52 ideas
8093 | Seek wisdom rather than truth; it is easier [Joubert] |
8095 | We must think with our entire body and soul [Joubert] |
21829 | Philosophy aims to understand how things (broadly understood) hang together (broadly understood) [Sellars] |
8107 | The love of certainty holds us back in metaphysics [Joubert] |
8099 | The truths of reason instruct, but they do not illuminate [Joubert] |
8098 | Truth consists of having the same idea about something that God has [Joubert] |
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] |
10225 | Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro] |
10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
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] |
6550 | Reduction requires that an object's properties consist of its constituents' properties and relations [Sellars] |
10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
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] |
8101 | To know is to see inside oneself [Joubert] |
8793 | If observation is knowledge, it is not just an experience; it is a justification in the space of reasons [Sellars] |
8792 | Observations like 'this is green' presuppose truths about what is a reliable symptom of what [Sellars] |
8094 | The imagination has made more discoveries than the eye [Joubert] |
6382 | The 'grain problem' says physical objects are granular, where sensations appear not to be [Sellars, by Polger] |
8103 | A thought is as real as a cannon ball [Joubert] |
8100 | Where does the bird's idea of a nest come from? [Joubert] |
8791 | The concept of 'green' involves a battery of other concepts [Sellars] |
8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos] |
8096 | He gives his body up to pleasure, but not his soul [Joubert] |
8104 | What will you think of pleasures when you no longer enjoy them? [Joubert] |
8097 | Virtue is hard if we are scorned; we need support [Joubert] |
8106 | In raising a child we must think of his old age [Joubert] |
8105 | We can't exactly conceive virtue without the idea of God [Joubert] |
8102 | We cannot speak against Christianity without anger, or speak for it without love [Joubert] |