133 ideas
| 19199 | Some say metaphysics is a highly generalised empirical study of objects [Tarski] |
| Full Idea: For some people metaphysics is a general theory of objects (ontology) - a discipline which is to be developed in a purely empirical way, and which differs from other empirical disciplines in its generality. | |
| From: Alfred Tarski (The Semantic Conception of Truth [1944], 19) | |
| A reaction: Tarski says some people despise it, but for him such metaphysics is 'not objectionable'. I subscribe to this view, but the empirical aspect is very remote, because it's too general for detail observation or experiment. Generality is the key to philosophy. |
| 19193 | Disputes that fail to use precise scientific terminology are all meaningless [Tarski] |
| Full Idea: Disputes like the vague one about 'the right conception of truth' occur in all domains where, instead of exact, scientific terminology, common language with its vagueness and ambiguity is used; and they are always meaningless, and therefore in vain. | |
| From: Alfred Tarski (The Semantic Conception of Truth [1944], 14) | |
| A reaction: Taski taught a large number of famous philosophers in California in the 1950s, and this approach has had a huge influence. Recently there has been a bit of a rebellion. E.g. Kit Fine doesn't think it can all be done in formal languages. |
| 19179 | For a definition we need the words or concepts used, the rules, and the structure of the language [Tarski] |
| Full Idea: We must specify the words or concepts which we wish to use in defining the notion of truth; and we must also give the formal rules to which the definition should conform. More generally, we must describe the formal structure of the language. | |
| From: Alfred Tarski (The Semantic Conception of Truth [1944], 01) | |
| A reaction: This, of course, is a highly formal view of how definition should be achieved, offered in anticipation of one of the most famous definitions in logic (of truth, by Tarski). Normally we assume English and classical logic. |
| 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. |
| 10153 | In everyday language, truth seems indefinable, inconsistent, and illogical [Tarski] |
| Full Idea: In everyday language it seems impossible to define the notion of truth or even to use this notion in a consistent manner and in agreement with the laws of logic. | |
| From: Alfred Tarski (works [1936]), quoted by Feferman / Feferman - Alfred Tarski: life and logic Int III | |
| A reaction: [1935] See Logic|Theory of Logic|Semantics of Logic for Tarski's approach to truth. |
| 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. |
| 19178 | Definitions of truth should not introduce a new version of the concept, but capture the old one [Tarski] |
| Full Idea: The desired definition of truth does not aim to specify the meaning of a familiar word used to denote a novel notion; on the contrary, it aims to catch hold of the actual meaning of an old notion. | |
| From: Alfred Tarski (The Semantic Conception of Truth [1944], 01) | |
| A reaction: Tarski refers back to Aristotle for an account of the 'old notion'. To many the definition of Tarski looks very weird, so it is important to see that he is trying to capture the original concept. |
| 19177 | A definition of truth should be materially adequate and formally correct [Tarski] |
| Full Idea: The main problem of the notion of truth is to give a satisfactory definition which is materially adequate and formally correct. | |
| From: Alfred Tarski (The Semantic Conception of Truth [1944], 01) | |
| A reaction: That is, I take it, that it covers all cases of being true and failing to be true, and it fits in with the logic. The logic is explicitly classical logic, and he is not aiming to give the 'nature' or natural language understanding of the concept. |
| 19186 | A rigorous definition of truth is only possible in an exactly specified language [Tarski] |
| Full Idea: The problem of the definition of truth obtains a precise meaning and can be solved in a rigorous way only for those languages whose structure has been exactly specified. | |
| From: Alfred Tarski (The Semantic Conception of Truth [1944], 06) | |
| A reaction: Taski has just stated how to exactly specify the structure of a language. He says definition can only be vague and approximate for natural languages. (The usual criticism of the correspondence theory is its vagueness). |
| 19194 | We may eventually need to split the word 'true' into several less ambiguous terms [Tarski] |
| Full Idea: A time may come when we find ourselves confronted with several incompatible, but equally clear and precise, conceptions of truth. It will then become necessary to abandon the ambiguous usage of the word 'true', and introduce several terms instead. | |
| From: Alfred Tarski (The Semantic Conception of Truth [1944], 14) | |
| A reaction: There may be a whiff of the pragmatic attitude to truth here, though that view is not necessarily pluralist. Analytic philosophy needs much more splitting of difficult terms into several more focused terms. |
| 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. |
| 19196 | Scheme (T) is not a definition of truth [Tarski] |
| Full Idea: It is a mistake to regard scheme (T) as a definition of truth. | |
| From: Alfred Tarski (The Semantic Conception of Truth [1944], 15) | |
| A reaction: The point is, I take it, that the definition is the multitude of sentences which are generated by the schema, not the schema itself. |
| 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 |
| 13338 | '"It is snowing" is true if and only if it is snowing' is a partial definition of the concept of truth [Tarski] |
| Full Idea: Statements of the form '"it is snowing" is true if and only if it is snowing' and '"the world war will begin in 1963" is true if and only if the world war will being in 1963' can be regarded as partial definitions of the concept of truth. | |
| From: Alfred Tarski (The Establishment of Scientific Semantics [1936], p.404) | |
| A reaction: The key word here is 'partial'. Truth is defined, presumably, when every such translation from the object language has been articulated, which is presumably impossible, given the infinity of concatenated phrases possible in a sentence. |
| 19180 | It is convenient to attach 'true' to sentences, and hence the language must be specified [Tarski] |
| Full Idea: For several reasons it appears most convenient to apply the term 'true' to sentences, and we shall follow this course. Consequently, we must always relate the notion of truth, like that of a sentence, to a specific language. | |
| From: Alfred Tarski (The Semantic Conception of Truth [1944], 02) | |
| A reaction: Personally I take truth to attach to propositions, since sentences are ambiguous. In Idea 17308 the one sentence expresses three different truths (in my opinion), even though a single sentence (given in the object language) specifies it. |
| 19181 | In the classical concept of truth, 'snow is white' is true if snow is white [Tarski] |
| Full Idea: If we base ourselves on the classical conception of truth, we shall say that the sentence 'snow is white' is true if snow is white, and it is false if snow is not white. | |
| From: Alfred Tarski (The Semantic Conception of Truth [1944], 04) | |
| A reaction: I had not realised, prior to his, how closely Tarski is sticking to Aristotle's famous formulation of truth. The point is that you can only specify 'what is' using a language. Putting 'true' in the metalanguage gives specific content to Aristotle. |
