66 ideas
10633 | 'Some critics admire only one another' cannot be paraphrased in singular first-order [Linnebo] |
18996 | A statement S is 'partly true' if it has some wholly true parts [Yablo] |
19006 | An 'enthymeme' is an argument with an indispensable unstated assumption [Yablo] |
8859 | The main modal logics disagree over three key formulae [Yablo] |
10779 | A comprehension axiom is 'predicative' if the formula has no bound second-order variables [Linnebo] |
23445 | Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo] |
18999 | y is only a proper part of x if there is a z which 'makes up the difference' between them [Yablo] |
10781 | A 'pure logic' must be ontologically innocent, universal, and without presuppositions [Linnebo] |
10638 | A pure logic is wholly general, purely formal, and directly known [Linnebo] |
19001 | 'Pegasus doesn't exist' is false without Pegasus, yet the absence of Pegasus is its truthmaker [Yablo] |
10640 | Instead of complex objects like tables, plurally quantify over mereological atoms tablewise [Linnebo] |
10778 | Can second-order logic be ontologically first-order, with all the benefits of second-order? [Linnebo] |
10636 | Plural plurals are unnatural and need a first-level ontology [Linnebo] |
10639 | Plural quantification may allow a monadic second-order theory with first-order ontology [Linnebo] |
10783 | Plural quantification depends too heavily on combinatorial and set-theoretic considerations [Linnebo] |
10635 | Second-order quantification and plural quantification are different [Linnebo] |
10641 | Traditionally we eliminate plurals by quantifying over sets [Linnebo] |
23447 | In classical semantics singular terms refer, and quantifiers range over domains [Linnebo] |
23443 | The axioms of group theory are not assertions, but a definition of a structure [Linnebo] |
23444 | To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo] |
9138 | An infinite series of sentences asserting falsehood produces the paradox without self-reference [Yablo, by Sorensen] |
8865 | If 'the number of Democrats is on the rise', does that mean that 50 million is on the rise? [Yablo] |
23446 | You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo] |
23448 | Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo] |
14085 | 'Deductivist' structuralism is just theories, with no commitment to objects, or modality [Linnebo] |
14084 | Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo] |
14086 | 'Modal' structuralism studies all possible concrete models for various mathematical theories [Linnebo] |
14087 | 'Set-theoretic' structuralism treats mathematics as various structures realised among the sets [Linnebo] |
14089 | Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure [Linnebo] |
14083 | Structuralism is right about algebra, but wrong about sets [Linnebo] |
14090 | In mathematical structuralism the small depends on the large, which is the opposite of physical structures [Linnebo] |
19002 | A nominalist can assert statements about mathematical objects, as being partly true [Yablo] |
8863 | We must treat numbers as existing in order to express ourselves about the arrangement of planets [Yablo] |
10580 | Mathematics is both necessary and a priori because it really consists of logical truths [Yablo] |
23441 | Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo] |
23442 | Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo] |
8862 | Platonic objects are really created as existential metaphors [Yablo] |
10579 | Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo] |
14091 | There may be a one-way direction of dependence among sets, and among natural numbers [Linnebo] |
10577 | Concrete objects have few essential properties, but properties of abstractions are mostly essential [Yablo] |
10578 | We are thought to know concreta a posteriori, and many abstracta a priori [Yablo] |
19489 | For me, fictions are internally true, without a significant internal or external truth-value [Yablo] |
19490 | Make-believe can help us to reason about facts and scientific procedures [Yablo] |
19491 | 'The clouds are angry' can only mean '...if one were attributing emotions to clouds' [Yablo] |
8864 | We quantify over events, worlds, etc. in order to make logical possibilities clearer [Yablo] |
19494 | Fictionalism allows that simulated beliefs may be tracking real facts [Yablo] |
10643 | We speak of a theory's 'ideological commitments' as well as its 'ontological commitments' [Linnebo] |
10637 | Ordinary speakers posit objects without concern for ontology [Linnebo] |
14088 | An 'intrinsic' property is either found in every duplicate, or exists independent of all externals [Linnebo] |
8858 | Philosophers keep finding unexpected objects, like models, worlds, functions, numbers, events, sets, properties [Yablo] |
10782 | The modern concept of an object is rooted in quantificational logic [Linnebo] |
14381 | A statue is essentially the statue, but its lump is not essentially a statue, so statue isn't lump [Yablo, by Rocca] |
18998 | Parthood lacks the restriction of kind which most relations have [Yablo] |
19493 | Governing possible worlds theory is the fiction that if something is possible, it happens in a world [Yablo] |
19004 | Gettier says you don't know if you are confused about how it is true [Yablo] |
19007 | A theory need not be true to be good; it should just be true about its physical aspects [Yablo] |
18993 | If sentences point to different evidence, they must have different subject-matter [Yablo] |
19003 | Most people say nonblack nonravens do confirm 'all ravens are black', but only a tiny bit [Yablo] |
10805 | A sentence should be recarved to reveal its content or implication relations [Yablo] |
18992 | Sentence-meaning is the truth-conditions - plus factors responsible for them [Yablo] |
10634 | Predicates are 'distributive' or 'non-distributive'; do individuals do what the group does? [Linnebo] |
18994 | The content of an assertion can be quite different from compositional content [Yablo] |
18997 | Truth-conditions as subject-matter has problems of relevance, short cut, and reversal [Yablo] |
19005 | Not-A is too strong to just erase an improper assertion, because it actually reverses A [Yablo] |
8861 | Hardly a word in the language is devoid of metaphorical potential [Yablo] |
4377 | Intellectualism is an excessive emphasis on reasoning in moral philosophy [Burnyeat] |