40 ideas
21360 | Unobservant thinkers tend to dogmatise using insufficient facts [Aristotle] |
13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
13021 | The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy] |
13022 | Infinite sets are essential for giving an account of the real numbers [Maddy] |
13023 | The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy] |
13024 | Efforts to prove the Axiom of Choice have failed [Maddy] |
13025 | Modern views say the Choice set exists, even if it can't be constructed [Maddy] |
13026 | A large array of theorems depend on the Axiom of Choice [Maddy] |
13019 | The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy] |
13018 | Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy] |
13212 | Infinity is only potential, never actual [Aristotle] |
13221 | Existence is either potential or actual [Aristotle] |
16100 | True change is in a thing's logos or its matter, not in its qualities [Aristotle] |
16101 | A change in qualities is mere alteration, not true change [Aristotle] |
12133 | If the substratum persists, it is 'alteration'; if it doesn't, it is 'coming-to-be' or 'passing-away' [Aristotle] |
13213 | All comings-to-be are passings-away, and vice versa [Aristotle] |
10496 | Monothetic categories have fixed defining features, and polythetic categories do not [Ellen] |
10497 | In symbolic classification, the categories are linked to rules [Ellen] |
10495 | Continuous experience sometimes needs imposition of boundaries to create categories [Ellen] |
12134 | Matter is the substratum, which supports both coming-to-be and alteration [Aristotle] |
16572 | Does the pure 'this' come to be, or the 'this-such', or 'so-great', or 'somewhere'? [Aristotle] |
16573 | Philosophers have worried about coming-to-be from nothing pre-existing [Aristotle] |
13214 | The substratum changing to a contrary is the material cause of coming-to-be [Aristotle] |
13215 | If a perceptible substratum persists, it is 'alteration'; coming-to-be is a complete change [Aristotle] |
16717 | Which of the contrary features of a body are basic to it? [Aristotle] |
10498 | Classification is no longer held to be rooted in social institutions [Ellen] |
13216 | Matter is the limit of points and lines, and must always have quality and form [Aristotle] |
17994 | The primary matter is the substratum for the contraries like hot and cold [Aristotle] |
13224 | There couldn't be just one element, which was both water and air at the same time [Aristotle] |
16594 | The Four Elements must change into one another, or else alteration is impossible [Aristotle] |
13223 | Fire is hot and dry; Air is hot and moist; Water is cold and moist; Earth is cold and dry [Aristotle] |
13220 | Bodies are endlessly divisible [Aristotle] |
13210 | Wood is potentially divided through and through, so what is there in the wood besides the division? [Aristotle] |
13211 | If a body is endlessly divided, is it reduced to nothing - then reassembled from nothing? [Aristotle] |
13228 | There is no time without movement [Aristotle] |
16595 | If each thing can cease to be, why hasn't absolutely everything ceased to be long ago? [Aristotle] |
13227 | Being is better than not-being [Aristotle] |
13226 | An Order controls all things [Aristotle] |