| 19183 | Each interpreted T-sentence is a partial definition of truth; the whole definition is their conjunction [Tarski] |
| Full Idea: In 'X is true iff p' if we replace X by the name of a sentence and p by a particular sentence this can be considered a partial definition of truth. The whole definition has to be ...a logical conjunction of all these partial definitions. | |
| From: Alfred Tarski (The Semantic Conception of Truth [1944], 04) | |
| A reaction: This seems an unprecedented and odd way to define something. Define 'red' by '"This tomato is red" iff this tomato is red', etc? Define 'stone' by collecting together all the stones? The complex T-sentences are infinite in number. |
| 19182 | Use 'true' so that all T-sentences can be asserted, and the definition will then be 'adequate' [Tarski] |
| Full Idea: We wish to use the term 'true' in such a way that all the equivalences of the form (T) [i.e. X is true iff p] can be asserted, and we shall call a definition of truth 'adequate' if all these equivalences follow from it. | |
| From: Alfred Tarski (The Semantic Conception of Truth [1944], 04) | |
| A reaction: The interpretation of Tarski's theory is difficult. From this I'm thinking that 'true' is simply being defined as 'assertible'. This is the status of each line in a logical proof, if there is a semantic dimension to the proof (and not mere syntax). |
| 19198 | We don't give conditions for asserting 'snow is white'; just that assertion implies 'snow is white' is true [Tarski] |
| Full Idea: Semantic truth implies nothing regarding the conditions under which 'snow is white' can be asserted. It implies only that, whenever we assert or reject this sentence, we must be ready to assert or reject the correlated sentence '"snow is white" is true'. | |
| From: Alfred Tarski (The Semantic Conception of Truth [1944], 18) | |
| A reaction: This appears to identify truth with assertibility, which is pretty much what modern pragmatists say. How do you distinguish 'genuine' assertion from rhetorical, teasing or lying assertions? Genuine assertion implies truth? Hm. |
| 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 |
| 19184 | The best truth definition involves other semantic notions, like satisfaction (relating terms and objects) [Tarski] |
| Full Idea: It turns out that the simplest and most natural way of obtaining an exact definition of truth is one which involves the use of other semantic notions, e.g. the notion of satisfaction (...which expresses relations between expressions and objects). | |
| From: Alfred Tarski (The Semantic Conception of Truth [1944], 05) | |
| A reaction: While the T-sentences appear to be 'minimal' and 'deflationary', it seems important to remember that 'satisfaction', which is basic to his theory, is a very robust notion. He actually mentions 'objects'. But see Idea 19185. |
| 19191 | Specify satisfaction for simple sentences, then compounds; true sentences are satisfied by all objects [Tarski] |
| Full Idea: To define satisfaction we indicate which objects satisfy the simplest sentential functions, then state the conditions for compound functions. This applies automatically to sentences (with no free variables) so a true sentence is satisfied by all objects. | |
| From: Alfred Tarski (The Semantic Conception of Truth [1944], 11) | |
| A reaction: I presume nothing in the domain of objects can conflict with a sentence that has been satisfied by some of them, so 'all' the objects satisfy the sentence. Tarski doesn't use the word 'domain'. Basic satisfaction seems to be stipulated. |
| 19188 | We can't use a semantically closed language, or ditch our logic, so a meta-language is needed [Tarski] |
| Full Idea: In a 'semantically closed' language all sentences which determine the adequate usage of 'true' can be asserted in the language. ...We can't change our logic, so we reject such languages. ...So must use two different languages to discuss truth. | |
| From: Alfred Tarski (The Semantic Conception of Truth [1944], 08-09) | |
| A reaction: This section explains why a meta-language is required. It rests entirely on the existence of the Liar paradox is a semantically closed language. |
| 19189 | The metalanguage must contain the object language, logic, and defined semantics [Tarski] |
| Full Idea: Every sentence which occurs in the object language must also occur in the metalanguage, or can be translated into the metalanguage. There must also be logical terms, ...and semantic terms can only be introduced in the metalanguage by definition. | |
| From: Alfred Tarski (The Semantic Conception of Truth [1944], 09) | |
| A reaction: He suggest that if the languages are 'typed', the meta-languag, to be 'richer', must contain variables of a higher logica type. Does this mean second-order logic? |
| 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'. |
| 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 naďve 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. |
| 10824 | If listing equivalences is a reduction of truth, witchcraft is just a list of witch-victim pairs [Field,H on Tarski] |
| Full Idea: By similar standards of reduction to Tarski's, one might prove witchcraft compatible with physicalism, as long as witches cast only a finite number of spells. We merely list witch-and-victim pairs, with no mention of the terms of witchcraft theory. | |
| From: comment on Alfred Tarski (The Semantic Conception of Truth [1944], 04) by Hartry Field - Tarski's Theory of Truth §4 |
| 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. |
| 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 |
| 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? |
| 19141 | Tarski thought axiomatic truth was too contingent, and in danger of inconsistencies [Tarski, by Davidson] |
| Full Idea: Tarski preferred an explicit definition of truth to axioms. He says axioms have a rather accidental character, only a definition can guarantee the continued consistency of the system, and it keeps truth in harmony with physical science and physicalism. | |
| From: report of Alfred Tarski (works [1936]) by Donald Davidson - Truth and Predication 2 n2 | |
| A reaction: Davidson's summary, gleaned from various sources in Tarski. A big challenge for modern axiom systems is to avoid inconsistency, which is extremely hard to do (given that set theory is not sure of having achieved it). |
| 19190 | We need an undefined term 'true' in the meta-language, specified by axioms [Tarski] |
| Full Idea: We have to include the term 'true', or some other semantic term, in the list of undefined terms of the meta-language, and to express fundamental properties of the notion of truth in a series of axioms. | |
| From: Alfred Tarski (The Semantic Conception of Truth [1944], 10) | |
| A reaction: It sounds as if Tarski semantic theory gives truth for the object language, but then an axiomatic theory of truth is also needed for the metalanguage. Halbch and Horsten seem to want an axiomatic theory in the object language. |
| 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 |
| 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'. |
| 19197 | Truth can't be eliminated from universal claims, or from particular unspecified claims [Tarski] |
| Full Idea: Truth can't be eliminated from universal statements saying all sentences of a certain type are true, or from the proof that 'all consequences of true sentences are true'. It is also needed if we can't name the sentence ('Plato's first sentence is true'). | |
