Combining Philosophers
Ideas for Thrasymachus, Alfred Tarski and Volker Halbach
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83 ideas
3. Truth / A. Truth Problems / 1. Truth
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16330
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Truth-value 'gluts' allow two truth values together; 'gaps' give a partial conception of truth [Halbach]
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16339
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Truth axioms prove objects exist, so truth doesn't seem to be a logical notion [Halbach]
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3. Truth / A. Truth Problems / 2. Defining Truth
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16295
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Tarski proved that truth cannot be defined from within a given theory [Tarski, by Halbach]
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15342
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Tarski proved that any reasonably expressive language suffers from the liar paradox [Tarski, by Horsten]
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19069
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'True sentence' has no use consistent with logic and ordinary language, so definition seems hopeless [Tarski]
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10153
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In everyday language, truth seems indefinable, inconsistent, and illogical [Tarski]
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19178
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Definitions of truth should not introduce a new version of the concept, but capture the old one [Tarski]
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19177
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A definition of truth should be materially adequate and formally correct [Tarski]
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19186
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A rigorous definition of truth is only possible in an exactly specified language [Tarski]
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19194
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We may eventually need to split the word 'true' into several less ambiguous terms [Tarski]
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16324
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Any definition of truth requires a metalanguage [Halbach]
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15647
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Truth definitions don't produce a good theory, because they go beyond your current language [Halbach]
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16293
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Traditional definitions of truth often make it more obscure, rather than less [Halbach]
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16301
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If people have big doubts about truth, a definition might give it more credibility [Halbach]
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3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
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16296
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Tarski's Theorem renders any precise version of correspondence impossible [Tarski, by Halbach]
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3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
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10672
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Tarskian semantics says that a sentence is true iff it is satisfied by every sequence [Tarski, by Hossack]
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13338
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'"It is snowing" is true if and only if it is snowing' is a partial definition of the concept of truth [Tarski]
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19135
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Tarski enumerates cases of truth, so it can't be applied to new words or languages [Davidson on Tarski]
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19138
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Tarski define truths by giving the extension of the predicate, rather than the meaning [Davidson on Tarski]
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4699
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Tarski made truth relative, by only defining truth within some given artificial language [Tarski, by O'Grady]
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19324
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Tarski has to avoid stating how truths relate to states of affairs [Kirkham on Tarski]
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19180
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It is convenient to attach 'true' to sentences, and hence the language must be specified [Tarski]
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19181
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In the classical concept of truth, 'snow is white' is true if snow is white [Tarski]
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19196
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Scheme (T) is not a definition of truth [Tarski]
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19183
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Each interpreted T-sentence is a partial definition of truth; the whole definition is their conjunction [Tarski]
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19182
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Use 'true' so that all T-sentences can be asserted, and the definition will then be 'adequate' [Tarski]
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19198
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We don't give conditions for asserting 'snow is white'; just that assertion implies 'snow is white' is true [Tarski]
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15339
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Tarski gave up on the essence of truth, and asked how truth is used, or how it functions [Tarski, by Horsten]
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16302
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Tarski did not just aim at a definition; he also offered an adequacy criterion for any truth definition [Tarski, by Halbach]
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3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth
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15410
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Truth only applies to closed formulas, but we need satisfaction of open formulas to define it [Burgess on Tarski]
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18811
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Tarski uses sentential functions; truly assigning the objects to variables is what satisfies them [Tarski, by Rumfitt]
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15365
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We can define the truth predicate using 'true of' (satisfaction) for variables and some objects [Tarski, by Horsten]
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19314
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For physicalism, reduce truth to satisfaction, then define satisfaction as physical-plus-logic [Tarski, by Kirkham]
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19316
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Insight: don't use truth, use a property which can be compositional in complex quantified sentence [Tarski, by Kirkham]
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19175
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Tarski gave axioms for satisfaction, then derived its explicit definition, which led to defining truth [Tarski, by Davidson]
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19184
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The best truth definition involves other semantic notions, like satisfaction (relating terms and objects) [Tarski]
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19191
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Specify satisfaction for simple sentences, then compounds; true sentences are satisfied by all objects [Tarski]
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3. Truth / F. Semantic Truth / 1. Tarski's Truth / c. Meta-language for truth
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19188
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We can't use a semantically closed language, or ditch our logic, so a meta-language is needed [Tarski]
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19189
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The metalanguage must contain the object language, logic, and defined semantics [Tarski]
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15649
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In semantic theories of truth, the predicate is in an object-language, and the definition in a metalanguage [Halbach]
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16297
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Semantic theories avoid Tarski's Theorem by sticking to a sublanguage [Halbach]
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3. Truth / F. Semantic Truth / 2. Semantic Truth
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19134
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Tarski defined truth for particular languages, but didn't define it across languages [Davidson on Tarski]
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16304
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Tarski didn't capture the notion of an adequate truth definition, as Convention T won't prove non-contradiction [Halbach on Tarski]
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2571
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Tarski says that his semantic theory of truth is completely neutral about all metaphysics [Tarski, by Haack]
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10821
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Physicalists should explain reference nonsemantically, rather than getting rid of it [Tarski, by Field,H]
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10822
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A physicalist account must add primitive reference to Tarski's theory [Field,H on Tarski]
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10824
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If listing equivalences is a reduction of truth, witchcraft is just a list of witch-victim pairs [Field,H on Tarski]
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16303
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Tarski made truth respectable, by proving that it could be defined [Tarski, by Halbach]
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10969
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Tarski had a theory of truth, and a theory of theories of truth [Tarski, by Read]
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17746
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Tarski's 'truth' is a precise relation between the language and its semantics [Tarski, by Walicki]
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10904
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Tarskian truth neglects the atomic sentences [Mulligan/Simons/Smith on Tarski]
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16337
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Disquotational truth theories are short of deductive power [Halbach]
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3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
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15650
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Axiomatic theories of truth need a weak logical framework, and not a strong metatheory [Halbach]
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15322
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Tarski's had the first axiomatic theory of truth that was minimally adequate [Tarski, by Horsten]
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16306
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Tarski defined truth, but an axiomatisation can be extracted from his inductive clauses [Tarski, by Halbach]
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19141
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Tarski thought axiomatic truth was too contingent, and in danger of inconsistencies [Tarski, by Davidson]
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19190
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We need an undefined term 'true' in the meta-language, specified by axioms [Tarski]
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15655
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Should axiomatic truth be 'conservative' - not proving anything apart from implications of the axioms? [Halbach]
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15648
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Instead of a truth definition, add a primitive truth predicate, and axioms for how it works [Halbach]
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16322
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CT proves PA consistent, which PA can't do on its own, so CT is not conservative over PA [Halbach]
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15654
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If truth is defined it can be eliminated, whereas axiomatic truth has various commitments [Halbach]
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16294
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Axiomatic truth doesn't presuppose a truth-definition, though it could admit it at a later stage [Halbach]
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16326
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The main semantic theories of truth are Kripke's theory, and revisions semantics [Halbach]
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16311
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To axiomatise Tarski's truth definition, we need a binary predicate for his 'satisfaction' [Halbach]
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16318
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Compositional Truth CT has the truth of a sentence depending of the semantic values of its constituents [Halbach]
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16299
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Gödel numbering means a theory of truth can use Peano Arithmetic as its base theory [Halbach]
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16340
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Truth axioms need a base theory, because that is where truth issues arise [Halbach]
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16305
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We know a complete axiomatisation of truth is not feasible [Halbach]
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16313
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A theory is 'conservative' if it adds no new theorems to its base theory [Halbach, by PG]
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16315
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The Tarski Biconditional theory TB is Peano Arithmetic, plus truth, plus all Tarski bi-conditionals [Halbach]
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16314
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Theories of truth are 'typed' (truth can't apply to sentences containing 'true'), or 'type-free' [Halbach]
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3. Truth / G. Axiomatic Truth / 2. FS Truth Axioms
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16327
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Friedman-Sheard is type-free Compositional Truth, with two inference rules for truth [Halbach]
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3. Truth / G. Axiomatic Truth / 3. KF Truth Axioms
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16329
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Kripke-Feferman theory KF axiomatises Kripke fixed-points, with Strong Kleene logic with gluts [Halbach]
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16332
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The KF theory is useful, but it is not a theory containing its own truth predicate [Halbach]
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16331
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The KF is much stronger deductively than FS, which relies on classical truth [Halbach]
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3. Truth / H. Deflationary Truth / 1. Redundant Truth
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19197
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Truth can't be eliminated from universal claims, or from particular unspecified claims [Tarski]
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3. Truth / H. Deflationary Truth / 2. Deflationary Truth
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19185
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Semantics is a very modest discipline which solves no real problems [Tarski]
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16320
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Some say deflationism is axioms which are conservative over the base theory [Halbach]
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15656
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Deflationists say truth merely serves to express infinite conjunctions [Halbach]
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16338
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Deflationism says truth is a disquotation device to express generalisations, adding no new knowledge [Halbach]
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16317
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The main problem for deflationists is they can express generalisations, but not prove them [Halbach]
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16316
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Deflationists say truth is just for expressing infinite conjunctions or generalisations [Halbach]
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16319
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Compositional Truth CT proves generalisations, so is preferred in discussions of deflationism [Halbach]
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