46 ideas
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] |
10147 | The Axiom of Choice is consistent with the other axioms of set theory [Feferman/Feferman] |
10148 | Axiom of Choice: a set exists which chooses just one element each of any set of sets [Feferman/Feferman] |
10149 | Platonist will accept the Axiom of Choice, but others want criteria of selection or definition [Feferman/Feferman] |
10150 | The Trichotomy Principle is equivalent to the Axiom of Choice [Feferman/Feferman] |
10146 | Cantor's theories needed the Axiom of Choice, but it has led to great controversy [Feferman/Feferman] |
18999 | y is only a proper part of x if there is a z which 'makes up the difference' between them [Yablo] |
19001 | 'Pegasus doesn't exist' is false without Pegasus, yet the absence of Pegasus is its truthmaker [Yablo] |
10158 | A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman] |
10162 | Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman] |
10160 | Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman] |
10159 | Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman] |
10161 | If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman] |
10156 | 'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman] |
10155 | Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman] |
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] |
13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
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] |
8862 | Platonic objects are really created as existential metaphors [Yablo] |
10579 | Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo] |
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] |
8858 | Philosophers keep finding unexpected objects, like models, worlds, functions, numbers, events, sets, properties [Yablo] |
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] |
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] |