9558
|
All scientific tests will verify mathematics, so it is a background, not something being tested [Sober]
|
|
Full Idea:
If mathematical statements are part of every competing hypothesis, then no matter which hypothesis comes out best in the light of observations, they will be part of the best hypothesis. They are not tested, but are a background assumption.
|
|
From:
Elliott Sober (Mathematics and Indispensibility [1993], 45), quoted by Charles Chihara - A Structural Account of Mathematics
|
|
A reaction:
This is a very nice objection to the Quine-Putnam thesis that mathematics is confirmed by the ongoing successes of science.
|
8790
|
The 'doctrine of the given' is correct; some beliefs or statements are self-justifying [Chisholm]
|
|
Full Idea:
In my opinion, the 'doctrine of the given' is correct in saying that there are some beliefs or statements which are 'self-justifying' and that among such beliefs are statements some of which concern appearances or 'ways of being appeared to'.
|
|
From:
Roderick Chisholm (The Myth of the Given [1964], §12)
|
|
A reaction:
To boldly assert that they are 'self-justifying' invites a landslide of criticisms, pointing at a regress. It might be better to say they are self-evident, or intuitively known, or primitive, or true by the natural light of reason.
|