Combining Texts

All the ideas for 'Philosophical Fragments', 'Matter and Motion Cannot Think' and 'Letters to Russell'

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6 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?

7. Existence / A. Nature of Existence / 5. Reason for Existence

16007	I assume existence, rather than reasoning towards it [Kierkegaard]
	Full Idea: I always reason from existence, not towards existence.
	From: Søren Kierkegaard (Philosophical Fragments [1844], p.40)
	A reaction: Kierkegaard's important premise to help show that theistic proofs for God's existence don't actually prove existence, but develop the content of a conception. [SY]

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.

10. Modality / A. Necessity / 2. Nature of Necessity

16013	Nothing necessary can come into existence, since it already 'is' [Kierkegaard]
	Full Idea: Can the necessary come into existence? That is a change, and everything that comes into existence demonstrates that it is not necessary. The necessary already 'is'.
	From: Søren Kierkegaard (Philosophical Fragments [1844], p.74)
	A reaction: [SY]

17. Mind and Body / A. Mind-Body Dualism / 3. Panpsychism

23224	That all matter thinks is absurd, and would make each part of our bodies a distinct self-consciousness [Bentley]
	Full Idea: [Belief in thinking matter] leads to monstrous absurdities. …Every stock and stone would be a percipient and rational creature. …every single Atom of our bodies would be a distinct Animal, endued with self-consciousness and personal sensation of its own.
	From: Richard Bentley (Matter and Motion Cannot Think [1692], p.14-15), quoted by Matthew Cobb - The Idea of the Brain 2
	A reaction: Sounds correct, though presumably panpsychists don't think the flickers of consciousness in my toenails and hair constitute full-blown persons. I can't imagine what awareness is being claimed for my toenails.