69 ideas
| 23367 | Even pointing a finger should only be done for a reason [Epictetus] |
| Full Idea: Philosophy says it is not right even to stretch out a finger without some reason. | |
| From: Epictetus (fragments/reports [c.57], 15) | |
| A reaction: The key point here is that philosophy concerns action, an idea on which Epictetus is very keen. He rather despise theory. This idea perfectly sums up the concept of the wholly rational life (which no rational person would actually want to live!). |
| 16295 | Tarski proved that truth cannot be defined from within a given theory [Tarski, by Halbach] |
| Full Idea: Tarski's Theorem states that under fairly generally applicable conditions, the assumption that there is a definition of truth within a given theory for the language of that same theory leads to a contradiction. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Volker Halbach - Axiomatic Theories of Truth 1 | |
| A reaction: That might leave room for a definition outside the given theory. I take the main motivation for the axiomatic approach to be a desire to get a theory of truth within the given theory, where Tarski's Theorem says traditional approaches are just wrong. |
| 15342 | Tarski proved that any reasonably expressive language suffers from the liar paradox [Tarski, by Horsten] |
| Full Idea: Tarski's Theorem on the undefinability of truth says in a language sufficiently rich to talk about itself (which Gödel proved possible, via coding) the liar paradox can be carried out. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Leon Horsten - The Tarskian Turn 02.2 | |
| A reaction: The point is that truth is formally indefinable if it leads inescapably to contradiction, which the liar paradox does. This theorem is the motivation for all modern attempts to give a rigorous account of truth. |
| 19069 | 'True sentence' has no use consistent with logic and ordinary language, so definition seems hopeless [Tarski] |
| Full Idea: The possibility of a consistent use of 'true sentence' which is in harmony with the laws of logic and the spirit of everyday language seems to be very questionable, so the same doubt attaches to the possibility of constructing a correct definition. | |
| From: Alfred Tarski (The Concept of Truth for Formalized Languages [1933], §1) | |
| A reaction: This is often cited as Tarski having conclusively proved that 'true' cannot be defined from within a language, but his language here is much more circumspect. Modern critics say the claim depends entirely on classical logic. |
| 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'. |
| 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. |
| 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. |
| 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. |
| 16296 | Tarski's Theorem renders any precise version of correspondence impossible [Tarski, by Halbach] |
| Full Idea: Tarski's Theorem applies to any sufficient precise version of the correspondence theory of truth, and all the other traditional theories of truth. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Volker Halbach - Axiomatic Theories of Truth 1 | |
| A reaction: This is the key reason why modern thinkers have largely dropped talk of the correspondence theory. See Idea 16295. |
| 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] |
| 15339 | Tarski gave up on the essence of truth, and asked how truth is used, or how it functions [Tarski, by Horsten] |
| Full Idea: Tarski emancipated truth theory from traditional philosophy, by no longer posing Pilate's question (what is truth? or what is the essence of truth?) but instead 'how is truth used?', 'how does truth function?' and 'how can its functioning be described?'. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Leon Horsten - The Tarskian Turn 02.2 | |
| A reaction: Horsten, later in the book, does not give up on the essence of truth, and modern theorists are trying to get back to that question by following Tarski's formal route. Modern analytic philosophy at its best, it seems to me. |
| 16302 | Tarski did not just aim at a definition; he also offered an adequacy criterion for any truth definition [Tarski, by Halbach] |
| Full Idea: Tarski did not settle for a definition of truth, taking its adequacy for granted. Rather he proposed an adequacy criterion for evaluating the adequacy of definitions of truth. The criterion is his famous Convention T. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Volker Halbach - Axiomatic Theories of Truth 3 | |
| A reaction: Convention T famously says the sentence is true if and only if a description of the sentence is equivalent to affirming the sentence. 'Snow is white' iff snow is white. |
| 19135 | Tarski enumerates cases of truth, so it can't be applied to new words or languages [Davidson on Tarski] |
| Full Idea: Tarski does not tell us how to apply his concept of truth to a new case, whether the new case is a new language or a word newly added to a language. This is because enumerating cases gives no clue for the next or general case. | |
| From: comment on Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Donald Davidson - Truth and Predication 1 | |
| A reaction: His account has been compared to a telephone directory. We aim to understand the essence of anything, so that we can fully know it, and explain and predict how it will behave. Either truth is primitive, or I demand to know its essence. |
| 19138 | Tarski define truths by giving the extension of the predicate, rather than the meaning [Davidson on Tarski] |
| Full Idea: Tarski defined the class of true sentences by giving the extension of the truth predicate, but he did not give the meaning. | |
