Another small step on the path to (someday) understanding calculus has clarified an aspect of Leibniz.
I basically got this before (as in the statement in an earlier post about "infinite density" replacing the "infinite series"), but it's clearer now. In Leibniz' metaphysics, infinity becomes the infinity of calculus. The series of numbers, by which we could "count" reality (and which would go on forever in space and time), is replaced by the function, the curve whose proximity to a line can never be reduced to a single number, but can only be expressed (like the curve itself), through a relational representation.
Anyone who gets calculus will, I'm sure, see that I have a long way to go.
Showing posts with label Leibniz. Show all posts
Showing posts with label Leibniz. Show all posts
10.22.2007
8.27.2007
a few quotes and fragments from Leibniz
(as much for their poetic or humorous potential as anything else. Pagination refers to G.W. Leibniz, Philosophical Texts, Oxford 1998.) (sorry about the font size crap--Blogger has its oddities, which I could probably fix with some time in the HTML region... but won't.)
So in order that our words should be as blameless as their meaning, it will be as well to link certain ways of speech with certain thoughts. (69)
Willebrord Snell, first formulator of the rules of refraction (75)
as if there were only it and God in the world (112)
Sleep, which is an image of death, and ecstasies; the enshrouding of a silkworm in its shell, which can be taken for death; the resuscitation of drowned flies brought about by covering them with some dry powder (whereas they remain completely dead if they are left unaided), and that of swallows which make their winter quarters in reeds and which are discovered with no semblance of life; experiments with people killed by cold, drowned or strangled, and who are then brought back to life... all these things confirm my opinion that these different states differ only in degree... (133).
nothing is empty, sterile, undeveloped or without perception... (135)
So in order that our words should be as blameless as their meaning, it will be as well to link certain ways of speech with certain thoughts. (69)
Willebrord Snell, first formulator of the rules of refraction (75)
as if there were only it and God in the world (112)
Sleep, which is an image of death, and ecstasies; the enshrouding of a silkworm in its shell, which can be taken for death; the resuscitation of drowned flies brought about by covering them with some dry powder (whereas they remain completely dead if they are left unaided), and that of swallows which make their winter quarters in reeds and which are discovered with no semblance of life; experiments with people killed by cold, drowned or strangled, and who are then brought back to life... all these things confirm my opinion that these different states differ only in degree... (133).
nothing is empty, sterile, undeveloped or without perception... (135)
8.26.2007
Leibniz--initial forays
The hidden motive of metaphysics from Leibniz on: the fear of infinite regress, lack of ground.
It persists in many scientistic (and embarrassing) strains of Anglo-American philosophy today, even as physics (the model for scientistic thinking) has long since moved into much more uncertain regions.
Descartes broke off a piece of metaphysics to found modern epistemology, grounding everything in the subject... and did a half-assed job of it.
Of course, philosophy has tried to find the ultimate basis of being since at least Thales ("everything is water"), but it wasn't until Leibniz's time (which was also Newton's) that reason began to open the gap that struck terror into the hearts of European thinkers, revealing vast and hitherto undreamed-of nothingnesses.
When metaphysics was metaphysics, though, the thinking of this flight away from groundlessness had fascinating results of a sort today's pseudoscientist philosophers can't match.
Leibniz tries to solve two problems of groundlessness:
1) The idea that the causal chain could extend forever into the past, without finding an ultimate beginning, necessitated God for Leibniz (and others). God is outside time (time, in fact, begins to lose its objective status in Leibniz and Kant, becoming a form of perception or reception), having set out the whole of being, within which each being's essence contains everything that will ever happen to it, all its relations with all other beings. Especially for an atheist like me, this problem looks dusty and goofy, and the predestinational solution just as ridiculous. But the implications in Leibniz are interesting: Leibniz spatializes time, so that it can have an outside, and he needs a concept (God) to catapult thought out of the dimension of time as we know it. The causal chain becomes a spatial series of systems of relationships.
This doesn't really solve the infinity problem, but changes its direction; now reality is infinitely dense.
