Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Causation in a Physical World' and 'Mathematics and the Metaphysicians'

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9 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.

23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues

7903	The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
	Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
	From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
	A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate').

26. Natural Theory / C. Causation / 1. Causation

8404	Explain single events by general rules, or vice versa, or probability explains both, or they are unconnected [Field,H]
	Full Idea: Some think singular causal claims should be explained in terms of general causal claims; some think the order should be reversed; some think a third thing (e.g. objective probability) will explain both; and some think they are only loosely connected.
	From: Hartry Field (Causation in a Physical World [2003], 2)
	A reaction: I think Ducasse gives the best account, which is the second option, of giving singular causal claims priority. Probability (Mellor) strikes me as a non-starter, and the idea that they are fairly independent seems rather implausible.

26. Natural Theory / C. Causation / 5. Direction of causation

8401	Physical laws are largely time-symmetric, so they make a poor basis for directional causation [Field,H]
	Full Idea: It is sometimes pointed out that (perhaps with a few minor exceptions) the fundamental physical laws are completely time-symmetric. If so, then if one is inclined to found causation on fundamental physical law, it isn't evident how directionality gets in.
	From: Hartry Field (Causation in a Physical World [2003], 1)
	A reaction: All my instincts tell me that causation is more fundamental than laws, and that directionality is there at the start. That, though, raises the nice question of how, if causation explains laws, the direction eventually gets left OUT!

8400	Identifying cause and effect is not just conventional; we explain later events by earlier ones [Field,H]
	Full Idea: It is not just that the earlier member of a cause-effect pair is conventionally called the cause; it is also connected with other temporal asymmetries that play an important role in our practices. We tend to explain later events in terms of earlier ones.
	From: Hartry Field (Causation in a Physical World [2003], 1)
	A reaction: We also interfere with the earlier one to affect the later one, and not vice versa (Idea 8363). I am inclined to think that attempting to explain the direction of causation is either pointless or hopeless.

8402	The only reason for adding the notion of 'cause' to fundamental physics is directionality [Field,H]
	Full Idea: Although it is true that the notion of 'cause' is not needed in fundamental physics, even statistical physics, still directionality considerations don't preclude this notion from being consistently added to fundamental physics.
	From: Hartry Field (Causation in a Physical World [2003], 1)
	A reaction: This only makes sense if the notion of cause already has directionality built into it, which I think is correct. The physicist might reply that they don't care about directionality, but the whole idea of an experiment seems to depend on it (Idea 8363).