22 ideas
12204 | The logic of metaphysical necessity is S5 [Rumfitt] |
17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
12195 | Soundness in argument varies with context, and may be achieved very informally indeed [Rumfitt] |
12199 | There is a modal element in consequence, in assessing reasoning from suppositions [Rumfitt] |
12201 | We reject deductions by bad consequence, so logical consequence can't be deduction [Rumfitt] |
17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
12194 | Contradictions include 'This is red and not coloured', as well as the formal 'B and not-B' [Rumfitt] |
12198 | Geometrical axioms in logic are nowadays replaced by inference rules (which imply the logical truths) [Rumfitt] |
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] |
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] |
17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
14532 | A distinctive type of necessity is found in logical consequence [Rumfitt, by Hale/Hoffmann,A] |
12200 | A logically necessary statement need not be a priori, as it could be unknowable [Rumfitt] |
12193 | Logical necessity is when 'necessarily A' implies 'not-A is contradictory' [Rumfitt] |
12202 | Narrow non-modal logical necessity may be metaphysical, but real logical necessity is not [Rumfitt] |
5040 | Necessary truths can be analysed into original truths; contingent truths are infinitely analysable [Leibniz] |
13159 | Only God sees contingent truths a priori [Leibniz] |
12203 | If a world is a fully determinate way things could have been, can anyone consider such a thing? [Rumfitt] |
5039 | If non-existents are possible, their existence would replace what now exists, which cannot therefore be necessary [Leibniz] |
5041 | God does everything in a perfect way, and never acts contrary to reason [Leibniz] |