118 ideas
| 19199 | Some say metaphysics is a highly generalised empirical study of objects [Tarski] |
| 19193 | Disputes that fail to use precise scientific terminology are all meaningless [Tarski] |
| 1812 | All discussion is full of uncertainty and contradiction (Mode 11) [Agrippa, by Diog. Laertius] |
| 1811 | Proofs often presuppose the thing to be proved (Mode 15) [Agrippa, by Diog. Laertius] |
| 1813 | All reasoning endlessly leads to further reasoning (Mode 12) [Agrippa, by Diog. Laertius] |
| 1815 | Reasoning needs arbitrary faith in preliminary hypotheses (Mode 14) [Agrippa, by Diog. Laertius] |
| 19179 | For a definition we need the words or concepts used, the rules, and the structure of the language [Tarski] |
| 9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
| 10153 | In everyday language, truth seems indefinable, inconsistent, and illogical [Tarski] |
| 16295 | Tarski proved that truth cannot be defined from within a given theory [Tarski, by Halbach] |
| 15342 | Tarski proved that any reasonably expressive language suffers from the liar paradox [Tarski, by Horsten] |
| 19069 | 'True sentence' has no use consistent with logic and ordinary language, so definition seems hopeless [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] |
| 19186 | A rigorous definition of truth is only possible in an exactly specified language [Tarski] |
| 19194 | We may eventually need to split the word 'true' into several less ambiguous terms [Tarski] |
| 16296 | Tarski's Theorem renders any precise version of correspondence impossible [Tarski, by Halbach] |
| 19196 | Scheme (T) is not a definition of truth [Tarski] |
| 15339 | Tarski gave up on the essence of truth, and asked how truth is used, or how it functions [Tarski, by Horsten] |
| 16302 | Tarski did not just aim at a definition; he also offered an adequacy criterion for any truth definition [Tarski, by Halbach] |
| 19135 | Tarski enumerates cases of truth, so it can't be applied to new words or languages [Davidson on Tarski] |
| 19138 | Tarski define truths by giving the extension of the predicate, rather than the meaning [Davidson on Tarski] |
| 4699 | Tarski made truth relative, by only defining truth within some given artificial language [Tarski, by O'Grady] |
| 19324 | Tarski has to avoid stating how truths relate to states of affairs [Kirkham on Tarski] |
| 10672 | Tarskian semantics says that a sentence is true iff it is satisfied by every sequence [Tarski, by Hossack] |
| 13338 | '"It is snowing" is true if and only if it is snowing' is a partial definition of the concept of truth [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] |
| 19182 | Use 'true' so that all T-sentences can be asserted, and the definition will then be 'adequate' [Tarski] |
| 19183 | Each interpreted T-sentence is a partial definition of truth; the whole definition is their conjunction [Tarski] |
| 19198 | We don't give conditions for asserting 'snow is white'; just that assertion implies 'snow is white' is true [Tarski] |
| 15410 | Truth only applies to closed formulas, but we need satisfaction of open formulas to define it [Burgess on Tarski] |
| 18811 | Tarski uses sentential functions; truly assigning the objects to variables is what satisfies them [Tarski, by Rumfitt] |
| 15365 | We can define the truth predicate using 'true of' (satisfaction) for variables and some objects [Tarski, by Horsten] |
| 19314 | For physicalism, reduce truth to satisfaction, then define satisfaction as physical-plus-logic [Tarski, by Kirkham] |
| 19316 | Insight: don't use truth, use a property which can be compositional in complex quantified sentence [Tarski, by Kirkham] |
| 19175 | Tarski gave axioms for satisfaction, then derived its explicit definition, which led to defining truth [Tarski, by Davidson] |
| 19184 | The best truth definition involves other semantic notions, like satisfaction (relating terms and objects) [Tarski] |
| 19191 | Specify satisfaction for simple sentences, then compounds; true sentences are satisfied by all objects [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] |
| 19134 | Tarski defined truth for particular languages, but didn't define it across languages [Davidson on Tarski] |
| 16304 | Tarski didn't capture the notion of an adequate truth definition, as Convention T won't prove non-contradiction [Halbach on Tarski] |
| 2571 | Tarski says that his semantic theory of truth is completely neutral about all metaphysics [Tarski, by Haack] |
| 10821 | Physicalists should explain reference nonsemantically, rather than getting rid of it [Tarski, by Field,H] |
| 10822 | A physicalist account must add primitive reference to Tarski's theory [Field,H on Tarski] |
| 10824 | If listing equivalences is a reduction of truth, witchcraft is just a list of witch-victim pairs [Field,H on Tarski] |
| 16303 | Tarski made truth respectable, by proving that it could be defined [Tarski, by Halbach] |
| 10969 | Tarski had a theory of truth, and a theory of theories of truth [Tarski, by Read] |
| 17746 | Tarski's 'truth' is a precise relation between the language and its semantics [Tarski, by Walicki] |
| 10904 | Tarskian truth neglects the atomic sentences [Mulligan/Simons/Smith on Tarski] |
| 16306 | Tarski defined truth, but an axiomatisation can be extracted from his inductive clauses [Tarski, by Halbach] |
| 15322 | Tarski's had the first axiomatic theory of truth that was minimally adequate [Tarski, by Horsten] |
| 19141 | Tarski thought axiomatic truth was too contingent, and in danger of inconsistencies [Tarski, by Davidson] |
| 19190 | We need an undefined term 'true' in the meta-language, specified by axioms [Tarski] |
| 19197 | Truth can't be eliminated from universal claims, or from particular unspecified claims [Tarski] |
| 19185 | Semantics is a very modest discipline which solves no real problems [Tarski] |
| 19195 | Truth tables give prior conditions for logic, but are outside the system, and not definitions [Tarski] |