| From: Alfred Tarski (The Semantic Conception of Truth [1944], 16) | |
| A reaction: This points to the deflationary view of truth, if its only role is in talking about other sentences in this way. Tarski gives the standard reason for rejecting the Redundancy view. |
| 19185 | Semantics is a very modest discipline which solves no real problems [Tarski] |
| Full Idea: Semantics as it is conceived in this paper is a sober and modest discipline which has no pretensions to being a universal patent-medicine for all the ills and diseases of mankind, whether imaginary or real. | |
| From: Alfred Tarski (The Semantic Conception of Truth [1944], 05) | |
| A reaction: Written in 1944. This remark encourages the minimal or deflationary interpretation of his theory of truth, but see the robust use of 'satisfaction' in Idea 19184. |
| 19195 | Truth tables give prior conditions for logic, but are outside the system, and not definitions [Tarski] |
| Full Idea: Logical sentences are often assigned preliminary conditions under which they are true or false (often given as truth tables). However, these are outside the system of logic, and should not be regarded as definitions of the terms involved. | |
| From: Alfred Tarski (The Semantic Conception of Truth [1944], 15) | |
| A reaction: Hence, presumably, the connectives are primitives (with no nature or meaning), and the truth tables are axioms for their use? This opinion of Tarski's may have helped shift the preference towards natural deduction introduction and elimination rules. |
| 10152 | Set theory and logic are fairy tales, but still worth studying [Tarski] |
| Full Idea: People have asked me, 'How can you, a nominalist, do work in set theory and in logic, which are theories about things you do not believe in?' ...I believe that there is a value even in fairy tales and the study of fairy tales. | |
| From: Alfred Tarski (talk [1965]), quoted by Feferman / Feferman - Alfred Tarski: life and logic | |
| A reaction: This is obviously an oversimplification. I don't think for a moment that Tarski literally believed that the study of fairy tales had as much value as the study of logic. Why do we have this particular logic, and not some other? |
| 10048 | There is no clear boundary between the logical and the non-logical [Tarski] |
| Full Idea: No objective grounds are known to me which permit us to draw a sharp boundary between the two groups of terms, the logical and the non-logical. | |
| From: Alfred Tarski (works [1936]), quoted by Alan Musgrave - Logicism Revisited §3 | |
| A reaction: Musgrave is pointing out that this is bad news if you want to 'reduce' something like arithmetic to logic. 'Logic' is a vague object. |
| 13337 | A language: primitive terms, then definition rules, then sentences, then axioms, and finally inference rules [Tarski] |
| Full Idea: For a language, we must enumerate the primitive terms, and the rules of definition for new terms. Then we must distinguish the sentences, and separate out the axioms from amng them, and finally add rules of inference. | |
| From: Alfred Tarski (The Establishment of Scientific Semantics [1936], p.402) | |
| A reaction: [compressed] This lays down the standard modern procedure for defining a logical language. Once all of this is in place, we then add a semantics and we are in business. Natural deduction tries to do without the axioms. |
| 10759 | There are at least seven possible systems of semantics for second-order logic [Rossberg] |
| Full Idea: In addition to standard and Henkin semantics for second-order logic, one might also employ substitutional or game-theoretical or topological semantics, or Boolos's plural interpretation, or even a semantics inspired by Lesniewski. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: This is helpful in seeing the full picture of what is going on in these logical systems. |
| 10751 | Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg] |
| Full Idea: Second-order logic raises doubts because of its ontological commitment to the set-theoretic hierarchy, and the allegedly problematic epistemic status of the second-order consequence relation. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §1) | |
| A reaction: The 'epistemic' problem is whether you can know the truths, given that the logic is incomplete, and so they cannot all be proved. Rossberg defends second-order logic against the second problem. A third problem is that it may be mathematics. |
| 10757 | Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg] |
| Full Idea: Henkin semantics (for second-order logic) specifies a second domain of predicates and relations for the upper case constants and variables. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: This second domain is restricted to predicates and relations which are actually instantiated in the model. Second-order logic is complete with this semantics. Cf. Idea 10756. |
| 18812 | Split out the logical vocabulary, make an assignment to the rest. It's logical if premises and conclusion match [Tarski, by Rumfitt] |
| Full Idea: Tarski made a division of logical and non-logical vocabulary. He then defined a model as a non-logical assignment satisfying the corresponding sentential function. Then a conclusion follows logically if every model of the premises models the conclusion. | |
| From: report of Alfred Tarski (The Concept of Logical Consequence [1936]) by Ian Rumfitt - The Boundary Stones of Thought 3.2 | |
| A reaction: [compressed] This is Tarski's account of logical consequence, which follows on from his account of truth. 'Logical validity' is then 'true in every model'. Rumfitt doubts whether Tarski has given the meaning of 'logical consequence'. |
| 10753 | Logical consequence is intuitively semantic, and captured by model theory [Rossberg] |
| Full Idea: Logical consequence is intuitively taken to be a semantic notion, ...and it is therefore the formal semantics, i.e. the model theory, that captures logical consequence. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §2) | |
| A reaction: If you come at the issue from normal speech, this seems right, but if you start thinking about the necessity of logical consequence, that formal rules and proof-theory seem to be the foundation. |
| 10752 | Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg] |
| Full Idea: Deductive consequence, written Γ|-S, is loosely read as 'the sentence S can be deduced from the sentences Γ', and semantic consequence Γ|=S says 'all models that make Γ true make S true as well'. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §2) | |
| A reaction: We might read |= as 'true in the same model as'. What is the relation, though, between the LHS and the RHS? They seem to be mutually related to some model, but not directly to one another. |
| 10694 | Logical consequence is when in any model in which the premises are true, the conclusion is true [Tarski, by Beall/Restall] |
| Full Idea: Tarski's 1936 definition of logical consequence is that in any model in which the premises are true, the conclusion is true too (so that no model can make the conclusion false). | |
| From: report of Alfred Tarski (works [1936]) by JC Beall / G Restall - Logical Consequence 3 | |
| A reaction: So the general idea is that a logical consequence is distinguished by being unstoppable. Sounds good. But then we have monotonic and non-monotonic logics, which (I'm guessing) embody different notions of consequence. |
| 10479 | Logical consequence: true premises give true conclusions under all interpretations [Tarski, by Hodges,W] |
