|
17807
|
To study formal systems, look at the whole thing, and not just how it is constructed in steps [Curry]
|
|
Full Idea:
In the study of formal systems we do not confine ourselves to the derivation of elementary propositions step by step. Rather we take the system, defined by its primitive frame, as datum, and then study it by any means at our command.
|
|
From:
Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'The formalist')
|
|
A reaction:
This is what may potentially lead to an essentialist view of such things. Focusing on bricks gives formalism, focusing on buildings gives essentialism.
|
|
17806
|
It is untenable that mathematics is general physical truths, because it needs infinity [Curry]
|
|
Full Idea:
According to realism, mathematical propositions express the most general properties of our physical environment. This is the primitive view of mathematics, yet on account of the essential role played by infinity in mathematics, it is untenable today.
|
|
From:
Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'The problem')
|
|
A reaction:
I resist this view, because Curry's view seems to imply a mad metaphysics. Hilbert resisted the role of the infinite in essential mathematics. If the physical world includes its possibilities, that might do the job. Hellman on structuralism?
|
|
17371
|
Some kinds are very explanatory, but others less so, and some not at all [Devitt]
|
|
Full Idea:
Explanatory significance, hence naturalness, comes in degrees: positing some kinds may be very explanatory, positing others, only a little bit explanatory, positing others still, not explanatory at all.
|
|
From:
Michael Devitt (Natural Kinds and Biological Realism [2009], 4)
|
|
A reaction:
He mentions 'cousin' as a natural kind that is not very explanatory of anything. It interests us as humans, but not at all in other animals, it seems. ...Nice thought, though, that two squirrels might be cousins...
|
|
4800
|
Natural laws result from eliminative induction, where enumerative induction gives generalisations [Cohen,LJ, by Psillos]
|
|
Full Idea:
Cohen contends that statements that express laws of nature are the products of eliminative induction, where accidentally true generalisations are the products of enumerative induction.
|
|
From:
report of L. Jonathan Cohen (The Problem of Natural Laws [1980], p.222) by Stathis Psillos - Causation and Explanation §7.1
|
|
A reaction:
The idea is that enumerative induction only offers the support of positive instances, where eliminative induction involves attempts to falsify a range of hypotheses. This still bases laws on observed regularities, rather than essences or mechanisms.
|