37 ideas
2352 | The job of the philosopher is to distinguish facts about the world from conventions [Putnam] |
15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
2345 | Semantic notions do not occur in Tarski's definitions, but assessing their correctness involves translation [Putnam] |
2347 | Asserting the truth of an indexical statement is not the same as uttering the statement [Putnam] |
17608 | We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo] |
17607 | Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo] |
10870 | ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg] |
13012 | Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy] |
17609 | Set theory can be reduced to a few definitions and seven independent axioms [Zermelo] |
13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy] |
13015 | Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy] |
13020 | The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy] |
13486 | Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD] |
13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
18178 | For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy] |
13027 | Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy] |
9627 | Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR] |
2349 | Realists believe truth is correspondence, independent of humans, is bivalent, and is unique [Putnam] |
2351 | Aristotle says an object (e.g. a lamp) has identity if its parts stay together when it is moved [Putnam] |
2331 | Functionalism says robots and people are the same at one level of abstraction [Putnam] |
2071 | If concepts have external meaning, computational states won't explain psychology [Putnam] |
2332 | Functionalism can't explain reference and truth, which are needed for logic [Putnam] |
2348 | Is there just one computational state for each specific belief? [Putnam] |
2344 | If we are going to eliminate folk psychology, we must also eliminate folk logic [Putnam] |
2074 | Can we give a scientific, computational account of folk psychology? [Putnam] |
2343 | Reference may be different while mental representation is the same [Putnam] |
2346 | Meaning and translation (which are needed to define truth) both presuppose the notion of reference [Putnam] |
2354 | "Meaning is use" is not a definition of meaning [Putnam] |
2336 | Holism seems to make fixed definition more or less impossible [Putnam] |
2334 | Meaning holism tried to show that you can't get fixed meanings built out of observation terms [Putnam] |
2335 | Understanding a sentence involves background knowledge and can't be done in isolation [Putnam] |
2340 | We should separate how the reference of 'gold' is fixed from its conceptual content [Putnam] |
2341 | Like names, natural kind terms have their meaning fixed by extension and reference [Putnam] |
2339 | Aristotle implies that we have the complete concepts of a language in our heads, but we don't [Putnam] |
2338 | Reference (say to 'elms') is a social phenomenon which we can leave to experts [Putnam] |
7667 | There are two sides to men - the pleasantly social, and the violent and creative [Diderot, by Berlin] |
2342 | "Water" is a natural kind term, but "H2O" is a description [Putnam] |