Combining Texts

All the ideas for 'fragments/reports', 'Mathematics and Indispensibility' and 'Aquinas, Thomas'

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4 ideas

7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems

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.

14. Science / A. Basis of Science / 2. Demonstration

22110	Demonstration provides depth of understanding and explanation (rather than foundations) [Kretzmann/Stump]
	Full Idea: According to Aquinas, what demonstration provides is not so much knowledge as conceived by foundationalists as depth of understanding and explanatory insight.
	From: Kretzmann/Stump (Aquinas, Thomas [2005]), quoted by Kretzmann/Stump - Aquinas, Thomas 11
	A reaction: It was noticeable that Aristotle didn't make clear what demonstration aims to achieve, and he didn't employ it elsewhere in his writings. We aim for understanding, not for well grounded propositions. Understanding needs implications and mechanisms.

26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature

1748	Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
	Full Idea: Archelaus was the first person to say that the universe is boundless.
	From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3

27. Natural Reality / G. Biology / 3. Evolution

5989	Archelaus said life began in a primeval slime [Archelaus, by Schofield]
	Full Idea: Archelaus wrote that life on Earth began in a primeval slime.
	From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus
	A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea.