51 ideas
10482 | The logic of ZF is classical first-order predicate logic with identity [Boolos] |
10492 | A few axioms of set theory 'force themselves on us', but most of them don't [Boolos] |
18192 | Do the Replacement Axioms exceed the iterative conception of sets? [Boolos, by Maddy] |
7785 | The use of plurals doesn't commit us to sets; there do not exist individuals and collections [Boolos] |
10485 | Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos] |
10484 | The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos] |
13547 | Limitation of Size is weak (Fs only collect is something the same size does) or strong (fewer Fs than objects) [Boolos, by Potter] |
10699 | Does a bowl of Cheerios contain all its sets and subsets? [Boolos] |
14249 | Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley] |
10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
10225 | Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro] |
10736 | Boolos showed how plural quantifiers can interpret monadic second-order logic [Boolos, by Linnebo] |
10780 | Any sentence of monadic second-order logic can be translated into plural first-order logic [Boolos, by Linnebo] |
10829 | A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos] |
10697 | Identity is clearly a logical concept, and greatly enhances predicate calculus [Boolos] |
10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
13671 | Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology [Boolos, by Shapiro] |
10267 | We should understand second-order existential quantifiers as plural quantifiers [Boolos, by Shapiro] |
10698 | Plural forms have no more ontological commitment than to first-order objects [Boolos] |
7806 | Boolos invented plural quantification [Boolos, by Benardete,JA] |
10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos] |
13841 | Why should compactness be definitive of logic? [Boolos, by Hacking] |
10491 | Infinite natural numbers is as obvious as infinite sentences in English [Boolos] |
10483 | Mathematics and science do not require very high orders of infinity [Boolos] |
10833 | Many concepts can only be expressed by second-order logic [Boolos] |
10490 | Mathematics isn't surprising, given that we experience many objects as abstract [Boolos] |
10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
4913 | Brain lesions can erase whole categories of perception, suggesting they are hard-wired [Carter,R] |
10488 | It is lunacy to think we only see ink-marks, and not word-types [Boolos] |
10487 | I am a fan of abstract objects, and confident of their existence [Boolos] |
10489 | We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos] |
12887 | A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim] |
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] |
4915 | In primates, brain size correlates closely with size of social group [Carter,R] |
4904 | Proper brains appear at seven weeks, and neonates have as many neurons as adults do [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] |
4912 | Out-of-body experiences may be due to temporary loss of proprioception [Carter,R] |
4920 | Thinking takes place on the upper side of the prefrontal cortex [Carter,R] |
4903 | Scans of brains doing similar tasks produce very similar patterns of activation [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] |
8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos] |
4907 | The 'locus coeruleus' is one of several candidates for the brain's 'pleasure centre' [Carter,R] |