13231
|
Explanatory proofs rest on 'characterizing properties' of entities or structure [Steiner,M]
|
|
Full Idea:
My proposal is that an explanatory proof makes reference to the 'characterizing property' of an entity or structure mentioned in the theorem, where the proof depends on the property. If we substitute a different object, the theory collapses.
|
|
From:
Mark Steiner (Mathematical Explanation [1978], p.34)
|
|
A reaction:
He prefers 'characterizing property' to 'essence', because he is not talking about necessary properties, since all properties are necessary in mathematics. He is, in fact, reverting to the older notion of an essence, as the core power of the thing.
|
4688
|
We imagine small and large objects scaled to the same size, suggesting a fixed capacity for imagination [Lavers]
|
|
Full Idea:
If we think of a pea, and then of the Eiffel Tower, they seem to occupy the same space in our consciousness, suggesting that we scale our images to fit the available hardware, just as computer imagery is limited by the screen and memory available.
|
|
From:
Michael Lavers (talk [2003]), quoted by PG - Db (ideas)
|
|
A reaction:
Nice point. It is especially good because it reinforces a physicalist view of the mind from introspection, where most other evidence is external observation of brains (as Nietzsche reinforces determinism by introspection).
|
15877
|
The aim of science is just to create a comprehensive, elegant language to describe brute facts [Poincaré, by Harré]
|
|
Full Idea:
In Poincaré's view, we try to construct a language within which the brute facts of experience are expressed as comprehensively and as elegantly as possible. The job of science is the forging of a language precisely suited to that purpose.
|
|
From:
report of Henri Poincaré (The Value of Science [1906], Pt III) by Rom Harré - Laws of Nature 2
|
|
A reaction:
I'm often struck by how obscure and difficult our accounts of self-evident facts can be. Chairs are easy, and the metaphysics of chairs is hideous. Why is that? I'm a robust realist, but I like Poincaré's idea. He permits facts.
|