131 ideas
| 12330 | In ontology, logic dominated language, until logic was mathematized [Badiou] |
| 9808 | Philosophy aims to reveal the grandeur of mathematics [Badiou] |
| 6575 | Philosophy may never find foundations, and may undermine our lives in the process [Fogelin] |
| 12318 | The female body, when taken in its entirety, is the Phallus itself [Badiou] |
| 19199 | Some say metaphysics is a highly generalised empirical study of objects [Tarski] |
| 12325 | Philosophy has been relieved of physics, cosmology, politics, and now must give up ontology [Badiou] |
| 19193 | Disputes that fail to use precise scientific terminology are all meaningless [Tarski] |
| 6585 | Rationality is threatened by fear of inconsistency, illusions of absolutes or relativism, and doubt [Fogelin] |
| 12324 | Consensus is the enemy of thought [Badiou] |
| 6557 | Humans may never be able to attain a world view which is both rich and consistent [Fogelin] |
| 6568 | A game can be played, despite having inconsistent rules [Fogelin] |
| 6560 | The law of noncontradiction is traditionally the most basic principle of rationality [Fogelin] |
| 6565 | The law of noncontradiction makes the distinction between asserting something and denying it [Fogelin] |
| 19179 | For a definition we need the words or concepts used, the rules, and the structure of the language [Tarski] |
| 6574 | Legal reasoning is analogical, not deductive [Fogelin] |
| 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] |
| 12337 | There is 'transivity' iff membership ∈ also means inclusion ⊆ [Badiou] |
| 12321 | The axiom of choice must accept an indeterminate, indefinable, unconstructible set [Badiou] |
| 12342 | Topos theory explains the plurality of possible logics [Badiou] |
| 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] |
| 12341 | Logic is a mathematical account of a universe of relations [Badiou] |
| 19192 | The truth definition proves semantic contradiction and excluded middle laws (not the logic laws) [Tarski] |
| 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] |
| 13341 | Using the definition of truth, we can prove theories consistent within sound logics [Tarski] |
| 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] |
| 9812 | In mathematics, if a problem can be formulated, it will eventually be solved [Badiou] |
| 12335 | Numbers are for measuring and for calculating (and the two must be consistent) [Badiou] |
| 12334 | There is no single unified definition of number [Badiou] |
| 12333 | Each type of number has its own characteristic procedure of introduction [Badiou] |
| 12322 | Must we accept numbers as existing when they no longer consist of units? [Badiou] |
| 9813 | Mathematics shows that thinking is not confined to the finite [Badiou] |
| 12327 | The undecidability of the Continuum Hypothesis may have ruined or fragmented set theory [Badiou] |
| 10157 | Tarski improved Hilbert's geometry axioms, and without set-theory [Tarski, by Feferman/Feferman] |
| 12329 | If mathematics is a logic of the possible, then questions of existence are not intrinsic to it [Badiou] |
| 12328 | Platonists like axioms and decisions, Aristotelians like definitions, possibilities and logic [Badiou] |
| 12331 | Logic is definitional, but real mathematics is axiomatic [Badiou] |
| 10154 | Tarski's theory of truth shifted the approach away from syntax, to set theory and semantics [Feferman/Feferman on Tarski] |
| 9809 | Mathematics inscribes being as such [Badiou] |
| 12340 | There is no Being as a whole, because there is no set of all sets [Badiou] |
| 12323 | Existence is Being itself, but only as our thought decides it [Badiou] |
| 12332 | The modern view of Being comes when we reject numbers as merely successions of One [Badiou] |
| 12326 | The primitive name of Being is the empty set; in a sense, only the empty set 'is' [Badiou] |
| 9811 | It is of the essence of being to appear [Badiou] |
| 12320 | Ontology is (and always has been) Cantorian mathematics [Badiou] |
| 10151 | I am a deeply convinced nominalist [Tarski] |
| 6582 | Conventions can only work if they are based on something non-conventional [Fogelin] |
| 6576 | My view is 'circumspect rationalism' - that only our intellect can comprehend the world [Fogelin] |
| 6589 | Knowledge is legitimate only if all relevant defeaters have been eliminated [Fogelin] |
| 6596 | For coherentists, circularity is acceptable if the circle is large, rich and coherent [Fogelin] |
| 6597 | A rule of justification might be: don't raise the level of scrutiny without a good reason [Fogelin] |
| 6588 | Scepticism is cartesian (sceptical scenarios), or Humean (future), or Pyrrhonian (suspend belief) [Fogelin] |
| 6590 | Scepticism deals in remote possibilities that are ineliminable and set the standard very high [Fogelin] |
| 6583 | Radical perspectivism replaces Kant's necessary scheme with many different schemes [Fogelin] |
| 6555 | We are also irrational, with a unique ability to believe in bizarre self-created fictions [Fogelin] |
| 13345 | Sentences are 'analytical' if every sequence of objects models them [Tarski] |
| 12338 | We must either assert or deny any single predicate of any single subject [Badiou] |
| 6605 | Critics must be causally entangled with their subject matter [Fogelin] |
| 20407 | Taste is the capacity to judge an object or representation which is thought to be beautiful [Tarski, by Schellekens] |
| 6607 | The word 'beautiful', when deprived of context, is nearly contentless [Fogelin] |
| 9814 | All great poetry is engaged in rivalry with mathematics [Badiou] |
| 6604 | Saying 'It's all a matter to taste' ignores the properties of the object discussed [Fogelin] |
| 6586 | Cynics are committed to morality, but disappointed or disgusted by human failings [Fogelin] |
| 6572 | Deterrence, prevention, rehabilitation and retribution can come into conflict in punishments [Fogelin] |
| 6573 | Retributivists say a crime can be 'paid for'; deterrentists still worry about potential victims [Fogelin] |
| 12316 | For Enlightenment philosophers, God was no longer involved in politics [Badiou] |
| 12317 | The God of religion results from an encounter, not from a proof [Badiou] |