51 ideas
18486 | We might define truth as arising from the truth-maker relation [MacBride] |
18484 | Phenomenalists, behaviourists and presentists can't supply credible truth-makers [MacBride] |
18466 | If truthmaking is classical entailment, then anything whatsoever makes a necessary truth [MacBride] |
18481 | Maximalism follows Russell, and optimalism (no negative or universal truthmakers) follows Wittgenstein [MacBride] |
18473 | 'Maximalism' says every truth has an actual truthmaker [MacBride] |
18483 | The main idea of truth-making is that what a proposition is about is what matters [MacBride] |
18479 | There are different types of truthmakers for different types of negative truth [MacBride] |
18477 | There aren't enough positive states out there to support all the negative truths [MacBride] |
18482 | Optimalists say that negative and universal are true 'by default' from the positive truths [MacBride] |
18485 | Even idealists could accept truthmakers, as mind-dependent [MacBride] |
18474 | Does 'this sentence has no truth-maker' have a truth-maker? Reductio suggests it can't have [MacBride] |
18490 | Maybe 'makes true' is not an active verb, but just a formal connective like 'because'? [MacBride] |
18493 | Truthmaker talk of 'something' making sentences true, which presupposes objectual quantification [MacBride] |
10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
13913 | The four 'perfect syllogisms' are called Barbara, Celarent, Darii and Ferio [Engelbretsen/Sayward] |
13914 | Syllogistic logic has one rule: what is affirmed/denied of wholes is affirmed/denied of their parts [Engelbretsen/Sayward] |
13915 | Syllogistic can't handle sentences with singular terms, or relational terms, or compound sentences [Engelbretsen/Sayward] |
13916 | Term logic uses expression letters and brackets, and '-' for negative terms, and '+' for compound terms [Engelbretsen/Sayward] |
10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
13850 | In modern logic all formal validity can be characterised syntactically [Engelbretsen/Sayward] |
13849 | Classical logic rests on truth and models, where constructivist logic rests on defence and refutation [Engelbretsen/Sayward] |
13851 | Unlike most other signs, = cannot be eliminated [Engelbretsen/Sayward] |
18489 | Connectives link sentences without linking their meanings [MacBride] |
18476 | 'A is F' may not be positive ('is dead'), and 'A is not-F' may not be negative ('is not blind') [MacBride] |
10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
13852 | Axioms are ω-incomplete if the instances are all derivable, but the universal quantification isn't [Engelbretsen/Sayward] |
8923 | Numbers are identified by their main properties and relations, involving the successor function [MacBride] |
10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
8926 | For mathematical objects to be positions, positions themselves must exist first [MacBride] |
18480 | Maybe it only exists if it is a truthmaker (rather than the value of a variable)? [MacBride] |
18471 | Different types of 'grounding' seem to have no more than a family resemblance relation [MacBride] |
18472 | Which has priority - 'grounding' or 'truth-making'? [MacBride] |
18475 | Russell allows some complex facts, but Wittgenstein only allows atomic facts [MacBride] |
21354 | It may be that internal relations like proportion exist, because we directly perceive it [MacBride] |
21353 | Internal relations are fixed by existences, or characters, or supervenience on characters [MacBride] |
21352 | 'Multigrade' relations are those lacking a fixed number of relata [MacBride] |
10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
18478 | Wittgenstein's plan to show there is only logical necessity failed, because of colours [MacBride] |