Combining Texts

All the ideas for 'fragments/reports', 'Review of Tait 'Provenance of Pure Reason'' and 'De Mundo Praesenti'

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7 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX

13418	The old problems with the axiom of choice are probably better ascribed to the law of excluded middle [Parsons,C]
	Full Idea: The difficulties historically attributed to the axiom of choice are probably better ascribed to the law of excluded middle.
	From: Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §2)
	A reaction: The law of excluded middle was a target for the intuitionists, so presumably the debate went off in that direction.

6. Mathematics / C. Sources of Mathematics / 8. Finitism

13419	If functions are transfinite objects, finitists can have no conception of them [Parsons,C]
	Full Idea: The finitist may have no conception of function, because functions are transfinite objects.
	From: Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §4)
	A reaction: He is offering a view of Tait's. Above my pay scale, but it sounds like a powerful objection to the finitist view. Maybe there is a finitist account of functions that could be given?

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

13417	If a mathematical structure is rejected from a physical theory, it retains its mathematical status [Parsons,C]
	Full Idea: If experience shows that some aspect of the physical world fails to instantiate a certain mathematical structure, one will modify the theory by sustituting a different structure, while the original structure doesn't lose its status as part of mathematics.
	From: Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §2)
	A reaction: This seems to be a beautifully simple and powerful objection to the Quinean idea that mathematics somehow only gets its authority from physics. It looked like a daft view to begin with, of course.

8. Modes of Existence / C. Powers and Dispositions / 4. Powers as Essence

12714	The substantial form is the principle of action or the primitive force of acting [Leibniz]
	Full Idea: The substantial form is the principle of action or the primitive force of acting.
	From: Gottfried Leibniz (De Mundo Praesenti [1686], A6.4.1507-8), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 3
	A reaction: The clearest statement of the modification of Aristotle's hylomorphism which Leibniz preferred in his middle period, and which strikes me as an improvement, and about right. Shame that monads got too much of a grip on him, but he was trying to dig deeper.

9. Objects / D. Essence of Objects / 1. Essences of Objects

12743	A true being must (unlike a chain) have united parts, with a substantial form as its subject [Leibniz]
	Full Idea: In a Being one per se a real union is required consisting not in the situation or motion of parts, as in a chain or a house, but in a unique individual principle and subject of attributes and operations, in us a soul and in a body a substantial form.
	From: Gottfried Leibniz (De Mundo Praesenti [1686], A6.4.1506), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 7
	A reaction: Leibniz is said not to be an essentialist, by making all properties essential, but he is certainly committed to substance, and it sounds like essence here (or one view of essence), when it makes identity possible. This idea is pure Aristotle.

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.