territory. |
| 18095 | Instead of by cuts or series convergence, real numbers could be defined by axioms [Bostock] |
| Full Idea: In addition to cuts, or converging series, Cantor suggests we can simply lay down a set of axioms for the real numbers, and this can be done without any explicit mention of the rational numbers [note: the axioms are those for a complete ordered field]. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.4) | |
| A reaction: It is interesting when axioms are best, and when not. Set theory depends entirely on axioms. Horsten and Halbach are now exploring treating truth as axiomatic. You don't give the 'nature' of the thing - just rules for its operation. |
| 18099 | The number of reals is the number of subsets of the natural numbers [Bostock] |
| Full Idea: It is not difficult to show that the number of the real numbers is the same as the number of all the subsets of the natural numbers. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.5) | |
| A reaction: The Continuum Hypothesis is that this is the next infinite number after the number of natural numbers. Why can't there be a number which is 'most' of the subsets of the natural numbers? |
| 18093 | For Eudoxus cuts in rationals are unique, but not every cut makes a real number [Bostock] |
| Full Idea: As Eudoxus claimed, two distinct real numbers cannot both make the same cut in the rationals, for any two real numbers must be separated by a rational number. He did not say, though, that for every such cut there is a real number that makes it. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.4) | |
| A reaction: This is in Bostock's discussion of Dedekind's cuts. It seems that every cut is guaranteed to produce a real. Fine challenges the later assumption. |
| 18110 | Infinitesimals are not actually contradictory, because they can be non-standard real numbers [Bostock] |
| Full Idea: Non-standard natural numbers will yield non-standard rational and real numbers. These will include reciprocals which will be closer to 0 than any standard real number. These are like 'infinitesimals', so that notion is not actually a contradiction. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.5) |
| 18156 | Modern axioms of geometry do not need the real numbers [Bostock] |
| Full Idea: A modern axiomatisation of geometry, such as Hilbert's (1899), does not need to claim the existence of real numbers anywhere in its axioms. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.B.5.ii) | |
| A reaction: This is despite the fact that geometry is reduced to algebra, and the real numbers are the equivalent of continuous lines. Bostock votes for a Greek theory of proportion in this role. |
| 18097 | The Peano Axioms describe a unique structure [Bostock] |
| Full Idea: The Peano Axioms are categorical, meaning that they describe a unique structure. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.4 n20) | |
| A reaction: So if you think there is nothing more to the natural numbers than their structure, then the Peano Axioms give the essence of arithmetic. If you think that 'objects' must exist to generate a structure, there must be more to the numbers. |
| 13358 | Ordinary or mathematical induction assumes for the first, then always for the next, and hence for all [Bostock] |
| Full Idea: The principle of mathematical (or ordinary) induction says suppose the first number, 0, has a property; suppose that if any number has that property, then so does the next; then it follows that all numbers have the property. | |
| From: David Bostock (Intermediate Logic [1997], 2.8) | |
| A reaction: Ordinary induction is also known as 'weak' induction. Compare Idea 13359 for 'strong' or complete induction. The number sequence must have a first element, so this doesn't work for the integers. |
| 13359 | Complete induction assumes for all numbers less than n, then also for n, and hence for all numbers [Bostock] |
| Full Idea: The principle of complete induction says suppose that for every number, if all the numbers less than it have a property, then so does it; it then follows that every number has the property. | |
| From: David Bostock (Intermediate Logic [1997], 2.8) | |
| A reaction: Complete induction is also known as 'strong' induction. Compare Idea 13358 for 'weak' or mathematical induction. The number sequence need have no first element. |
| 18148 | Hume's Principle is a definition with existential claims, and won't explain numbers [Bostock] |
| Full Idea: Hume's Principle will not do as an implicit definition because it makes a positive claim about the size of the universe (which no mere definition can do), and because it does not by itself explain what the numbers are. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) |
| 18145 | Many things will satisfy Hume's Principle, so there are many interpretations of it [Bostock] |
| Full Idea: Hume's Principle gives a criterion of identity for numbers, but it is obvious that many other things satisfy that criterion. The simplest example is probably the numerals (in any notation, decimal, binary etc.), giving many different interpretations. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) |
| 18149 | There are many criteria for the identity of numbers [Bostock] |
| Full Idea: There is not just one way of giving a criterion of identity for numbers. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) |
| 18143 | Frege makes numbers sets to solve the Caesar problem, but maybe Caesar is a set! [Bostock] |
| Full Idea: The Julius Caesar problem was one reason that led Frege to give an explicit definition of numbers as special sets. He does not appear to notice that the same problem affects his Axiom V for introducing sets (whether Caesar is or is not a set). | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) | |
| A reaction: The Julius Caesar problem is a sceptical acid that eats into everything in philosophy of mathematics. You give all sorts of wonderful accounts of numbers, but at what point do you know that you now have a number, and not something else? |
| 18116 | Numbers can't be positions, if nothing decides what position a given number has [Bostock] |
| Full Idea: There is no ground for saying that a number IS a position, if the truth is that there is nothing to determine which number is which position. | |
| From: David Bostock (Philosophy of Mathematics [2009], 6.4) | |
| A reaction: If numbers lose touch with the empirical ability to count physical objects, they drift off into a mad world where they crumble away. |
| 18117 | Structuralism falsely assumes relations to other numbers are numbers' only properties [Bostock] |
| Full Idea: Structuralism begins from a false premise, namely that numbers have no properties other than their relations to other numbers. | |
| From: David Bostock (Philosophy of Mathematics [2009], 6.5) | |
| A reaction: Well said. Describing anything purely relationally strikes me as doomed, because you have to say why those things relate in those ways. |
| 18141 | Nominalism about mathematics is either reductionist, or fictionalist [Bostock] |
| Full Idea: Nominalism has two main versions, one which tries to 'reduce' the objects of mathematics to something simpler (Russell and Wittgenstein), and another which claims that such objects are mere 'fictions' which have no reality (Field). | |
| From: David Bostock (Philosophy of Mathematics [2009], 9) |
| 18157 | Nominalism as based on application of numbers is no good, because there are too many applications [Bostock] |
| Full Idea: The style of nominalism which aims to reduce statements about numbers to statements about their applications does not work for the natural numbers, because they have many applications, and it is arbitrary to choose just one of them. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.B.5.iii) |
| 18150 | Actual measurement could never require the precision of the real numbers [Bostock] |
| Full Idea: We all know that in practice no physical measurement can be 100 per cent accurate, and so it cannot require the existence of a genuinely irrational number, rather than some of the rational numbers close to it. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.3) |
| 18158 | Ordinals are mainly used adjectively, as in 'the first', 'the second'... [Bostock] |
| Full Idea: The basic use of the ordinal numbers is their use as ordinal adjectives, in phrases such as 'the first', 'the second' and so on. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.5.iii) | |
| A reaction: That is because ordinals seem to attach to particulars, whereas cardinals seem to attach to groups. Then you say 'three is greater than four', it is not clear which type you are talking about. |
| 18127 | Simple type theory has 'levels', but ramified type theory has 'orders' [Bostock] |
| Full Idea: The simple theory of types distinguishes sets into different 'levels', but this is quite different from the distinction into 'orders' which is imposed by the ramified theory. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.1) | |
| A reaction: The ramified theory has both levels and orders (p.235). Russell's terminology is, apparently, inconsistent. |
| 18147 | Neo-logicists meet the Caesar problem by saying Hume's Principle is unique to number [Bostock] |
| Full Idea: The response of neo-logicists to the Julius Caesar problem is to strengthen Hume's Principle in the hope of ensuring that only numbers will satisfy it. They say the criterion of identity provided by HP is essential to number, and not to anything else. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) |
| 18144 | Neo-logicists agree that HP introduces number, but also claim that it suffices for the job [Bostock] |
| Full Idea: The neo-logicists take up Frege's claim that Hume's Principle introduces a new concept (of a number), but unlike Frege they go on to claim that it by itself gives a complete account of that concept. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) | |
| A reaction: So the big difference between Frege and neo-logicists is the Julius Caesar problem. |
| 18111 | Treating numbers as objects doesn't seem like logic, since arithmetic fixes their totality [Bostock] |
| Full Idea: If logic is neutral on the number of objects there are, then logicists can't construe numbers as objects, for arithmetic is certainly not neutral on the number of numbers there are. They must be treated in some other way, perhaps as numerical quantifiers. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.5) |
| 18146 | If Hume's Principle is the whole story, that implies structuralism [Bostock] |
| Full Idea: If Hume's Principle is all we are given, by way of explanation of what the numbers are, the only conclusion to draw would seem to be the structuralists' conclusion, ...studying all systems that satisfy that principle. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) | |
| A reaction: Any approach that implies a set of matching interpretations will always imply structuralism. To avoid it, you need to pin the target down uniquely. |
| 18129 | Many crucial logicist definitions are in fact impredicative [Bostock] |
| Full Idea: Many of the crucial definitions in the logicist programme are in fact impredicative. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.2) |
| 18159 | Higher cardinalities in sets are just fairy stories [Bostock] |
