130 ideas
| 6779 | Instrumentalists say distinctions between observation and theory vanish with ostensive definition [Bird] |
| 9449 | The plausible Barcan formula implies modality in the actual world [Bird] |
| 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] |
| 10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
| 10225 | Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro] |
| 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] |
| 9501 | If all existents are causally active, that excludes abstracta and causally isolated objects [Bird] |
| 9500 | If naturalism refers to supervenience, that leaves necessary entities untouched [Bird] |
| 6780 | Anti-realism is more plausible about laws than about entities and theories [Bird] |
| 10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
| 9502 | There might be just one fundamental natural property [Bird] |
| 9477 | Categorical properties are not modally fixed, but change across possible worlds [Bird] |
| 9490 | The categoricalist idea is that a property is only individuated by being itself [Bird] |
| 9495 | If we abstractly define a property, that doesn't mean some object could possess it [Bird] |
| 9492 | Categoricalists take properties to be quiddities, with no essential difference between them [Bird] |
| 9503 | To name an abundant property is either a Fregean concept, or a simple predicate [Bird] |
| 14540 | Only real powers are fundamental [Bird, by Mumford/Anjum] |
| 9450 | If all properties are potencies, and stimuli and manifestation characterise them, there is a regress [Bird] |
| 9498 | The essence of a potency involves relations, e.g. mass, to impressed force and acceleration [Bird] |
| 9474 | A disposition is finkish if a time delay might mean the manifestation fizzles out [Bird] |
| 9475 | A robust pot attached to a sensitive bomb is not fragile, but if struck it will easily break [Bird] |
| 9499 | Megarian actualists deny unmanifested dispositions [Bird] |
| 10488 | It is lunacy to think we only see ink-marks, and not word-types [Boolos] |
| 9486 | Why should a universal's existence depend on instantiation in an existing particular? [Bird] |
| 9472 | Resemblance itself needs explanation, presumably in terms of something held in common [Bird] |
| 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] |
| 9482 | If the laws necessarily imply p, that doesn't give a new 'nomological' necessity [Bird] |
| 9481 | Logical necessitation is not a kind of necessity; George Orwell not being Eric Blair is not a real possibility [Bird] |
| 6796 | Subjective probability measures personal beliefs; objective probability measures the chance of an event happening [Bird] |
| 6797 | Objective probability of tails measures the bias of the coin, not our beliefs about it [Bird] |
| 9505 | Empiricist saw imaginability and possibility as close, but now they seem remote [Bird] |
| 9491 | Haecceitism says identity is independent of qualities and without essence [Bird] |
| 6800 | Many philosophers rate justification as a more important concept than knowledge [Bird] |
| 6786 | As science investigates more phenomena, the theories it needs decreases [Bird] |
| 6792 | If theories need observation, and observations need theories, how do we start? [Bird] |
| 6757 | Explanation predicts after the event; prediction explains before the event [Bird] |
| 6805 | Relativity ousted Newtonian mechanics despite a loss of simplicity [Bird] |
| 6777 | Realists say their theories involve truth and the existence of their phenomena [Bird] |
| 6804 | There is no agreement on scientific method - because there is no such thing [Bird] |
| 6778 | Instrumentalists regard theories as tools for prediction, with truth being irrelevant [Bird] |
| 6775 | Induction is inference to the best explanation, where the explanation is a law [Bird] |
| 6791 | If Hume is right about induction, there is no scientific knowledge [Bird] |
| 6790 | Anything justifying inferences from observed to unobserved must itself do that [Bird] |
| 6738 | Any conclusion can be drawn from an induction, if we use grue-like predicates [Bird] |
| 6739 | Several months of observing beech trees supports the deciduous and evergreen hypotheses [Bird] |
| 6799 | We normally learn natural kinds from laws, but Goodman shows laws require prior natural kinds [Bird] |
| 6798 | Bayesianism claims to find rationality and truth in induction, and show how science works [Bird] |
| 6752 | The objective component of explanations is the things that must exist for the explanation [Bird] |
| 6754 | We talk both of 'people' explaining things, and of 'facts' explaining things [Bird] |
| 9487 | We can't reject all explanations because of a regress; inexplicable A can still explain B [Bird] |
| 6750 | Explanations are causal, nomic, psychological, psychoanalytic, Darwinian or functional [Bird] |
| 6761 | Contrastive explanations say why one thing happened but not another [Bird] |
| 6758 | 'Covering law' explanations only work if no other explanations are to be found [Bird] |
| 6759 | Livers always accompany hearts, but they don't explain hearts [Bird] |