| From: comment on Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Donald Davidson - Truth and Predication 1 | |
| A reaction: This is analogous to giving an account of the predicate 'red' as the set of red objects. Since I regard that as a hopeless definition of 'red', I am inclined to think the same of Tarski's account of truth. It works in the logic, but so what? |
| 4699 | Tarski made truth relative, by only defining truth within some given artificial language [Tarski, by O'Grady] |
| Full Idea: Tarski's account doesn't hold for natural languages. The general notion of truth is replaced by "true-in-L", where L is a formal language. Hence truth is relativized to each artificial language. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Paul O'Grady - Relativism Ch.2 | |
| A reaction: This is a pretty good indication that Tarski's theory is NOT a correspondence theory, even if its structure may sometimes give that impression. |
| 19324 | Tarski has to avoid stating how truths relate to states of affairs [Kirkham on Tarski] |
| Full Idea: Tarski has to define truths so as not to make explicit the relation between a true sentence and an obtaining state of affairs. ...He has to list each sentence separately, and simply assign it a state of affairs. | |
| From: comment on Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Richard L. Kirkham - Theories of Truth: a Critical Introduction 5.8 | |
| A reaction: He has to avoid semantic concepts like 'reference', because he wants a physicalist theory, according to Kirkham. Thus the hot interest in theories of reference in the 1970s/80s. And also attempts to give a physicalist account of meaning. |
| 10672 | Tarskian semantics says that a sentence is true iff it is satisfied by every sequence [Tarski, by Hossack] |
| Full Idea: Tarskian semantics says that a sentence is true iff it is satisfied by every sequence, where a sequence is a set-theoretic individual, a set of ordered pairs each with a natural number as its first element and an object from the domain for its second. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Keith Hossack - Plurals and Complexes 3 |
| 15410 | Truth only applies to closed formulas, but we need satisfaction of open formulas to define it [Burgess on Tarski] |
| Full Idea: In Tarski's theory of truth, although the notion of truth is applicable only to closed formulas, to define it we must define a more general notion of satisfaction applicable to open formulas. | |
| From: comment on Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by John P. Burgess - Philosophical Logic 1.8 | |
| A reaction: This is a helpful pointer to what is going on in the Tarski definition. It culminates in the 'satisfaction of all sequences', which presumable delivers the required closed formula. |
| 18811 | Tarski uses sentential functions; truly assigning the objects to variables is what satisfies them [Tarski, by Rumfitt] |
| Full Idea: Tarski invoked the notion of a sentential function, where components are replaced by appropriate variables. A function is then satisfied by assigning objects to variables. An assignment satisfies if the function is true of the things assigned. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Ian Rumfitt - The Boundary Stones of Thought 3.2 | |
| A reaction: [very compressed] This use of sentential functions, rather than sentences, looks like the key to Tarski's definition of truth. |
| 15365 | We can define the truth predicate using 'true of' (satisfaction) for variables and some objects [Tarski, by Horsten] |
| Full Idea: The truth predicate, says Tarski, should be defined in terms of the more primitive satisfaction relation: the relation of being 'true of'. The fundamental notion is a formula (containing the free variables) being true of a sequence of objects as values. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Leon Horsten - The Tarskian Turn 06.3 |
| 19314 | For physicalism, reduce truth to satisfaction, then define satisfaction as physical-plus-logic [Tarski, by Kirkham] |
| Full Idea: Tarski, a physicalist, reduced semantics to physical and/or logicomathematical concepts. He defined all semantic concepts, save satisfaction, in terms of truth. Then truth is defined in terms of satisfaction, and satisfaction is given non-semantically. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Richard L. Kirkham - Theories of Truth: a Critical Introduction 5.1 | |
| A reaction: The term 'logicomathematical' is intended to cover set theory. Kirkham says you can remove these restrictions from Tarski's theory, and the result is a version of the correspondence theory. |
| 19316 | Insight: don't use truth, use a property which can be compositional in complex quantified sentence [Tarski, by Kirkham] |
| Full Idea: Tarski's great insight is find another property, since open sentences are not truth. It must be had by open and genuine sentences. Clauses having it must generate it for the whole sentence. Truth can be defined for sentences by using it. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Richard L. Kirkham - Theories of Truth: a Critical Introduction 5.4 | |
| A reaction: The proposed property is 'satisfaction', which can (unlike truth) be a feature open sentences (such as 'x is green', which is satisfied by x='grass'), |
| 19175 | Tarski gave axioms for satisfaction, then derived its explicit definition, which led to defining truth [Tarski, by Davidson] |
