30 ideas
| 8013 | In the Reformation, morality became unconditional but irrational, individually autonomous, and secular [MacIntyre] |
| Full Idea: Three concepts about morality emerge from the Reformation period: that moral rules are unconditional demands that lack rational justification; that moral agents are sovereign in choices; and that secular powers have their own norms and justifications. | |
| From: Alasdair MacIntyre (A Short History of Ethics [1967], Ch.10) | |
| A reaction: I get the impression that a rather frank admission of the role of self-interest emerged at that time as well. It is only in the late seventeenth century that the possibility of a secular altruism begins to be investigated. But there's Shakespeare... |
| 8021 | The Levellers and the Diggers mark a turning point in the history of morality [MacIntyre] |
| Full Idea: The Levellers and the Diggers mark a turning point in the history of morality. | |
| From: Alasdair MacIntyre (A Short History of Ethics [1967], Ch.11) | |
| A reaction: John Lilburne, the Leveller, 'Free-Born John', was the most important of them. They mainly fought for rights of religious conscience, but it quickly escalated into a demand for economic and social rights. It spread to France and the United States. |
| 9572 | Realists about sets say there exists a null set in the real world, with no members [Chihara] |
| Full Idea: In the Gödelian realistic view of set theory the statement that there is a null set as the assertion of the existence in the real world of a set that has no members. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 11.6) | |
| A reaction: It seems to me obvious that such a claim is nonsense on stilts. 'In the beginning there was the null set'? |
| 9550 | We only know relational facts about the empty set, but nothing intrinsic [Chihara] |
| Full Idea: Everything we know about the empty set is relational; we know that nothing is the membership relation to it. But what do we know about its 'intrinsic properties'? | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 01.5) | |
| A reaction: Set theory seems to depend on the concept of the empty set. Modern theorists seem over-influenced by the Quine-Putnam view, that if science needs it, we must commit ourselves to its existence. |
| 9562 | In simple type theory there is a hierarchy of null sets [Chihara] |
| Full Idea: In simple type theory, there is a null set of type 1, a null set of type 2, a null set of type 3..... (Quine has expressed his distaste for this). | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 07.4) | |
| A reaction: It is bad enough trying to individuate the unique null set, without whole gangs of them drifting indistinguishably through the logical fog. All rational beings should share Quine's distaste, even if Quine is wrong. |
| 9573 | The null set is a structural position which has no other position in membership relation [Chihara] |
| Full Idea: In the structuralist view of sets, in structures of a certain sort the null set is taken to be a position (or point) that will be such that no other position (or point) will be in the membership relation to it. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 11.6) | |
| A reaction: It would be hard to conceive of something having a place in a structure if nothing had a relation to it, so is the null set related to singeton sets but not there members. It will be hard to avoid Platonism here. Set theory needs the null set. |
| 9551 | What is special about Bill Clinton's unit set, in comparison with all the others? [Chihara] |
| Full Idea: What is it about the intrinsic properties of just that one unit set in virtue of which Bill Clinton is related to just it and not to any other unit sets in the set-theoretical universe? | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 01.5) | |
| A reaction: If we all kept pet woodlice, we had better not hold a wood louse rally, or we might go home with the wrong one. My singleton seems seems remarkably like yours. Could we, perhaps, swap, just for a change? |
| 9549 | The set theorist cannot tell us what 'membership' is [Chihara] |
| Full Idea: The set theorist cannot tell us anything about the true relationship of membership. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 01.5) | |
| A reaction: If three unrelated objects suddenly became members of a set, it is hard to see how the world would have changed, except in the minds of those thinking about it. |
| 9571 | ZFU refers to the physical world, when it talks of 'urelements' [Chihara] |
| Full Idea: ZFU set theory talks about physical objects (the urelements), and hence is in some way about the physical world. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 11.5) | |
| A reaction: This sounds a bit surprising, given that the whole theory would appear to be quite unaffected if God announced that idealism is true and there are no physical objects. |
| 9563 | A pack of wolves doesn't cease when one member dies [Chihara] |
| Full Idea: A pack of wolves is not thought to go out of existence just because some member of the pack is killed. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 07.5) | |
| A reaction: The point is that the formal extensional notion of a set doesn't correspond to our common sense notion of a group or class. Even a highly scientific theory about wolves needs a loose notion of a wolf pack. |
| 9561 | The mathematics of relations is entirely covered by ordered pairs [Chihara] |
| Full Idea: Everything one needs to do with relations in mathematics can be done by taking a relation to be a set of ordered pairs. (Ordered triples etc. can be defined as order pairs, so that <x,y,z> is <x,<y,z>>). | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 07.2) | |