| 9634 | Set theory says that natural numbers are an actual infinity (to accommodate their powerset) [Brown,JR] |
| 9615 | Nowadays conditions are only defined on existing sets [Brown,JR] |
| 9613 | Naïve set theory assumed that there is a set for every condition [Brown,JR] |
| 9617 | The 'iterative' view says sets start with the empty set and build up [Brown,JR] |
| 9642 | A flock of birds is not a set, because a set cannot go anywhere [Brown,JR] |
| 10152 | Set theory and logic are fairy tales, but still worth studying [Tarski] |
| 10048 | There is no clear boundary between the logical and the non-logical [Tarski] |
| 13337 | A language: primitive terms, then definition rules, then sentences, then axioms, and finally inference rules [Tarski] |
| 18812 | Split out the logical vocabulary, make an assignment to the rest. It's logical if premises and conclusion match [Tarski, by Rumfitt] |
| 10694 | Logical consequence is when in any model in which the premises are true, the conclusion is true [Tarski, by Beall/Restall] |
| 10479 | Logical consequence: true premises give true conclusions under all interpretations [Tarski, by Hodges,W] |
| 13344 | X follows from sentences K iff every model of K also models X [Tarski] |
| 19192 | The truth definition proves semantic contradiction and excluded middle laws (not the logic laws) [Tarski] |
| 9605 | If a proposition is false, then its negation is true [Brown,JR] |
| 18759 | Identity is invariant under arbitrary permutations, so it seems to be a logical term [Tarski, by McGee] |
| 10823 | A name denotes an object if the object satisfies a particular sentential function [Tarski] |
| 18756 | Tarski built a compositional semantics for predicate logic, from dependent satisfactions [Tarski, by McGee] |
| 19313 | Tarksi invented the first semantics for predicate logic, using this conception of truth [Tarski, by Kirkham] |
| 13335 | Semantics is the concepts of connections of language to reality, such as denotation, definition and truth [Tarski] |
| 13336 | A language containing its own semantics is inconsistent - but we can use a second language [Tarski] |
| 13339 | A sentence is satisfied when we can assert the sentence when the variables are assigned [Tarski] |
| 13340 | Satisfaction is the easiest semantical concept to define, and the others will reduce to it [Tarski] |
| 13343 | A 'model' is a sequence of objects which satisfies a complete set of sentential functions [Tarski] |
| 16323 | The object language/ metalanguage distinction is the basis of model theory [Tarski, by Halbach] |
| 9649 | Axioms are either self-evident, or stipulations, or fallible attempts [Brown,JR] |
| 13341 | Using the definition of truth, we can prove theories consistent within sound logics [Tarski] |
| 9638 | Berry's Paradox finds a contradiction in the naming of huge numbers [Brown,JR] |
| 8940 | Tarski avoids the Liar Paradox, because truth cannot be asserted within the object language [Tarski, by Fisher] |
| 19187 | The Liar makes us assert a false sentence, so it must be taken seriously [Tarski] |
| 9604 | Mathematics is the only place where we are sure we are right [Brown,JR] |
| 9622 | 'There are two apples' can be expressed logically, with no mention of numbers [Brown,JR] |
| 9648 | π is a 'transcendental' number, because it is not the solution of an equation [Brown,JR] |
| 9621 | Mathematics represents the world through structurally similar models. [Brown,JR] |
| 9646 | There is no limit to how many ways something can be proved in mathematics [Brown,JR] |
| 9647 | Computers played an essential role in proving the four-colour theorem of maps [Brown,JR] |
| 10157 | Tarski improved Hilbert's geometry axioms, and without set-theory [Tarski, by Feferman/Feferman] |
| 9643 | Set theory may represent all of mathematics, without actually being mathematics [Brown,JR] |
| 9644 | When graphs are defined set-theoretically, that won't cover unlabelled graphs [Brown,JR] |
| 9625 | To see a structure in something, we must already have the idea of the structure [Brown,JR] |
| 9628 | Sets seem basic to mathematics, but they don't suit structuralism [Brown,JR] |
| 9606 | The irrationality of root-2 was achieved by intellect, not experience [Brown,JR] |
| 9610 | Numbers are not abstracted from particulars, because each number is a particular [Brown,JR] |
| 9612 | There is an infinity of mathematical objects, so they can't be physical [Brown,JR] |
| 9620 | Empiricists base numbers on objects, Platonists base them on properties [Brown,JR] |
| 10154 | Tarski's theory of truth shifted the approach away from syntax, to set theory and semantics [Feferman/Feferman on Tarski] |
| 9630 | The most brilliant formalist was Hilbert [Brown,JR] |
| 9629 | For nomalists there are no numbers, only numerals [Brown,JR] |
| 9639 | Does some mathematics depend entirely on notation? [Brown,JR] |
| 9608 | There are no constructions for many highly desirable results in mathematics [Brown,JR] |
| 9645 | Constructivists say p has no value, if the value depends on Goldbach's Conjecture [Brown,JR] |
| 9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
| 10151 | I am a deeply convinced nominalist [Tarski] |
| 8850 | Agrippa's Trilemma: justification is infinite, or ends arbitrarily, or is circular [Agrippa, by Williams,M] |
| 1814 | Everything is perceived in relation to another thing (Mode 13) [Agrippa, by Diog. Laertius] |
| 9611 | 'Abstract' nowadays means outside space and time, not concrete, not physical [Brown,JR] |
| 9609 | The older sense of 'abstract' is where 'redness' or 'group' is abstracted from particulars [Brown,JR] |
| 9640 | A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR] |
| 13345 | Sentences are 'analytical' if every sequence of objects models them [Tarski] |
| 20407 | Taste is the capacity to judge an object or representation which is thought to be beautiful [Tarski, by Schellekens] |
| 9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |