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All the ideas for 'fragments/reports', 'Letters to Samuel Masson' and 'On Body and Force, Against the Cartesians'

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8 ideas

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite

13190	I don't admit infinite numbers, and consider infinitesimals to be useful fictions [Leibniz]
	Full Idea: Notwithstanding my infinitesimal calculus, I do not admit any real infinite numbers, even though I confess that the multitude of things surpasses any finite number, or rather any number. ..I consider infinitesimal quantities to be useful fictions.
	From: Gottfried Leibniz (Letters to Samuel Masson [1716], 1716)
	A reaction: With the phrase 'useful fictions' we seem to have jumped straight into Harty Field. I'm with Leibniz on this one. The history of mathematics is a series of ingenious inventions, whenever they seem to make further exciting proofs possible.

14. Science / D. Explanation / 2. Types of Explanation / h. Explanations by function

13195	To explain a house we must describe its use, as well as its parts [Leibniz]
	Full Idea: A house would be badly explained if we were to describe only the arrangement of its parts, but not its use.
	From: Gottfried Leibniz (On Body and Force, Against the Cartesians [1702], p.255)
	A reaction: This must partly fall under pragmatics (i.e. what the enquirer is interested in). But function plays a genuine role in artefacts, and also in evolved biological organs.

15. Nature of Minds / C. Capacities of Minds / 10. Conatus/Striving

13193	Active force is not just potential for action, since it involves a real effort or striving [Leibniz]
	Full Idea: Active force should not be thought of as the simple and common potential [potentia] or receptivity to action of the schools. Rather, active force involves an effort [conatus] or striving [tendentia] toward action.
	From: Gottfried Leibniz (On Body and Force, Against the Cartesians [1702], p.252)
	A reaction: This is why Leibniz is lured into making his active forces more and more animistic, till they end up like proto-minds (though never, remember, conscious and willing minds).

25. Social Practice / E. Policies / 5. Education / b. Education principles

13304	Learned men gain more in one day than others do in a lifetime [Posidonius]
	Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes.
	From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078
	A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book.

26. Natural Theory / D. Laws of Nature / 1. Laws of Nature

13194	God's laws would be meaningless without internal powers for following them [Leibniz]
	Full Idea: To say that, in creation, God gave bodies a law for acting means nothing, unless, at the same time, he gave them something by means of which it could happen that the law is followed.
	From: Gottfried Leibniz (On Body and Force, Against the Cartesians [1702], p.253)
	A reaction: This is the beginning of the modern rebellion against the medieval view of laws as imposed from outside on passive matter. Unfortunately for Leibniz, once you have postulated active internal powers, the external laws become redundant.

27. Natural Reality / A. Classical Physics / 1. Mechanics / c. Forces

13196	All qualities of bodies reduce to forces [Leibniz]
	Full Idea: All qualities of bodies .....are in the end reduced [revoco] to forces.
	From: Gottfried Leibniz (On Body and Force, Against the Cartesians [1702], p.256)
	A reaction: The dots conceal a long qualification, but he is essentially standing by this simple remark. If you substitute the word 'powers' for 'forces', I think that is just about right.

13192	Power is passive force, which is mass, and active force, which is entelechy or form [Leibniz]
	Full Idea: The dynamicon or power [potentia] in bodies is twofold, passive and active. Passive force [vis] constitutes matter or mass [massa], and active force constitutes entelechy or form.
	From: Gottfried Leibniz (On Body and Force, Against the Cartesians [1702], p.252)
	A reaction: This is explicitly equating the innate force understood in physics with Aristotelian form. The passive force is to explain the resistance of bodies. I like the equation of force with power. He says the entelechy is 'analogous' to a soul.

27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure

20820	Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]
	Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness.
	From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42
	A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them.