| A reaction: How do we distinguish 'I own my cat' from 'I love my cat'? Or 'I quite like my cat' from 'I adore my cat'? Nevertheless, this is an interesting starting point for a discussion of relations. |
| 9552 | Sentences are consistent if they can all be true; for Frege it is that no contradiction can be deduced [Chihara] |
| Full Idea: In first-order logic a set of sentences is 'consistent' iff there is an interpretation (or structure) in which the set of sentences is true. ..For Frege, though, a set of sentences is consistent if it is not possible to deduce a contradiction from it. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 02.1) | |
| A reaction: The first approach seems positive, the second negative. Frege seems to have a higher standard, which is appealing, but the first one seems intuitively right. There is a possible world where this could work. |
| 9553 | Analytic geometry gave space a mathematical structure, which could then have axioms [Chihara] |
| Full Idea: With the invention of analytic geometry (by Fermat and then Descartes) physical space could be represented as having a mathematical structure, which could eventually lead to its axiomatization (by Hilbert). | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 02.3) | |
| A reaction: The idea that space might have axioms seems to be pythagoreanism run riot. I wonder if there is some flaw at the heart of Einstein's General Theory because of this? |
| 10192 | We can replace existence of sets with possibility of constructing token sentences [Chihara, by MacBride] |
| Full Idea: Chihara's 'constructability theory' is nominalist - mathematics is reducible to a simple theory of types. Instead of talk of sets {x:x is F}, we talk of open sentences Fx defining them. Existence claims become constructability of sentence tokens. | |
| From: report of Charles Chihara (A Structural Account of Mathematics [2004]) by Fraser MacBride - Review of Chihara's 'Structural Acc of Maths' p.81 | |
| A reaction: This seems to be approaching the problem in a Fregean way, by giving an account of the semantics. Chihara is trying to evade the Quinean idea that assertion is ontological commitment. But has Chihara retreated too far? How does he assert existence? |
| 9559 | If a successful theory confirms mathematics, presumably a failed theory disconfirms it? [Chihara] |
| Full Idea: If mathematics shares whatever confirmation accrues to the theories using it, would it not be reasonable to suppose that mathematics shares whatever disconfirmation accrues to the theories using it? | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 05.8) | |
| A reaction: Presumably Quine would bite the bullet here, although maths is much closer to the centre of his web of belief, and so far less likely to require adjustment. In practice, though, mathematics is not challenged whenever an experiment fails. |
| 9566 | No scientific explanation would collapse if mathematical objects were shown not to exist [Chihara] |
| Full Idea: Evidently, no scientific explanations of specific phenomena would collapse as a result of any hypothetical discovery that no mathematical objects exist. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 09.1) | |
| A reaction: It is inconceivable that anyone would challenge this claim. A good model seems to be drama; a play needs commitment from actors and audience, even when we know it is fiction. The point is that mathematics doesn't collapse either. |
| 8006 | When Aristotle speaks of soul he means something like personality [MacIntyre] |
| Full Idea: When Aristotle speaks of the soul we could very often retain his meaning by speaking of personality. | |
| From: Alasdair MacIntyre (A Short History of Ethics [1967], Ch. 7) | |
| A reaction: MacIntyre contrasts this strongly with Plato's dualist view. Famously Aristotle thinks the soul is the 'form' of the body, but this implies that he also includes the higher-level functions of the body. Soul is character? |
| 9568 | I prefer the open sentences of a Constructibility Theory, to Platonist ideas of 'equivalence classes' [Chihara] |
| Full Idea: What I refer to as an 'equivalence class' (of line segments of a particular length) is an open sentence in my Constructibility Theory. I just use this terminology of the Platonist for didactic purposes. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 09.10) | |
| A reaction: This is because 'equivalence classes' is committed to the existence of classes, which is Quinean Platonism. I am with Chihara in wanting a story that avoids such things. Kit Fine is investigating similar notions of rules of construction. |
| 9547 | Mathematical entities are causally inert, so the causal theory of reference won't work for them [Chihara] |
| Full Idea: Causal theories of reference seem doomed to failure for the case of reference to mathematical entities, since such entities are evidently causally inert. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 01.3) | |
| A reaction: Presumably you could baptise a fictional entity such as 'Polonius', and initiate a social causal chain, with a tradition of reference. You could baptise a baby in absentia. |
| 8002 | Sophists don't distinguish a person outside one social order from someone outside all order [MacIntyre] |
| Full Idea: The sophist tradition failed to distinguish the difference between the concept of a man who stands outside and is able to question the conventions of some one given social order, and the concept of a man who stands outside social life as such. | |
| From: Alasdair MacIntyre (A Short History of Ethics [1967], Ch. 3) | |
| A reaction: A very nice distinction. Compare foreigners in Athens with Diogenes of Sinope, who renounced all cities. This is the germ of MacIntyre's view that morality is essentially dependent on some sort of social order. He is a reviver of virtue theory. |
| 8012 | The value/fact logical gulf is misleading, because social facts involve values [MacIntyre] |
