46 ideas
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] |
4913 | Brain lesions can erase whole categories of perception, suggesting they are hard-wired [Carter,R] |
4910 | Sense organs don't discriminate; they reduce various inputs to the same electrical pulses [Carter,R] |
4911 | The recognition sequence is: classify, name, locate, associate, feel [Carter,R, by PG] |
4919 | There seems to be no dividing line between a memory and a thought [Carter,R] |
4908 | No one knows if animals are conscious [Carter,R] |
4902 | Pain doesn't have one brain location, but is linked to attention and emotion [Carter,R] |
4904 | Proper brains appear at seven weeks, and neonates have as many neurons as adults do [Carter,R] |
4915 | In primates, brain size correlates closely with size of social group [Carter,R] |
4917 | Consciousness involves awareness, perception, self-awareness, attention and reflection [Carter,R] |
4916 | There is enormous evidence that consciousness arises in the frontal lobes of the brain [Carter,R] |
4905 | Normal babies seem to have overlapping sense experiences [Carter,R] |
4918 | In blindsight V1 (normal vision) is inactive, but V5 (movement) lights up [Carter,R] |
18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
4912 | Out-of-body experiences may be due to temporary loss of proprioception [Carter,R] |
4903 | Scans of brains doing similar tasks produce very similar patterns of activation [Carter,R] |
4920 | Thinking takes place on the upper side of the prefrontal cortex [Carter,R] |
4906 | Babies show highly emotional brain events, but may well be unaware of them [Carter,R] |
4909 | The only way we can control our emotions is by manipulating the outside world that influences them [Carter,R] |
4914 | A frog will starve to death surrounded by dead flies [Carter,R] |
7258 | The forefather of modern intuitionism is Richard Price [Price,R, by Dancy,J] |
4907 | The 'locus coeruleus' is one of several candidates for the brain's 'pleasure centre' [Carter,R] |