| Full Idea: In its higher reaches, which posit sets of huge cardinalities, set theory is just a fairy story. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.5.iii) | |
| A reaction: You can't say the higher reaches are fairy stories but the lower reaches aren't, if the higher is directly derived from the lower. The empty set and the singleton are fairy stories too. Bostock says the axiom of infinity triggers the fairy stories. |
| 18155 | A fairy tale may give predictions, but only a true theory can give explanations [Bostock] |
| Full Idea: A common view is that although a fairy tale may provide very useful predictions, it cannot provide explanations for why things happen as they do. In order to do that a theory must also be true (or, at least, an approximation to the truth). | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.B.5) | |
| A reaction: Of course, fictionalism offers an explanation of mathematics as a whole, but not of the details (except as the implications of the initial fictional assumptions). |
| 18140 | The best version of conceptualism is predicativism [Bostock] |
| Full Idea: In my personal opinion, predicativism is the best version of conceptualism that we have yet discovered. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.4) | |
| A reaction: Since conceptualism is a major player in the field, this makes predicativism a very important view. I won't vote Predicativist quite yet, but I'm tempted. |
| 18138 | Conceptualism fails to grasp mathematical properties, infinity, and objective truth values [Bostock] |
| Full Idea: Three simple objections to conceptualism in mathematics are that we do not ascribe mathematical properties to our ideas, that our ideas are presumably finite, and we don't think mathematics lacks truthvalue before we thought of it. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.4) | |
| A reaction: [compressed; Bostock refers back to his Ch 2] Plus Idea 18134. On the whole I sympathise with conceptualism, so I will not allow myself to be impressed by any of these objections. (So, what's actually wrong with them.....?). |
| 18131 | If abstracta only exist if they are expressible, there can only be denumerably many of them [Bostock] |
| Full Idea: If an abstract object exists only when there is some suitable way of expressing it, then there are at most denumerably many abstract objects. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.2) | |
| A reaction: Fine by me. What an odd view, to think there are uncountably many abstract objects in existence, only a countable portion of which will ever be expressed! [ah! most people agree with me, p.243-4] |
| 18134 | Predicativism makes theories of huge cardinals impossible [Bostock] |
| Full Idea: Classical mathematicians say predicative mathematics omits areas of great interest, all concerning non-denumerable real numbers, such as claims about huge cardinals. There cannot be a predicative version of this theory. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) | |
| A reaction: I'm not sure that anyone will really miss huge cardinals if they are prohibited, though cryptography seems to flirt with such things. Are we ever allowed to say that some entity conjured up by mathematicians is actually impossible? |
| 18135 | If mathematics rests on science, predicativism may be the best approach [Bostock] |
| Full Idea: It has been claimed that only predicative mathematics has a justification through its usefulness to science (an empiricist approach). | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) | |
| A reaction: [compressed. Quine is the obvious candidate] I suppose predicativism gives your theory roots, whereas impredicativism is playing an abstract game. |
| 18136 | If we can only think of what we can describe, predicativism may be implied [Bostock] |
| Full Idea: If we accept the initial idea that we can think only of what we ourselves can describe, then something like the theory of predicativism quite naturally results | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) | |
| A reaction: I hate the idea that we can only talk of what falls under a sortal, but 'what we can describe' is much more plausible. Whether or not you agree with this approach (I'm pondering it), this makes predicativism important. |
| 18132 | The predicativity restriction makes a difference with the real numbers [Bostock] |
| Full Idea: It is with the real numbers that the restrictions imposed by predicativity begin to make a real difference. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) |
| 18133 | The usual definitions of identity and of natural numbers are impredicative [Bostock] |
| Full Idea: The predicative approach cannot accept either the usual definition of identity or the usual definition of the natural numbers, for both of these definitions are impredicative. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) | |
| A reaction: [Bostock 237-8 gives details] |
| 7771 | We need 'events' to explain adverbs, which are adjectival predicates of events [Davidson, by Lycan] |
| Full Idea: To deal with the truth conditions for some adverbs, Davidson introduced a domain of 'events', and made adverbs into adjectival predicates of events. | |
| From: report of Donald Davidson (The Logical Form of Action Sentences [1967]) by William Lycan - Philosophy of Language Ch.9 | |
| A reaction: This seems to be a striking case of a procedure of which I heartily disapprove - deriving you ontology from your semantics. Do all languages have adverbs? |
| 8860 | Language-learning is not good enough evidence for the existence of events [Yablo on Davidson] |
| Full Idea: One needs a better reason for believing in events than the help they provide with language-learning. | |
| From: comment on Donald Davidson (The Logical Form of Action Sentences [1967], §8) by Stephen Yablo - Apriority and Existence §8 | |
| A reaction: I can almost believe in micro-events at the quantum level, but I cannot believe that the Renaissance (made of events within events within events) is an event, even though I may 'quantify over it', and discuss its causes and effects. |
| 7949 | Varied descriptions of an event will explain varied behaviour relating to it [Davidson, by Macdonald,C] |
| Full Idea: Davidson points out that we can only make sense of patterns of behaviour such as excuses if events can have more than one description. So I flip the light switch, turn on the light, illuminate the room, and alert a prowler, but I do only one thing. | |
| From: report of Donald Davidson (Action, Reasons and Causes [1963]) by Cynthia Macdonald - Varieties of Things Ch.5 | |
| A reaction: We can distinguish an event as an actual object, and as an intentional object. We can probably individuate intentional events quite well (according to our interests), but actual 'events' seem to flow into one another and overlap. |
| 8348 | If we don't assume that events exist, we cannot make sense of our common talk [Davidson] |
| Full Idea: The assumption, ontological and metaphysical, that there are events, is one without which we cannot make sense of much of our most common talk. | |
| From: Donald Davidson (Causal Relations [1967], §4) | |
| A reaction: He considers events to be unanalysable basics. Explanation of normal talk also needs ghosts, premonitions, telepathy and Father Christmas. It is extremely hard to individuate events, unless they are subatomic, and rather numerous. |
| 9843 | You can't identify events by causes and effects, as the event needs to be known first [Dummett on Davidson] |
| Full Idea: Davidson's criterion for the identity of events is a mistake, because we cannot know the causes and effects of an event until we know what that event comprises. | |
| From: comment on Donald Davidson (The Individuation of Events [1969]) by Michael Dummett - Frege philosophy of mathematics Ch.10 | |
| A reaction: How many attempts by analytical philosophers to give necessary and sufficient conditions for things seem to founder in this way. Their predecessor is at the end of 'Theaetetus'; you have to know what the sun is before you can define it. |
| 14602 | Events can only be individuated causally [Davidson, by Schaffer,J] |
| Full Idea: Davidson claims that events can only be individuated causally. | |
| From: report of Donald Davidson (The Individuation of Events [1969], 3) by Jonathan Schaffer - Causation and Laws of Nature 3 | |
| A reaction: Schaffer rejects this in favour of individuating events by their spatiotemporal locations and intrinsic natures (which seem to be property instantiations, a la Kim). Schaffer was a pupil of David Lewis. |
| 14004 | We need events for action statements, causal statements, explanation, mind-and-body, and adverbs [Davidson, by Bourne] |
| Full Idea: Davidson claims that we require the existence of events in order to make sense of a) action statements, b) causal statements, c) explanation, d) the mind-body problem, and e) the logic of adverbial modification. | |
| From: report of Donald Davidson (The Individuation of Events [1969], Intro IIb) by Craig Bourne - A Future for Presentism | |
| A reaction: Events are a nice shorthand, but I don't like them in a serious ontology. Prior says there objects and what happens to them; Kim reduces events to other things. Processes are more clearly individuated than events. |
| 8278 | The claim that events are individuated by their causal relations to other events is circular [Lowe on Davidson] |
| Full Idea: Davidson has urged that events are individuated by the causal relations which they bear to one another, in accordance with the principle that events are identical just in case they have the same causes and effects. But the principle is viciously circular. | |
| From: comment on Donald Davidson (The Individuation of Events [1969]) by E.J. Lowe - The Possibility of Metaphysics 7.4 | |
| A reaction: You wouldn't want to identify a person just by their relationships, even though those will certainly be unique. Generally it is what I am (right now) naming as the Functional Fallacy: believing that specifying the function of x explains x. |
| 23285 | If we try to identify facts precisely, they all melt into one (as the Slingshot Argument proves) [Davidson] |
| Full Idea: If we try to provide a serious semantics for reference to facts, we discover that they melt into one; there is no telling them apart. The relevant argument (the 'Slingshot') was credited to Frege by Alonso Church. | |
| From: Donald Davidson (Truth Rehabilitated [1997], p.5) | |
| A reaction: This sounds like good grounds for not attempting to be too precise. 'There are bluebells in my local wood' identifies a fact by words, but even an animal can distinguish this fact. Only a logician dreams of making its content precise. |
| 15002 | If the best theory of adverbs refers to events, then our ontology should include events [Davidson, by Sider] |
| Full Idea: Davidson argued that the best linguistic theory of adverbial modification assigns truth-conditions quantifying over events; thus we must embrace an ontology of events. | |
| From: report of Donald Davidson (The Logical Form of Action Sentences [1967]) by Theodore Sider - Writing the Book of the World 07.8 | |
| A reaction: Sider is critical and I agree. This is just the sort of linguistic manoeuvre that gets philosophy a bad name. As Yablo remarks, we have a terrible tendency to want to thingify everything. |
