|
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.
|
|
10579
|
Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo]
|
|
Full Idea:
Saying 'the number of Fs is 5', instead of using five quantifiers, puts the numeral in quantifiable position, which brings expressive advantages. 'There are more sheep in the field than cows' is an infinite disjunction, expressible in finite compass.
|
|
From:
Stephen Yablo (Abstract Objects: a Case Study [2002], 08)
|
|
A reaction:
See Hofweber with similar thoughts. This idea I take to be a key one in explaining many metaphysical confusions. The human mind just has a strong tendency to objectify properties, relations, qualities, categories etc. - for expression and for reasoning.
|
|
16391
|
Indexical thoughts are about themselves, and ascribe properties to themselves [Perry, by Recanati]
|
|
Full Idea:
Perry's newer token-reflexive framework says indexical thoughts have token-reflexive content, that is, thoughts that are about themselves and ascribe properties to themselves. …They relate not to the subject, but to the occurrence of a thought.
|
|
From:
report of John Perry (Reference and Reflexivity [2001]) by François Recanati - Mental Files 18.1
|
|
A reaction:
[There seem to be four indexical theories: this one, Recanati's, the earlier Kaplan-Perry one, and Lewis's] Is Perry thinking of second-level thoughts? 'I'm bored' has the content 'boredom' plus 'felt in here'? How does 'I'm bored' refer to 'I'm bored'?
|