| Full Idea: One reason why it is highly misleading to talk of a logical gulf between value and fact....is that we cannot characterize the social life of a tribe in their factual terms and escape their evaluations. | |
| From: Alasdair MacIntyre (A Short History of Ethics [1967], Ch.10) | |
| A reaction: Personally I like the objection that facts about functions cannot avoid the value of good functions, but this is very good. It is much better than simply trying to find a specific counterexample, such as facts about promises. Values just are facts. |
| 8005 | 'Happiness' is a bad translation of 'eudaimonia', which includes both behaving and faring well [MacIntyre] |
| Full Idea: The name 'eudaimonia' is badly but inevitably translated by 'happiness', badly because it includes both the notion of behaving well and the notion of faring well. | |
| From: Alasdair MacIntyre (A Short History of Ethics [1967], Ch. 7) | |
| A reaction: This seems to imply that it does not include the notion of feeling good. Aristotle, however, concludes that pleasure is part of eudaimonia. I take our 'happiness' to be an internal notion, while the Greek word is an external notion. |
| 8001 | 'Dikaiosune' is justice, but also fairness and personal integrity [MacIntyre] |
| Full Idea: The Greek 'dikaiosune' is inadequately translated as 'justice', but also as any other word; it combines the notion of fairness in externals with that of personal integrity in a way that no English word does. | |
| From: Alasdair MacIntyre (A Short History of Ethics [1967], Ch. 1) | |
| A reaction: 'Dikaiosune' is said to be the main topic of Plato's 'Republic'. Plato seems to have meant it to cover whatever makes a good character. Justice in behaviour presumably flows from internal justice of character (which is, roughly, inner harmony). |
| 8023 | My duties depend on my identity, which depends on my social relations [MacIntyre] |
| Full Idea: I cannot answer the question 'What ought I to do?' until I have answered the question 'Who am I?', and any answer to this question will specify my place in a nexus of social relationships. | |
| From: Alasdair MacIntyre (A Short History of Ethics [1967], Ch.13) | |
| A reaction: This is the beginning of the modern critique of deontological ethics coming from revived virtue theory. As it stands, MacIntyre's idea sounds contractual, but I think he intends it in a more organic way. I am a fan. |
| 8022 | I am naturally free if I am not tied to anyone by a contract [MacIntyre] |
| Full Idea: The essence of the claim to natural rights is that no one has a right against me unless he can cite some contract, my consent to it, and his performance of his obligations under it. | |
| From: Alasdair MacIntyre (A Short History of Ethics [1967], Ch.11) | |
| A reaction: This has become the foundation of western democracy, and the rebellious teenager's charter. Children have not consented to a contract with their parents. Close and loving relationships cease to be contractual. |
| 8031 | Fans of natural rights or laws can't agree on what the actual rights or laws are [MacIntyre] |
| Full Idea: It is notorious that adherents of theories about natural rights or natural laws offer lists of rights or laws which differ in substance from each other. | |
| From: Alasdair MacIntyre (A Short History of Ethics [1967], Ch.17) | |
| A reaction: There seems to have been a consensus early on that self-defence was a natural right, but divergence presumably occurs when you get bolder and more complex. There is a lot of divergence over which is Shakespeare's best play. |
| 8416 | Reductionists can't explain accidents, uninstantiated laws, probabilities, or the existence of any laws [Tooley] |
| Full Idea: Reductionist accounts of causation cannot distinguish laws from accidental uniformities, cannot allow for basic uninstantiated laws, can't explain probabilistic laws, and cannot even demonstrate the existence of laws. | |
| From: Michael Tooley (Causality: Reductionism versus Realism [1990], 2) | |
| A reaction: I am tempted to say that this is so much the worse for the idea of laws. Extensive regularities only occur for a reason. Probabilities aren't laws. Hypothetical facts will cover uninstantiated laws. Laws are just patterns. |
| 8418 | Quantum physics suggests that the basic laws of nature are probabilistic [Tooley] |
| Full Idea: Quantum physics seems to lend strong support to the idea that the basic laws of nature may well be probabilistic. | |
| From: Michael Tooley (Causality: Reductionism versus Realism [1990], 3.2.1) | |
| A reaction: Groan. Quantum physics should be outlawed from all philosophical discussions. The scientists don't understand it themselves. I'm certainly not going to build my worldview on it. I don't accept that these probabilities could count as 'laws'. |
| 9574 | 'Gunk' is an individual possessing no parts that are atoms [Chihara] |
| Full Idea: An 'atomless gunk' is defined to be an individual possessing no parts that are atoms. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], App A) | |
| A reaction: [Lewis coined it] If you ask what are a-toms made of and what are ideas made of, the only answer we can offer is that the a-toms are made of gunk, and the ideas aren't made of anything, which is still bad news for the existence of ideas. |
| 8008 | The Bible is a story about God in which humans are incidental characters [MacIntyre] |
| Full Idea: The Bible is a story about God in which human beings appear as incidental characters. | |
| From: Alasdair MacIntyre (A Short History of Ethics [1967], Ch. 9) | |
| A reaction: Very illuminating. He creates man, is betrayed by man, drowns him and starts again, sends a redeemer who gets murdered, and finally enlightens a small band who continue the uphill struggle to promote God's way. What next? |