Ideas from 'The Semantic Conception of Truth' by Alfred Tarski [1944], by Theme Structure

[found in 'Semantics and the Philosophy of Language' (ed/tr Linsky,Leonard) [University of Illinois 1972,0-252-00093-5]].

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1. Philosophy / E. Nature of Metaphysics / 5. Metaphysics beyond Science
Some say metaphysics is a highly generalised empirical study of objects
                        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.
1. Philosophy / F. Analytic Philosophy / 1. Nature of Analysis
Disputes that fail to use precise scientific terminology are all meaningless
                        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.
2. Reason / D. Definition / 1. Definitions
For a definition we need the words or concepts used, the rules, and the structure of the language
                        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.
3. Truth / A. Truth Problems / 2. Defining Truth
Definitions of truth should not introduce a new version of the concept, but capture the old one
                        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.
A definition of truth should be materially adequate and formally correct
                        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.
A rigorous definition of truth is only possible in an exactly specified language
                        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).
We may eventually need to split the word 'true' into several less ambiguous terms
                        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.
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
Scheme (T) is not a definition of truth
                        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.
It is convenient to attach 'true' to sentences, and hence the language must be specified
                        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.
In the classical concept of truth, 'snow is white' is true if snow is white
                        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.
Use 'true' so that all T-sentences can be asserted, and the definition will then be 'adequate'
                        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).
Each interpreted T-sentence is a partial definition of truth; the whole definition is their conjunction
                        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.
We don't give conditions for asserting 'snow is white'; just that assertion implies 'snow is white' is true
                        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.
3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth
The best truth definition involves other semantic notions, like satisfaction (relating terms and objects)
                        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.
Specify satisfaction for simple sentences, then compounds; true sentences are satisfied by all objects
                        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.
3. Truth / F. Semantic Truth / 1. Tarski's Truth / c. Meta-language for truth
We can't use a semantically closed language, or ditch our logic, so a meta-language is needed
                        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.
The metalanguage must contain the object language, logic, and defined semantics
                        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?
3. Truth / F. Semantic Truth / 2. Semantic Truth
If listing equivalences is a reduction of truth, witchcraft is just a list of witch-victim pairs
                        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
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
We need an undefined term 'true' in the meta-language, specified by axioms
                        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.
3. Truth / H. Deflationary Truth / 1. Redundant Truth
Truth can't be eliminated from universal claims, or from particular unspecified claims
                        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.
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
Semantics is a very modest discipline which solves no real problems
                        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.
4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
Truth tables give prior conditions for logic, but are outside the system, and not definitions
                        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.
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
The truth definition proves semantic contradiction and excluded middle laws (not the logic laws)
                        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.
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
The Liar makes us assert a false sentence, so it must be taken seriously
                        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?