| 6756 | Probabilistic-statistical explanations don't entail the explanandum, but makes it more likely [Bird] |
| 6760 | An operation might reduce the probability of death, yet explain a death [Bird] |
| 6785 | Inference to the Best Explanation is done with facts, so it has to be realist [Bird] |
| 6788 | Maybe bad explanations are the true ones, in this messy world [Bird] |
| 6787 | Which explanation is 'best' is bound to be subjective, and no guide to truth [Bird] |
| 6751 | Maybe explanation is so subjective that it cannot be a part of science [Bird] |
| 17527 | Causation seems to be an innate concept (or acquired very early) [Bird] |
| 8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos] |
| 6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |
| 6776 | Natural kinds are those that we use in induction [Bird] |
| 6767 | Rubies and sapphires are both corundum, with traces of metals varying their colours [Bird] |
| 6768 | Tin is not one natural kind, but appears to be 21, depending on isotope [Bird] |
| 6771 | Natural kinds may overlap, or be sub-kinds of one another [Bird] |
| 6770 | Membership of a purely random collection cannot be used as an explanation [Bird] |
| 6773 | If F is a universal appearing in a natural law, then Fs form a natural kind [Bird] |
| 6769 | In the Kripke-Putnam view only nuclear physicists can know natural kinds [Bird] |
| 6774 | Darwinism suggests that we should have a native ability to detect natural kinds [Bird] |
| 6764 | Nominal essence of a natural kind is the features that make it fit its name [Bird] |
| 6766 | Jadeite and nephrite are superficially identical, but have different composition [Bird] |
| 6808 | Reference to scientific terms is by explanatory role, not by descriptions [Bird] |
| 17528 | The dispositional account explains causation, as stimulation and manifestation of dispositions [Bird] |
| 9493 | We should explain causation by powers, not powers by causation [Bird] |
| 6753 | Laws are more fundamental in science than causes, and laws will explain causes [Bird] |
| 9494 | Singularism about causes is wrong, as the universals involved imply laws [Bird] |
| 17526 | The counterfactual approach makes no distinction between cause and pre-condition [Bird] |
| 6762 | Newton's laws cannot be confirmed individually, but only in combinations [Bird] |
| 6763 | Parapsychology is mere speculation, because it offers no mechanisms for its working [Bird] |
| 6772 | Existence requires laws, as inertia or gravity are needed for mass or matter [Bird] |
| 9507 | Laws are explanatory relationships of things, which supervene on their essences [Bird] |
| 9488 | Laws are either disposition regularities, or relations between properties [Bird] |
| 6746 | There may be many laws, each with only a few instances [Bird] |
| 6740 | 'All uranium lumps are small' is a law, but 'all gold lumps are small' is not [Bird] |
| 6741 | There can be remarkable uniformities in nature that are purely coincidental [Bird] |
| 6742 | A law might have no instances, if it was about things that only exist momentarily [Bird] |
| 6743 | If laws are just instances, the law should either have gaps, or join the instances arbitrarily [Bird] |
| 6744 | Where is the regularity in a law predicting nuclear decay? [Bird] |
| 6747 | Laws cannot explain instances if they are regularities, as something can't explain itself [Bird] |
| 6748 | Similar appearance of siblings is a regularity, but shared parents is what links them [Bird] |
| 6749 | We can only infer a true regularity if something binds the instances together [Bird] |
| 6803 | If we only infer laws from regularities among observations, we can't infer unobservable entities. [Bird] |
| 6801 | Accidental regularities are not laws, and an apparent regularity may not be actual [Bird] |
| 9496 | That other diamonds are hard does not explain why this one is [Bird] |
| 9479 | Dispositional essentialism says laws (and laws about laws) are guaranteed regularities [Bird] |
| 6745 | A regularity is only a law if it is part of a complete system which is simple and strong [Bird] |
| 6802 | With strange enough predicates, anything could be made out to be a regularity [Bird] |
| 9473 | Laws cannot offer unified explanations if they don't involve universals [Bird] |
| 9484 | If the universals for laws must be instantiated, a vanishing particular could destroy a law [Bird] |
| 9506 | Salt necessarily dissolves in water, because of the law which makes the existence of salt possible [Bird] |
| 23713 | Most laws supervene on fundamental laws, which are explained by basic powers [Bird, by Friend/Kimpton-Nye] |
| 6789 | If flame colour is characteristic of a metal, that is an empirical claim needing justification [Bird] |
| 9489 | Essentialism can't use conditionals to explain regularities, because of possible interventions [Bird] |
| 6807 | In Newton mass is conserved, but in Einstein it can convert into energy [Bird] |
| 9504 | The relational view of space-time doesn't cover times and places where things could be [Bird] |