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13165
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Geometrical proofs do not show causes, as when we prove a triangle contains two right angles [Proclus]
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Full Idea:
Geometry does not ask 'why?' ..When from the exterior angle equalling two opposite interior angles it is shown that the interior angles make two right angles, this is not a causal demonstration. With no exterior angle they still equal two right angles.
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From:
Proclus (Commentary on Euclid's 'Elements' [c.452], p.161-2), quoted by Paolo Mancosu - Explanation in Mathematics §5
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A reaction:
A very nice example. It is hard to imagine how one might demonstrate the cause of the angles making two right angles. If you walk, turn left x°, then turn left y°, then turn left z°, and x+y+z=180°, you end up going in the original direction.
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9569
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The origin of geometry started in sensation, then moved to calculation, and then to reason [Proclus]
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Full Idea:
It is unsurprising that geometry was discovered in the necessity of Nile land measurement, since everything in the world of generation goes from imperfection to perfection. They would naturally pass from sense-perception to calculation, and so to reason.
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From:
Proclus (Commentary on Euclid's 'Elements' [c.452]), quoted by Charles Chihara - A Structural Account of Mathematics 9.12 n55
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A reaction:
The last sentence is the core of my view on abstraction, that it proceeds by moving through levels of abstraction, approaching more and more general truths.
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2854
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Prescriptivism says 'ought' without commitment to act is insincere, or weakly used [Hooker,B]
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Full Idea:
Prescriptivism holds that if you think one 'ought' to do a certain kind of act, and yet you are not committed to doing that act in the relevant circumstances, then you either spoke insincerely, or are using the word 'ought' in a weak sense.
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From:
Brad W. Hooker (Prescriptivism [1995], p.640)
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A reaction:
So that's an 'ought', but not a 'genuine ought', then? (No True Scotsman move). Someone ought to rescue that drowning child, but I can't be bothered.
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20883
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Modern utilitarians value knowledge, friendship, autonomy, and achievement, as well as pleasure [Hooker,B]
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Full Idea:
Most utilitarians now think that pleasure, even if construed widely, is not the only thing desirable in itself. ...Goods also include important knowledge, friendship, autonomy, achievement and so on.
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From:
Brad W. Hooker (Rule Utilitarianism and Euthanasia [1997], 2)
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A reaction:
That pleasure is desired is empirically verifiable, which certainly motivated Bentham. A string of other desirables each needs to be justified - but how? What would be the value of a 'friendship' if neither party got pleasure from it?
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20885
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Euthanasia is active or passive, and voluntary, non-voluntary or involuntary [Hooker,B]
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Full Idea:
Six types of euthanasia: 1) Active voluntary (knowing my wishes), 2) Active non-voluntary (not knowing my wishes), 3) Active involuntary (against my wishes), 4) Passive voluntary, 5) Passive non-voluntary, 6) Passive involuntary.
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From:
Brad W. Hooker (Rule Utilitarianism and Euthanasia [1997], 5)
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A reaction:
'Active' is intervening, and 'passive' is not intervening. A helpful framework.
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20882
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Euthanasia may not involve killing, so it is 'killing or not saving, out of concern for that person' [Hooker,B]
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Full Idea:
Passive euthanasia is arguably not killing, and the death involved is often painful, so let us take the term 'euthanasia' to mean 'either killing or passing up opportunities to save someone, out of concern for that person'.
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From:
Brad W. Hooker (Rule Utilitarianism and Euthanasia [1997], 1)
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A reaction:
This sounds good, and easily settled, until you think concern for that person could have two different outcomes, depending on whether the criteria are those of the decider or of the patient. Think of religious decider and atheist patient, or vice versa.
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