20 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. |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| Full Idea: One feature of the Axiom of Choice that troubled many mathematicians was the so-called Banach-Tarski paradox: using the Axiom, a sphere can be decomposed into finitely many parts and those parts reassembled into two spheres the same size as the original. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) | |
| A reaction: (The key is that the parts are non-measurable). To an outsider it is puzzling that the Axiom has been universally accepted, even though it produces such a result. Someone can explain that, I'm sure. |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| Full Idea: If-thenism denies that mathematics is in the business of discovering truths about abstracta. ...[their opponents] obviously don't regard any starting point, even a consistent one, as equally worthy of investigation. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.3) | |
| A reaction: I have some sympathy with if-thenism, in that you can obviously study the implications of any 'if' you like, but deep down I agree with the critics. |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| Full Idea: At the end of the nineteenth century there was a renewed emphasis on rigor, the central tool of which was axiomatization, along the lines of Hilbert's axioms for geometry and Dedekind's axioms for real numbers. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| Full Idea: The fact that two apparently fruitful mathematical themes turn out to coincide makes it all the more likely that they're tracking a genuine strain of mathematical depth. | |
| From: Penelope Maddy (Defending the Axioms [2011], 5.3ii) |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| Full Idea: One form of the Continuum Hypothesis is the claim that every infinite set of reals is either countable or of the same size as the full set of reals. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.4 n40) |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| Full Idea: Our set-theoretic methods track the underlying contours of mathematical depth. ...What sets are, most fundamentally, is markers for these contours ...they are maximally effective trackers of certain trains of mathematical fruitfulness. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.4) | |
| A reaction: This seems to make it more like a map of mathematics than the actual essence of mathematics. |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| Full Idea: Ordinary perceptual cognition is most likely involved in our grasp of elementary arithmetic, but ...this connection to the physical world has long since been idealized away in the infinitary structures of contemporary pure mathematics. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.3) | |
| A reaction: Despite this, Maddy's quest is for a 'naturalistic' account of mathematics. She ends up defending 'objectivity' (and invoking Tyler Burge), rather than even modest realism. You can't 'idealise away' the counting of objects. I blame Cantor. |
| 14082 | No sortal could ever exactly pin down which set of particles count as this 'cup' [Schaffer,J] |
| Full Idea: Many decent candidates could the referent of this 'cup', differing over whether outlying particles are parts. No further sortal I could invoke will be selective enough to rule out all but one referent for it. | |
| From: Jonathan Schaffer (Deflationary Metaontology of Thomasson [2009], 3.1 n8) | |
| A reaction: I never had much faith in sortals for establishing individual identity, so this point comes as no surprise. The implication is strongly realist - that the cup has an identity which is permanently beyond our capacity to specify it. |
| 14081 | Identities can be true despite indeterminate reference, if true under all interpretations [Schaffer,J] |
| Full Idea: There can be determinately true identity claims despite indeterminate reference of the terms flanking the identity sign; these will be identity claims true under all admissible interpretations of the flanking terms. | |
| From: Jonathan Schaffer (Deflationary Metaontology of Thomasson [2009], 3.1) | |
| A reaction: In informal contexts there might be problems with the notion of what is 'admissible'. Is 'my least favourite physical object' admissible? |
| 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? |
| 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. |
| 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? |