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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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21947
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Power is localised, so we either have totalitarian centralisation, or local politics [Foucault, by Gutting]
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Full Idea:
Foucault's analysis suggests that meaningful revolution, hence genuine liberation, is impossible: the only alternative to the modern net of micro-centres of power is totalitatian domination. Hence his politics, even when revolutionary, is always local.
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From:
report of Michel Foucault (Discipline and Punish [1977]) by Gary Gutting - Foucault: a very short introduction 8
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A reaction:
It is hard to disagree with this.
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21946
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Prisons gradually became our models for schools, hospitals and factories [Foucault, by Gutting]
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Full Idea:
Foucault's thesis is that disciplinary techniques introduced for criminals became the model for other modern sites of control (schools, hospitals, factories), so that prison discipline pervades all of society.
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From:
report of Michel Foucault (Discipline and Punish [1977]) by Gary Gutting - Foucault: a very short introduction 8
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A reaction:
Someone recently designed Foucault Monopoly, where every location is a prison. All tightly controlled organisations, such as a medieval monastery, or the Roman army, will inevitably share many features.
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