1933 | The Concept of Truth for Formalized Languages |
p.1 | 15322 | Tarski's had the first axiomatic theory of truth that was minimally adequate |
p.4 | 16295 | Tarski proved that truth cannot be defined from within a given theory |
p.15 | 16302 | Tarski did not just aim at a definition; he also offered an adequacy criterion for any truth definition |
p.15 | 15339 | Tarski gave up on the essence of truth, and asked how truth is used, or how it functions |
p.17 | 16303 | Tarski made truth respectable, by proving that it could be defined |
p.19 | 16304 | Tarski didn't capture the notion of an adequate truth definition, as Convention T won't prove non-contradiction |
p.22 | 10969 | Tarski had a theory of truth, and a theory of theories of truth |
p.23 | 16306 | Tarski defined truth, but an axiomatisation can be extracted from his inductive clauses |
p.31 | 17746 | Tarski's 'truth' is a precise relation between the language and its semantics |
p.37 | 18756 | Tarski built a compositional semantics for predicate logic, from dependent satisfactions |
p.60 | 10904 | Tarskian truth neglects the atomic sentences |
p.72 | 18811 | Tarski uses sentential functions; truly assigning the objects to variables is what satisfies them |
p.74 | 15365 | We can define the truth predicate using 'true of' (satisfaction) for variables and some objects |
p.141 | 19313 | Tarksi invented the first semantics for predicate logic, using this conception of truth |
p.377 | 10821 | Physicalists should explain reference nonsemantically, rather than getting rid of it |
p.381 | 10822 | A physicalist account must add primitive reference to Tarski's theory |
§1 | p.165 | 19069 | 'True sentence' has no use consistent with logic and ordinary language, so definition seems hopeless |
p.194 | p.382 | 10823 | A name denotes an object if the object satisfies a particular sentential function |
1936 | The Establishment of Scientific Semantics |
p.401 | p.401 | 13335 | Semantics is the concepts of connections of language to reality, such as denotation, definition and truth |
p.402 | p.402 | 13336 | A language containing its own semantics is inconsistent - but we can use a second language |
p.402 | p.402 | 13337 | A language: primitive terms, then definition rules, then sentences, then axioms, and finally inference rules |
p.404 | p.404 | 13338 | '"It is snowing" is true if and only if it is snowing' is a partial definition of the concept of truth |
p.405 | p.405 | 13339 | A sentence is satisfied when we can assert the sentence when the variables are assigned |
p.406 | p.406 | 13340 | Satisfaction is the easiest semantical concept to define, and the others will reduce to it |
p.407 | p.407 | 13341 | Using the definition of truth, we can prove theories consistent within sound logics |
1936 | The Concept of Logical Consequence |
p.73 | 18812 | Split out the logical vocabulary, make an assignment to the rest. It's logical if premises and conclusion match |
p.417 | p.417 | 13343 | A 'model' is a sequence of objects which satisfies a complete set of sentential functions |
p.417 | p.417 | 13344 | X follows from sentences K iff every model of K also models X |
p.418 | p.418 | 13345 | Sentences are 'analytical' if every sequence of objects models them |
1936 | works |
p.6 | 10694 | Logical consequence is when in any model in which the premises are true, the conclusion is true |
p.9 | 10479 | Logical consequence: true premises give true conclusions under all interpretations |
p.31 | 19141 | Tarski thought axiomatic truth was too contingent, and in danger of inconsistencies |
p.103 | 10048 | There is no clear boundary between the logical and the non-logical |
p.112 | 10153 | In everyday language, truth seems indefinable, inconsistent, and illogical |
p.230 | 10157 | Tarski improved Hilbert's geometry axioms, and without set-theory |
1944 | The Semantic Conception of Truth |
01 | p.13 | 19177 | A definition of truth should be materially adequate and formally correct |
01 | p.13 | 19178 | Definitions of truth should not introduce a new version of the concept, but capture the old one |
01 | p.14 | 19179 | For a definition we need the words or concepts used, the rules, and the structure of the language |
02 | p.14 | 19180 | It is convenient to attach 'true' to sentences, and hence the language must be specified |
04 | p.15 | 19181 | In the classical concept of truth, 'snow is white' is true if snow is white |
04 | p.16 | 19182 | Use 'true' so that all T-sentences can be asserted, and the definition will then be 'adequate' |
04 | p.16 | 19183 | Each interpreted T-sentence is a partial definition of truth; the whole definition is their conjunction |
04 | p.387 | 10824 | If listing equivalences is a reduction of truth, witchcraft is just a list of witch-victim pairs |
05 | p.17 | 19184 | The best truth definition involves other semantic notions, like satisfaction (relating terms and objects) |
05 | p.17 | 19185 | Semantics is a very modest discipline which solves no real problems |
06 | p.19 | 19186 | A rigorous definition of truth is only possible in an exactly specified language |
07 | p.20 | 19187 | The Liar makes us assert a false sentence, so it must be taken seriously |
08-09 | p.20 | 19188 | We can't use a semantically closed language, or ditch our logic, so a meta-language is needed |
09 | p.22 | 19189 | The metalanguage must contain the object language, logic, and defined semantics |
10 | p.24 | 19190 | We need an undefined term 'true' in the meta-language, specified by axioms |
11 | p.25 | 19191 | Specify satisfaction for simple sentences, then compounds; true sentences are satisfied by all objects |
12 | p.26 | 19192 | The truth definition proves semantic contradiction and excluded middle laws (not the logic laws) |
14 | p.27 | 19193 | Disputes that fail to use precise scientific terminology are all meaningless |
14 | p.28 | 19194 | We may eventually need to split the word 'true' into several less ambiguous terms |
15 | p.29 | 19196 | Scheme (T) is not a definition of truth |
15 | p.29 | 19195 | Truth tables give prior conditions for logic, but are outside the system, and not definitions |
16 | p.31 | 19197 | Truth can't be eliminated from universal claims, or from particular unspecified claims |
18 | p.33 | 19198 | We don't give conditions for asserting 'snow is white'; just that assertion implies 'snow is white' is true |
19 | p.35 | 19199 | Some say metaphysics is a highly generalised empirical study of objects |
1965 | talk |
p.52 | 10152 | Set theory and logic are fairy tales, but still worth studying |
p.52 | 10151 | I am a deeply convinced nominalist |