| 13543 | A relation is not reflexive, just because it is transitive and symmetrical [Bostock] |
| Full Idea: It is easy to fall into the error of supposing that a relation which is both transitive and symmetrical must also be reflexive. | |
| From: David Bostock (Intermediate Logic [1997], 4.7) | |
| A reaction: Compare Idea 14430! Transivity will take you there, and symmetricality will get you back, but that doesn't entitle you to take the shortcut? |
| 13802 | Relations can be one-many (at most one on the left) or many-one (at most one on the right) [Bostock] |
| Full Idea: A relation is 'one-many' if for anything on the right there is at most one on the left (∀xyz(Rxz∧Ryz→x=y), and is 'many-one' if for anything on the left there is at most one on the right (∀xyz(Rzx∧Rzy→x=y). | |
| From: David Bostock (Intermediate Logic [1997], 8.1) |
| 19173 | Treating predicates as sets drops the predicate for a new predicate 'is a member of', which is no help [Davidson] |
| Full Idea: 'Theaetetus is a member of the set of seated objects' doesn't mention the predicate 'sits', but has a new predicate 'is a member of', with no given semantic role. We are back with Plato's problem with the predicate 'instantiates'. | |
| From: Donald Davidson (Truth and Predication [2005], 7) | |
| A reaction: Plato's problem is the 'third man' problem - a regress in the explanation. In other words, if we are trying to explain predication, treating predicates as sets gets us nowhere. Just as I always thought. But you have to want explanations. |
| 13847 | If non-existent things are self-identical, they are just one thing - so call it the 'null object' [Bostock] |
| Full Idea: If even non-existent things are still counted as self-identical, then all non-existent things must be counted as identical with one another, so there is at most one non-existent thing. We might arbitrarily choose zero, or invent 'the null object'. | |
| From: David Bostock (Intermediate Logic [1997], 8.6) |
| 13820 | The idea that anything which can be proved is necessary has a problem with empty names [Bostock] |
| Full Idea: The common Rule of Necessitation says that what can be proved is necessary, but this is incorrect if we do not permit empty names. The most straightforward answer is to modify elementary logic so that only necessary truths can be proved. | |
| From: David Bostock (Intermediate Logic [1997], 8.4) |
| 19142 | Probability can be constrained by axioms, but that leaves open its truth nature [Davidson] |
| Full Idea: Kolmogorov's axiomatisation of probability puts clear constraints on the concept of probability, but leaves open whether probability is further characterised as relative frequency, degree of belief, or something else. | |
| From: Donald Davidson (Truth and Predication [2005], 2) | |
| A reaction: Davidson cites this to show the limitations of axiomatic approaches to any topic (e.g. sets, truth, arithmetic). The item in question must be treated as a 'primitive'. This always has the feeling of second-best. |
| 11145 | Having a belief involves the possibility of being mistaken [Davidson] |
| Full Idea: Someone cannot have a belief unless he understands the possibility of being mistaken. | |
| From: Donald Davidson (Thought and Talk [1975], p.170) | |
| A reaction: If you pretend to throw a ball for a dog, but don't release it, the dog experiences being mistaken very dramatically. |
| 8806 | The concepts of belief and truth are linked, since beliefs are meant to fit reality [Davidson] |
| Full Idea: Knowing what a belief is brings with it the concept of objective truth, for the notion of a belief is the notion of a state that may or may not jibe with reality. | |
| From: Donald Davidson (Coherence Theory of Truth and Knowledge [1983], p.162) | |
| A reaction: I find any discussion of belief that makes no reference to truth (as in Hume) quite puzzling. I can understand it when a belief is just triggered by a sensation ('this is hot'), but not when a belief arrives after careful comparison of reasons. |
| 6397 | The concept of belief can only derive from relationship to a speech community [Davidson] |
| Full Idea: We have the idea of belief from its role in the interpretation of language; as a private attitude it is not intelligible except in relation to public language. So a creature must be a member of a speech community to have the concept of belief. | |
| From: Donald Davidson (Thought and Talk [1975], p.22) | |
| A reaction: This shows how Wittgenstein's Private Language Argument (e.g. Idea 4152) hovers behind Davidson's philosophy. The idea is quite persuasive. A solitary creature just follows its mental states. The question of whether it believes them is a meta-thought. |
| 8867 | A belief requires understanding the distinctions of true-and-false, and appearance-and-reality [Davidson] |
| Full Idea: Having a belief demands in addition appreciating the contrast between true belief and false, between appearance and reality, mere seeming and being. | |
| From: Donald Davidson (Three Varieties of Knowledge [1991], p.209) | |
| A reaction: This sets the bar very high for belief (never mind knowledge), and seems to imply that animals don't have beliefs. How should we describe their cognitive states then? I would say these criteria only apply to actual knowledge. |
| 8252 | Davidson believes experience is non-conceptual, and outside the space of reasons [Davidson, by McDowell] |
| Full Idea: Davidson thinks that experience can be nothing but an extra-conceptual impact on sensibility. So he concludes that experience must be outside the space of reasons. | |
| From: report of Donald Davidson (Coherence Theory of Truth and Knowledge [1983], I.6) by John McDowell - Mind and World I | |
| A reaction: McDowell's challenge to the view that experience is extra-conceptual seems to be the key debate among modern empiricists. My only intuition in this area is that we should beware of all-or-nothing solutions to such problems. |
| 6400 | Without the dualism of scheme and content, not much is left of empiricism [Davidson] |
| Full Idea: The third dogma of empiricism is the dualism of scheme and content, of organizing system and something waiting to be organized, which cannot be made intelligible and defensible. If we give it up, it is not clear that any distinctive empiricism remains. | |
| From: Donald Davidson (The Very Idea of a Conceptual Scheme [1974], p.189) | |
| A reaction: The first two dogmas were 'analyticity' and 'reductionism', as identified by Quine in 1953. Presumably Hume's Principles of Association (Idea 2189) would be an example of a scheme. A key issue is whether there is any 'pure' content. |
| 8255 | Davidson says the world influences us causally; I say it influences us rationally [McDowell on Davidson] |
| Full Idea: Davidson urges that we should hold that the world exerts a merely causal influence on our thinking, but I am trying to describe a way in which the world exerts a rational influence on our thinking. | |
| From: comment on Donald Davidson (Coherence Theory of Truth and Knowledge [1983]) by John McDowell - Mind and World II.5 | |
| A reaction: McDowell seems to be fighting for the existence of 'pure' reason in a way that is hard to defend with a thoroughly materialist view of human brains. If the world is coherent, then maybe it is rational, and so has reasons to offer us? |
| 23294 | It is common to doubt truth when discussing it, but totally accept it when discussing knowledge [Davidson] |
| Full Idea: You are following Plato's lead if you worry about the concept of truth when it is the focus of your attention, but you pretend you understand it when trying to cope with knowledge (or belief, memory, perception etc.). | |
| From: Donald Davidson (The Folly of Trying to Define Truth [1999], p.20) | |
| A reaction: Nice to find someone pointing out this absurdity. He says Hume does the same with doubts about the external world, which he ignores when discussing other minds. Belief is holding true; only truths are actually remembered…. |
| 8804 | Reasons for beliefs are not the same as evidence [Davidson] |
| Full Idea: We must find a reason for supposing most of our beliefs are true that is not a form of evidence. | |
| From: Donald Davidson (Coherence Theory of Truth and Knowledge [1983], p.158) | |
| A reaction: This simple observation strikes me as being a key truth in epistemology. It is the same confusion that creates Jackson's Knowledge Argument (Idea 7377) against physicalism (that experiencing red can be thought to be knowledge). |
| 8802 | Sensations lack the content to be logical; they cause beliefs, but they cannot justify them [Davidson] |
| Full Idea: The relation between a sensation and a belief cannot be logical, since sensations are not beliefs or propositional attitudes. The relation must be causal. Sensations cause some beliefs, but they do not show why the belief is justified. | |
| From: Donald Davidson (Coherence Theory of Truth and Knowledge [1983], p.157) | |
| A reaction: This is, I am beginning to think, the single most important idea in the whole of modern epistemology. Animals have beliefs caused in this way, and because they only have simple beliefs about immediate things, most of their beliefs are true. |
| 8801 | Coherent justification says only beliefs can be reasons for holding other beliefs [Davidson] |
| Full Idea: What distinguishes a coherence theory of justification is simply the claim that nothing can count as a reason for holding a belief except another belief. | |
| From: Donald Davidson (Coherence Theory of Truth and Knowledge [1983], p.156) | |
| A reaction: I think I agree fully with this. Red patches and headaches I count as evidence rather than as reasons. Since a red patch can be hallucinatory, and a headache can be dreamed, they can't possibly embody true propositions without critical evaluation. |
| 8805 | Skepticism is false because our utterances agree, because they are caused by the same objects [Davidson] |
| Full Idea: What stands in the way of global skepticism of the senses is the fact that we must take the objects of a belief to be the causes of that belief. And our utterances mean the same thing because belief in their truth is caused by the same objects. | |
| From: Donald Davidson (Coherence Theory of Truth and Knowledge [1983], p.161) | |
| A reaction: This is hardly a knock-down argument against scepticism, but it builds a nice picture. The second half extends the Private Language Argument (e.g. Idea 4158). But I still have non-existent conversations about non-existent things in my dreams. |
| 10347 | Objectivity is intersubjectivity [Davidson] |
| Full Idea: An entity is objective in so far as it is intersubjective. | |
| From: Donald Davidson (Three Varieties of Knowledge [1991]), quoted by Martin Kusch - Knowledge by Agreement Ch.10 | |
| A reaction: This thought baffled me until I saw it in the context of socialised epistemology. Effectively objectivity is subsumed under justification, which in turn is seen in a social context, not private to individuals. |
| 6398 | Different points of view make sense, but they must be plotted on a common background [Davidson] |
| Full Idea: Different points of view make sense, but only if there is a common co-ordinate system on which to plot them. | |
| From: Donald Davidson (The Very Idea of a Conceptual Scheme [1974], p.184) | |
