10529
|
If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K]
|
|
Full Idea:
Neo-Fregeans have thought that Hume's Principle, and the like, might be definitive of number and therefore not subject to the usual epistemological worries over its truth.
|
|
From:
Kit Fine (Precis of 'Limits of Abstraction' [2005], p.310)
|
|
A reaction:
This seems to be the underlying dream of logicism - that arithmetic is actually brought into existence by definitions, rather than by truths derived from elsewhere. But we must be able to count physical objects, as well as just counting numbers.
|
10530
|
Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K]
|
|
Full Idea:
The fundamental difficulty facing the neo-Fregean is to either adopt the predicative reading of Hume's Principle, defining numbers, but inadequate, or the impredicative reading, which is adequate, but not really a definition.
|
|
From:
Kit Fine (Precis of 'Limits of Abstraction' [2005], p.312)
|
|
A reaction:
I'm not sure I understand this, but the general drift is the difficulty of building a system which has been brought into existence just by definition.
|
10527
|
An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K]
|
|
Full Idea:
If an abstraction principle is going to be acceptable, then it should not 'inflate', i.e. it should not result in there being more abstracts than there are objects. By this mark Hume's Principle will be acceptable, but Frege's Law V will not.
|
|
From:
Kit Fine (Precis of 'Limits of Abstraction' [2005], p.307)
|
|
A reaction:
I take this to be motivated by my own intuition that abstract concepts had better be rooted in the world, or they are not worth the paper they are written on. The underlying idea this sort of abstraction is that it is 'shared' between objects.
|
18202
|
The concept of a field gradually replaced the substances in explaining relations between charges [Einstein/Infeld]
|
|
Full Idea:
In the beginning the field concept was no more than a means of facilitating the understanding of phenomena. ...In the new field language it is the field and not the charges themselves which is essential. The substance was overshadowed by the field.
|
|
From:
Einstein,A/Infeld,L (The Evolution of Physics [1938], p.151), quoted by Penelope Maddy - Naturalism in Mathematics II.4
|
|
A reaction:
This is very important for philosophical metaphysicians, especially those like me who want to explain the universe by the nature of the stuff that composes it. The 'stuff' had better not be simplistic individual 'substances'.
|