31 ideas
2352 | The job of the philosopher is to distinguish facts about the world from conventions [Putnam] |
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] |
6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
6304 | Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik] |
13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
6300 | Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik] |
6303 | Sets are positions in patterns [Resnik] |
6302 | Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik] |
6295 | There are too many mathematical objects for them all to be mental or physical [Resnik] |
6296 | Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik] |
6301 | Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik] |
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] |
2342 | "Water" is a natural kind term, but "H2O" is a description [Putnam] |