| A reaction: This seems right to me. I am very struck by the close similarities between people from wildly differing cultural backgrounds, as seen, for example, at the Olympic Games. |
| 8347 | Explanations typically relate statements, not events [Davidson] |
| Full Idea: Explanations typically relate statements, not events. | |
| From: Donald Davidson (Causal Relations [1967], §4) | |
| A reaction: An oddly linguistic way of putting our attempts to understand the world. Presumably the statements are supposed to be about the events (or whatever), and they are supposed to be true, so we are trying to relate features of the world. |
| 3960 | There are no such things as minds, but people have mental properties [Davidson] |
| Full Idea: There are no such things as minds, but people have mental properties. | |
| From: Donald Davidson (Davidson on himself [1994], p.231) | |
| A reaction: I think this is right. It fits with Searle's notion of consciousness as a property, like the liquidity of water. I don't panic if I think "I have no mind, but I have extraordinary properties". |
| 8866 | If we know other minds through behaviour, but not our own, we should assume they aren't like me [Davidson] |
| Full Idea: If the mental states of others are known only through their behavioral and other outward manifestations, while this is not true of our own mental states, why should we think our own mental states are anything like those of others? | |
| From: Donald Davidson (Three Varieties of Knowledge [1991], p.207) | |
| A reaction: His point is that if you seriously doubt other minds, you should follow through on the implications. But that is to treat it as a theory about other minds, rather an a sceptical worry. Descartes didn't walk into walls while writing Meditation 1. |
| 10346 | Knowing other minds rests on knowing both one's own mind and the external world [Davidson, by Dummett] |
| Full Idea: Davidson argues that knowledge of other minds presupposes knowledge of one's own mind, and that there is no knowledge of other minds without knowledge of the external world. | |
| From: report of Donald Davidson (Three Varieties of Knowledge [1991]) by Michael Dummett - Common Sense and Physics Ch.10 | |
| A reaction: Davidson't argument is actually hard to swallow because it is so long and complex. Compressing the point makes it begin to sound like a variant of the argument from analogy. |
| 19169 | Predicates are a source of generality in sentences [Davidson] |
| Full Idea: Predicates introduce generality into sentences. | |
| From: Donald Davidson (Truth and Predication [2005], 7) | |
| A reaction: Not sure about this. Most words introduce generality. 'From' is a very general word about direction. 'Dogs bark' is as generally about dogs as it is generally about barking. |
| 4042 | Metaphysics requires the idea of people (speakers) located in space and time [Davidson] |
| Full Idea: An intelligible metaphysics will assign a central place to the idea of people (= speakers) with a location in public space and time. | |
| From: Donald Davidson (The Method of Truth in Metaphysics [1977], §III) | |
| A reaction: The 'location' is the interesting bit, requiring people to be bodies, not abstractions. A big, plausible claim, but hard to prove. |
| 4983 | There are no rules linking thought and behaviour, because endless other thoughts intervene [Davidson] |
| Full Idea: We know too much about thought and behaviour to trust exact and universal statements linking them. Beliefs and desires issue in behaviour only as modified and mediated by further beliefs and desires, attitudes and attendings, without limit. | |
| From: Donald Davidson (Mental Events [1970], p.217) | |
| A reaction: Now seen as a key objection to behaviourism, and rightly so. However, I am not sure about "without limit", which implies an implausible absolute metaphysical freedom. Davidson goes too far in denying any nomological link between thought and brain. |
| 3529 | Reduction is impossible because mind is holistic and brain isn't [Davidson, by Maslin] |
| Full Idea: Davidson rejects ontological reduction of mental to physical because propositional attitudes are holistic; there must be extensive coherence among someone's attitudes to treat them as a rational person, and this has no counterpart in physical theory. | |
| From: report of Donald Davidson (Mental Events [1970]) by Keith T. Maslin - Introduction to the Philosophy of Mind 7.5 | |
| A reaction: I don't find this view persuasive. We treat the weather in simple terms, even though it is almost infinitely complex. Davidson has a Kantian overconfidence in our rationality. A coherence among the parts is needed to be a tree. |
| 3964 | If the mind is an anomaly, this makes reduction of the mental to the physical impossible [Davidson] |
| Full Idea: If there are no strict psychophysical laws, this rules out reductionism, either by definition of mental predicates in physical terms, or by way of bridging laws. | |
| From: Donald Davidson (Davidson on himself [1994], p.231) | |
| A reaction: But it is by no means clear that there are no psycho-physical laws. How could this be known a priori? |
| 2307 | Anomalous monism says nothing at all about the relationship between mental and physical [Davidson, by Kim] |
| Full Idea: Davidson's anomalous monism says no more about the relationship between the mental and the physical than the claim that all objects with a colour have a shape says about the relationship between colours and shapes. | |
| From: report of Donald Davidson (Mental Events [1970]) by Jaegwon Kim - Mind in a Physical World §1 p.005 | |
| A reaction: Indeed, I find the enthusiasm for property dualism etc. quite baffling, given that we are merely told that mind is 'an anomaly'. I take it to be old fashioned dualism in trendy clothes. |
| 5497 | Mind is outside science, because it is humanistic and partly normative [Davidson, by Lycan] |
| Full Idea: For Davidson, mental types are individuated by considerations that are nonscientific, distinctly humanistic, and part normative, so will not coincide with any types that are designated in scientific terms. | |
| From: report of Donald Davidson (Mental Events [1970]) by William Lycan - Introduction - Ontology p.8 | |
| A reaction: I just don't believe this, mainly because I don't accept that there is a category called 'nonscientific'. All we are saying is that a brain is a hugely complicated object, and we don't properly understand its operations, though we relate to it very well. |
| 4081 | Anomalous monism says causes are events, so the mental and physical are identical, without identical properties [Davidson, by Crane] |
| Full Idea: Davidson's anomalous monism says that events are causes, so we can identify mental and physical events without having to identify their properties. | |
| From: report of Donald Davidson (Mental Events [1970]) by Tim Crane - Elements of Mind 2.18 | |
| A reaction: As Fodor insists, a thing like a mountain has properties at different levels of description. We can have 'property dualism' and full-blown reductive identity. |
| 2321 | If rule-following and reason are 'anomalies', does that make reductionism impossible? [Davidson, by Kim] |
| Full Idea: Davidson takes mental anomalism (that the mind exhibits normativity and rationality), and in particular his claim that there are no laws connecting mental and physical properties, to undermine mind-body reductionism. | |
| From: report of Donald Davidson (Mental Events [1970]) by Jaegwon Kim - Mind in a Physical World §4 p.092 | |
| A reaction: A nice summary of the core idea of property dualism. Personally I expect the whole lot to be reducible, and to follow laws, but the sheer complexity of the brain permanently bars us from actually doing the reduction. |
| 3404 | Davidson claims that mental must be physical, to make mental causation possible [Davidson, by Kim] |
| Full Idea: Davidson's thesis is that if mental events of a particular kind cause physical events of a particular kind, and the two kinds are connected by a law, then they must both be physical kinds. | |
| From: report of Donald Davidson (Mental Events [1970]) by Jaegwon Kim - Philosophy of Mind p.137 | |
| A reaction: Davidson would pretty obviously be right. The whole problem here is the idea of a 'law'. You can only have strict law for simple entities, like particles and natural kinds. The brain is a mess, like weather or explosions. |
| 3963 | There are no strict psychophysical laws connecting mental and physical events [Davidson] |
| Full Idea: There are no strict psychophysical laws (that is, laws connecting mental events under their mental descriptions with physical events under their physical descriptions). | |
| From: Donald Davidson (Davidson on himself [1994], p.231) | |
| A reaction: This is clearly open to question. It may be just that no human mind could ever grasp such laws, given their probable complexity. |
| 3961 | Obviously all mental events are causally related to physical events [Davidson] |
| Full Idea: All mental events are causally related to physical events. ..This seems obvious. | |
| From: Donald Davidson (Davidson on himself [1994], p.231) | |
| A reaction: All mental events are physically caused. Some bodily physical events result from mental events. Probably all mental events have some effect of other mental events (all of which are in some sense physical). |
| 3965 | Mental entities do not add to the physical furniture of the world [Davidson] |
| Full Idea: Mental entities do not add to the physical furniture of the world. | |
| From: Donald Davidson (Davidson on himself [1994], p.231) | |
| A reaction: This seems to me clearly true, however we propose to characterise mental events. |
| 3405 | If mental causation is lawless, it is only possible if mental events have physical properties [Davidson, by Kim] |
| Full Idea: Since no laws exist connecting mental and physical properties, purely physical laws must do the causal work, which means mental events enter into causal relations only because they possess physical properties that figure in laws. | |
| From: report of Donald Davidson (Mental Events [1970]) by Jaegwon Kim - Philosophy of Mind p.138 | |
| A reaction: Surely no such laws exist 'yet'? I can see no plausible argument that psycho-physical laws are impossible. However, the conclusion of this remark seems right. Interaction requires some sort of equality. |
| 3966 | The correct conclusion is ontological monism combined with conceptual dualism [Davidson] |
| Full Idea: My basic premises lead to the conclusion of ontological monism coupled with conceptual dualism (like Spinoza, except that he denied mental causation). | |
| From: Donald Davidson (Davidson on himself [1994], p.231) | |
| A reaction: 'Conceptual dualism' implies no real difference, but 'property dualism' is better, suggesting different properties when viewed from different angles. |
| 16041 | Supervenience of the mental means physical changes mental, and mental changes physical [Davidson] |
| Full Idea: The supervenience [of mental characteristics on the physical] might be taken to mean that there cannot be two events alike in all physical respects but differing in some mental respect, or an object cannot differ mentally without altering physically. | |
| From: Donald Davidson (Mental Events [1970], I) | |
