85 ideas
| 24069 | Much metaphysical debate concerns what is fundamental, rather than what exists [Koslicki] |
| 15118 | A successful Aristotelian 'definition' is what sciences produces after an investigation [Koslicki] |
| 17311 | Real definitions don't just single out a thing; they must also explain its essence [Koslicki] |
| 15116 | Essences cause necessary features, and definitions describe those necessary features [Koslicki] |
| 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] |
| 13258 | The 'aggregative' objections says mereology gets existence and location of objects wrong [Koslicki] |
| 15926 | Second-order logic presupposes a set of relations already fixed by the first-order domain [Lavine] |
| 13288 | Consequence is truth-preserving, either despite substitutions, or in all interpretations [Koslicki] |
| 14506 | 'Roses are red; therefore, roses are colored' seems truth-preserving, but not valid in a system [Koslicki] |
| 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] |
| 17435 | Objects do not naturally form countable units [Koslicki] |
| 17433 | We can still count squares, even if they overlap [Koslicki] |
| 15912 | Counting results in well-ordering, and well-ordering makes counting possible [Lavine] |
| 17439 | There is no deep reason why we count carrots but not asparagus [Koslicki] |
| 17434 | We struggle to count branches and waves because our concepts lack clear boundaries [Koslicki] |
| 15949 | The theory of infinity must rest on our inability to distinguish between very large sizes [Lavine] |
| 15947 | The infinite is extrapolation from the experience of indefinitely large size [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] |
| 17312 | It is more explanatory if you show how a number is constructed from basic entities and relations [Koslicki] |
| 15929 | Set theory will found all of mathematics - except for the notion of proof [Lavine] |
| 14505 | Some questions concern mathematical entities, rather than whole structures [Koslicki] |
| 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] |
| 17314 | The relata of grounding are propositions or facts, but for dependence it is objects and their features [Koslicki] |
| 16062 | A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow] |
| 16061 | If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow] |
| 17436 | We talk of snow as what stays the same, when it is a heap or drift or expanse [Koslicki] |
| 16060 | Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow] |
| 16064 | The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow] |
| 13289 | Structures have positions, constituent types and number, and some invariable parts [Koslicki] |
| 14501 | 'Categorical' properties exist in the actual world, and 'hypothetical' properties in other worlds [Koslicki] |
| 14495 | I aim to put the notion of structure or form back into the concepts of part, whole and object [Koslicki] |
| 13264 | If a whole is just a structure, a dinner party wouldn't need the guests to turn up [Koslicki] |
| 24065 | Structured wholes are united by the teamwork needed for their capacities [Koslicki] |
| 14497 | The clay is just a part of the statue (its matter); the rest consists of its form or structure [Koslicki] |
| 13280 | Statue and clay differ in modal and temporal properties, and in constitution [Koslicki] |
| 24066 | The form explains kind, structure, unity and activity [Koslicki] |
| 14496 | Structure or form are right at the centre of modern rigorous modes of enquiry [Koslicki] |
| 13279 | There are at least six versions of constitution being identity [Koslicki] |
| 14498 | For three-dimensionalist parthood must be a three-place relation, including times [Koslicki] |
| 13283 | The parts may be the same type as the whole, like a building made of buildings [Koslicki] |
| 13266 | Wholes in modern mereology are intended to replace sets, so they closely resemble them [Koslicki] |
| 14500 | Wholes are entities distinct from their parts, and have different properties [Koslicki] |
| 13281 | Wholes are not just their parts; a whole is an entity distinct from the proper parts [Koslicki] |
| 15110 | An essence and what merely follow from it are distinct [Koslicki] |
| 17313 | Modern views want essences just to individuate things across worlds and times [Koslicki] |
| 15113 | Individuals are perceived, but demonstration and definition require universals [Koslicki] |
| 24067 | Hylomorphic compounds need an individual form for transworld identity [Koslicki] |
| 17309 | For Fine, essences are propositions true because of identity, so they are just real definitions [Koslicki] |
| 17315 | We need a less propositional view of essence, and so must distinguish it clearly from real definitions [Koslicki] |
| 15112 | If an object exists, then its essential properties are necessary [Koslicki] |
| 15111 | In demonstration, the explanatory order must mirror the causal order of the phenomena [Koslicki] |
| 15115 | In a demonstration the middle term explains, by being part of the definition [Koslicki] |
| 17317 | A good explanation captures the real-world dependence among the phenomena [Koslicki] |
| 15117 | Greek uses the same word for 'cause' and 'explanation' [Koslicki] |
| 15114 | Discovering the Aristotelian essence of thunder will tell us why thunder occurs [Koslicki] |
| 17316 | We can abstract to a dependent entity by blocking out features of its bearer [Koslicki] |
| 14504 | The Kripke/Putnam approach to natural kind terms seems to give them excessive stability [Koslicki] |
| 13285 | Natural kinds support inductive inferences, from previous samples to the next one [Koslicki] |
| 13287 | Concepts for species are either intrinsic structure, or relations like breeding or ancestry [Koslicki] |
| 13284 | Should vernacular classifications ever be counted as natural kind terms? [Koslicki] |
| 13286 | There are apparently no scientific laws concerning biological species [Koslicki] |