24 ideas
10017 | Truth in a model is more tractable than the general notion of truth [Hodes] |
10018 | Truth is quite different in interpreted set theory and in the skeleton of its language [Hodes] |
17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
10015 | Higher-order logic may be unintelligible, but it isn't set theory [Hodes] |
17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
10011 | Identity is a level one relation with a second-order definition [Hodes] |
10016 | When an 'interpretation' creates a model based on truth, this doesn't include Fregean 'sense' [Hodes] |
17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
10027 | Mathematics is higher-order modal logic [Hodes] |
10026 | Arithmetic must allow for the possibility of only a finite total of objects [Hodes] |
17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
10021 | It is claimed that numbers are objects which essentially represent cardinality quantifiers [Hodes] |
10022 | Numerical terms can't really stand for quantifiers, because that would make them first-level [Hodes] |
17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
10023 | Talk of mirror images is 'encoded fictions' about real facts [Hodes] |
19544 | Closure says if you know P, and also know P implies Q, then you must know Q [Dretske] |
19545 | We needn't regret the implications of our regrets; regretting drinking too much implies the past is real [Dretske] |
19547 | Reasons for believing P may not transmit to its implication, Q [Dretske] |
19546 | Knowing by visual perception is not the same as knowing by implication [Dretske] |
19548 | The only way to preserve our homely truths is to abandon closure [Dretske] |
19549 | P may imply Q, but evidence for P doesn't imply evidence for Q, so closure fails [Dretske] |
19550 | We know past events by memory, but we don't know the past is real (an implication) by memory [Dretske] |