Puzzling over Leibniz’s substances

-Liebniz: a substance is that from which all true predicates can be deduced.


This is certainly true in mathematics. A circle is self-evidently that from which all true predicates of a circle can be deduced. What would one deduce properties from, if not their subject?

1.) A complete science is the complete deduction of properties of a subject.

2.) The complete science of individuals is possible.

3.) So it is possible to completely deduce the properties of some individual subject.

The complete science of Caesar would deduce that he would cross the Rubicon. A complete science of me would allow you to finish this post all by yourself without anyone having to go to the trouble of reading it.

Before Leibniz, the argument was a reductio ad absurdum showing the impossibility of (2), though Leibniz probably accepted it since (a) the PSR seems to demand a perfectly intelligible account of every individual as such (b) the perfection of the universe requires the complete intelligibility of the individuals composing it and, most importantly, (c) even though we have no science of individuals, God certainly does, and not just from his omniscience but because all is a procession from his own idea.

If we could deduce the whole universe from the creator’s idea of it, it seems like small potatoes to deduce the life of Alexander, and the basis for this deduction within nature seems to be simply Alexander himself.

Aristotle would respond that the substance of Alexander is not just intelligible, but is constituted by matter which is unintelligible to us. Leibniz might point out that what is intelligible to us is not the issue, and unless one is ready to deny that matter is intelligible even to God the response has no merit. Nevertheless, Aristotle can distinguish science into certain knowledge and the mode of certain knowledge which abstracts from the particular, and if we place deduction from concepts firmly on the side of science in the second sense, we are mistaken to think there is some possible deduction of Alexander’s properties. The price of this is to lose the divine ideas, or at least ideas understood as being ruled by laws of deduction. But can an idea be understood in this way?




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