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13412
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Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf]
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Full Idea:
Not all numbers could possibly have been learned à la Frege-Russell, because we could not have performed that many distinct acts of abstraction. Somewhere along the line a rule had to come in to enable us to obtain more numbers, in the natural order.
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From:
Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.165)
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A reaction:
Follows on from Idea 13411. I'm not sure how Russell would deal with this, though I am sure his account cannot be swept aside this easily. Nevertheless this seems powerful and convincing, approaching the problem through the epistemology.
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13413
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We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf]
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Full Idea:
Both ordinalists and cardinalists, to account for our number words, have to account for the fact that we know so many of them, and that we can 'recognize' numbers which we've neither seen nor heard.
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From:
Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.166)
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A reaction:
This seems an important contraint on any attempt to explain numbers. Benacerraf is an incipient structuralist, and here presses the importance of rules in our grasp of number. Faced with 42,578,645, we perform an act of deconstruction to grasp it.
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13411
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If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf]
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Full Idea:
If we accept the Frege-Russell analysis of number (the natural numbers are the cardinals) as basic and correct, one thing which seems to follow is that one could know, say, three, seventeen, and eight, but no other numbers.
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From:
Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.164)
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A reaction:
It seems possible that someone might only know those numbers, as the patterns of members of three neighbouring families (the only place where they apply number). That said, this is good support for the priority of ordinals. See Idea 13412.
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14753
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The 'dominant' of two coinciding sortals is the one that entails the widest range of properties [Burke,M, by Sider]
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Full Idea:
Burke claims that the 'dominant' sortal is the one whose satisfaction entails possession of the widest range of properties. For example, the statue (unlike the lump of clay) also possesses aesthetic properties, and hence is dominant.
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From:
report of Michael Burke (Dion and Theon: an essentialist solution [1994]) by Theodore Sider - Four Dimensionalism 5.4
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A reaction:
[there are three papers by Burke on this; see all the quotations from Burke] Presumably one sortal could entail a single very important property, and the other sortal entail a huge range of trivial properties. What does being a 'thing' entail?
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16072
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'The rock' either refers to an object, or to a collection of parts, or to some stuff [Burke,M, by Wasserman]
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Full Idea:
Burke distinguishes three different readings of 'the rock'. It can be a singular description denoting an object, or a plural description denoting all the little pieces of rock, or a mass description the relevant rocky stuff.
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From:
report of Michael Burke (Dion and Theon: an essentialist solution [1994]) by Ryan Wasserman - Material Constitution 5
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A reaction:
Idea 16068 is an objection to the second reading. Only the first reading seems plausible, so we must just get over all the difficulties philosophers have unearthed about knowing exactly what an 'object' is. I offer you essentialism. Rocks have unity.
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4304
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Descartes says there are two substance, Spinoza one, and Leibniz infinitely many [Cottingham]
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Full Idea:
Descartes was a dualist about substance, Spinoza was a monist, and Leibniz was a pluralist (an infinity of substances).
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From:
John Cottingham (The Rationalists [1988], p.76)
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A reaction:
Spinoza is appealing. We posit a substance, as the necessary basis for existence, but it is unclear how more than one substance can be differentiated. If mind is a separate substance, why isn't iron? Why aren't numbers?
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16234
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Burke says when two object coincide, one of them is destroyed in the process [Burke,M, by Hawley]
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Full Idea:
Michael Burke argues that a sweater is identical with the thread that consitutes it, that both were created at the moment when they began to coincide, and that the original thread was destroyed in the process.
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From:
report of Michael Burke (Dion and Theon: an essentialist solution [1994]) by Katherine Hawley - How Things Persist 5.3
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A reaction:
[Burke's ideas are spread over three articles] It is the thread which is destroyed, because the sweater is the 'dominant sortal' (which strikes me as a particularlyd desperate concept).
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14750
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Two entities can coincide as one, but only one of them (the dominant sortal) fixes persistence conditions [Burke,M, by Sider]
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Full Idea:
Michael Burke has given an account that avoids distinguishing coinciding entities. ...The statue/lump satisfies both 'lump' and 'statue', but only the latter determines that object's persistence conditions, and so is that object's 'dominant sortal'.
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From:
report of Michael Burke (Dion and Theon: an essentialist solution [1994]) by Theodore Sider - Four Dimensionalism 5.4
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A reaction:
Presumably a lump on its own can have its own persistance conditions (as a 'lump'), but those would presumably be lost if you shaped it into a statue. Burke concedes that. Can of worms. Using a book as a doorstop...
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