2) The dread newer in Leibniz's time: that material being could be subdivided, broken down ad infinitum. Here's where the monad comes in. The ultimate substance, the monad is incorporeal, no longer spatial. Its changes are self-caused, the result of its "perceptions." The monad, in a way, is simply the locus of perspectives, of relations that respond to other relations, with a given density. I'll wait for a later post to get deeply into the question of what the hell the monad is supposed to "be." Here I'll just note that the monad is outside space. As Leibniz's response to the infinite regress of decomposition, the perpetual zoom to a smaller and smaller scale, the monad is outside that scale, or is outside scale entirely. Again, a new dimension is added; space and scale, in fact, are called into question, since ultimate reality is an absolute fullness of monadic perspectives on one another.
In both cases, Leibniz's solution is simply to make a leap--one could even consider this a Kierkegaardian "leap of faith" in a more radical sense than Kierkegaard, with his ethico-religious focus, ever achieved. These leaps are thoroughly absurd, and as such are so easy to pick apart that centuries have been wasted doing it in books, pamphlets and classroom discussions. At the same time, the failure to think along with Leibniz, to trace the movements of his thought in these leaps and the strange propositions he makes, bouncing language off of the perimeter of the void, has meant that his real contemporary offer (I conjecture, in mid-study)--an offer of one way of thinking that at least faces the lack of ground, that tries to retain deductive/scientific reason while pushing it beyond its own limits (and this almost at the inception of modern reason)--has been missed.
It persists in many scientistic (and embarrassing) strains of Anglo-American philosophy today, even as physics (the model for scientistic thinking) has long since moved into much more uncertain regions.
Descartes broke off a piece of metaphysics to found modern epistemology, grounding everything in the subject... and did a half-assed job of it.
Of course, philosophy has tried to find the ultimate basis of being since at least Thales ("everything is water"), but it wasn't until Leibniz's time (which was also Newton's) that reason began to open the gap that struck terror into the hearts of European thinkers, revealing vast and hitherto undreamed-of nothingnesses.
When metaphysics was metaphysics, though, the thinking of this flight away from groundlessness had fascinating results of a sort today's pseudoscientist philosophers can't match.
Leibniz tries to solve two problems of groundlessness:
1) The idea that the causal chain could extend forever into the past, without finding an ultimate beginning, necessitated God for Leibniz (and others). God is outside time (time, in fact, begins to lose its objective status in Leibniz and Kant, becoming a form of perception or reception), having set out the whole of being, within which each being's essence contains everything that will ever happen to it, all its relations with all other beings. Especially for an atheist like me, this problem looks dusty and goofy, and the predestinational solution just as ridiculous. But the implications in Leibniz are interesting: Leibniz spatializes time, so that it can have an outside, and he needs a concept (God) to catapult thought out of the dimension of time as we know it. The causal chain becomes a spatial series of systems of relationships.
This doesn't really solve the infinity problem, but changes its direction; now reality is infinitely dense.
2) The dread newer in Leibniz's time: that material being could be subdivided, broken down ad infinitum. Here's where the monad comes in. The ultimate substance, the monad is incorporeal, no longer spatial. Its changes are self-caused, the result of its "perceptions." The monad, in a way, is simply the locus of perspectives, of relations that respond to other relations, with a given density. I'll wait for a later post to get deeply into the question of what the hell the monad is supposed to "be." Here I'll just note that the monad is outside space. As Leibniz's response to the infinite regress of decomposition, the perpetual zoom to a smaller and smaller scale, the monad is outside that scale, or is outside scale entirely. Again, a new dimension is added; space and scale, in fact, are called into question, since ultimate reality is an absolute fullness of monadic perspectives on one another.
In both cases, Leibniz's solution is simply to make a leap--one could even consider this a Kierkegaardian "leap of faith" in a more radical sense than Kierkegaard, with his ethico-religious focus, ever achieved. These leaps are thoroughly absurd, and as such are so easy to pick apart that centuries have been wasted doing it in books, pamphlets and classroom discussions. At the same time, the failure to think along with Leibniz, to trace the movements of his thought in these leaps and the strange propositions he makes, bouncing language off of the perimeter of the void, has meant that his real contemporary offer (I conjecture, in mid-study)--an offer of one way of thinking that at least faces the lack of ground, that tries to retain deductive/scientific reason while pushing it beyond its own limits (and this almost at the inception of modern reason)--has been missed.
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