Combining Texts

All the ideas for 'Substance and Individuation in Leibniz', 'Mathematics: Form and Function' and 'The Semantic Tradition from Kant to Carnap'

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18 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

18189	ZFC could contain a contradiction, and it can never prove its own consistency [MacLane]
	Full Idea: We have at hand no proof that the axioms of ZFC for set theory will never yield a contradiction, while Gödel's second theorem tells us that such a consistency proof cannot be conducted within ZFC.
	From: Saunders MacLane (Mathematics: Form and Function [1986], p.406), quoted by Penelope Maddy - Naturalism in Mathematics
	A reaction: Maddy quotes this, while defending set theory as the foundation of mathematics, but it clearly isn't the most secure foundation that could be devised. She says the benefits of set theory do not need guaranteed consistency (p.30).

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX

18270	Choice suggests that intensions are not needed to ensure classes [Coffa]
	Full Idea: The axiom of choice was an assumption that implicitly questioned the necessity of intensions to guarantee the presence of classes.
	From: J. Alberto Coffa (The Semantic Tradition from Kant to Carnap [1991], 7 'Log')
	A reaction: The point is that Choice just picks out members for no particular reason. So classes, it seems, don't need a reason to exist.

8. Modes of Existence / A. Relations / 1. Nature of Relations

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?

9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation

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.

9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity

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?

9. Objects / B. Unity of Objects / 2. Substance / a. Substance

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.

9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance

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.

9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined

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.

9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties

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.

9. Objects / E. Objects over Time / 12. Origin as Essential

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).

10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity

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!

12. Knowledge Sources / A. A Priori Knowledge / 8. A Priori as Analytic

18263	The semantic tradition aimed to explain the a priori semantically, not by Kantian intuition [Coffa]
	Full Idea: The semantic tradition's problem was the a priori; its enemy, Kantian pure intuition; its purpose, to develop a conception of the a priori in which pure intuition played no role; its strategy, to base that theory on a development of semantics.
	From: J. Alberto Coffa (The Semantic Tradition from Kant to Carnap [1991], 2 Intro)
	A reaction: It seems to me that intuition, in the modern sense, has been unnecessarily demonised. I would define it as 'rational insights which cannot be fully articulated'. Sherlock Holmes embodies it.

12. Knowledge Sources / A. A Priori Knowledge / 11. Denying the A Priori

18272	Platonism defines the a priori in a way that makes it unknowable [Coffa]
	Full Idea: The trouble with Platonism had always been its inability to define a priori knowledge in a way that made it possible for human beings to have it.
	From: J. Alberto Coffa (The Semantic Tradition from Kant to Carnap [1991], 7 'What')
	A reaction: This is the famous argument of Benacerraf 1973.

14. Science / D. Explanation / 2. Types of Explanation / c. Explanations by coherence

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.

15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind

18266	Mathematics generalises by using variables [Coffa]
	Full Idea: The instrument of generality in mathematics is the variable.
	From: J. Alberto Coffa (The Semantic Tradition from Kant to Carnap [1991], 4 'The conc')
	A reaction: I like the idea that there are variables in ordinary speech, pronouns being the most obvious example. 'Cats' is a variable involving quantification over a domain of lovable fluffy mammals.

27. Natural Reality / D. Time / 1. Nature of Time / a. Absolute time

18279	Relativity is as absolutist about space-time as Newton was about space [Coffa]
	Full Idea: If the theory of relativity might be thought to support an idealist construal of space and time, it is no less absolutistic about space-time than Newton's theory was about space.
	From: J. Alberto Coffa (The Semantic Tradition from Kant to Carnap [1991])
	A reaction: [He cites Minkowski, Weyl and Cartan for this conclusion] Coffa is clearly a bit cross about philosophers who draw naive idealist and relativist conclusions from relativity.