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17807
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To study formal systems, look at the whole thing, and not just how it is constructed in steps [Curry]
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Full Idea:
In the study of formal systems we do not confine ourselves to the derivation of elementary propositions step by step. Rather we take the system, defined by its primitive frame, as datum, and then study it by any means at our command.
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From:
Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'The formalist')
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A reaction:
This is what may potentially lead to an essentialist view of such things. Focusing on bricks gives formalism, focusing on buildings gives essentialism.
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8865
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If 'the number of Democrats is on the rise', does that mean that 50 million is on the rise? [Yablo]
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Full Idea:
If someone says 'the number of Democrats is on the rise', he or she wants to focus on Democrats, not numbers. If the number is 50 million, is 50 million really on the rise?
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From:
Stephen Yablo (Apriority and Existence [2000], §14)
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A reaction:
This is a very nice warning from Yablo, against easy platonism, or any sort of platonism at all. We routinely say that numbers are 'increasing', but the real meaning needs entangling. Here it refers to people joining a party.
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17806
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It is untenable that mathematics is general physical truths, because it needs infinity [Curry]
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Full Idea:
According to realism, mathematical propositions express the most general properties of our physical environment. This is the primitive view of mathematics, yet on account of the essential role played by infinity in mathematics, it is untenable today.
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From:
Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'The problem')
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A reaction:
I resist this view, because Curry's view seems to imply a mad metaphysics. Hilbert resisted the role of the infinite in essential mathematics. If the physical world includes its possibilities, that might do the job. Hellman on structuralism?
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8864
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We quantify over events, worlds, etc. in order to make logical possibilities clearer [Yablo]
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Full Idea:
It is not that the contents of sentences are inexpressible without quantifying over events, worlds, etc. (they aren't). But the logical relations become much more tractable if we represent them quantificationally.
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From:
Stephen Yablo (Apriority and Existence [2000], §13)
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A reaction:
Yablo is explaining why we find ourselves committed to abstract objects. It is essentially, as I am beginning to suspect, a conspiracy of logicians. What on earth is 'the empty set' when it is at home? What's it made of?
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8858
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Philosophers keep finding unexpected objects, like models, worlds, functions, numbers, events, sets, properties [Yablo]
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Full Idea:
There's a tradition in philosophy of finding 'unexpected objects' in truth-conditions, such as countermodels, possible worlds, functions, numbers, events, sets and properties.
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From:
Stephen Yablo (Apriority and Existence [2000], §02)
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A reaction:
This is a very nice perspective on the whole matter of abstract objects. If we find ourselves reluctantly committed to the existence of something which is ontologically peculiar, we should go back to the philosophical drawing-board.
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16764
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The soul conserves the body, as we see by its dissolution when the soul leaves [Toletus]
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Full Idea:
Every accident of a living thing, as well as all its organs and temperaments and its dispositions are conserved by the soul. We see this from experience, since when that soul recedes, all these dissolve and become corrupted.
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From:
Franciscus Toletus (Commentary on 'De Anima' [1572], II.1.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 24.5
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A reaction:
A nice example of observing a phenemonon, but not being able to observe the dependence relation the right way round. Compare Descartes in Idea 16763.
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