| Full Idea: Tarski's definition of logical consequence (1936) is that in a fully interpreted formal language an argument is valid iff under any allowed interpretation of its nonlogical symbols, if the premises are true then so is the conclusion. | |
| From: report of Alfred Tarski (works [1936]) by Wilfrid Hodges - Model Theory 3 | |
| A reaction: The idea that you can only make these claims 'under an interpretation' seems to have had a huge influence on later philosophical thinking. |
| 13344 | X follows from sentences K iff every model of K also models X [Tarski] |
| Full Idea: The sentence X follows logically from the sentences of the class K if and only if every model of the class K is also a model of the sentence X. | |
| From: Alfred Tarski (The Concept of Logical Consequence [1936], p.417) | |
| A reaction: [see Idea 13343 for his account of a 'model'] He is offering to define logical consequence in general, but this definition fits what we now call 'semantic consequence', written |=. This it is standard practice to read |= as 'models'. |
| 19192 | The truth definition proves semantic contradiction and excluded middle laws (not the logic laws) [Tarski] |
| Full Idea: With our definition of truth we can prove the laws of contradiction and excluded middle. These semantic laws should not be identified with the related logical laws, which belong to the sentential calculus, and do not involve 'true' at all. | |
| From: Alfred Tarski (The Semantic Conception of Truth [1944], 12) | |
| A reaction: Very illuminating. I wish modern thinkers could be so clear about this matter. The logic contains 'P or not-P'. The semantics contains 'P is either true or false'. Critics say Tarski has presupposed 'classical' logic. |
| 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 '='). |
| 10754 | In proof-theory, logical form is shown by the logical constants [Rossberg] |
| Full Idea: A proof-theorist could insist that the logical form of a sentence is exhibited by the logical constants that it contains. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §2) | |
| A reaction: You have to first get to the formal logical constants, rather than the natural language ones. E.g. what is the truth table for 'but'? There is also the matter of the quantifiers and the domain, and distinguishing real objects and predicates from bogus. |
| 14650 | Maybe proper names involve essentialism [Plantinga] |
| Full Idea: Perhaps the notion of a proper name itself involves essentialism. | |
| From: Alvin Plantinga (De Re and De Dicto [1969], p.43) | |
| A reaction: This is just before Kripke's announcement of 'rigid designation', which seems to have relaunched modern essentialism. The thought is that you can't name something, if you don't have a stable notion of what is (and isn't) being named. |
| 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 |
| 13335 | Semantics is the concepts of connections of language to reality, such as denotation, definition and truth [Tarski] |
| Full Idea: Semantics is the totality of considerations concerning concepts which express connections between expressions of a language and objects and states of affairs referred to by these expressions. Examples are denotation, satisfaction, definition and truth. | |
| From: Alfred Tarski (The Establishment of Scientific Semantics [1936], p.401) | |
| A reaction: Interestingly, he notes that it 'is not commonly recognised' that truth is part of semantics. Nowadays truth seems to be the central concept in most semantics. |
| 13336 | A language containing its own semantics is inconsistent - but we can use a second language [Tarski] |
| Full Idea: People have not been aware that the language about which we speak need by no means coincide with the language in which we speak. ..But the language which contains its own semantics must inevitably be inconsistent. | |
| From: Alfred Tarski (The Establishment of Scientific Semantics [1936], p.402) | |
| A reaction: It seems that Tarski was driven to propose the metalanguage approach mainly by the Liar Paradox. |
| 13339 | A sentence is satisfied when we can assert the sentence when the variables are assigned [Tarski] |
| Full Idea: Here is a partial definition of the concept of satisfaction: John and Peter satisfy the sentential function 'X and Y are brothers' if and only if John and Peter are brothers. | |
| From: Alfred Tarski (The Establishment of Scientific Semantics [1936], p.405) | |
| A reaction: Satisfaction applies to open sentences and truth to closed sentences (with named objects). He uses the notion of total satisfaction to define truth. The example is a partial definition, not just an illustration. |
| 13340 | Satisfaction is the easiest semantical concept to define, and the others will reduce to it [Tarski] |
| Full Idea: It has been found useful in defining semantical concepts to deal first with the concept of satisfaction; both because the definition of this concept presents relatively few difficulties, and because the other semantical concepts are easily reduced to it. | |
| From: Alfred Tarski (The Establishment of Scientific Semantics [1936], p.406) | |
| A reaction: See Idea 13339 for his explanation of satisfaction. We just say that a open sentence is 'acceptable' or 'assertible' (or even 'true') when particular values are assigned to the variables. Then sentence is then 'satisfied'. |
| 13343 | A 'model' is a sequence of objects which satisfies a complete set of sentential functions [Tarski] |
| Full Idea: An arbitrary sequence of objects which satisfies every sentential function of the sentences L' will be called a 'model' or realization of the class L of sentences. There can also be a model of a single sentence is this way. | |
| From: Alfred Tarski (The Concept of Logical Consequence [1936], p.417) | |
| A reaction: [L' is L with the constants replaced by variables] Tarski is the originator of model theory, which is central to modern logic. The word 'realization' is a helpful indicator of what he has in mind. A model begins to look like a possible world. |
| 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 |
| 10756 | A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg] |
| Full Idea: A standard model is a set of objects called the 'domain', and an interpretation function, assigning objects in the domain to names, subsets to predicate letters, subsets of the Cartesian product of the domain with itself to binary relation symbols etc. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: The model actually specifies which objects have which predicates, and which objects are in which relations. Tarski's account of truth in terms of 'satisfaction' seems to be just a description of those pre-decided facts. |
| 10758 | If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model [Rossberg] |
| Full Idea: A mathematical theory is 'categorical' if, and only if, all of its models are isomorphic. Such a theory then essentially has just one model, the standard one. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: So the term 'categorical' is gradually replacing the much-used phrase 'up to isomorphism'. |
| 13341 | Using the definition of truth, we can prove theories consistent within sound logics [Tarski] |
| Full Idea: Using the definition of truth we are in a position to carry out the proof of consistency for deductive theories in which only (materially) true sentences are (formally) provable. | |
| From: Alfred Tarski (The Establishment of Scientific Semantics [1936], p.407) | |
| A reaction: This is evidently what Tarski saw as the most important first fruit of his new semantic theory of truth. |
