46 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] |
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] |
18680 | To avoid misunderstandings supervenience is often expressed negatively: no A-change without B-change [Orsi] |
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] |
7295 | Maybe induction is only reliable IF reality is stable [Mitchell,A] |
8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos] |
18684 | Rather than requiring an action, a reason may 'entice' us, or be 'eligible', or 'justify' it [Orsi] |
18666 | Value-maker concepts (such as courageous or elegant) simultaneously describe and evaluate [Orsi] |
18667 | The '-able' concepts (like enviable) say this thing deserves a particular response [Orsi] |
18685 | Final value is favoured for its own sake, and personal value for someone's sake [Orsi] |
18679 | Things are only valuable if something makes it valuable, and we can ask for the reason [Orsi] |
18682 | A complex value is not just the sum of the values of the parts [Orsi] |
18683 | Trichotomy Thesis: comparable values must be better, worse or the same [Orsi] |
18686 | The Fitting Attitude view says values are fitting or reasonable, and values are just byproducts [Orsi] |
18672 | Values from reasons has the 'wrong kind of reason' problem - admiration arising from fear [Orsi] |
18677 | A thing may have final value, which is still derived from other values, or from relations [Orsi] |
18668 | Truths about value entail normative truths about actions or attitudes [Orsi] |
18670 | The Buck-Passing view of normative values says other properties are reasons for the value [Orsi] |
18669 | Values can be normative in the Fitting Attitude account, where 'good' means fitting favouring [Orsi] |