| A reaction: This is the first occasion on which Davidson introduced his notion of supervenience. Supervenience is often taken to be one-way. The first implies physical causing mental; his second implies that mental causes physical. |
| 6620 | Davidson sees identity as between events, not states, since they are related in causation [Davidson, by Lowe] |
| Full Idea: Davidson's version of the identity theory is couched in terms of events rather than states, because he regards causation as a relation between events. | |
| From: report of Donald Davidson (Mental Events [1970]) by E.J. Lowe - Introduction to the Philosophy of Mind Ch.2 n12 | |
| A reaction: I think it may be more to the point that the mind is a dynamic thing, and so it consists of events rather than states, and hence we want to know what those events are made up from. I think my chair is causing me to rest above the floor… |
| 6383 | Cause unites our picture of the universe; without it, mental and physical will separate [Davidson] |
| Full Idea: The concept of cause is what holds together our picture of the universe, a picture that would otherwise disintegrate into a diptych of the mental and the physical. | |
| From: Donald Davidson (Intro to 'Essays on Actions and Events' [1980], p.xi) | |
| A reaction: Davidson seems to be the one who put mental causation at the centre of philosophy. By then denying that there are any 'psycho-physical' laws, he seems to me to have re-opened the metaphysical gap he says he was trying to close. |
| 3429 | Multiple realisability was worse news for physicalism than anomalous monism was [Davidson, by Kim] |
| Full Idea: Davidson's argument about psychophysical anomalism has not been embraced by everyone; multiple realisability of mental properties has had a much greater impact in undermining reductionism (and hence type physicalism). | |
| From: report of Donald Davidson (Mental Events [1970]) by Jaegwon Kim - Philosophy of Mind p.218 | |
| A reaction: My view is that functional states are multiply realisable, but phenomenal states aren't. Fear functions in frogs much as it does in us, but being a frightened frog is nothing like being a frightened human. Their brains are different! |
| 6392 | Thought depends on speech [Davidson] |
| Full Idea: The thesis I want to refine and then argue for is that thought depends on speech. | |
| From: Donald Davidson (Thought and Talk [1975], p.8) | |
| A reaction: This has the instant and rather implausible implication that animals don't think. He is not, of course, saying that all thought is speech, which would leave out thinking in images. You can't do much proper thought without concepts and propositions. |
| 3967 | Absence of all rationality would be absence of thought [Davidson] |
| Full Idea: To imagine a totally irrational animal is to imagine an animal without thought. | |
| From: Donald Davidson (Davidson on himself [1994], p.232) | |
| A reaction: This wouldn't be so clear without the theory of evolution, which suggests that only the finders of truth last long enough to breed. |
| 6393 | A creature doesn't think unless it interprets another's speech [Davidson] |
| Full Idea: A creature cannot have a thought unless it is an interpreter of the speech of another. | |
| From: Donald Davidson (Thought and Talk [1975], p.9) | |
| A reaction: His use of the word 'creature' shows that he is perfectly aware of the issue of whether animals think, and he is, presumably, denying it. At first glance this sounds silly, but maybe animals don't really 'think', in our sense of the word. |
| 6386 | In no important way can psychology be reduced to the physical sciences [Davidson] |
| Full Idea: There is no important sense in which psychology can be reduced to the physical sciences. | |
| From: Donald Davidson (The Material Mind [1973], p.259) | |
| A reaction: In no 'important' way can the beauty of the Lake District be reduced to geology - but it is geology. 'Important' to whom? To a metaphysician, I would say psychology does reduce to physics, and that is important, but it is not important to a psychologist. |
| 6175 | External identification doesn't mean external location, as with sunburn [Davidson, by Rowlands] |
| Full Idea: Davidson observes that the inference from a thought being identified by a relation to something outside the head does not entail that the thought is not wholly in the head, just as sunburn is identified by external factors, but is still in the skin. | |
| From: report of Donald Davidson (Knowing One's Own Mind [1987]) by Mark Rowlands - Externalism Ch.8 | |
| A reaction: Rowlands (an externalist) agrees, and this strikes me as correct, and it needs to be one of the fixed points in any assessment of externalism. |
| 3974 | Our meanings are partly fixed by events of which we may be ignorant [Davidson] |
| Full Idea: What we mean by what we say is partly fixed by events of which we may be ignorant. | |
| From: Donald Davidson (Davidson on himself [1994], p.235) | |
| A reaction: There is 'strict and literal meaning', which is fixed by the words, even if I don't know what I am saying. But 'speaker's meaning' is surely a pure matter of a state of mind? |
| 8872 | It is widely supposed that externalism cannot be reconciled with first-person authority [Davidson] |
| Full Idea: It has been widely supposed that externalism, which holds that the contents of a person's propositional attitudes are partly determined by factors of which the person may be ignorant, cannot be reconciled with first-person authority. | |
| From: Donald Davidson (Epistemology Externalized [1990], p.197) | |
| A reaction: It is certainly a bit puzzling if you go around saying 'Actually, people don't know their own thoughts'. Davidson aims to defend first-person authority. The full story is developed in Tyler Burge's views on 'anti-individualism'. |
| 8874 | It is hard to interpret a speaker's actions if we take a broad view of the content [Davidson] |
| Full Idea: It will explain a speaker's actions far better if we interpret him as he intended to be interpreted, than if we suppose he means and thinks what someone else might mean and think who used the same words 'correctly'. | |
| From: Donald Davidson (Epistemology Externalized [1990], p.199) | |
| A reaction: This comes down to the fact that our actions have to be motivated by internal meanings. If I defer to experts on the essence of gold, I still buy gold according to how I myself understand it. So meaning has two components? |
| 11144 | Concepts are only possible in a language community [Davidson] |
| Full Idea: A private attitude is not intelligible except as an adjustment to the public norms provided by language. It follows that a creature must be a member of speech community if it is to have the concept of belief. | |
| From: Donald Davidson (Thought and Talk [1975], p.170) | |
| A reaction: This obviously draws on Wittgenstein's private language argument, and strikes me as blatantly wrong, because I take higher animals to have concepts without language. Pure vision gives rise to concepts. I don't even think they are necessarily conscious. |
| 6387 | A minimum requirement for a theory of meaning is that it include an account of truth [Davidson] |
| Full Idea: Whatever else it embraces, a theory of meaning must include an account of truth - a statement of the conditions under which an arbitrary sentence of the language is true. | |
| From: Donald Davidson (Reality without Reference [1977], p.132) | |
| A reaction: It is a moot point whether we can define meaning if we assume truth, or if we can define truth by assuming meaning. Tarski seems to presuppose meaning when he defines truth (Idea 2345). I like Davidson's taking of truth as basic. |
| 19149 | If we reject corresponding 'facts', we should also give up the linked idea of 'representations' [Davidson] |
| Full Idea: If we give up facts that make entities true, we ought to give up representations at the same time, for the legitimacy of each depends on the legitimacy of the other. | |
| From: Donald Davidson (Truth and Predication [2005], 2) | |
| A reaction: Not sure about this, because I'm not sure I know what he means by 'representations'. Surely every sentence is 'about' something? Is that just the references within the sentence, but not the sentence as a whole? |
| 19163 | You only understand an order if you know what it is to obey it [Davidson] |
| Full Idea: We understand an imperative if and only if we know under what conditions what it orders or commands is obeyed. | |
| From: Donald Davidson (Truth and Predication [2005], 6) | |
| A reaction: How could this be wrong? 'Do you understand the order?' 'Yes sir!' 'Well do it then!' 'Do what sir?' |
| 15160 | Davidson rejected ordinary meaning, and just used truth and reference instead [Davidson, by Soames] |
| Full Idea: Davidson held that knowledge of truth and reference could give us a notion of meaning. He embraced Quine's rejection of analyticity, synonymy and ordinary meaning, and substituted truth and reference, when there was something genuine to capture. | |
| From: report of Donald Davidson (Semantics for Natural Languages [1970]) by Scott Soames - Philosophy of Language 2.3 | |
| A reaction: I always get a warm glow when anyone suggests that the concept of meaning involves the concept of truth. I largely reject Quine. Davidson made a helpful suggestion! |
| 14612 | Davidson aimed to show that language is structured by first-order logic [Davidson, by Smart] |
| Full Idea: Davidson's program was to show the underlying structure of natural languages as that of first-order logic. | |
| From: report of Donald Davidson (Semantics for Natural Languages [1970], 2) by J.J.C. Smart - The Tenseless Theory of Time 2 | |
| A reaction: First order logic just reasons about a domain of objects with predicates attached to them. Language appears to refer to properties and relations as well as objects. |
| 4041 | Sentences held true determine the meanings of the words they contain [Davidson] |
| Full Idea: Sentences held true (the linguistic representatives of beliefs) determine the meanings of the words they contain. | |
| From: Donald Davidson (The Method of Truth in Metaphysics [1977], §II) | |
| A reaction: Maybe. Historically, truth and belief presumably precede words and sentences. But words separate off from beliefs very easily. I'm not convinced. Words initiate language, not beliefs? |
| 6391 | A theory of truth tells us how communication by language is possible [Davidson] |
| Full Idea: A theory of truth lets us answer the underlying question how communication by language is possible. | |
| From: Donald Davidson (Reality without Reference [1977], p.137) | |
| A reaction: If, instead, you explain communication by understood intentions (á la Grice), you have to say more about what sort of intentions are meant. If you use reference, you still have more to say about the meaning of sentences. Davidson looks good. |
| 23289 | Knowing the potential truth conditions of a sentence is necessary and sufficient for understanding [Davidson] |
| Full Idea: It is clear that someone who knows under what conditions a sentence would be true understands that sentence, …and if someone does not know under what conditions it would be true then they do not understand it. | |
| From: Donald Davidson (Truth Rehabilitated [1997], p.13) | |
