45 ideas
1642 | We must fight fiercely for knowledge, understanding and intelligence [Plato] |
1645 | The desire to split everything into its parts is unpleasant and unphilosophical [Plato] |
287 | Good analysis involves dividing things into appropriate forms without confusion [Plato] |
1644 | Dialectic should only be taught to those who already philosophise well [Plato] |
20478 | In discussion a person's opinions are shown to be in conflict, leading to calm self-criticism [Plato] |
4901 | Truth has to be correspondence to facts, and a match between relations of ideas and relations in the world [Perry] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
11278 | What does 'that which is not' refer to? [Plato] |
1643 | If statements about non-existence are logically puzzling, so are statements about existence [Plato] |
7022 | To be is to have a capacity, to act on other things, or to receive actions [Plato] |
1641 | Some alarming thinkers think that only things which you can touch exist [Plato] |
10784 | Whenever there's speech it has to be about something [Plato] |
16122 | Good thinkers spot forms spread through things, or included within some larger form [Plato] |
10422 | The not-beautiful is part of the beautiful, though opposed to it, and is just as real [Plato] |
15855 | If we see everything as separate, we can then give no account of it [Plato] |
4885 | Identity is a very weak relation, which doesn't require interdefinability, or shared properties [Perry] |
4899 | Possible worlds thinking has clarified the logic of modality, but is problematic in epistemology [Perry] |
4898 | Possible worlds are indices for a language, or concrete realities, or abstract possibilities [Perry] |
1637 | A soul without understanding is ugly [Plato] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
4887 | We try to cause other things to occur by causing mental events to occur [Perry] |
4884 | Brain states must be in my head, and yet the pain seems to be in my hand [Perry] |
4888 | It seems plausible that many animals have experiences without knowing about them [Perry] |
4891 | If epiphenomenalism just says mental events are effects but not causes, it is consistent with physicalism [Perry] |
4900 | Prior to Kripke, the mind-brain identity theory usually claimed that the identity was contingent [Perry] |
4892 | If physicalists stick with identity (not supervenience), Martian pain will not be like ours [Perry] |
4889 | Although we may classify ideas by content, we individuate them differently, as their content can change [Perry] |
4896 | The intension of an expression is a function from possible worlds to an appropriate extension [Perry] |
4897 | A proposition is a set of possible worlds for which its intension delivers truth [Perry] |
4890 | A sharp analytic/synthetic line can rarely be drawn, but some concepts are central to thought [Perry] |
1636 | Wickedness is an illness of the soul [Plato] |
1638 | Didactic education is hard work and achieves little [Plato] |