62 ideas
15375 | If terms change their designations in different states, they are functions from states to objects [Fitting] |
15376 | Intensional logic adds a second type of quantification, over intensional objects, or individual concepts [Fitting] |
15378 | Awareness logic adds the restriction of an awareness function to epistemic logic [Fitting] |
15379 | Justication logics make explicit the reasons for mathematical truth in proofs [Fitting] |
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] |
11026 | Classical logic is deliberately extensional, in order to model mathematics [Fitting] |
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] |
11028 | λ-abstraction disambiguates the scope of modal operators [Fitting] |
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] |
22121 | The concept of being has only one meaning, whether talking of universals or of God [Duns Scotus, by Dumont] |
22122 | Being (not sensation or God) is the primary object of the intellect [Duns Scotus, by Dumont] |
16660 | Are things distinct if they are both separate, or if only one of them can be separate? [Duns Scotus, by Pasnau] |
10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
16648 | Accidents must have formal being, if they are principles of real action, and of mental action and thought [Duns Scotus] |
10488 | It is lunacy to think we only see ink-marks, and not word-types [Boolos] |
22125 | Duns Scotus was a realist about universals [Duns Scotus, by Dumont] |
15386 | If only the singular exists, science is impossible, as that relies on true generalities [Duns Scotus, by Panaccio] |
15387 | If things were singular they would only differ numerically, but horse and tulip differ more than that [Duns Scotus, by Panaccio] |
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] |
16632 | We distinguish one thing from another by contradiction, because this is, and that is not [Duns Scotus] |
22127 | Scotus said a substantial principle of individuation [haecceitas] was needed for an essence [Duns Scotus, by Dumont] |
13094 | The haecceity is the featureless thing which gives ultimate individuality to a substance [Duns Scotus, by Cover/O'Leary-Hawthorne] |
16650 | 'Unity' is a particularly difficult word, because things can have hidden unity [Duns Scotus] |
16770 | It is absurd that there is no difference between a genuinely unified thing, and a mere aggregate [Duns Scotus] |
16776 | Substance is an intrinsic thing, so parts of substances can't also be intrinsic things [Duns Scotus] |
16626 | Substance is only grasped under the general heading of 'being' [Duns Scotus] |
16614 | Matter and form give true unity; subject and accident is just unity 'per accidens' [Duns Scotus] |
10919 | What prevents a stone from being divided into parts which are still the stone? [Duns Scotus] |
22126 | Avicenna and Duns Scotus say essences have independent and prior existence [Duns Scotus, by Dumont] |
16768 | Two things are different if something is true of one and not of the other [Duns Scotus] |
15377 | Definite descriptions pick out different objects in different possible worlds [Fitting] |
22129 | Certainty comes from the self-evident, from induction, and from self-awareness [Duns Scotus, by Dumont] |
22130 | Scotus defended direct 'intuitive cognition', against the abstractive view [Duns Scotus, by Dumont] |
22128 | Augustine's 'illumination' theory of knowledge leads to nothing but scepticism [Duns Scotus, by Dumont] |
22131 | The will retains its power for opposites, even when it is acting [Duns Scotus, by Dumont] |
8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos] |
22123 | The concept of God is the unique first efficient cause, final cause, and most eminent being [Duns Scotus, by Dumont] |
22124 | We can't infer the infinity of God from creation ex nihilo [Duns Scotus, by Dumont] |