76 ideas
9161 | Maybe reasonableness requires circular justifications - that is one coherentist view [Field,H] |
10825 | The notion of truth is to help us make use of the utterances of others [Field,H] |
10820 | In the early 1930s many philosophers thought truth was not scientific [Field,H] |
13499 | Tarski reduced truth to reference or denotation [Field,H, by Hart,WD] |
10818 | Tarski really explained truth in terms of denoting, predicating and satisfied functions [Field,H] |
10817 | Tarski just reduced truth to some other undefined semantic notions [Field,H] |
10482 | The logic of ZF is classical first-order predicate logic with identity [Boolos] |
10492 | A few axioms of set theory 'force themselves on us', but most of them don't [Boolos] |
18192 | Do the Replacement Axioms exceed the iterative conception of sets? [Boolos, by Maddy] |
7785 | The use of plurals doesn't commit us to sets; there do not exist individuals and collections [Boolos] |
10485 | Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos] |
10484 | The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos] |
13547 | Limitation of Size is weak (Fs only collect is something the same size does) or strong (fewer Fs than objects) [Boolos, by Potter] |
10699 | Does a bowl of Cheerios contain all its sets and subsets? [Boolos] |
9570 | In Field's Platonist view, set theory is false because it asserts existence for non-existent things [Field,H, by Chihara] |
14249 | Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley] |
10225 | Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro] |
10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
10736 | Boolos showed how plural quantifiers can interpret monadic second-order logic [Boolos, by Linnebo] |
10780 | Any sentence of monadic second-order logic can be translated into plural first-order logic [Boolos, by Linnebo] |
10260 | Logical consequence is defined by the impossibility of P and ¬q [Field,H, by Shapiro] |
10829 | A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos] |
10697 | Identity is clearly a logical concept, and greatly enhances predicate calculus [Boolos] |
10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
13671 | Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology [Boolos, by Shapiro] |
10267 | We should understand second-order existential quantifiers as plural quantifiers [Boolos, by Shapiro] |
10698 | Plural forms have no more ontological commitment than to first-order objects [Boolos] |
7806 | Boolos invented plural quantification [Boolos, by Benardete,JA] |
10819 | Tarski gives us the account of truth needed to build a group of true sentences in a model [Field,H] |
10827 | Model theory is unusual in restricting the range of the quantifiers [Field,H] |
10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos] |
13841 | Why should compactness be definitive of logic? [Boolos, by Hacking] |
9226 | If mathematical theories conflict, it may just be that they have different subject matter [Field,H] |
8958 | In Field's version of science, space-time points replace real numbers [Field,H, by Szabó] |
10491 | Infinite natural numbers is as obvious as infinite sentences in English [Boolos] |
10483 | Mathematics and science do not require very high orders of infinity [Boolos] |
18221 | 'Metric' axioms uses functions, points and numbers; 'synthetic' axioms give facts about space [Field,H] |
10833 | Many concepts can only be expressed by second-order logic [Boolos] |
10490 | Mathematics isn't surprising, given that we experience many objects as abstract [Boolos] |
8757 | The Indispensability Argument is the only serious ground for the existence of mathematical entities [Field,H] |
18212 | Nominalists try to only refer to physical objects, or language, or mental constructions [Field,H] |
10261 | The application of mathematics only needs its possibility, not its truth [Field,H, by Shapiro] |
18218 | Hilbert explains geometry, by non-numerical facts about space [Field,H] |
9623 | Field needs a semantical notion of second-order consequence, and that needs sets [Brown,JR on Field,H] |
18215 | It seems impossible to explain the idea that the conclusion is contained in the premises [Field,H] |
18216 | Abstractions can form useful counterparts to concrete statements [Field,H] |
18214 | Mathematics is only empirical as regards which theory is useful [Field,H] |
8714 | Fictionalists say 2+2=4 is true in the way that 'Oliver Twist lived in London' is true [Field,H] |
18210 | Why regard standard mathematics as truths, rather than as interesting fictions? [Field,H] |
18211 | You can reduce ontological commitment by expanding the logic [Field,H] |
10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
8959 | Field presumes properties can be eliminated from science [Field,H, by Szabó] |
10488 | It is lunacy to think we only see ink-marks, and not word-types [Boolos] |
10487 | I am a fan of abstract objects, and confident of their existence [Boolos] |
10489 | We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos] |
18213 | Abstract objects are only applicable to the world if they are impure, and connect to the physical [Field,H] |
9160 | Lots of propositions are default reasonable, but the a priori ones are empirically indefeasible [Field,H] |
9164 | We treat basic rules as if they were indefeasible and a priori, with no interest in counter-evidence [Field,H] |
9165 | Reliability only makes a rule reasonable if we place a value on the truth produced by reliable processes [Field,H] |
9162 | Believing nothing, or only logical truths, is very reliable, but we want a lot more than that [Field,H] |
9166 | People vary in their epistemological standards, and none of them is 'correct' [Field,H] |
9163 | If we only use induction to assess induction, it is empirically indefeasible, and hence a priori [Field,H] |
18222 | Beneath every extrinsic explanation there is an intrinsic explanation [Field,H] |
16861 | A false theory could hardly rival the explanatory power of natural selection [Darwin] |
10826 | 'Valence' and 'gene' had to be reduced to show their compatibility with physicalism [Field,H] |
9917 | 'Abstract' is unclear, but numbers, functions and sets are clearly abstract [Field,H] |
8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos] |
22244 | 'Partial reference' is when the subject thinks two objects are one object [Field,H, by Recanati] |
7615 | Field says reference is a causal physical relation between mental states and objects [Field,H, by Putnam] |
8404 | Explain single events by general rules, or vice versa, or probability explains both, or they are unconnected [Field,H] |
8401 | Physical laws are largely time-symmetric, so they make a poor basis for directional causation [Field,H] |
8400 | Identifying cause and effect is not just conventional; we explain later events by earlier ones [Field,H] |
8402 | The only reason for adding the notion of 'cause' to fundamental physics is directionality [Field,H] |
18223 | In theories of fields, space-time points or regions are causal agents [Field,H] |
18220 | Both philosophy and physics now make substantivalism more attractive [Field,H] |
18219 | Relational space is problematic if you take the idea of a field seriously [Field,H] |