72 ideas
| 11912 | Substantive metaphysics says what a property is, not what a predicate means [Molnar] |
| 11920 | A real definition gives all the properties that constitute an identity [Molnar] |
| 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] |
| 11919 | Ontological dependence rests on essential connection, not necessary connection [Molnar] |
| 10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
| 11929 | The three categories in ontology are objects, properties and relations [Molnar] |
| 11927 | Reflexive relations are syntactically polyadic but ontologically monadic [Molnar] |
| 11915 | If atomism is true, then all properties derive from ultimate properties [Molnar] |
| 11916 | 'Being physical' is a second-order property [Molnar] |
| 11956 | 'Categorical properties' are those which are not powers [Molnar] |
| 11928 | Are tropes transferable? If they are, that is a version of Platonism [Molnar] |
| 11933 | A power's type-identity is given by its definitive manifestation [Molnar] |
| 11932 | Powers have Directedness, Independence, Actuality, Intrinsicality and Objectivity [Molnar] |
| 11934 | The physical world has a feature very like mental intentionality [Molnar] |
| 11947 | Dispositions and external powers arise entirely from intrinsic powers in objects [Molnar] |
| 11952 | The Standard Model suggest that particles are entirely dispositional, and hence are powers [Molnar] |
| 11953 | Some powers are ungrounded, and others rest on them, and are derivative [Molnar] |
| 11943 | Dispositions can be causes, so they must be part of the actual world [Molnar] |
| 11939 | If powers only exist when actual, they seem to be nomadic, and indistinguishable from non-powers [Molnar] |
| 10488 | It is lunacy to think we only see ink-marks, and not word-types [Boolos] |
| 11914 | Platonic explanations of universals actually diminish our understanding [Molnar] |
| 11913 | For nominalists, predicate extensions are inexplicable facts [Molnar] |
| 11962 | Nominalists only accept first-order logic [Molnar] |
| 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] |
| 11917 | Structural properties are derivate properties [Molnar] |
| 11955 | There are no 'structural properties', as properties with parts [Molnar] |
| 11918 | The essence of a thing need not include everything that is necessarily true of it [Molnar] |
| 11963 | What is the truthmaker for a non-existent possible? [Molnar] |
| 21513 | We can no more expect a precise definition of coherence than we can of the moral ideal [Ewing] |
| 21497 | If undetailed, 'coherence' is just a vague words that covers all possible arguments [Ewing] |
| 11951 | Hume allows interpolation, even though it and extrapolation are not actually valid [Molnar] |
| 11936 | The two ways proposed to distinguish mind are intentionality or consciousness [Molnar] |
| 11935 | Physical powers like solubility and charge also have directedness [Molnar] |
| 11944 | Rule occasionalism says God's actions follow laws, not miracles [Molnar] |
| 8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos] |
| 18671 | The ground for an attitude is not a thing's 'goodness', but its concrete characteristics [Ewing] |
| 11960 | Singular causation is prior to general causation; each aspirin produces the aspirin generalization [Molnar] |
| 11937 | We should analyse causation in terms of powers, not vice versa [Molnar] |
| 11954 | We should analyse causation in terms of powers [Molnar] |
| 11961 | Causal dependence explains counterfactual dependence, not vice versa [Molnar] |
| 11959 | Science works when we assume natural kinds have essences - because it is true [Molnar] |
| 9448 | Location in space and time are non-power properties [Molnar, by Mumford] |
| 11930 | One essential property of a muon doesn't entail the others [Molnar] |
| 11957 | It is contingent which kinds and powers exist in the world [Molnar] |
| 11921 | The laws of nature depend on the powers, not the other way round [Molnar] |
| 11931 | Energy fields are discontinuous at the very small [Molnar] |