27 ideas
| 10571 | Concern for rigour can get in the way of understanding phenomena [Fine,K] |
| Full Idea: It is often the case that the concern for rigor gets in the way of a true understanding of the phenomena to be explained. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) | |
| A reaction: This is a counter to Timothy Williamson's love affair with rigour in philosophy. It strikes me as the big current question for analytical philosophy - of whether the intense pursuit of 'rigour' will actually deliver the wisdom we all seek. |
| 10565 | There is no stage at which we can take all the sets to have been generated [Fine,K] |
| Full Idea: There is no stage at which we can take all the sets to have been generated, since the set of all those sets which have been generated at a given stage will itself give us something new. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
| 10564 | We might combine the axioms of set theory with the axioms of mereology [Fine,K] |
| Full Idea: We might combine the standard axioms of set theory with the standard axioms of mereology. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
| 10569 | If you ask what F the second-order quantifier quantifies over, you treat it as first-order [Fine,K] |
| Full Idea: We are tempted to ask of second-order quantifiers 'what are you quantifying over?', or 'when you say "for some F" then what is the F?', but these questions already presuppose that the quantifiers are first-order. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005]) |
| 10570 | Assigning an entity to each predicate in semantics is largely a technical convenience [Fine,K] |
| Full Idea: In doing semantics we normally assign some appropriate entity to each predicate, but this is largely for technical convenience. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) |
| 10573 | Dedekind cuts lead to the bizarre idea that there are many different number 1's [Fine,K] |
| Full Idea: Because of Dedekind's definition of reals by cuts, there is a bizarre modern doctrine that there are many 1's - the natural number 1, the rational number 1, the real number 1, and even the complex number 1. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) | |
| A reaction: See Idea 10572. |
| 10575 | Why should a Dedekind cut correspond to a number? [Fine,K] |
| Full Idea: By what right can Dedekind suppose that there is a number corresponding to any pair of irrationals that constitute an irrational cut? | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) |
| 10574 | Unless we know whether 0 is identical with the null set, we create confusions [Fine,K] |
| Full Idea: What is the union of the singleton {0}, of zero, and the singleton {φ}, of the null set? Is it the one-element set {0}, or the two-element set {0, φ}? Unless the question of identity between 0 and φ is resolved, we cannot say. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) |
| 10560 | Set-theoretic imperialists think sets can represent every mathematical object [Fine,K] |
| Full Idea: Set-theoretic imperialists think that it must be possible to represent every mathematical object as a set. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
| 10568 | Logicists say mathematics can be derived from definitions, and can be known that way [Fine,K] |
| Full Idea: Logicists traditionally claim that the theorems of mathematics can be derived by logical means from the relevant definitions of the terms, and that these theorems are epistemically innocent (knowable without Kantian intuition or empirical confirmation). | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) |
| 10563 | A generative conception of abstracts proposes stages, based on concepts of previous objects [Fine,K] |
| Full Idea: It is natural to have a generative conception of abstracts (like the iterative conception of sets). The abstracts are formed at stages, with the abstracts formed at any given stage being the abstracts of those concepts of objects formed at prior stages. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) | |
| A reaction: See 10567 for Fine's later modification. This may not guarantee 'levels', but it implies some sort of conceptual priority between abstract entities. |
| 13076 | Scholastics treat relations as two separate predicates of the relata [Cover/O'Leary-Hawthorne] |
| Full Idea: The scholastics treated it as a step in the right explanatory direction to analyze a relational statement of the form 'aRb' into two subject-predicate statements, attributing different relational predicates to a and to b. | |
| From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 2.2.1) | |
| A reaction: The only alternative seems to be Russell's view of relations as pure universals, having a life of their own, quite apart from their relata. Or you could take them as properties of space, time (and powers?), external to the relata? |
| 13102 | If you individuate things by their origin, you still have to individuate the origins themselves [Cover/O'Leary-Hawthorne] |
| Full Idea: If we go for the necessity-of-origins view, A and B are different if the origin of A is different from the origin of B. But one is left with the further question 'When is the origin of A distinct from the origin of B?' | |
| From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 7.4.1) | |
| A reaction: There may be an answer to this, in a regress of origins that support one another, but in the end the objection is obviously good. You can't begin to refer to an 'origin' if you can't identify anything in the first place. |
| 13103 | Numerical difference is a symmetrical notion, unlike proper individuation [Cover/O'Leary-Hawthorne] |
| Full Idea: Scholastics distinguished criteria of numerical difference from questions of individuation proper, since numerical difference is a symmetrical notion. | |
| From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 7.4.1) | |
| A reaction: This apparently old-fashioned point appears to be conclusively correct. Modern thinkers, though, aren't comfortable with proper individuation, because they don't believe in concepts like 'essence' and 'substance' that are needed for the job. |
| 13104 | Haecceity as property, or as colourless thisness, or as singleton set [Cover/O'Leary-Hawthorne] |
| Full Idea: There is a contemporary property construal of haecceities, ...and a Scotistic construal as primitive, 'colourless' thisnesses which, unlike singleton-set haecceities, are aimed to do some explanatory work. | |
| From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 7.4.4) | |
