13412
|
Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf]
|
|
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.
|
|
From:
Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.165)
|
|
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.
|
13413
|
We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf]
|
|
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.
|
|
From:
Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.166)
|
|
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.
|
13411
|
If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf]
|
|
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.
|
|
From:
Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.164)
|
|
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.
|
16648
|
Accidents must have formal being, if they are principles of real action, and of mental action and thought [Duns Scotus]
|
|
Full Idea:
Accidents are principles of acting and principles of cognizing substance, and are the per se objects of the senses. But it is ridiculous to say that something is a principle of acting (either real or intentional) and yet does not have any formal being.
|
|
From:
John Duns Scotus (Ordinatio [1302], IV.12.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 10.5
|
|
A reaction:
Pasnau cites this as the key scholastic argument for accidental properties having some independent and real existence (as required for Transubstantiation). Rival views say accidents are just 'modes' of a thing's existence. Aquinas compromised.
|
15386
|
If only the singular exists, science is impossible, as that relies on true generalities [Duns Scotus, by Panaccio]
|
|
Full Idea:
Scotus argued that if everything is singular, with no objective common feature, science would be impossible, as it proceeds from general concepts. General is the opposite of singular, so it would be inadequate to understand a singular reality.
|
|
From:
report of John Duns Scotus (Ordinatio [1302]) by Claude Panaccio - Medieval Problem of Universals 'John Duns'
|
|
A reaction:
[compressed] It is a fact that if you generalise about 'tigers', you are glossing over the individuality of each singular tiger. That is OK for 'electron', if they really are identical, but our general predicates may be imposing identity on electrons.
|
16632
|
We distinguish one thing from another by contradiction, because this is, and that is not [Duns Scotus]
|
|
Full Idea:
What is it [that establishes distinctness of things]? It is, to be sure, that which is universally the reason for distinguishing one thing from another: namely, a contradiction…..If this is, and that is not, then they are not the same entity in being.
|
|
From:
John Duns Scotus (Ordinatio [1302], IV.11.3), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 08.2
|
|
A reaction:
This is a remarkably intellectualist view of such things. John Wycliff, apparently, enquired about how animals were going to manage all this sort of thing. It should appeal to the modern logical approach to metaphysics.
|
13094
|
The haecceity is the featureless thing which gives ultimate individuality to a substance [Duns Scotus, by Cover/O'Leary-Hawthorne]
|
|
Full Idea:
For Scotus, the haecceity of an individual was a positive non-quidditative entity which, together with a common nature from which it was formally distinct, played the role of the ultimate differentia, thus individuating the substance.
|
|
From:
report of John Duns Scotus (Ordinatio [1302]) by Cover,J/O'Leary-Hawthorne,J - Substance and Individuation in Leibniz 6.1.3
|
|
A reaction:
Most thinkers seem to agree (with me) that this is a non-starter, an implausible postulate designed to fill a gap in a metaphysic that hasn't been properly worked out. Leibniz is the hero who faces the problem and works around it.
|
16770
|
It is absurd that there is no difference between a genuinely unified thing, and a mere aggregate [Duns Scotus]
|
|
Full Idea:
It seems absurd …that there should be no difference between a whole that is one thing per se, and a whole that is one thing by aggregation, like a cloud or a heap.
|
|
From:
John Duns Scotus (Ordinatio [1302], III.2.2), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 25.5
|
|
A reaction:
Leibniz invented monads because he was driven crazy by the quest for 'true unity' in things. Objective unity may be bogus, but I suspect that imposing plausible unity on things is the only way we can grasp the world.
|