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Single Idea 19195

[filed under theme 4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables ]

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.

Gist of Idea

Truth tables give prior conditions for logic, but are outside the system, and not definitions

Source

Alfred Tarski (The Semantic Conception of Truth [1944], 15)

Book Ref

'Semantics and the Philosophy of Language', ed/tr. Linsky,Leonard [University of Illinois 1972], p.29

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.

The 24 ideas from 'The Semantic Conception of Truth'

19179 For a definition we need the words or concepts used, the rules, and the structure of the language [Tarski]
19178 Definitions of truth should not introduce a new version of the concept, but capture the old one [Tarski]
19177 A definition of truth should be materially adequate and formally correct [Tarski]
19180 It is convenient to attach 'true' to sentences, and hence the language must be specified [Tarski]
19181 In the classical concept of truth, 'snow is white' is true if snow is white [Tarski]
19183 Each interpreted T-sentence is a partial definition of truth; the whole definition is their conjunction [Tarski]
19182 Use 'true' so that all T-sentences can be asserted, and the definition will then be 'adequate' [Tarski]
10824 If listing equivalences is a reduction of truth, witchcraft is just a list of witch-victim pairs [Field,H on Tarski]
19184 The best truth definition involves other semantic notions, like satisfaction (relating terms and objects) [Tarski]
19185 Semantics is a very modest discipline which solves no real problems [Tarski]
19186 A rigorous definition of truth is only possible in an exactly specified language [Tarski]
19187 The Liar makes us assert a false sentence, so it must be taken seriously [Tarski]
19188 We can't use a semantically closed language, or ditch our logic, so a meta-language is needed [Tarski]
19189 The metalanguage must contain the object language, logic, and defined semantics [Tarski]
19190 We need an undefined term 'true' in the meta-language, specified by axioms [Tarski]
19191 Specify satisfaction for simple sentences, then compounds; true sentences are satisfied by all objects [Tarski]
19192 The truth definition proves semantic contradiction and excluded middle laws (not the logic laws) [Tarski]
19194 We may eventually need to split the word 'true' into several less ambiguous terms [Tarski]
19193 Disputes that fail to use precise scientific terminology are all meaningless [Tarski]
19196 Scheme (T) is not a definition of truth [Tarski]
19195 Truth tables give prior conditions for logic, but are outside the system, and not definitions [Tarski]
19197 Truth can't be eliminated from universal claims, or from particular unspecified claims [Tarski]
19198 We don't give conditions for asserting 'snow is white'; just that assertion implies 'snow is white' is true [Tarski]
19199 Some say metaphysics is a highly generalised empirical study of objects [Tarski]