196 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] |
19179 | For a definition we need the words or concepts used, the rules, and the structure of the language [Tarski] |
16295 | Tarski proved that truth cannot be defined from within a given theory [Tarski, by Halbach] |
10153 | In everyday language, truth seems indefinable, inconsistent, and illogical [Tarski] |
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] |
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] |
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] |
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] |
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] |
19134 | Tarski defined truth for particular languages, but didn't define it across languages [Davidson on Tarski] |
16303 | Tarski made truth respectable, by proving that it could be defined [Tarski, by Halbach] |
16304 | Tarski didn't capture the notion of an adequate truth definition, as Convention T won't prove non-contradiction [Halbach on Tarski] |
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] |
16306 | Tarski defined truth, but an axiomatisation can be extracted from his inductive clauses [Tarski, by Halbach] |
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] |
9535 | 'Contradictory' propositions always differ in truth-value [Lemmon] |
9512 | We write the 'negation' of P (not-P) as ¬ [Lemmon] |
9511 | We write the conditional 'if P (antecedent) then Q (consequent)' as P→Q [Lemmon] |
9510 | That proposition that either P or Q is their 'disjunction', written P∨Q [Lemmon] |
9508 | The sign |- may be read as 'therefore' [Lemmon] |
9509 | That proposition that both P and Q is their 'conjunction', written P∧Q [Lemmon] |
9514 | If A and B are 'interderivable' from one another we may write A -||- B [Lemmon] |
9513 | We write 'P if and only if Q' as P↔Q; it is also P iff Q, or (P→Q)∧(Q→P) [Lemmon] |
9532 | 'Subcontrary' propositions are never both false, so that A∨B is a tautology [Lemmon] |
9533 | A 'implies' B if B is true whenever A is true (so that A→B is tautologous) [Lemmon] |
9517 | The 'scope' of a connective is the connective, the linked formulae, and the brackets [Lemmon] |
9529 | A wff is 'inconsistent' if all assignments to variables result in the value F [Lemmon] |
9519 | A 'substitution-instance' is a wff formed by consistent replacing variables with wffs [Lemmon] |
9531 | 'Contrary' propositions are never both true, so that ¬(A∧B) is a tautology [Lemmon] |
9516 | A 'well-formed formula' follows the rules for variables, ¬, →, ∧, ∨, and ↔ [Lemmon] |
9518 | A 'theorem' is the conclusion of a provable sequent with zero assumptions [Lemmon] |
9528 | A wff is a 'tautology' if all assignments to variables result in the value T [Lemmon] |
9530 | A wff is 'contingent' if produces at least one T and at least one F [Lemmon] |
9534 | Two propositions are 'equivalent' if they mirror one another's truth-value [Lemmon] |
9401 | ∨E: Derive C from A∨B, if C can be derived both from A and from B [Lemmon] |
9397 | CP: Given a proof of B from A as assumption, we may derive A→B [Lemmon] |
9393 | A: we may assume any proposition at any stage [Lemmon] |
9399 | ∧E: Given A∧B, we may derive either A or B separately [Lemmon] |
9398 | ∧I: Given A and B, we may derive A∧B [Lemmon] |
9394 | MPP: Given A and A→B, we may derive B [Lemmon] |
9402 | RAA: If assuming A will prove B∧¬B, then derive ¬A [Lemmon] |
9395 | MTT: Given ¬B and A→B, we derive ¬A [Lemmon] |
9396 | DN: Given A, we may derive ¬¬A [Lemmon] |
9400 | ∨I: Given either A or B separately, we may derive A∨B [Lemmon] |
9522 | 'Modus ponendo tollens' (MPT) says P, ¬(P ∧ Q) |- ¬Q [Lemmon] |
9521 | 'Modus tollendo ponens' (MTP) says ¬P, P ∨ Q |- Q [Lemmon] |
9525 | We can change conditionals into negated conjunctions with P→Q -||- ¬(P ∧ ¬Q) [Lemmon] |
9524 | We can change conditionals into disjunctions with P→Q -||- ¬P ∨ Q [Lemmon] |
9523 | De Morgan's Laws make negated conjunctions/disjunctions into non-negated disjunctions/conjunctions [Lemmon] |
9527 | The Distributive Laws can rearrange a pair of conjunctions or disjunctions [Lemmon] |
9526 | We can change conjunctions into negated conditionals with P→Q -||- ¬(P → ¬Q) [Lemmon] |
9537 | Truth-tables are good for showing invalidity [Lemmon] |
9538 | A truth-table test is entirely mechanical, but this won't work for more complex logic [Lemmon] |
19195 | Truth tables give prior conditions for logic, but are outside the system, and not definitions [Tarski] |
9536 | If any of the nine rules of propositional logic are applied to tautologies, the result is a tautology [Lemmon] |