| A reaction: I've always subscribed to this view. Langauge is meaningless if you can't relate it to reality, and I don't think there could be a language without an intuitive notion of truth. |
| 19152 | Utterances have the truth conditions intended by the speaker [Davidson] |
| Full Idea: An utterance has certain truth conditions only if the speaker intends it to be interpreted as having those truth conditions. | |
| From: Donald Davidson (Truth and Predication [2005], 3) | |
| A reaction: This seems to be a concession to the rather sensible things that Grice said about meaning. What about malapropisms? Surely there the speaker does not understand the truth conditions of her own utterance? Truth conditions are in the head? |
| 19162 | Meaning involves use, but a sentence has many uses, while meaning stays fixed [Davidson] |
| Full Idea: Meaning depends on use, but it is not easy to say how, for uses to which we may put the utterance of a sentence are endless while its meaning remains fixed. | |
| From: Donald Davidson (Truth and Predication [2005], 6) | |
| A reaction: Quite so. The password is 'Swordfish' (or 'Sweet marjoram', if you prefer). |
| 6395 | An understood sentence can be used for almost anything; it isn't language if it has only one use [Davidson] |
| Full Idea: Once a sentence is understood, an utterance of it may be used to serve almost any extra-linguistic purpose; an instrument that could be put to only one use would lack autonomy of meaning, which means it should not be counted as language. | |
| From: Donald Davidson (Thought and Talk [1975], p.17) | |
| A reaction: I find this point very appealing, in opposition to the Wittgenstein view of meaning as use. Passwords seem to me a striking case of the separation of meaning and use. I like the phrase 'autonomy of meaning'. Random sticks can form a word. |
| 23290 | It could be that the use of a sentence is explained by its truth conditions [Davidson] |
| Full Idea: It may be that sentences are used as they are because of their truth conditions, and they have the truth conditions they do because of how they are used. | |
| From: Donald Davidson (Truth Rehabilitated [1997], p.13) | |
| A reaction: I've always taken the attempt to explain meaning by use as absurd. It is similar to trying to explain mind in terms of function. In each case, what is the intrinsic nature of the thing, which makes that use or that function possible? |
| 19131 | We recognise sentences at once as linguistic units; we then figure out their parts [Davidson] |
| Full Idea: Our interest in the parts of sentences is derivative; we recognise at once that sentences are effective linguistic units, while we must figure out or decide what constitutes the meaningful words and particles. | |
| From: Donald Davidson (Truth and Predication [2005], Intro) | |
| A reaction: It depends on whether linguistic priority goes to complete thoughts that require expression, or to naming and ostensive definition to relate to elements of the environment. I find it hard to have a strong view on this one. Just So stories? |
| 6394 | The pattern of sentences held true gives sentences their meaning [Davidson] |
| Full Idea: Although most utterances are not concerned with truth, it is the pattern of sentences held true that gives sentences their meaning. | |
| From: Donald Davidson (Thought and Talk [1975], p.14) | |
| A reaction: Davidson's distinctive version of meaning holism, as opposed to Quine's rather behaviouristic version. I agree that we relate to people through the pattern of sentences they hold true, but I am unconvinced that this 'gives sentences their meaning'. |
| 6388 | Is reference the key place where language and the world meet? [Davidson] |
| Full Idea: The essential question is whether reference is the, or at least one, place where there is direct contact between linguistic theory and events, actions, or objects described in nonlinguistic terms. | |
| From: Donald Davidson (Reality without Reference [1977], p.134) | |
| A reaction: How do you 'describe objects in nonlinguistic terms'? The causal theory of reference (e.g. Idea 4957) is designed to plug language straight into the world via reference. It simplifies things nicely, but I don't quite believe it. |
| 6390 | With a holistic approach, we can give up reference in empirical theories of language [Davidson] |
| Full Idea: I defend a version of the holistic approach, and urge that we must give up the concept of reference as basic to an empirical theory of language. | |
| From: Donald Davidson (Reality without Reference [1977], p.136) | |
| A reaction: He proposes to connect language to the world via the concept of truth, rather than of reference. It is a brilliant idea, and is the key issue in philosophy of language. I go back to animals, which seem to care about situations rather than things. |
| 6389 | To explain the reference of a name, you must explain its sentence-role, so reference can't be defined nonlinguistically [Davidson] |
| Full Idea: It is inconceivable that one should be able to explain the relationship between 'Kilimanjiro' and Kilimanjiro without first explaining the role of the word in sentences; hence there is no chance of explaining reference directly in nonlinguistic terms. | |
| From: Donald Davidson (Reality without Reference [1977], p.135) | |
| A reaction: I point at the mountain, and a local says 'Kilimanjiro'? There is a 'gavagai'-type problem with that. The prior question might be 'what is it about this word that enables it to have a role in sentences?' Unlike whimpering or belching. |
| 19156 | Modern predicates have 'places', and are sentences with singular terms deleted from the places [Davidson] |
| Full Idea: The notion of 'places' in a predicate is the key to the modern concept of a predicate. Any expression obtained from a sentence by deleting one or more singular terms from the sentence counts as a predicate. | |
| From: Donald Davidson (Truth and Predication [2005], 4) |
| 13363 | A (modern) predicate is the result of leaving a gap for the name in a sentence [Bostock] |
| Full Idea: A simple way of approaching the modern notion of a predicate is this: given any sentence which contains a name, the result of dropping that name and leaving a gap in its place is a predicate. Very different from predicates in Aristotle and Kant. | |
| From: David Bostock (Intermediate Logic [1997], 3.2) | |
| A reaction: This concept derives from Frege. To get to grips with contemporary philosophy you have to relearn all sorts of basic words like 'predicate' and 'object'. |
| 19176 | The concept of truth can explain predication [Davidson] |
| Full Idea: My strategy is to show how our grasp of the concept of truth can explain predication. | |
| From: Donald Davidson (Truth and Predication [2005], 7) | |
| A reaction: His account of the concept of truth centres on Tarski's theory, but he clearly thinks more is needed than the bare bones offered by Tarski. The point, I think, is that predication is what makes a sentence 'truth-apt'. |
| 7772 | Compositionality explains how long sentences work, and truth conditions are the main compositional feature [Davidson, by Lycan] |
| Full Idea: Davidson's main argument in favour of his truth conditions theory of meaning is that compositionality is needed to account for our understanding of long, novel sentences, and a sentence's truth condition is its most obviously compositional feature. | |
| From: report of Donald Davidson (Truth and Meaning [1967]) by William Lycan - Philosophy of Language Ch.9 | |
| A reaction: This seems to me exactly right. As we hear a new long sentence unfold, we piece together the meaning. At the end we may spot that the meaning is silly, or an unverifiable speculation, or not what the speaker intended - but it is too late! It means. |
| 19133 | If you assign semantics to sentence parts, the sentence fails to compose a whole [Davidson] |
| Full Idea: The puzzle is that once plausible assignments of semantic roles have been made to parts of sentences, the parts do not seem to compose a united whole. | |
| From: Donald Davidson (Truth and Predication [2005], Intro) | |
| A reaction: It's not clear to me that a sentence does compose a 'whole', given that you can often add or remove bits from sentences, sometimes without changing the meaning. We often, in speech, assemble sentences before we have thought of their full meaning. |
| 7327 | Davidson thinks Frege lacks an account of how words create sentence-meaning [Davidson, by Miller,A] |
| Full Idea: Davidson thinks that Frege's model for a theory of semantic value (and thereby for a systematic theory of sense) is unsatisfactory, because it provides no useful or explanatory account of how sentence-meaning can be a function of word-meaning. | |
| From: report of Donald Davidson (Truth and Meaning [1967]) by Alexander Miller - Philosophy of Language 8.1 | |
| A reaction: Put like that, it is not clear to me how you could even start to explain how word-meaning contributes to sentence meaning. Try speaking any sentence slowly, and observe how the sentence meaning builds up. Truth is, of course, relevant. |
| 7331 | A theory of meaning comes down to translating sentences into Fregean symbolic logic [Davidson, by Macey] |
| Full Idea: For a theory of meaning for a fragment of natural language, what Davidson requires, in effect, is that the sentences be translatable into the language of Frege's symbolic logic. | |
| From: report of Donald Davidson (In Defence of Convention T [1973]) by David Macey - Penguin Dictionary of Critical Theory | |
| A reaction: This assumes the adequacy of Fregean logic, which seems unlikely. Is this the culmination of Leibniz's dream of a fully logical language - so that anything that won't fit into our logical form is ruled (logical positivist style) as meaningless? |
| 19132 | Top-down semantic analysis must begin with truth, as it is obvious, and explains linguistic usage [Davidson] |
| Full Idea: Truth is the essential semantic concept with which to begin a top-down analysis of sentences, since truth, or lack of it, is the most obvious semantic property of sentences, and provides the clearest explanation of judging and conveying information. | |
| From: Donald Davidson (Truth and Predication [2005], Intro) | |
| A reaction: [a bit compressed] Presumably this goes with giving sentences semantic priority. The alternative approach is compositional, and is likely to give reference of terms priority over truth of the sentence. But accurate reference is a sort of truth. |
| 7769 | You can state truth-conditions for "I am sick now" by relativising it to a speaker at a time [Davidson, by Lycan] |
| Full Idea: Davidson's response to the problem of how you would state truth conditions for "I am sick now" ...is to relativize its truth to a particular speaker and a time. | |
| From: report of Donald Davidson (Truth and Meaning [1967]) by William Lycan - Philosophy of Language Ch.9 | |
| A reaction: Lycan is not happy with this, but it seems a reasonable way to treat the truth of any statement containing indexicals. Never mind the 'truth conditions theory of meaning' - just ask whether "I am sick now" is true. |
| 19158 | 'Humanity belongs to Socrates' is about humanity, so it's a different proposition from 'Socrates is human' [Davidson] |