| 10761 | Completeness can always be achieved by cunning model-design [Rossberg] |
| Full Idea: All that should be required to get a semantics relative to which a given deductive system is complete is a sufficiently cunning model-theorist. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §5) |
| 10755 | A deductive system is only incomplete with respect to a formal semantics [Rossberg] |
| Full Idea: No deductive system is semantically incomplete in and of itself; rather a deductive system is incomplete with respect to a specified formal semantics. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: This important point indicates that a system might be complete with one semantics and incomplete with another. E.g. second-order logic can be made complete by employing a 'Henkin semantics'. |
| 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. |
| 19187 | The Liar makes us assert a false sentence, so it must be taken seriously [Tarski] |
| Full Idea: In my judgement, it would be quite wrong and dangerous from the point of view of scientific progress to depreciate the importance of nhtinomies like the Liar Paradox, and treat them as jokes. The fact is we have been compelled to assert a false sentence. | |
| From: Alfred Tarski (The Semantic Conception of Truth [1944], 07) | |
| A reaction: This is the heartfelt cry of the perfectionist, who wants everything under control. It was the dream of the age of Frege to Hilbert, which gradually eroded after Gödel's Incompleteness proof. Short ordinary folk panic about the Liar? |
| 14648 | Could I name all of the real numbers in one fell swoop? Call them all 'Charley'? [Plantinga] |
| Full Idea: Can't I name all the real numbers in the interval (0,1) at once? Couldn't I name them all 'Charley', for example? | |
| From: Alvin Plantinga (De Re and De Dicto [1969], p.40) | |
| A reaction: Plantinga is nervous about such a sweeping move, but can't think of an objection. This addresses a big problem, I think - that you are supposed to accept the real numbers when we cannot possibly name them all. |
| 10157 | Tarski improved Hilbert's geometry axioms, and without set-theory [Tarski, by Feferman/Feferman] |
| Full Idea: Tarski found an elegant new axiom system for Euclidean geometry that improved Hilbert's earlier version - and he formulated it without the use of set-theoretical notions. | |
| From: report of Alfred Tarski (works [1936]) by Feferman / Feferman - Alfred Tarski: life and logic Ch.9 |
| 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 |
| 14664 | Necessary beings (numbers, properties, sets, propositions, states of affairs, God) exist in all possible worlds [Plantinga] |
| Full Idea: A 'necessary being' is one that exists in every possible world; and only some objects - numbers, properties, pure sets, propositions, states of affairs, God - have this distinction. | |
| From: Alvin Plantinga (Actualism and Possible Worlds [1976], 2) | |
| A reaction: This a very odd list, though it is fairly orthodox among philosophers trained in modern modal logic. At the very least it looks rather parochial to me. |
| 10151 | I am a deeply convinced nominalist [Tarski] |
| Full Idea: I am a nominalist. This is a very deep conviction of mine. ...I am a tortured nominalist. | |
| From: Alfred Tarski (talk [1965]), quoted by Feferman / Feferman - Alfred Tarski: life and logic Int I | |
| A reaction: I too am of the nominalist persuasion, but I don't feel justified in such a strong commitment. |
| 16435 | Plantinga proposes necessary existent essences as surrogates for the nonexistent things [Plantinga, by Stalnaker] |
| Full Idea: Plantinga proposes surrogates for nonexistent things - individual essences that are themselves necessary existents and that correspond one-to-one with all the 'things' that might exist. | |
| From: report of Alvin Plantinga (World and Essence [1970]) by Robert C. Stalnaker - Mere Possibilities 1 | |
| A reaction: There are an awful lot of competing concepts of essence flying around these days. This one seems to require some abstract 'third realm' (or worse) in which these essences can exist, awaiting the arrival of thinkers. Not for me. |
| 14655 | The 'identity criteria' of a name are a group of essential and established facts [Plantinga] |
| Full Idea: What we might call 'identity criteria' associated with a name such as 'Aristotle' are what the users of the name regard as essential and established facts about him. | |
| From: Alvin Plantinga (World and Essence [1970], I) | |
| A reaction: The problem here is that identifying something is superficial, whereas essences run deep. Plantinga is, in fact, talking about Lockean 'nominal essence' (and seems unaware of the fact, and never mentions the Lockean real/nominal distinction). |
| 14647 | Surely self-identity is essential to Socrates? [Plantinga] |
| Full Idea: If anything is essential to Socrates, surely self-identity is. | |
| From: Alvin Plantinga (De Re and De Dicto [1969], p.37) | |
| A reaction: This is the modern move of Plantinga and Adams, to make 'is identical with Socrates' the one property which assures the identity of Socrates (his 'haecceity'). My view is that self-identity is not a property. Plantinga wonders about that on p.44. |
| 14658 | 'Being Socrates' and 'being identical with Socrates' characterise Socrates, so they are among his properties [Plantinga] |
| Full Idea: Surely it is true of Socrates that he is Socrates and he is identical with Socrates. If these are true of him, then 'being Socrates' and 'being identical with Socrates' characterize him; they are among his properties or attributes. | |
| From: Alvin Plantinga (World and Essence [1970], II) | |
| A reaction: As far as I can see (if you insist on accepting self-identity as meaningful) the most you get here is that these are predicates that can attach to Socrates. If you identify predicates with properties you are in deep metaphysical trouble. |
| 13132 | A snowball's haecceity is the property of being identical with itself [Plantinga, by Westerhoff] |
| Full Idea: Plantinga assumes that being identical with that snowball names a property which is that snowball's haecceity. | |
| From: report of Alvin Plantinga (De Essentia [1979]) by Jan Westerhoff - Ontological Categories §52 | |
| A reaction: Only a philosopher would suggest such a bizarre way of establishing the unique individuality of a given snowball. You could hardly keep track of the snowball with just that criterion. How do you decide whether something has Plantinga's property? |
| 14666 | Socrates is a contingent being, but his essence is not; without Socrates, his essence is unexemplified [Plantinga] |
| Full Idea: Socrates is a contingent being; his essence, however, is not. Properties, like propositions and possible worlds, are necessary beings. If Socrates had not existed, his essence would have been unexemplified, but not non-existent. | |
| From: Alvin Plantinga (Actualism and Possible Worlds [1976], 4) | |
| A reaction: This is a distinctive Plantinga view, of which I can make little sense. I take it that Socrates used to have an essence. Being dead, the essence no longer exists, but when we talk about Socrates it is largely this essence to which we refer. OK? |
| 14656 | Does Socrates have essential properties, plus a unique essence (or 'haecceity') which entails them? [Plantinga] |
| Full Idea: Does Socrates have, in addition to his essential properties, an 'essence' or 'haecceity' - a property essential to him that entails each of his essential properties and that nothing distinct from him has in the world? | |