9539 | Propositional logic is complete, since all of its tautologous sequents are derivable [Lemmon] |
13909 | Write '(∀x)(...)' to mean 'take any x: then...', and '(∃x)(...)' to mean 'there is an x such that....' [Lemmon] |
13902 | 'Gm' says m has property G, and 'Pmn' says m has relation P to n [Lemmon] |
13911 | The 'symbols' are bracket, connective, term, variable, predicate letter, reverse-E [Lemmon] |
13910 | Our notation uses 'predicate-letters' (for 'properties'), 'variables', 'proper names', 'connectives' and 'quantifiers' [Lemmon] |
13904 | Universal Elimination (UE) lets us infer that an object has F, from all things having F [Lemmon] |
13901 | Predicate logic uses propositional connectives and variables, plus new introduction and elimination rules [Lemmon] |
13903 | Universal elimination if you start with the universal, introduction if you want to end with it [Lemmon] |
13906 | With finite named objects, we can generalise with &-Intro, but otherwise we need ∀-Intro [Lemmon] |
13908 | UE all-to-one; UI one-to-all; EI arbitrary-to-one; EE proof-to-one [Lemmon] |
13905 | If there is a finite domain and all objects have names, complex conjunctions can replace universal quantifiers [Lemmon] |
13900 | 'Some Frenchmen are generous' is rendered by (∃x)(Fx→Gx), and not with the conditional → [Lemmon] |
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] |
9520 | The paradoxes of material implication are P |- Q → P, and ¬P |- P → Q [Lemmon] |
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] |
10157 | Tarski improved Hilbert's geometry axioms, and without set-theory [Tarski, by Feferman/Feferman] |
10154 | Tarski's theory of truth shifted the approach away from syntax, to set theory and semantics [Feferman/Feferman on Tarski] |
22355 | In the realist view, the real external world explains how it (and perceptions of it) are possible [Williams,B] |
10151 | I am a deeply convinced nominalist [Tarski] |
23283 | Necessity implies possibility, but in experience it matters which comes first [Williams,B] |
4243 | Our ability to react to an alien culture shows that ethical thought extends beyond cultural boundaries [Williams,B] |
4244 | It is very confused to deduce a nonrelativist morality of universal toleration from relativism [Williams,B] |
3238 | 'Dead person' isn't a contradiction, so 'person' is somewhat vague [Williams,B] |
3239 | You can only really love a person as a token, not as a type [Williams,B] |
7946 | The memory criterion has a problem when one thing branches into two things [Williams,B, by Macdonald,C] |
2176 | There is only a problem of free will if you think the notion of 'voluntary' can be metaphysically deepened [Williams,B] |
2181 | It is an absurd Kantian idea that at the limit rationality and freedom coincide [Williams,B] |
24008 | Reference to a person's emotions is often essential to understanding their actions [Williams,B] |
24009 | Moral education must involve learning about various types of feeling towards things [Williams,B] |
13345 | Sentences are 'analytical' if every sequence of objects models them [Tarski] |
4317 | We judge weakness of will by an assessment after the event is concluded [Williams,B, by Cottingham] |
9284 | Reasons are 'internal' if they give a person a motive to act, but 'external' otherwise [Williams,B] |
2174 | Responsibility involves cause, intention, state of mind, and response after the event [Williams,B] |
22455 | Many ethical theories neglect the power of regretting the ought not acted upon [Williams,B] |
20407 | Taste is the capacity to judge an object or representation which is thought to be beautiful [Tarski, by Schellekens] |
4114 | Philosophers try to produce ethical theories because they falsely assume that ethics can be simple [Williams,B] |
22453 | Moral conflicts have a different feeling and structure from belief conflicts [Williams,B, by Foot] |
22454 | We tolerate inconsistency in ethics but not in other beliefs (which reflect an independent order) [Williams,B, by Foot] |
22450 | If moral systems can't judge other moral systems, then moral relativism is true [Williams,B, by Foot] |
2178 | In bad actions, guilt points towards victims, and shame to the agent [Williams,B] |
20168 | Blame usually has no effect if the recipient thinks it unjustified [Williams,B] |
20167 | Blame partly rests on the fiction that blamed agents always know their obligations [Williams,B] |
4128 | Intuitionism has been demolished by critics, and no longer looks interesting [Williams,B] |
