53 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 | Naďve 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] |
| 16062 | A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow] |
| 16061 | If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow] |
| 16060 | Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow] |
| 16064 | The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow] |
| 10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
| 16665 | There are entities, and then positive 'modes', modifying aspects outside the thing's essence [Suárez] |
| 16666 | A mode determines the state and character of a quantity, without adding to it [Suárez] |
| 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] |
| 16667 | Substances are incomplete unless they have modes [Suárez, by Pasnau] |
| 17007 | Forms must rule over faculties and accidents, and are the source of action and unity [Suárez] |
| 16780 | Partial forms of leaf and fruit are united in the whole form of the tree [Suárez] |
| 16758 | The best support for substantial forms is the co-ordinated unity of a natural being [Suárez] |
| 16743 | We can get at the essential nature of 'quantity' by knowing bulk and extension [Suárez] |
| 13074 | Only natural kinds and their members have real essences [Suárez, by Cover/O'Leary-Hawthorne] |
| 16742 | We only know essences through non-essential features, esp. those closest to the essence [Suárez] |
| 22143 | Identity does not exclude possible or imagined difference [Suárez, by Boulter] |
| 22144 | Real Essential distinction: A and B are of different natural kinds [Suárez, by Boulter] |
| 22146 | Minor Real distinction: B needs A, but A doesn't need B [Suárez, by Boulter] |
| 22145 | Major Real distinction: A and B have independent existences [Suárez, by Boulter] |
| 22147 | Conceptual/Mental distinction: one thing can be conceived of in two different ways [Suárez, by Boulter] |
| 22148 | Modal distinction: A isn't B or its property, but still needs B [Suárez, by Boulter] |
| 22149 | Scholastics assess possibility by what has actually happened in reality [Suárez, by Boulter] |
| 8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos] |
| 7563 | The old 'influx' view of causation says it is a flow of accidental properties from A to B [Suárez, by Jolley] |
| 16682 | Other things could occupy the same location as an angel [Suárez] |