41 ideas
8893 | For any given area, there seem to be a huge number of possible coherent systems of beliefs [Bonjour] |
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] |
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] |
18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [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] |
18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
15797 | All structures are dispositional, objects are dispositions sets, and events manifest dispositions [Fetzer] |
15800 | All events and objects are dispositional, and hence all structural properties are dispositional [Fetzer] |
8888 | The concept of knowledge is so confused that it is best avoided [Bonjour] |
8887 | It is hard to give the concept of 'self-evident' a clear and defensible characterization [Bonjour] |
8897 | The adverbial account will still be needed when a mind apprehends its sense-data [Bonjour] |
8896 | Conscious states have built-in awareness of content, so we know if a conceptual description of it is correct [Bonjour] |
8891 | My incoherent beliefs about art should not undermine my very coherent beliefs about physics [Bonjour] |
8892 | Coherence seems to justify empirical beliefs about externals when there is no external input [Bonjour] |
8894 | Coherentists must give a reason why coherent justification is likely to lead to the truth [Bonjour] |
8889 | Reliabilists disagree over whether some further requirement is needed to produce knowledge [Bonjour] |
8890 | If the reliable facts producing a belief are unknown to me, my belief is not rational or responsible [Bonjour] |
8895 | If neither the first-level nor the second-level is itself conscious, there seems to be no consciousness present [Bonjour] |
18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
15798 | Kinds are arrangements of dispositions [Fetzer] |
15799 | Lawlike sentences are general attributions of disposition to all members of some class [Fetzer] |