|
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?
|
|
5020
|
Our thoughts are either dependent, or self-evident. All thoughts seem to end in the self-evident [Leibniz]
|
|
Full Idea:
Whatever is thought by us is either conceived through itself, or involves the concept of another. …Thus one must proceed to infinity, or all thoughts are resolved into those which are conceived through themselves.
|
|
From:
Gottfried Leibniz (Of Organum or Ars Magna of Thinking [1679], p.1)
|
|
A reaction:
This seems to embody the rationalist attitude to foundations. I am sympathetic. Experiences just come to us as basic, but they don't qualify as 'thoughts', let alone knowledge. Experiences are more 'given' than 'conceptual'.
|
|
14080
|
Are causal descriptions part of the causal theory of reference, or are they just metasemantic? [Kaplan, by Schaffer,J]
|
|
Full Idea:
Kaplan notes that the causal theory of reference can be understood in two quite different ways, as part of the semantics (involving descriptions of causal processes), or as metasemantics, explaining why a term has the referent it does.
|
|
From:
report of David Kaplan (Dthat [1970]) by Jonathan Schaffer - Deflationary Metaontology of Thomasson 1
|
|
A reaction:
[Kaplan 'Afterthought' 1989] The theory tends to be labelled as 'direct' rather than as 'causal' these days, but causal chains are still at the heart of the story (even if more diffused socially). Nice question. Kaplan takes the meta- version as orthodox.
|