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18284
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Particulars can be verified or falsified, but general statements can only be falsified (conclusively) [Popper]
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Full Idea:
Whereas particular reality statements are in principle completely verifiable or falsifiable, things are different for general reality statements: they can indeed be conclusively falsified, they can acquire a negative truth value, but not a positive one.
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From:
Karl Popper (Two Problems of Epistemology [1932], p.256), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 18 'Laws'
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A reaction:
This sounds like a logician's approach to science, but I prefer to look at coherence, where very little is actually conclusive, and one tinkers with the theory instead.
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16736
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Explanation is generally to deduce it from something better known, which comes in degrees [Boyle]
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Full Idea:
Generally speaking, to render a reason of an effect or phenomenon is to deduce it from something else in nature more known than itself, and consequently there may be diverse kinds of degrees of explication of the same thing.
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From:
Robert Boyle (Certain Physical Essays [1672], II:21), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 23.4
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A reaction:
There is a picture of a real explanatory structure to nature, from which we pick bits that interest us for entirely pragmatic reasons. Boyle and I are as one on this matter.
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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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16737
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The best explanations get down to primary basics, but others go less deep [Boyle]
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Full Idea:
Explications be most satisfactory that show how the effect is produced by the more primitive affects of matter (bulk, shape and motion) but are not to be despised that deduce them from more familiar qualities such as heat, weight, fluidity, fermentation.
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From:
Robert Boyle (Certain Physical Essays [1672], II:22), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 23.4
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A reaction:
[Compressed, and continued from Idea 16736] So there is a causal structure, and the best explanations go to the bottom of it, but lesser explanations only go half way down. So a very skimpy explanation ('dormative power') is still an explanation.
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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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