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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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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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12759
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There are atoms of substance, but no atoms of bulk or extension [Leibniz]
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Full Idea:
Although there are atoms of substance, namely monads, which lack parts, there are no atoms of bulk [moles], that is, atoms of the least possible extension, nor are there any ultimate elements, since a continuum cannot be composed out of points.
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From:
Gottfried Leibniz (On Nature Itself (De Ipsa Natura) [1698], §11)
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A reaction:
Leibniz has a constant battle for the rest of his career to explain what these 'atoms of substance' are, since they have location but no extension, they are self-sufficient yet generate force, and are non-physical but interact with matter.
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12718
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Secondary matter is active and complete; primary matter is passive and incomplete [Leibniz]
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Full Idea:
I understand matter as either secondary or primary. Secondary matter is, indeed, a complete substance, but it is not merely passive; primary matter is merely passive, but it is not a complete substance. So we must add a soul or form...
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From:
Gottfried Leibniz (On Nature Itself (De Ipsa Natura) [1698], §12), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 4
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A reaction:
It sounds as if primary matter is redundant, but Garber suggests that secondary matter is just the combination of primary matter with form.
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11854
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If there is some trace of God in things, that would explain their natural force [Leibniz]
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Full Idea:
If the law of God does indeed leave some vestige of him expressed in things...then it must be granted that there is a certain efficacy residing in things, a form or force such as we usually designate by the name of nature, from which the phenomena follow.
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From:
Gottfried Leibniz (On Nature Itself (De Ipsa Natura) [1698], §06)
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A reaction:
I wouldn't rate this as a very promising theory of powers, but it seems to me important that Leibniz recognises the innate power in things as needing explanation. If you remove divine power, you are left with unexplained intrinsic powers.
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12758
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It is plausible to think substances contain the same immanent force seen in our free will [Leibniz]
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Full Idea:
If we attribute an inherent force to our mind, a force acting immanently, then nothing forbids us to suppose that the same force would be found in other souls or forms, or, if you prefer, in the nature of substances.
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From:
Gottfried Leibniz (On Nature Itself (De Ipsa Natura) [1698], §10)
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A reaction:
This is the kind of bizarre idea that you are driven to, once you start thinking that God must have a will outside nature, and then that we have the same thing. Why shouldn't such a thing pop up all over the place? Only Leibniz spots the slippery slope.
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17367
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Species are phenetic, biological, niche, or phylogenetic-cladistic [Devitt, by PG]
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Full Idea:
The four main concepts of a species are 'phenetic' (similarity of traits), 'biological species' (interbreeding and isolated), 'ecological niche' (occupying an adaptive zone), or 'phylogenetic-cladistic' (start and finish at splits in lineage)
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From:
report of Michael Devitt (Resurrecting Biological Essentialism [2008], 4) by PG - Db (ideas)
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A reaction:
[my summary of Devitt's list] Devitt attacks the whole lot, in favour of essentialism - the species being fixed by its underlying explanatory mechanisms.
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19408
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To say that nature or the one universal substance is God is a pernicious doctrine [Leibniz]
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Full Idea:
To say that nature itself or the substance of all things is God is a pernicious doctrine, recently introduced into the world or renewed by a subtle or profane author.
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From:
Gottfried Leibniz (On Nature Itself (De Ipsa Natura) [1698], 8)
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A reaction:
The dastardly profane author is, of course, Spinoza, whom Leibniz had met in 1676. The doctrine may be pernicious to religious orthodoxy, but to me it is rather baffling, since in my understanding nature and God have almost nothing in common.
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