| A reaction: [He associates the contemporary account with David Kaplan] I suppose I would say that individuation is done by properties, but not by some single property, so I take it that I don't believe in haecceities at all. What individuates a haecceity? |
| 13100 | Maybe 'substance' is more of a mass-noun than a count-noun [Cover/O'Leary-Hawthorne] |
| Full Idea: We could think of 'substance' on the model of a mass noun, rather than a count noun. | |
| From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 7.3) | |
| A reaction: They offer this to help Leibniz out of a mess, but I think he would be appalled. The proposal seems close to 'prime matter' in Aristotle, which never quite does the job required of it. The idea is nice, though, and should be taken seriously. |
| 13068 | We can ask for the nature of substance, about type of substance, and about individual substances [Cover/O'Leary-Hawthorne] |
| Full Idea: In the 'blueprint' approach to substance, we confront at least three questions: What is it for a thing to be an individual substance? What is it for a thing to be the kind of substance that it is? What is it to be that very individual substance? | |
| From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 1.1.1) | |
| A reaction: My working view is that the answer to the first question is that substance is essence, that the second question is overrated and parasitic on the third, and that the third is the key question, and also reduces to essence. |
| 13069 | The general assumption is that substances cannot possibly be non-substances [Cover/O'Leary-Hawthorne] |
| Full Idea: There is a widespread assumption, now and in the past, that substances are essentially substances: nothing is actually a substance but possibly a non-substance. | |
| From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 1.1.2) | |
| A reaction: It seems to me that they clearly mean, in this context, that substances are 'necessarily' substances, not that they are 'essentially' substances. I would just say that substances are essences, and leave the necessity question open. |
| 13072 | Modern essences are sets of essential predicate-functions [Cover/O'Leary-Hawthorne] |
| Full Idea: The modern view of essence is that the essence of a particular thing is given by the set of predicate-functions essential to it, and the essence of any kind is given by the set of predicate-functions essential to every possible member of that kind. | |
| From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 1.2.2) | |
| A reaction: Thus the modern view has elided the meanings of 'essential' and 'necessary' when talking of properties. They are said to be 'functions' from possible worlds to individuals. The old view (and mine) demands real essences, not necessary properties. |
| 17080 | Modern essentialists express essence as functions from worlds to extensions for predicates [Cover/O'Leary-Hawthorne] |
| Full Idea: The modern essentialist gives the same metaphysical treatment to every grammatical predicate - by associating a function from worlds to extensions for each. | |
| From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 2.2) | |
| A reaction: I take this to mean that essentialism is the view that if some predicate attaches to an object then that predicate is essential if there is an extension of that predicate in all possible worlds. In English, essential predicates are necessary predicates. |
| 4869 | Experience does not teach us any essences of things [Spinoza] |
| Full Idea: Experience does not teach us any essences of things. | |
| From: Baruch de Spinoza (Letters to De Vries [1664], 1664?) | |
| A reaction: This, along with Leibniz's claim that experience cannot reveal necessities, may constitute a striking criticism of empiricism, but it invites the obvious reply 'so much the worse for essences'. An essence seems to be a theoretical concept, not a priori. |
| 13101 | Necessity-of-origin won't distinguish ex nihilo creations, or things sharing an origin [Cover/O'Leary-Hawthorne] |
| Full Idea: A necessity-of-origins approach cannot work to distinguish things that come into being genuinely ex nihilo, and cannot work to distinguish things sharing a single origin. | |
| From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 7.4.1) | |
| A reaction: Since I am deeply suspicious of essentiality or necessity of origin (and they are not, I presume, the same thing) I like these two. Twins have always bothered me with the second case (where order of birth seems irrelevant). |
| 13081 | Even extreme modal realists might allow transworld identity for abstract objects [Cover/O'Leary-Hawthorne] |
| Full Idea: It might be suggested that even the extreme modal realist can countenance transworld identity for abstract objects. | |
| From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 3.2.2 n46) | |
| A reaction: This may sound right for uncontroversial or well-defined abstracta such as numbers and circles, but even 'or' is ambiguous, and heaven knows what the transworld identity of 'democracy' is! |
| 13071 | We can go beyond mere causal explanations if we believe in an 'order of being' [Cover/O'Leary-Hawthorne] |
| Full Idea: The philosopher comfortable with an 'order of being' has richer resources to make sense of the 'in virtue of' relation than that provided only by causal relations between states of affairs, positing in addition other sorts of explanatory relationships. | |
| From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 1.1.2) | |
| A reaction: This might best be characterised as 'ontological dependence', and could be seen as a non-causal but fundamental explanatory relationship, and not one that has to depend on a theistic world view. |
| 10561 | Abstraction-theoretic imperialists think Fregean abstracts can represent every mathematical object [Fine,K] |
| Full Idea: Abstraction-theoretic imperialists think that it must be possible to represent every mathematical object as a Fregean abstract. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
| 10562 | We can combine ZF sets with abstracts as urelements [Fine,K] |
| Full Idea: I propose a unified theory which is a version of ZF or ZFC with urelements, where the urelements are taken to be the abstracts. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
| 10567 | We can create objects from conditions, rather than from concepts [Fine,K] |
| Full Idea: Instead of viewing the abstracts (or sums) as being generated from objects, via the concepts from which they are defined, we can take them to be generated from conditions. The number of the universe ∞ is the number of self-identical objects. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) | |
| A reaction: The point is that no particular object is now required to make the abstraction. |