Combining Texts

All the ideas for 'fragments/reports', 'Cantorian Abstraction: Recon. and Defence' and 'On the Necessity of Origin'

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8 ideas

5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic

9148	I think of variables as objects rather than as signs [Fine,K]
	Full Idea: It is natural nowadays to think of variables as a certain kind of sign, but I wish to think of them as a certain kind of object.
	From: Kit Fine (Cantorian Abstraction: Recon. and Defence [1998], §2)
	A reaction: Fine has a theory based on 'arbitrary objects', which is a rather charming idea. The cell of a spreadsheet is a kind of object, I suppose. A variable might be analogous to a point in space, where objects can locate themselves.

9. Objects / C. Structure of Objects / 6. Constitution of an Object

6019	If someone squashed a horse to make a dog, something new would now exist [Mnesarchus]
	Full Idea: If, for the sake of argument, someone were to mould a horse, squash it, then make a dog, it would be reasonable for us on seeing this to say that this previously did not exist but now does exist.
	From: Mnesarchus (fragments/reports [c.120 BCE]), quoted by John Stobaeus - Anthology 179.11
	A reaction: Locke would say it is new, because the substance is the same, but a new life now exists. A sword could cease to exist and become a new ploughshare, I would think. Apply this to the Ship of Theseus. Is form more important than substance?

9. Objects / E. Objects over Time / 10. Beginning of an Object

18892	Suppose a world where I'm from different gametes; add my gametes; which one is more me? [McGinn]
	Full Idea: It seems essential that you come from your gametes. Suppose (for reductio) that I come from Nixon's actual gametes. Now add my actual gametes to that possible world, and suppose they become an adult. Which has the stronger title to be me?
	From: Colin McGinn (On the Necessity of Origin [1976], p.132), quoted by Nathan Salmon - Reference and Essence (1st edn) 7.25.5
	A reaction: [See Nathan Salmon 1981:209] Feels like the Ship of Theseus. You say 'that's Theseus Ship', until the rival ship appears around the headland. Confusion. If Nixon's gametes can produce McGinn, the second gametes could produce a Nixon! Then what?

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

12019	McGinn falsely claims necessity of origin is a special case of the necessity of identity [Forbes,G on McGinn]
	Full Idea: McGinn assimilates the origin relation among organisms to the identity relation, so that the necessity of origin becomes a special case of the necessity of identity. We argue that this assimilation is illegitimate.
	From: comment on Colin McGinn (On the Necessity of Origin [1976]) by Graeme Forbes - The Metaphysics of Modality 6.1
	A reaction: Not sure about this. I have long suspected what McGinn suspects. Once you have identified the organism with a particular origin, it hardly seems surprising that this particular origin has become inescapable.

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

9152	If green is abstracted from a thing, it is only seen as a type if it is common to many things [Fine,K]
	Full Idea: In traditional abstraction, the colour green merely has the intrinsic property of being green, other properties of things being abstracted away. But why should that be regarded as a type? It must be because the property is common to the instances.
	From: Kit Fine (Cantorian Abstraction: Recon. and Defence [1998], §5)
	A reaction: A nice question which shows that the much-derided single act of abstraction is not sufficient to arrive at a concept, so that abstraction is a more complex matter (perhaps even a rational one) than simple empiricists believe.

18. Thought / E. Abstraction / 2. Abstracta by Selection

9149	To obtain the number 2 by abstraction, we only want to abstract the distinctness of a pair of objects [Fine,K]
	Full Idea: In abstracting from the elements of a doubleton to obtain 2, we do not wish to abstract away from all features of the objects. We wish to take account of the fact that the two objects are distinct; this alone should be preserved under abstraction.
	From: Kit Fine (Cantorian Abstraction: Recon. and Defence [1998], §3)
	A reaction: This is Fine's strategy for meeting Frege's objection to abstraction, summarised in Idea 9146. It seems to use the common sense idea that abstraction is not all-or-nothing. Abstraction has degrees (and levels).

9150	We should define abstraction in general, with number abstraction taken as a special case [Fine,K]
	Full Idea: Number abstraction can be taken to be a special case of abstraction in general, which can then be defined without recourse to the concept of number.
	From: Kit Fine (Cantorian Abstraction: Recon. and Defence [1998], §3)
	A reaction: At last, a mathematical logician recognising that they don't have a monopoly on abstraction. It is perfectly obvious that abstractions of simple daily concepts must be chronologically and logically prior to number abstraction. Number of what?

18. Thought / E. Abstraction / 8. Abstractionism Critique

9146	After abstraction all numbers seem identical, so only 0 and 1 will exist! [Fine,K]
	Full Idea: In Cantor's abstractionist account there can only be two numbers, 0 and 1. For abs(Socrates) = abs(Plato), since their numbers are the same. So the number of {Socrates,Plato} is {abs(Soc),abs(Plato)}, which is the same number as {Socrates}!
	From: Kit Fine (Cantorian Abstraction: Recon. and Defence [1998], §1)
	A reaction: Fine tries to answer this objection, which arises from §45 of Frege's Grundlagen. Fine summarises that "indistinguishability without identity appears to be impossible". Maybe we should drop talk of numbers in terms of sets.