| Full Idea: Tarski turned his axiomatic characterisation of satisfaction into an explicit definition of the satisfaction-predicate using some fancy set theoretical apparatus, and this in turn leads to the explicit definition of the truth predicate. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Donald Davidson - Truth and Predication 7 |
| 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. |
| 16303 | Tarski made truth respectable, by proving that it could be defined [Tarski, by Halbach] |
| Full Idea: Tarski's proof of the definability of truth allowed him to establish truth as a respectable notion by his standards. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Volker Halbach - Axiomatic Theories of Truth 3 |
| 19134 | Tarski defined truth for particular languages, but didn't define it across languages [Davidson on Tarski] |
| Full Idea: Tarski defined various predicates of the form 's is true in L', each applicable to a single language, but he failed to define a predicate of the form 's is true in L' for variable 'L'. | |
| From: comment on Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Donald Davidson - Truth and Predication 1 | |
| A reaction: You might say that no one defines 'tree' to be just 'in English', but we might define 'multiplies' to be in Peano Arithmetic. This indicates the limited and formal nature of what Tarski was trying to achieve. |
| 16304 | Tarski didn't capture the notion of an adequate truth definition, as Convention T won't prove non-contradiction [Halbach on Tarski] |
| Full Idea: Every really adequate theory of truth should also prove the law of non-contradiction. Therefore Tarski's notion of adequacy in Convention T fails to capture the intuitive notion of adequacy he is after. | |
| From: comment on Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Volker Halbach - Axiomatic Theories of Truth 3 | |
| A reaction: Tarski points out this weakness, in a passage quoted by Halbach. This obviously raises the question of what truth theories should prove, and this is explored by Halbach. If they start to prove arithmetic, we get nervous. Non-contradiction and x-middle? |
| 2571 | Tarski says that his semantic theory of truth is completely neutral about all metaphysics [Tarski, by Haack] |
| Full Idea: Tarski says "we may remain naïve realists or idealists, empiricists or metaphysicians… The semantic conception is completely neutral toward all these issues." | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Susan Haack - Philosophy of Logics 7.5 |
| 10821 | Physicalists should explain reference nonsemantically, rather than getting rid of it [Tarski, by Field,H] |
| Full Idea: Tarski work was to persuade physicalist that eliminating semantics was on the wrong track, and that we should explicate notions in the theory of reference nonsemantically rather than simply get rid of them. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Hartry Field - Tarski's Theory of Truth §3 |
| 10822 | A physicalist account must add primitive reference to Tarski's theory [Field,H on Tarski] |
| Full Idea: We need to add theories of primitive reference to Tarski's account if we are to establish the notion of truth as a physicalistically acceptable notion. | |
| From: comment on Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Hartry Field - Tarski's Theory of Truth §4 | |
| A reaction: This is the main point of Field's paper, and sounds very plausible to me. There is something major missing from Tarski, and at some point there needs to be a 'primitive' notion of thought and language making contact with the world, as it can't be proved. |
| 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. |
| 10969 | Tarski had a theory of truth, and a theory of theories of truth [Tarski, by Read] |
| Full Idea: Besides a theory of truth of his own, Tarski developed a theory of theories of truth. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Stephen Read - Thinking About Logic Ch.1 | |
| A reaction: The famous snow biconditional is the latter, and the recursive account based on satisfaction is the former. |
| 17746 | Tarski's 'truth' is a precise relation between the language and its semantics [Tarski, by Walicki] |
| Full Idea: Tarski's analysis of the concept of 'truth' ...is given a precise treatment as a particular relation between syntax (language) and semantics (the world). | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Michal Walicki - Introduction to Mathematical Logic History E.1 | |
| A reaction: My problem is that the concept of truth seems to apply to animal minds, which are capable of making right or wrong judgements, and of realising their errors. Tarski didn't make universal claims for his account. |
| 10904 | Tarskian truth neglects the atomic sentences [Mulligan/Simons/Smith on Tarski] |
| Full Idea: The Tarskian account of truth neglects the atomic sentences. | |
| From: comment on Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Mulligan/Simons/Smith - Truth-makers §1 | |
| A reaction: Yes! The whole Tarskian edifice is built on a foundation which it is taboo even to mention. If truth is just the assignment of 'T' and 'F', that isn't even the beginnings of a theory of 'truth'. |
| 15322 | Tarski's had the first axiomatic theory of truth that was minimally adequate [Tarski, by Horsten] |
| Full Idea: Tarski's work is the earliest axiomatic theory of truth that meets minimal adequacy conditions. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Leon Horsten - The Tarskian Turn 01.1 | |
| A reaction: This shows a way in which Tarski gave a new direction to the study of truth. Subsequent theories have been 'stronger'. |
| 16306 | Tarski defined truth, but an axiomatisation can be extracted from his inductive clauses [Tarski, by Halbach] |