| Full Idea: The sentence 'Humanity belongs to Socrates' is about the concept of humanity, unlike the "equivalent" 'Socrates is human', so they express different propositions. | |
| From: Donald Davidson (Truth and Predication [2005], 5) | |
| A reaction: [compressed] I like this a lot, because it shows why we should focus on propositions rather than on sentences, or even utterances. And asking what the sentence is 'about' focuses us on the underlying proposition or thought. |
| 3968 | Propositions explain nothing without an explanation of how sentences manage to name them [Davidson] |
| Full Idea: The idea of a proposition is unhelpful, until it is explained how exactly the words in the contained sentence manage to name or describe a proposition (which even Frege failed to achieve). | |
| From: Donald Davidson (Davidson on himself [1994], p.232) | |
| A reaction: It seems obvious to me that there are brain events best labelled as propositions, even if their fit with language is puzzling. |
| 18121 | In logic a proposition means the same when it is and when it is not asserted [Bostock] |
| Full Idea: In Modus Ponens where the first premise is 'P' and the second 'P→Q', in the first premise P is asserted but in the second it is not. Yet it must mean the same in both premises, or it would be guilty of the fallacy of equivocation. | |
| From: David Bostock (Philosophy of Mathematics [2009], 7.2) | |
| A reaction: This is Geach's thought (leading to an objection to expressivism in ethics, that P means the same even if it is not expressed). |
| 3970 | Thought is only fully developed if we communicate with others [Davidson] |
| Full Idea: We would have no fully-fledge thoughts if we were not in communication with others. | |
| From: Donald Davidson (Davidson on himself [1994], p.233) | |
| A reaction: This seems a plausible empirical observation, though I would doubt any a priori proof of it. If animals could speak, they would become intellectuals? |
| 8870 | Content of thought is established through communication, so knowledge needs other minds [Davidson] |
| Full Idea: Until a baseline has been established by communication with someone else, there is no point is saying one's own thoughts have a propositional content. Hence knowledge of another mind is essential all thought and all knowledge. | |
| From: Donald Davidson (Three Varieties of Knowledge [1991], p.213) | |
| A reaction: This really is building a skyscraper on the slightly shaky claims of the Private Language Argument (e.g. Idea 4158). Animals are so important in discussions of this kind. Is an albatross more or less devoid of thought and belief? |
| 6179 | Should we assume translation to define truth, or the other way around? [Blackburn on Davidson] |
| Full Idea: The concern of some philosophers has been expressed by saying that whereas Tarski took translation for granted, and sought to understand truth, Davidson takes truth for granted, and seeks to understand translation. | |
| From: comment on Donald Davidson (Truth and Meaning [1967]) by Simon Blackburn - Oxford Dictionary of Philosophy p.82 | |
| A reaction: We can just say that the two concepts are interdependent, but my personal intuitions side with Davidson. If you are going to take something as fundamental and axiomatic, truth looks a better bet than translation. |
| 6399 | Criteria of translation give us the identity of conceptual schemes [Davidson] |
| Full Idea: Studying the criteria of translation is a way of focusing on criteria of identity for conceptual schemes. | |
| From: Donald Davidson (The Very Idea of a Conceptual Scheme [1974], p.184) | |
| A reaction: This is why it was an inspired idea of Quine's to make translation a central topic in philosophy. We must be cautious, though, about saying that the language is the conceptual scheme, as that leaves animals with no scheme at all. |
| 18703 | Davidson's Cogito: 'I think, therefore I am generally right' [Davidson, by Button] |
| Full Idea: Davidson's Cogito has the form 'I think, therefore I am generally right'. | |
| From: report of Donald Davidson (Coherence Theory of Truth and Knowledge [1983], 16.6) by Tim Button - The Limits of Reason | |
| A reaction: On the whole I would subscribe to this Cogito (as Button calls it), from an evolutionary perspective. There would just be no point in thought if it wasn't generally right in everyday activity. |
| 8869 | The principle of charity attributes largely consistent logic and largely true beliefs to speakers [Davidson] |
| Full Idea: Concerning charity, the Principle of Coherence seeks logical consistency in the thought of the speaker, and the Principle of Correspondence seeks a similar response to features of the world to that of an interpreter. The speaker has logic and true belief. | |
| From: Donald Davidson (Three Varieties of Knowledge [1991], p.211) | |
| A reaction: Davidson adds a Kantian commitment to pure and universal reason to the very sceptical framework created by Quine. I agree with Davidson, but it seems more like faith than like an argument or an empirical observation. |
| 3971 | There is simply no alternative to the 'principle of charity' in interpreting what others do [Davidson] |
| Full Idea: The 'principle of charity' is a misleading term, since there is no alternative if we want to make sense of the attitudes and actions of the agents around us. | |
| From: Donald Davidson (Davidson on himself [1994], p.233) | |
| A reaction: I suppose so, but only with a background of evolutionary theory. I would necessarily assume charity if a robot spoke to me. |
| 19154 | The principle of charity says an interpreter must assume the logical constants [Davidson] |
| Full Idea: The principle of charity says that it is unavoidable that the pattern of sentences to which a speaker assents reflects the semantics of the logical constants. | |
| From: Donald Davidson (Truth and Predication [2005], 3) | |
| A reaction: That is not all the principle says, of course. Davidson seems to assume classical logic here, with a bivalent semantics. I wonder if all speakers use 'false' in the normal way, as well as 'true'? Do all languages even contain 'true'? |
| 19161 | We indicate use of a metaphor by its obvious falseness, or trivial truth [Davidson] |
| Full Idea: The sentences that contain metaphors are typically obviously false or trivially true, because these are typically indications that something is intended as a metaphor. | |
| From: Donald Davidson (Truth and Predication [2005], 6) | |
| A reaction: A nice point which sounds correct. Metaphors are famous being false, but the 'obvious' falseness signals the metaphor. If a metaphor is only obscurely false, that makes it difficult to read. |
| 7776 | Metaphors just mean what their words literally mean [Davidson] |
| Full Idea: Metaphors mean what the words, in their most literal interpretation, mean, and nothing more. | |
| From: Donald Davidson (What Metaphors Mean [1978], p.30) | |
| A reaction: This pronouncement must be the result of Davidson anguishing over the truth conditions for metaphors, which are usually either taken to have a 'metaphorical meaning', or to be abbreviated similes. He solved his problem at a stroke! Plausible. |
| 7775 | Understanding a metaphor is a creative act, with no rules [Davidson] |
| Full Idea: Understanding a metaphor is as much a creative endeavour as making a metaphor, and as little guided by rules. | |
| From: Donald Davidson (What Metaphors Mean [1978], p.29) | |
| A reaction: This is good news for literature studies courses. Davidson's point is that the metaphor itself only gives you a literal meaning, so it doesn't tell you how to interpret it. It seems an attractive proposal. |
| 7777 | We accept a metaphor when we see the sentence is false [Davidson] |
| Full Idea: It is only when a sentence is taken to be false that we accept it as a metaphor. | |
| From: Donald Davidson (What Metaphors Mean [1978], p.40) | |
| A reaction: This strikes me as a very nice and true generalisation, even though Davidson mentions "no man is an island" as a counterexample. We thirst for meaning, and switch to a second meaning when the first one looks peculiar. |
| 20020 | If one action leads directly to another, they are all one action [Davidson, by Wilson/Schpall] |
| Full Idea: Davidson (1980 ess 1) agreed with Anscombe that if a person Fs by G-ing, then her act F = her act G. For example, if someone accidentally alerts a burglar, by deliberately turning on a light, by flipping a switch, these are all the same action. | |
| From: report of Donald Davidson (Action, Reasons and Causes [1963]) by Wilson,G/Schpall,S - Action 1.2 | |
| A reaction: I would have thought there was obviously a strong conventional element in individuating actions, depending on interest. An electrician is only interest in whether the light worked. The police are only interested in the disturbance of the burglar. |
| 20072 | We explain an intention by giving an account of acting with an intention [Davidson, by Stout,R] |
| Full Idea: The early Davidson championed the approach that we explain the idea of having an intention by providing an account of what it is to act with an intention. | |
| From: report of Donald Davidson (Action, Reasons and Causes [1963]) by Rowland Stout - Action 7 'Conclusion' | |
| A reaction: This eliminates the distinction between a prior intention, and the intention that maintains a process such as speech. It sounds almost behaviourist. |
| 20076 | An intending is a judgement that the action is desirable [Davidson] |
| Full Idea: We can identify an intentional action ...with an all-out conditional judgement that the action is desirable. ...In the case of pure intending, I now suggest that the intention simply is an all-out judgement. | |
| From: Donald Davidson (Intending [1978], p.99), quoted by Rowland Stout - Action 8 'Davidson's' | |
| A reaction: 'Pure' intending seems to be what Stout calls 'prior' intending, which is clearer. This still strikes me as obviously false. I judge that it is desirable that I make a cup of coffee, but secretly I'm hoping someone else will make it for me. |
| 20074 | We can keep Davidson's account of intentions in action, by further explaining prior intentions [Davidson, by Stout,R] |
| Full Idea: Davidson's original account of intentions might still stand if we could accept that prior intentions are different in kind from intentions with which one acts. | |
| From: report of Donald Davidson (Problems in the Explanation of Action [1987]) by Rowland Stout - Action 8 'Davidson's' | |
| A reaction: Davidson says prior intention is all-out judgement of desirability. Prior intentions are more deliberate, with the other intentions as a presumed background to action. Compare Sartre's dual account of the self. |
| 20024 | Davidson gave up reductive accounts of intention, and said it was a primitive [Davidson, by Wilson/Schpall] |
| Full Idea: Later Davidson dropped his reductive treatment of intentions (in terms of 'pro-attitudes' and other beliefs), and accepted that intentions are irreducible, and distinct from pro-attitudes. | |
| From: report of Donald Davidson (Intending [1978]) by Wilson,G/Schpall,S - Action 2 | |
| A reaction: Only a philosopher would say that intentions cannot be reduced to something else. Since I have a very physicalist view of the mind, I incline to reduce them to powers and dispositions of physical matter. |
| 6385 | The causally strongest reason may not be the reason the actor judges to be best [Davidson] |