| From: Alvin Plantinga (World and Essence [1970], II) | |
| A reaction: Plantinga says yes, and offers 'Socrateity' (borrowed from Boethius) as his candidate. This is a very odd use of the word 'essence'. I take an essence to be a complex set of fundamental properties. I am also puzzled by his use of the word 'entails'. |
| 14646 | An object has a property essentially if it couldn't conceivably have lacked it [Plantinga] |
| Full Idea: An object has a property essentially just in case it couldn't conceivably have lacked that property. | |
| From: Alvin Plantinga (De Re and De Dicto [1969], p.35) | |
| A reaction: Making it depend on what we can conceive seems a bit dubious, for someone committed to real essences. The key issue is how narrowly or broadly you interpret the word 'property'. The word 'object' needs a bit of thought, too! |
| 14653 | X is essentially P if it is P in every world, or in every X-world, or in the actual world (and not ¬P elsewhere) [Plantinga] |
| Full Idea: Socrates has P essentially if he has P in every world, or has it in every world in which he exists, or - most plausible of all - has P in the actual world and has its complement [non-P] in no world. | |
| From: Alvin Plantinga (World and Essence [1970], Intro) | |
| A reaction: These strike me as mere necessary properties, which are not the same thing at all. Essences give rise to the other properties, but Plantinga offers nothing to do the job (and especially not 'Socrateity'!). Essences must explain, say I! |
| 14660 | If a property is ever essential, can it only ever be an essential property? [Plantinga] |
| Full Idea: Is it the case that any property had essentially by anything is had essentially by everything that has it? | |
| From: Alvin Plantinga (World and Essence [1970], III) | |
| A reaction: Plantinga says it is not true, but the only example he can give is Socrates having the property of 'being Socrates or Greek'. I take it to be universally false. There are not two types of property here. Properties sometimes play an essential role. |
| 14661 | Essences are instantiated, and are what entails a thing's properties and lack of properties [Plantinga] |
| Full Idea: E is an essence if and only if (a) 'has E essentially' is instantiated in some world or other, and (b) for any world W and property P, E entails 'has P in W' or 'does not have P in W'. | |
| From: Alvin Plantinga (World and Essence [1970], IV) | |
| A reaction: 'Entail' strikes me as a very odd word when you are talking about the structure of the physical world (or are we??). Why would a unique self-identity (his candidate for essence) do the necessary entailing? |
| 14654 | Properties are 'trivially essential' if they are instantiated by every object in every possible world [Plantinga] |
| Full Idea: Let us call properties that enjoy the distinction of being instantiated by every object in every possible world 'trivially essential properties'. | |
| From: Alvin Plantinga (World and Essence [1970], I) | |
| A reaction: These would appear to be trivially 'necessary' rather than 'essential'. This continual need for the qualifier 'trivial' shows that they are not talking about proper essences. |
| 14657 | Does 'being identical with Socrates' name a property? I can think of no objections to it [Plantinga] |
| Full Idea: Is there any reason to suppose that 'being identical with Socrates' names a property? Well, is there any reason to suppose that it does not? I cannot think of any, nor have I heard any that are at all impressive. | |
| From: Alvin Plantinga (World and Essence [1970], II) | |
| A reaction: Is there any reason to think that a planet somewhere is entirely under the control of white mice? Extraordinary. No wonder Plantinga believes in God and the Ontological Argument, as well as the existence of 'Socrateity' etc. |
| 14642 | Expressing modality about a statement is 'de dicto'; expressing it of property-possession is 'de re' [Plantinga] |
| Full Idea: Some statements predicate modality of another statement (modality 'de dicto'); but others predicate of an object the necessary or essential possession of a property; these latter express modality 'de re'. | |
| From: Alvin Plantinga (De Re and De Dicto [1969], p.26) | |
| A reaction: The distinction seems to originate in Aquinas, concerning whether God knows the future (or, how he knows the future). 'De dicto' is straightforward, but possibly the result of convention. 'De re' is controversial, and implies deep metaphysics. |
| 14643 | 'De dicto' true and 'de re' false is possible, and so is 'de dicto' false and 'de re' true [Plantinga] |
| Full Idea: Aquinas says if a 'de dicto' statement is true, the 'de re' version may be false. The opposite also applies: 'What I am thinking of [17] is essentially prime' is true, but 'The proposition "what I am thinking of is prime" is necessarily true' is false. | |
| From: Alvin Plantinga (De Re and De Dicto [1969], p.27) | |
| A reaction: In his examples the first is 'de re' (about the number), and the second is 'de dicto' (about that proposition). |
| 14649 | Can we find an appropriate 'de dicto' paraphrase for any 'de re' proposition? [Plantinga] |
| Full Idea: To explain the 'de re' via the 'de dicto' is to provide a rule enabling us to find, for each de re proposition, an equivalent de dicto proposition. | |
| From: Alvin Plantinga (De Re and De Dicto [1969], p.41) | |
| A reaction: Many 'de dicto' paraphrases will change the modality of a 'de re' statement, so the challenge is to find the right equivalent version. Plantinga takes up this challenge. The 'de dicto' statement says the object has the property, and must have it. |
| 14652 | 'De re' modality is as clear as 'de dicto' modality, because they are logically equivalent [Plantinga] |
| Full Idea: The idea of modality 'de re' is no more (although no less) obscure that the idea of modality 'de dicto'; for I think we can see that any statement of the former type is logically equivalent to some statement of the latter. | |
| From: Alvin Plantinga (World and Essence [1970], Intro) | |
| A reaction: If two things are logically equivalent, that doesn't ensure that they are equally clear! Personally I am on the side of de re modality. |
| 14659 | We can imagine being beetles or alligators, so it is possible we might have such bodies [Plantinga] |
| Full Idea: We easily understand Kafka's story about the man who wakes up to discover that he now has the body of a beetle; and in fact the state of affairs depicted is entirely possible. I can imagine being an alligator, so Socrates could have had an alligator body. | |
| From: Alvin Plantinga (World and Essence [1970], III) | |
| A reaction: This really is going the whole hog with accepting whatever is conceivable as being possible. I take this to be shocking nonsense, and it greatly reduces Plantinga in my esteem, despite his displays of intelligence and erudition. |
| 11984 | Asserting a possible property is to say it would have had the property if that world had been actual [Plantinga] |
| Full Idea: To say than x has a property in a possible world is simply to say that x would have had the property if that world had been actual. | |
| From: Alvin Plantinga (Transworld Identity or worldbound Individuals? [1973], I) | |
| A reaction: Plantinga tries to defuse all the problems with identity across possible worlds, by hanging on to subjunctive verbs and modal modifiers. The point, though, was to explain these, or at least to try to give their logical form. |
