48 ideas
7113 | Phenomenology assumes that all consciousness is of something [Sartre] |
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] |
7112 | The Cogito depends on a second-order experience, of being conscious of consciousness [Sartre] |
7114 | The consciousness that says 'I think' is not the consciousness that thinks [Sartre] |
7119 | Is the Cogito reporting an immediate experience of doubting, or the whole enterprise of doubting? [Sartre] |
7122 | We can never, even in principle, grasp other minds, because the Ego is self-conceiving [Sartre] |
7125 | A consciousness can conceive of no other consciousness than itself [Sartre] |
7108 | The eternal truth of 2+2=4 is what gives unity to the mind which regularly thinks it [Sartre] |
7111 | Consciousness exists as consciousness of itself [Sartre] |
22226 | Since we are a consciousness, Sartre entirely rejected the unconscious mind [Sartre, by Daigle] |
7107 | Intentionality defines, transcends and unites consciousness [Sartre] |
18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
7109 | If you think of '2+2=4' as the content of thought, the self must be united transcendentally [Sartre] |
7106 | The Ego is not formally or materially part of consciousness, but is outside in the world [Sartre] |
7117 | How could two I's, the reflective and the reflected, communicate with each other? [Sartre] |
7123 | Knowing yourself requires an exterior viewpoint, which is necessarily false [Sartre] |
22225 | My ego is more intimate to me, but not more certain than other egos [Sartre] |
7124 | The Ego never appears except when we are not looking for it [Sartre] |
7116 | When we are unreflective (as when chasing a tram) there is no 'I' [Sartre] |
7120 | It is theoretically possible that the Ego consists entirely of false memories [Sartre] |
7110 | If the 'I' is transcendental, it unnecessarily splits consciousness in two [Sartre] |
7115 | Maybe it is the act of reflection that brings 'me' into existence [Sartre] |
7121 | The Ego only appears to reflection, so it is cut off from the World [Sartre] |
3031 | The greatest good is not the achievement of desire, but to desire what is proper [Menedemus, by Diog. Laertius] |