| Full Idea: I defend my causal view of action by arguing that a reason that is causally strongest need not be a reason deemed by the actor to provide the strongest (best) grounds for acting. | |
| From: Donald Davidson (Intro to 'Essays on Actions and Events' [1980], p.xii) | |
| A reaction: If I smoke a cigarette against my better judgement, it is not clear to me how the desire to smoke it, which overcomes my judgement not to smoke it, counts as the causally strongest 'reason'. We seem to have two different senses of 'reason' here. |
| 20045 | Acting for a reason is a combination of a pro attitude, and a belief that the action is appropriate [Davidson] |
| Full Idea: Whenever someone does something for a reason he can be characterised as (a) having some sort of pro attitude towards action of a certain kind, and (b) believing (or knowing, perceiving, noticing, remembering) that his action is of that kind. | |
| From: Donald Davidson (Action, Reasons and Causes [1963], p.3-4), quoted by Rowland Stout - Action 3 'The belief-' | |
| A reaction: This is the earlier Davidson roughly endorsing the traditional belief-desire account of action. He is giving a reductive account of reasons. Deciding reasons were not reducible may have led him to property dualism. |
| 6384 | The notion of cause is essential to acting for reasons, intentions, agency, akrasia, and free will [Davidson] |
| Full Idea: My thesis is that the ordinary notion of cause is essential to understanding what it is to act with a reason, to have an intention to act, to be an agent, to act counter to one's own best judgement, or to act freely. | |
| From: Donald Davidson (Intro to 'Essays on Actions and Events' [1980], p.xi) | |
| A reaction: I cautiously agree, particularly with idea that causation is essential to acting as an agent. Since I believe 'free will' to be a complete delusion, that part of his thesis doesn't interest me. The hard part is understanding acting for a reason. |
| 20075 | Early Davidson says intentional action is caused by reasons [Davidson, by Stout,R] |
| Full Idea: In Davidson's earlier approach, intentional action requires causation by reasons. | |
| From: report of Donald Davidson (Action, Reasons and Causes [1963]) by Rowland Stout - Action 8 'Weakness' | |
| A reaction: A very Kantian idea, and one that seems to bestow causal powers on something which I take to be highly abstract. Thus Davidson was wrong (but in a nice way). |
| 3395 | Davidson claims that what causes an action is the reason for doing it [Davidson, by Kim] |
| Full Idea: Davidson defends the simple thesis that the reason for which an action is done is the one that causes it, …which means that agency is possible only if mental causation is possible. | |
| From: report of Donald Davidson (Action, Reasons and Causes [1963]) by Jaegwon Kim - Philosophy of Mind p.127 |
| 23734 | The best explanation of reasons as purposes for actions is that they are causal [Davidson, by Smith,M] |
| Full Idea: Davidson argues that the best interpretation of the teleological character of reason explanations is an intepretation in causal terms. | |
| From: report of Donald Davidson (Action, Reasons and Causes [1963]) by Michael Smith - The Moral Problem 4.4 | |
| A reaction: That is, this is the explanation of someone doing something 'because' they have this reason (rather than happening to have a reason). Smith observes that other mental states (such as beliefs) may also have this causal power. |
| 23737 | Reasons can give purposes to actions, without actually causing them [Smith,M on Davidson] |
| Full Idea: Only the Humean theory is able to make sense of reason explanation as a species of teleological explanation, and one may accept that reason explanations are teleological without accepting that they are causal. | |
| From: comment on Donald Davidson (Action, Reasons and Causes [1963]) by Michael Smith - The Moral Problem 4.6 | |
| A reaction: That is, reasons can give a purpose to an action, and thereby motivate it, without actually causing it. I agree with Smith. I certainly don't (usually, at least) experience reasons as directly producing my actions. Hume says desires are needed. |
| 6664 | Reasons must be causes when agents act 'for' reasons [Davidson, by Lowe] |
| Full Idea: It can be argued (by Davidson) that far from it being the case that reasons for and causes of action are quite distinct, reasons must be causes when agents act 'for' reasons. | |
| From: report of Donald Davidson (Action, Reasons and Causes [1963]) by E.J. Lowe - Introduction to the Philosophy of Mind Ch.9 | |
| A reaction: Lowe argues against this view. The rival views to Davidson would be either that reasons are no more than desires-plus-beliefs in disguise, or that the will causes actions, and strong reasons carry a great weight with the will. I like the will. |
| 19698 | Deviant causal chain: a reason causes an action, but isn't the reason for which it was performed [Davidson, by Neta] |
| Full Idea: A 'deviant causal chain' is when an agent has a reason for performing an action, and for the reason to cause the performance, without that being the reason for which the agent performed it. | |
| From: report of Donald Davidson (Freedom to Act [1973]) by Ram Neta - The Basing Relation II | |
| A reaction: Davidson's thesis is that 'reasons are causes'. This was a problem he faced. I think this discussion is now obscured by the complex and multi-layered account of action which is emerging from neuroscience. |
| 20166 | A man is a responsible agent to the extent he has an intention, and knows what he is doing [Hampshire] |
| Full Idea: A man becomes more and more a free and responsible agent the more he at all times knows what he is doing, in every sense of this phrase, and the more he acts with a definite and clearly formed intention. | |
| From: Stuart Hampshire (Thought and Responsibility [1960], p.178), quoted by John Kekes - The Human Condition 07.1 | |
| A reaction: Kekes quote this (along with Frankfurt, Hart etc) as the 'received view' of responsibility, which he attacks. |
| 3973 | Without a teacher, the concept of 'getting things right or wrong' is meaningless [Davidson] |
| Full Idea: Without a 'teacher', nothing would give content to the idea that there is a difference between getting things right and getting them wrong. | |
| From: Donald Davidson (Davidson on himself [1994], p.234) | |
| A reaction: Seems right. A group of speculators with no one in the role of 'teacher' would seem to be paralysed with uncertain (except where judgements are very obvious). |
| 8873 | The cause of a usage determines meaning, but why is the microstructure of water relevant? [Davidson] |
| Full Idea: While I agree that the usual cause of the use of the word determines what it means, I do not see why sameness of microstructure is necessarily the relevant similarity that determines my reference of the word 'water'. | |
| From: Donald Davidson (Epistemology Externalized [1990], p.198) | |
| A reaction: This is a problem for essentialists who build their views on semantic considerations. But the stability of what causes 'water' thoughts is the microstructure of water. However, that is an explantion of meaning, not a definition of it. |
| 10371 | Distinguish causation, which is in the world, from explanations, which depend on descriptions [Davidson, by Schaffer,J] |
| Full Idea: Davidson distinguishes between causation, an extensional relation that holds between coarse events, and explanation, which is an intensional relation that holds between the coarse events under a description. | |
| From: report of Donald Davidson (Causal Relations [1967]) by Jonathan Schaffer - The Metaphysics of Causation 1.2 | |
| A reaction: I'm unclear why everything has to be so coarse, when reality and causal events seem to fine-grained, but the distinction strikes me as good. Explanations relate to human understanding and human interests. Cf. Anscombe's view. |
| 8403 | Either facts, or highly unspecific events, serve better as causes than concrete events [Field,H on Davidson] |
| Full Idea: It is best to avoid Davidson's view that only quite concrete events can serve as causes; we should either say that facts as well as events can serve as causes; or that the events can be highly unspecific, including 'omissions'. | |
| From: comment on Donald Davidson (Causal Relations [1967]) by Hartry Field - Causation in a Physical World 1 | |
| A reaction: Something NOT happening might be the main cause of an effect (drought), or an effect may mainly result from a situation rather than an event (famine). |
| 3524 | Causation is either between events, or between descriptions of events [Davidson, by Maslin] |
| Full Idea: According to Davidson analyses of causality proceed at two different levels: at the lower level it holds between events regardless of how they are described; higher level explanations hold between descriptions of events, which pick out properties. | |
| From: report of Donald Davidson (Mental Events [1970]) by Keith T. Maslin - Introduction to the Philosophy of Mind 7.4 |
| 3526 | Whether an event is a causal explanation depends on how it is described [Davidson, by Maslin] |
| Full Idea: Davidson says causal explanations hold between descriptions of events and not between the events themselves, so the possibility of events as explanations depends on how they are described (e.g. a wind collapsing a bridge). | |
| From: report of Donald Davidson (Mental Events [1970]) by Keith T. Maslin - Introduction to the Philosophy of Mind 7.4 |
| 8346 | Full descriptions can demonstrate sufficiency of cause, but not necessity [Davidson] |
| Full Idea: The fuller we make the description of a cause, the better our chances of demonstrating that it was sufficient (as described) to produce the effect, and the worse our chances of demonstrating that it was necessary. (For the effect, it is the opposite). | |
| From: Donald Davidson (Causal Relations [1967], §3) | |
| A reaction: If the fullness of description is relevant, this suggests that Davidson is focusing on human explanations, rather than on the ontology of causation. If the cause IS necessary, why wouldn't a better description make that clearer? |
| 4778 | A singular causal statement is true if it is held to fall under a law [Davidson, by Psillos] |
| Full Idea: For Davidson, what makes singular causal statements true is the existence of some regularities or laws. All causal is nomological: c causes e iff there is a law that connects events like c with events like e. | |
| From: report of Donald Davidson (Causal Relations [1967]) by Stathis Psillos - Causation and Explanation §2.6 | |
| A reaction: I wonder if the cart is before the horse here. Scriven says this is just a claim that there are "phantom laws". It is the Humean view of causation, but surely the laws come after the causation, so can't be used to explain it? |
| 3962 | Cause and effect relations between events must follow strict laws [Davidson] |
| Full Idea: If two events are related as cause and effect, there is a strict law under which they may be subsumed. | |
| From: Donald Davidson (Davidson on himself [1994], p.231) | |
| A reaction: Davidson admits that this is open to challenge (though Hume and Kant supported it). It does seem to be central to our understanding of nature. |