51 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] |
| 18194 | 'Forcing' can produce new models of ZFC from old models [Maddy] |
| 18195 | A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy] |
| 18191 | Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy] |
| 18193 | The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy] |
| 18169 | Axiom of Reducibility: propositional functions are extensionally predicative [Maddy] |
| 18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
| 18190 | Completed infinities resulted from giving foundations to calculus [Maddy] |
| 18171 | Cantor and Dedekind brought completed infinities into mathematics [Maddy] |
| 18172 | Infinity has degrees, and large cardinals are the heart of set theory [Maddy] |
| 18175 | For any cardinal there is always a larger one (so there is no set of all sets) [Maddy] |
| 18196 | An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy] |
| 18187 | Theorems about limits could only be proved once the real numbers were understood [Maddy] |
| 18182 | The extension of concepts is not important to me [Maddy] |
| 18177 | In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy] |
| 18164 | Frege solves the Caesar problem by explicitly defining each number [Maddy] |
| 18184 | Making set theory foundational to mathematics leads to very fruitful axioms [Maddy] |
| 18185 | Unified set theory gives a final court of appeal for mathematics [Maddy] |
| 18183 | Set theory brings mathematics into one arena, where interrelations become clearer [Maddy] |
| 18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy] |
| 18186 | Identifying geometric points with real numbers revealed the power of set theory [Maddy] |
| 18188 | The line of rationals has gaps, but set theory provided an ordered continuum [Maddy] |
| 18207 | Maybe applications of continuum mathematics are all idealisations [Maddy] |
| 18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
| 18167 | We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy] |
| 2349 | Realists believe truth is correspondence, independent of humans, is bivalent, and is unique [Putnam] |
| 18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
| 2351 | Aristotle says an object (e.g. a lamp) has identity if its parts stay together when it is moved [Putnam] |
| 19727 | Reliabilist knowledge is evidence based belief, with high conditional probability [Comesaña] |
| 19725 | In a sceptical scenario belief formation is unreliable, so no beliefs at all are justified? [Comesaña] |
| 19726 | How do we decide which exact process is the one that needs to be reliable? [Comesaña] |
| 18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
| 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] |