| Full Idea: Tarski preferred a definition of truth, but from that an axiomatisation can be extracted. His induction clauses can be turned into axioms. Hence he opened the way to axiomatic theories of truth. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Volker Halbach - Axiomatic Theories of Truth 3 |
| 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) |
| 18759 | Identity is invariant under arbitrary permutations, so it seems to be a logical term [Tarski, by McGee] |
| Full Idea: Tarski showed that the only binary relations invariant under arbitrary permutations are the universal relation, the empty relation, identity and non-identity, thus giving us a reason to include '=' among the logical terms. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Vann McGee - Logical Consequence 6 | |
| A reaction: Tarski was looking for a criterion to distinguish logical from non-logical terms, since his account of logical validity depended on it. This idea lies behind whether a logic is or is not specified to be 'with identity' (i.e. using '='). |
| 10823 | A name denotes an object if the object satisfies a particular sentential function [Tarski] |
| Full Idea: To say that the name x denotes a given object a is the same as to stipulate that the object a ... satisfies a sentential function of a particular type. | |
| From: Alfred Tarski (The Concept of Truth for Formalized Languages [1933], p.194) |
| 18756 | Tarski built a compositional semantics for predicate logic, from dependent satisfactions [Tarski, by McGee] |
| Full Idea: Tarski discovered how to give a compositional semantics for predicate calculus, defining truth in terms of satisfaction, and showing how satisfaction for a complicated formula depends on satisfaction of the simple subformulas. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Vann McGee - Logical Consequence 4 | |
| A reaction: The problem was that the subformulas may contain free variables, and thus not be sentences with truth values. 'Satisfaction' can handle this, where 'truth' cannot (I think). |
| 19313 | Tarksi invented the first semantics for predicate logic, using this conception of truth [Tarski, by Kirkham] |
| Full Idea: Tarski invented a formal semantics for quantified predicate logic, the logic of reasoning about mathematics. The heart of this great accomplishment is his theory of truth. It has been called semantic 'theory' of truth, but Tarski preferred 'conception'. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Richard L. Kirkham - Theories of Truth: a Critical Introduction 5.1 |
| 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. |
| 16323 | The object language/ metalanguage distinction is the basis of model theory [Tarski, by Halbach] |
| Full Idea: Tarski's distinction between object and metalanguage forms the basis of model theory. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Volker Halbach - Axiomatic Theories of Truth 11 |
| 8940 | Tarski avoids the Liar Paradox, because truth cannot be asserted within the object language [Tarski, by Fisher] |
| Full Idea: In Tarski's account of truth, self-reference (as found in the Liar Paradox) is prevented because the truth predicate for any given object language is never a part of that object language, and so a sentence can never predicate truth of itself. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Jennifer Fisher - On the Philosophy of Logic 03.I | |
| A reaction: Thus we solve the Liar Paradox by ruling that 'you are not allowed to say that'. Hm. The slightly odd result is that in any conversation about whether p is true, we end up using (logically speaking) two different languages simultaneously. Hm. |
| 10154 | Tarski's theory of truth shifted the approach away from syntax, to set theory and semantics [Feferman/Feferman on Tarski] |
| Full Idea: Tarski's theory of truth has been most influential in eventually creating a shift from the entirely syntactic way of doing things in metamathematics (promoted by Hilbert in the 1920s, in his theory of proofs), towards a set-theoretical, semantic approach. | |
| From: comment on Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Feferman / Feferman - Alfred Tarski: life and logic Int III |
| 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. |
| 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. |
| 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. |
| 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?' |
| 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). |
| 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? |
| 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) |
| 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'. |
| 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. |
| 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. |
| 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. |
| 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. |
| 20407 | Taste is the capacity to judge an object or representation which is thought to be beautiful [Tarski, by Schellekens] |
| Full Idea: Taste is the faculty for judging an object or a kind of representation through a satisfaction or a dissatisfaction, ...where the object of such a satisfaction is called beautiful. | |
| From: report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Elizabeth Schellekens - Immanuel Kant (aesthetics) 1 | |
| A reaction: We usually avoid the word 'faculty' nowadays, because it implies a specific mechanism, but 'capacity' will do. Kant is said to focus specifically on beauty, whereas modern aestheticians have a broader view of the type of subject matter. |