Combining Texts

All the ideas for 'Mind and Its Place in Nature', 'Letters to Russell' and 'Structure and Ontology'

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5 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers

18253	I wish to go straight from cardinals to reals (as ratios), leaving out the rationals [Frege]
	Full Idea: You need a double transition, from cardinal numbes (Anzahlen) to the rational numbers, and from the latter to the real numbers generally. I wish to go straight from the cardinal numbers to the real numbers as ratios of quantities.
	From: Gottlob Frege (Letters to Russell [1902], 1903.05.21), quoted by Michael Dummett - Frege philosophy of mathematics 21 'Frege's'
	A reaction: Note that Frege's real numbers are not quantities, but ratios of quantities. In this way the same real number can refer to lengths, masses, intensities etc.

6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism

18166	The loss of my Rule V seems to make foundations for arithmetic impossible [Frege]
	Full Idea: With the loss of my Rule V, not only the foundations of arithmetic, but also the sole possible foundations of arithmetic, seem to vanish.
	From: Gottlob Frege (Letters to Russell [1902], 1902.06.22)
	A reaction: Obviously he was stressed, but did he really mean that there could be no foundation for arithmetic, suggesting that the subject might vanish into thin air?

9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta

18269	Logical objects are extensions of concepts, or ranges of values of functions [Frege]
	Full Idea: How are we to conceive of logical objects? My only answer is, we conceive of them as extensions of concepts or, more generally, as ranges of values of functions ...what other way is there?
	From: Gottlob Frege (Letters to Russell [1902], 1902.07.28), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 7 epigr
	A reaction: This is the clearest statement I have found of what Frege means by an 'object'. But an extension is a collection of things, so an object is a group treated as a unity, which is generally how we understand a 'set'. Hence Quine's ontology.

12. Knowledge Sources / B. Perception / 6. Inference in Perception

7628	Broad rejects the inferential component of the representative theory [Broad, by Maund]
	Full Idea: Broad, one of the most important modern defenders of the representative theory of perception, explicitly rejects the inferential component of the theory.
	From: report of C.D. Broad (Mind and Its Place in Nature [1925]) by Barry Maund - Perception Ch.1
	A reaction: Since the supposed inferences happen much too quickly to be conscious, it is hard to see how we could distinguish an inference from an interpretation mechanism. Personally I interpret things long before the question of truth arises.

18. Thought / E. Abstraction / 3. Abstracta by Ignoring

9626	A structure is an abstraction, focussing on relationships, and ignoring other features [Shapiro]
	Full Idea: A structure is the abstract form of a system, focussing on the interrelationships among the objects, and ignoring any features of them that do not affect how they relate to other objects in the system.
	From: Stewart Shapiro (Structure and Ontology [1989], 146), quoted by James Robert Brown - Philosophy of Mathematics Ch.4
	A reaction: I find this account very attractive, even though it appeals to supposedly outmoded psychological abstractionism. It seems pretty close to Aristotle's view of things. Shapiro's account must face up to Frege's worries about these matters.