| 14662 | Possible worlds clarify possibility, propositions, properties, sets, counterfacts, time, determinism etc. [Plantinga] |
| Full Idea: The idea of possible worlds has delivered insights on logical possibility (de dicto and de re), propositions, properties and sets, counterfactuals, time and temporal relations, causal determinism, the ontological argument, and the problem of evil. | |
| From: Alvin Plantinga (Actualism and Possible Worlds [1976], Intro) | |
| A reaction: This date (1976) seems to be the high-water mark for enthusiasm about possible worlds. I suppose if we just stick to 'insights' rather than 'answers' then the big claim might still be acceptable. Which problems are created by possible worlds? |
| 18383 | Plantinga says there is just this world, with possibilities expressed in propositions [Plantinga, by Armstrong] |
| Full Idea: Plantinga rejects other possible worlds, but adds to our world an uncountable multitude of sets of propositions, each set a way that the world might have been, but is in fact not. (Roughly, for each Lewis world, Plantinga has such a set). | |
| From: report of Alvin Plantinga (The Nature of Necessity [1974]) by David M. Armstrong - Truth and Truthmakers 07.2 | |
| A reaction: To me it seems as ontologically extravagant to postulate unexpressed propositions as to postulate concrete possible worlds. I think the best line is that there is just the actual world, with the possibilities implied in its dispositions. |
| 16472 | Plantinga's actualism is nominal, because he fills actuality with possibilia [Stalnaker on Plantinga] |
| Full Idea: Plantinga's critics worry that the metaphysics is actualist in name only, since it is achieved only by populating the actual world with entities whose nature is explained in terms of merely possible things that would exemplify them if anything did. | |
| From: comment on Alvin Plantinga (Actualism and Possible Worlds [1976]) by Robert C. Stalnaker - Mere Possibilities 4.4 | |
| A reaction: Plantinga seems a long way from the usual motivation for actualism, which is probably sceptical empiricism, and building a system on what is smack in front of you. Possibilities have to be true, though. That's why you need dispositions in actuality. |
| 11980 | A possible world is a maximal possible state of affairs [Plantinga] |
| Full Idea: A possible world is just a maximal possible state of affairs. | |
| From: Alvin Plantinga (Transworld Identity or worldbound Individuals? [1973], I) | |
| A reaction: The key point here is that Plantinga includes the word 'possible' in his definition. Possibility defines the worlds, and so worlds cannot be used on their own to define possibility. |
| 14651 | What Socrates could have been, and could have become, are different? [Plantinga] |
| Full Idea: Is there a difference between what Socrates could have been, and what he could have become? | |
| From: Alvin Plantinga (De Re and De Dicto [1969], p.44) | |
| A reaction: That is, I take it, 1) how different might he have been in the past, given how he is now?, and 2) how different might he have been in the past, and now, if he had permanently diverged from how he is now? 1) has tight constraints on it. |
| 11982 | If possible Socrates differs from actual Socrates, the Indiscernibility of Identicals says they are different [Plantinga] |
| Full Idea: If the Socrates of the actual world has snubnosedness but Socrates-in-W does not, this is surely inconsistent with the Indiscernibility of Identicals, a principle than which none sounder can be conceived. | |
| From: Alvin Plantinga (Transworld Identity or worldbound Individuals? [1973], I) | |
| A reaction: However, we allow Socrates to differ over time while remaining the same Socrates, so some similar approach should apply here. In both cases we need some notion of what is essential to Socrates. But what unites aged 3 with aged 70? |
| 11983 | It doesn't matter that we can't identify the possible Socrates; we can't identify adults from baby photos [Plantinga] |
| Full Idea: We may say it makes no sense to say that Socrates exists at a world, if there is in principle no way of identifying him. ...But this is confused. To suppose Agnew was a precocious baby, we needn't be able to pick him from a gallery of babies. | |
| From: Alvin Plantinga (Transworld Identity or worldbound Individuals? [1973], I) | |
| A reaction: This seems a good point, and yet we have a space-time line joining adult Agnew with baby Agnew, and no such causal link is available between persons in different possible worlds. What would be the criterion in each case? |
| 11985 | If individuals can only exist in one world, then they can never lack any of their properties [Plantinga] |
| Full Idea: The Theory of Worldbound Individuals contends that no object exists in more than one possible world; this implies the outrageous view that - taking properties in the broadest sense - no object could have lacked any property that it in fact has. | |
| From: Alvin Plantinga (Transworld Identity or worldbound Individuals? [1973], II) | |
| A reaction: Leibniz is the best known exponent of this 'outrageous view', though Plantinga shows that Lewis may be seen in the same light, since only counterparts are found in possible worlds, not the real thing. The Theory does seem wrong. |
| 11891 | Possibilities for an individual can only refer to that individual, in some possible world [Plantinga, by Mackie,P] |
| Full Idea: Plantinga says for an individual to exist with certain properties in some possible world is simply for it to be true that, had that possible world obtained, that individual would have existed with those properties. | |
| From: report of Alvin Plantinga (The Nature of Necessity [1974]) by Penelope Mackie - How Things Might Have Been 5.1 | |
| A reaction: This is intended to dissolve the problem of transworld identity, and is certainly a flat rejection of counterparts. I take the point to be that the individual is the key element in defining the possible world, so can't possibly be different. |
| 11986 | The counterparts of Socrates have self-identity, but only the actual Socrates has identity-with-Socrates [Plantinga] |
| Full Idea: While Socrates has no counterparts that lack self-identity, he does have counterparts that lack identity-with-Socrates. He alone has that - the property, that is, of being identical with the object that in fact instantiates Socrateity. | |
| From: Alvin Plantinga (Transworld Identity or worldbound Individuals? [1973], II) | |
| A reaction: I am never persuaded by arguments which rest on such dubious pseudo-properties. Whether or not a counterpart of Socrates has any sort of identity with Socrates cannot be prejudged, as it would beg the question. |
| 11987 | Counterpart Theory absurdly says I would be someone else if things went differently [Plantinga] |
| Full Idea: It makes no sense to say I could have been someone else, yet Counterpart Theory implies not merely that I could have been distinct from myself, but that I would have been distinct from myself had things gone differently in even the most miniscule detail. | |
| From: Alvin Plantinga (Transworld Identity or worldbound Individuals? [1973], II) | |
| A reaction: A counterpart doesn't appear to be 'me being distinct from myself'. We have to combine counterparts over possible worlds with perdurance over time. I am a 'worm' of time-slices. Anything not in that worm is not strictly me. |
