85 ideas
| 15477 | Ontology is highly abstract physics, containing placeholders and exclusions [Martin,CB] |
| 15471 | Truth is a relation between a representation ('bearer') and part of the world ('truthmaker') [Martin,CB] |
| 15945 | Second-order set theory just adds a version of Replacement that quantifies over functions [Lavine] |
| 15914 | An 'upper bound' is the greatest member of a subset; there may be several of these, so there is a 'least' one [Lavine] |
| 15921 | Collections of things can't be too big, but collections by a rule seem unlimited in size [Lavine] |
| 15937 | Those who reject infinite collections also want to reject the Axiom of Choice [Lavine] |
| 15936 | The Power Set is just the collection of functions from one collection to another [Lavine] |
| 15899 | Replacement was immediately accepted, despite having very few implications [Lavine] |
| 15930 | Foundation says descending chains are of finite length, blocking circularity, or ungrounded sets [Lavine] |
| 15920 | Pure collections of things obey Choice, but collections defined by a rule may not [Lavine] |
| 15898 | The controversy was not about the Axiom of Choice, but about functions as arbitrary, or given by rules [Lavine] |
| 15919 | The 'logical' notion of class has some kind of definition or rule to characterise the class [Lavine] |
| 15900 | The iterative conception of set wasn't suggested until 1947 [Lavine] |
| 15931 | The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine] |
| 15932 | The iterative conception doesn't unify the axioms, and has had little impact on mathematical proofs [Lavine] |
| 15933 | Limitation of Size: if it's the same size as a set, it's a set; it uses Replacement [Lavine] |
| 15913 | A collection is 'well-ordered' if there is a least element, and all of its successors can be identified [Lavine] |
| 15926 | Second-order logic presupposes a set of relations already fixed by the first-order domain [Lavine] |
| 15934 | Mathematical proof by contradiction needs the law of excluded middle [Lavine] |
| 15907 | Mathematics is nowadays (thanks to set theory) regarded as the study of structure, not of quantity [Lavine] |
| 15942 | Every rational number, unlike every natural number, is divisible by some other number [Lavine] |
| 15922 | For the real numbers to form a set, we need the Continuum Hypothesis to be true [Lavine] |
| 18250 | Cauchy gave a necessary condition for the convergence of a sequence [Lavine] |
| 15904 | The two sides of the Cut are, roughly, the bounding commensurable ratios [Lavine] |
| 15912 | Counting results in well-ordering, and well-ordering makes counting possible [Lavine] |
| 15947 | The infinite is extrapolation from the experience of indefinitely large size [Lavine] |
| 15949 | The theory of infinity must rest on our inability to distinguish between very large sizes [Lavine] |
| 15940 | The intuitionist endorses only the potential infinite [Lavine] |
| 15909 | 'Aleph-0' is cardinality of the naturals, 'aleph-1' the next cardinal, 'aleph-ω' the ω-th cardinal [Lavine] |
| 15915 | Ordinals are basic to Cantor's transfinite, to count the sets [Lavine] |
| 15917 | Paradox: the class of all ordinals is well-ordered, so must have an ordinal as type - giving a bigger ordinal [Lavine] |
| 15918 | Paradox: there is no largest cardinal, but the class of everything seems to be the largest [Lavine] |
| 15929 | Set theory will found all of mathematics - except for the notion of proof [Lavine] |
| 15935 | Modern mathematics works up to isomorphism, and doesn't care what things 'really are' [Lavine] |
| 15928 | Intuitionism rejects set-theory to found mathematics [Lavine] |
| 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] |
| 16648 | Accidents must have formal being, if they are principles of real action, and of mental action and thought [Duns Scotus] |
| 15484 | A property is a combination of a disposition and a quality [Martin,CB] |
| 15478 | Properties are the respects in which objects resemble, which places them in classes [Martin,CB] |
| 15483 | Properties are ways particular things are, and so they are tied to the identity of their possessor [Martin,CB] |
| 15480 | Objects are not bundles of tropes (which are ways things are, not parts of things) [Martin,CB] |
| 15489 | A property that cannot interact is worse than inert - it isn't there at all [Martin,CB] |
| 15487 | If unmanifested partnerless dispositions are still real, and are not just qualities, they can explain properties [Martin,CB] |
| 15488 | Qualities and dispositions are aspects of properties - what it exhibits, and what it does [Martin,CB] |
| 15479 | Properties endow a ball with qualities, and with powers or dispositions [Martin,CB] |
| 15469 | Dispositions in action can be destroyed, be recovered, or remain unchanged [Martin,CB] |
| 15467 | Powers depend on circumstances, so can't be given a conditional analysis [Martin,CB] |
| 15466 | 'The wire is live' can't be analysed as a conditional, because a wire can change its powers [Martin,CB] |
| 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] |
| 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] |
| 15476 | Structural properties involve dispositionality, so cannot be used to explain it [Martin,CB] |
| 15465 | Structures don't explain dispositions, because they consist of dispositions [Martin,CB] |
| 16614 | Matter and form give true unity; subject and accident is just unity 'per accidens' [Duns Scotus] |
| 15481 | I favour the idea of a substratum for properties; spacetime seems to be just a bearer of properties [Martin,CB] |
| 15474 | Properly understood, wholes do no more causal work than their parts [Martin,CB] |
| 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] |
| 15486 | Only abstract things can have specific and full identity specifications [Martin,CB] |
| 15475 | The concept of 'identity' must allow for some changes in properties or parts [Martin,CB] |
| 16768 | Two things are different if something is true of one and not of the other [Duns Scotus] |
| 15472 | It is pointless to say possible worlds are truthmakers, and then deny that possible worlds exist [Martin,CB] |
| 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] |
| 15492 | Explanations are mind-dependent, theory-laden, and interest-relative [Martin,CB] |
| 15495 | Analogy works, as when we eat food which others seem to be relishing [Martin,CB] |
| 15493 | Memory requires abstraction, as reminders of what cannot be fully remembered [Martin,CB] |
| 22131 | The will retains its power for opposites, even when it is acting [Duns Scotus, by Dumont] |
| 15485 | Instead of a cause followed by an effect, we have dispositions in reciprocal manifestation [Martin,CB] |
| 15491 | Causation should be explained in terms of dispositions and manifestations [Martin,CB] |
| 15468 | Causal counterfactuals are just clumsy linguistic attempts to indicate dispositions [Martin,CB] |
| 15470 | Causal laws are summaries of powers [Martin,CB] |
| 15482 | We can't think of space-time as empty and propertyless, and it seems to be a substratum [Martin,CB] |
| 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] |