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All the ideas for 'Ethical Studies', 'Mathematics and the Metaphysicians' and 'The Sceptical Chemist'

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6 ideas

5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox

7557	To solve Zeno's paradox, reject the axiom that the whole has more terms than the parts [Russell]
	Full Idea: Presumably Zeno appealed to the axiom that the whole has more terms than the parts; so if Achilles were to overtake the tortoise, he would have been in more places than the tortoise, which he can't be; but the conclusion is absurd, so reject the axiom.
	From: Bertrand Russell (Mathematics and the Metaphysicians [1901], p.89)
	A reaction: The point is that the axiom is normally acceptable (a statue contains more particles than the arm of the statue), but it breaks down when discussing infinity (Idea 7556). Modern theories of infinity are needed to solve Zeno's Paradoxes.

6. Mathematics / A. Nature of Mathematics / 1. Mathematics

10059	In mathematic we are ignorant of both subject-matter and truth [Russell]
	Full Idea: Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.
	From: Bertrand Russell (Mathematics and the Metaphysicians [1901], p.76)
	A reaction: A famous remark, though Musgrave is rather disparaging about Russell's underlying reasoning here.

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / b. Mark of the infinite

7556	A collection is infinite if you can remove some terms without diminishing its number [Russell]
	Full Idea: A collection of terms is infinite if it contains as parts other collections which have as many terms as it has; that is, you can take away some terms of the collection without diminishing its number; there are as many even numbers as numbers all together.
	From: Bertrand Russell (Mathematics and the Metaphysicians [1901], p.86)
	A reaction: He cites Dedekind and Cantor as source for these ideas. If it won't obey the rule that subtraction makes it smaller, then it clearly isn't a number, and really it should be banned from all mathematics.

12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence

7554	Self-evidence is often a mere will-o'-the-wisp [Russell]
	Full Idea: Self-evidence is often a mere will-o'-the-wisp, which is sure to lead us astray if we take it as our guide.
	From: Bertrand Russell (Mathematics and the Metaphysicians [1901], p.78)
	A reaction: The sort of nice crisp remark you would expect from a good empiricist philosopher. Compare Idea 4948. However Russell qualifies it with the word 'often', and all philosophers eventually realise that you have to start somewhere.

22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness

5655	Happiness is not satisfaction of desires, but fulfilment of values [Bradley, by Scruton]
	Full Idea: For Bradley, the happiness of the individual is not to be understood in terms of his desires and needs, but rather in terms of his values - which is to say, in terms of those of his desires which he incorporates into his self.
	From: report of F.H. Bradley (Ethical Studies [1876]) by Roger Scruton - Short History of Modern Philosophy Ch.16
	A reaction: Good. Bentham will reduce the values to a further set of desires, so that a value is a complex (second-level?) desire. I prefer to think of values as judgements, but I like Scruton's phrase of 'incorporating into his self'. Kant take note (Idea 1452).

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

15961	I don't see how mere moving matter can lead to the bodies of men and animals, and especially their seeds [Boyle]
	Full Idea: I confess I cannot well conceive how from matter, barely put into motion and left to itself, there could emerge such curious fabricks as the bodies of men and perfect animals, and more admirably contrived parcels of matter, as seeds of living creatures.
	From: Robert Boyle (The Sceptical Chemist [1661], p.569), quoted by Peter Alexander - Ideas, Qualities and Corpuscles
	A reaction: This is here to show that one of the most brilliant intellects of the seventeenth century thought carefully about this question and couldn't answer it. Natural selection really was a rather clever idea.