| 6356 | Maybe a reliable justification must come from a process working with its 'proper function' [Plantinga, by Pollock/Cruz] |
| Full Idea: A modified version of reliabilism proposes that a belief is justified in case it is the product of a process that is working according to its 'proper function' in the environment for which it is appropriate. | |
| From: report of Alvin Plantinga (Warrant and Proper Function [1993]) by J Pollock / J Cruz - Contemporary theories of Knowledge (2nd) §1.5.4 | |
| A reaction: Something might infallibly indicate something without that being its proper function (e.g. 'Red sky at night/ Shepherds' delight'). An inaccurate clock is fulfilling its proper function (telling the time), but not very well. |
| 9086 | The idea of abstract objects is not ontological; it comes from the epistemological idea of abstraction [Plantinga] |
| Full Idea: The notion of an abstract object comes from the notion of abstraction; it is in origin an epistemological rather than an ontological category. | |
| From: Alvin Plantinga (Why Propositions cannot be concrete [1993], p.232) | |
| A reaction: Etymology doesn't prove anything. However, if you define abstract objects as not existing in space or time, you must recognise that this may only be because that is how humans imaginatively created them in the first place. |
| 9087 | Theists may see abstract objects as really divine thoughts [Plantinga] |
| Full Idea: Theists may find attractive a view popular among medieval philosophers from Augustine on: that abstract objects are really divine thoughts. More exactly, propositions are divine thoughts, properties divine concepts, and sets divine collections. | |
| From: Alvin Plantinga (Why Propositions cannot be concrete [1993], p.233) | |
| A reaction: Hm. I pass this on because we should be aware that there is a theological history to discussions of abstract objects, and some people have vested interests in keeping them outside of the natural world. Aren't properties natural? Does God gerrymander sets? |
| 16469 | Plantinga has domains of sets of essences, variables denoting essences, and predicates as functions [Plantinga, by Stalnaker] |
| Full Idea: The domains in Plantinga's interpretation of Kripke's semantics are sets of essences, and the values of variables are essences. The values of predicates have to be functions from possible worlds to essences. | |
| From: report of Alvin Plantinga (Actualism and Possible Worlds [1976]) by Robert C. Stalnaker - Mere Possibilities 4.4 | |
| A reaction: I begin to think this is quite nice, as long as one doesn't take the commitment to the essences too seriously. For 'essence' read 'minimal identity'? But I take essences to be more than minimal, so use identities (which Kripke does?). |
| 16470 | Plantinga's essences have their own properties - so will have essences, giving a hierarchy [Stalnaker on Plantinga] |
| Full Idea: For Plantinga, essences are entities in their own right and will have properties different from what instantiates them. Hence he will need individual essences of individual essences, distinct from the essences. I see no way to avoid a hierarchy of them. | |
| From: comment on Alvin Plantinga (Actualism and Possible Worlds [1976]) by Robert C. Stalnaker - Mere Possibilities 4.4 | |
| A reaction: This sounds devastating for Plantinga, but it is a challenge for traditional Aristotelians. Only a logician suffers from a hierarchy, but a scientist might have to live with an essence, which contains a super-essence. |
| 14663 | Are propositions and states of affairs two separate things, or only one? I incline to say one [Plantinga] |
| Full Idea: Are there two sorts of thing, propositions and states of affairs, or only one? I am inclined to the former view on the ground that propositions have a property, truth or falsehood, not had by states of affairs. | |
| From: Alvin Plantinga (Actualism and Possible Worlds [1976], 1) | |
| A reaction: Might a proposition be nothing more than an assertion that a state of affairs obtains? It would then pass his test. The idea that a proposition is a complex of facts in the external world ('Russellian' propositions?) quite baffles me. |
| 9085 | If propositions are concrete they don't have to exist, and so they can't be necessary truths [Plantinga] |
| Full Idea: Someone who believes propositions are concrete cannot agree that some propositions are necessary. For propositions are contingent beings, and could have failed to exist. But if they fail to exist, then they fail to be true. | |
| From: Alvin Plantinga (Why Propositions cannot be concrete [1993], p.230) | |
| A reaction: [compressed] He implies the actual existence of an infinity of trivial, boring or ridiculous necessary truths. I suspect that he is just confusing a thought with its content. Or we might just treat necessary propositions as hypothetical. |
| 9084 | Propositions can't just be in brains, because 'there are no human beings' might be true [Plantinga] |
| Full Idea: If propositions are brain inscriptions, then if there had been no human beings there would have been no propositions. But then 'there are no human beings' would have been true, so there would have been at least one truth (and thus one proposition). | |
| From: Alvin Plantinga (Why Propositions cannot be concrete [1993], p.229) | |
| A reaction: This would make 'there are no x's' true for any value of x apart from actual objects, which implies an infinity of propositions. Does Plantinga really believe that these all exist? He may be confusing propositions with facts. |
| 13345 | Sentences are 'analytical' if every sequence of objects models them [Tarski] |
| Full Idea: A class of sentences can be called 'analytical' if every sequence of objects is a model of it. | |
| From: Alfred Tarski (The Concept of Logical Consequence [1936], p.418) | |
| A reaction: See Idea 13344 and Idea 13343 for the context of this assertion. |
| 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. |
| 20704 | A possible world contains a being of maximal greatness - which is existence in all worlds [Plantinga, by Davies,B] |
| Full Idea: Plantinga reformulates Malcolm's argument thus: 1) There is a possible world in which there exists a being with maximal greatness, 2) A being has maximal greatness in a world only if it exists in every world. | |
| From: report of Alvin Plantinga (The Nature of Necessity [1974], p.213) by Brian Davies - Introduction to the Philosophy of Religion 4 'b Descartes' | |
| A reaction: This is only Plantinga's starting point, which says nothing about the nature of God, but only that this 'great' being exists in all worlds. I would like to know why it is a 'being' rather than a 'thing'. Malcolm says if it is possible it is necessary. |
| 1474 | Moral evil may be acceptable to God because it allows free will (even though we don't see why this is necessary) [Plantinga, by PG] |
| Full Idea: Moral evil may be acceptable to a benevolent God because it is the only way to allow genuine free will, which may have a supreme value in creation (even if we are unsure what it is). | |
| From: report of Alvin Plantinga (Free Will Defence [1965], Pref.) by PG - Db (ideas) |
| 1475 | It is logically possible that natural evil like earthquakes is caused by Satan [Plantinga, by PG] |
| Full Idea: Physical evil (e.g. earthquakes) may be attributable to a fallen angel (Satan), who is the enemy of God, and this is enough to retain the idea that God is omnipotent and benevolent, and yet evil exists. | |
| From: report of Alvin Plantinga (Free Will Defence [1965], III) by PG - Db (ideas) |