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13453
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Perhaps second-order quantifications cover concepts of objects, rather than plain objects [Rayo/Uzquiano]
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Full Idea:
If one thought of second-order quantification as quantification over first-level Fregean concepts [note: one under which only objects fall], talk of domains might be regimented as talk of first-level concepts, which are not objects.
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From:
Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.2.2)
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A reaction:
That is (I take it), don't quantify over objects, but quantify over concepts, but only those under which known objects fall. One might thus achieve naïve comprehension without paradoxes. Sound like fun.
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16051
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Life has a new supervenient relation, which alters its underlying physical events [Morgan,L]
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Full Idea:
When some new kind of relatedness is supervenient (say at the level of life), the way in which the physical events which are involved run their course is different in virtue of its presence.
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From:
Lloyd Morgan (Emergent Evolution [1923], pp.15-16), quoted by Terence Horgan - From Supervenience to Superdupervenience 1
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A reaction:
This is a clear assertion of 'downward causation' at the first introduction of 'supervenience', supporting 'emergentism' about life and mind. That is, the newly-emerged feature has new causal powers that affect the physical system from outside. Wrong!
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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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13448
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The domain of an assertion is restricted by context, either semantically or pragmatically [Rayo/Uzquiano]
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Full Idea:
We generally take an assertion's domain of discourse to be implicitly restricted by context. [Note: the standard approach is that this restriction is a semantic phenomenon, but Kent Bach (2000) argues that it is a pragmatic phenomenon]
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From:
Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.1)
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A reaction:
I think Kent Bach is very very right about this. Follow any conversation, and ask what the domain is at any moment. The reference of a word like 'they' can drift across things, with no semantics to guide us, but only clues from context and common sense.
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