4366 | We can't accept Aristotle's naturalism about persons, because it is normative and unscientific [Williams,B, by Hursthouse] |
4132 | The category of person is a weak basis for ethics, because it is not fixed but comes in degrees [Williams,B] |
24007 | Emotivism saw morality as expressing emotions, and influencing others' emotions [Williams,B] |
4134 | The weakness of prescriptivism is shown by "I simply don't like staying at good hotels" [Williams,B] |
4135 | Some ethical ideas, such as 'treachery' and 'promise', seem to express a union of facts and values [Williams,B] |
22410 | Maybe the unthinkable is a moral category, and considering some options is dishonourable or absurd [Williams,B] |
22408 | Consequentialism assumes that situations can be compared [Williams,B] |
22411 | For a consequentialist massacring 7 million must be better than massacring 7 million and one [Williams,B] |
4120 | It is an error of consequentialism to think we just aim at certain states of affairs; we also want to act [Williams,B] |
23282 | If all that matters in morality is motive and intention, that makes moral luck irrelevant [Williams,B] |
4252 | Promise keeping increases reliability, by making deliberation focus on something which would be overlooked [Williams,B] |
4116 | A weakness of contractual theories is the position of a person of superior ability and power [Williams,B] |
2169 | Greek moral progress came when 'virtue' was freed from social status [Williams,B] |
4112 | A crucial feature of moral thought is second-order desire - the desire to have certain desires [Williams,B] |
24010 | An admirable human being should have certain kinds of emotional responses [Williams,B] |
23279 | It is important that a person can change their character, and not just be successive 'selves' [Williams,B] |
23280 | Kantians have an poor account of individuals, and insist on impartiality, because they ignore character [Williams,B] |
3236 | Equality of opportunity without equality of respect would create a very inhuman society [Williams,B] |
4113 | 'Deon' in Greek means what one must do; there was no word meaning 'duty' [Williams,B] |
4110 | Obligation and duty look backwards (because of a promise or job), although the acts are in the future [Williams,B] |
4250 | The concept of a 'duty to myself' is fraudulent [Williams,B] |
4249 | "Ought implies can" is a famous formula in connection with moral obligation [Williams,B] |
4248 | Not all moral deliberations lead to obligations; some merely reveal what 'may' be done [Williams,B] |
2172 | The modern idea of duty is unknown in archaic Greece [Williams,B] |
4121 | Why should I think of myself as both the legislator and the citizen who follows the laws? [Williams,B] |
22409 | We don't have a duty to ensure that others do their duty [Williams,B] |
4122 | If the self becomes completely impartial, it no longer has enough identity to worry about its interests [Williams,B] |
2180 | If reason cannot lead people to good, we must hope they have an internal voice [Williams,B] |
24012 | Kant's love of consistency is too rigid, and it even overrides normal fairness [Williams,B] |
2179 | If the moral self is seen as characterless, then other people have a very limited role in our moral lives [Williams,B] |
22407 | Utilitarianism cannot make any serious sense of integrity [Williams,B] |
23278 | For utilitarians states of affairs are what have value, not matter who produced them [Williams,B] |
4124 | Utilitarian benevolence involves no particular attachments, and is immune to the inverse square law [Williams,B] |
4245 | Ethical conviction must be to some extent passive, and can't just depend on the will and decisions [Williams,B] |
4246 | Taking responsibility won't cure ethical uncertainty by; we are uncertain what to decide [Williams,B] |
3233 | Equality implies that people are alike in potential as well as in needs [Williams,B] |
3234 | Equality seems to require that each person be acknowledged as having a significant point of view [Williams,B] |
3235 | It is a mark of extreme exploitation that the sufferers do not realise their plight [Williams,B] |
4247 | It is a mark of our having ethical values that we aim to reproduce them in our children [Williams,B] |
4131 | Most women see an early miscarriage and a late stillbirth as being very different in character [Williams,B] |
4133 | Speciesism isn't like racism, because the former implies a viewpoint which belongs to no one [Williams,B] |
2175 | There is a problem of evil only if you expect the world to be good [Williams,B] |