Key Arguments

• Phenomena now count only insofar as they can be reduced to mathematical order, not to disclose true being but to fit the measure of the human mind.
• This requires ‘removing the eyes’ of body and mind from phenomena, using the ‘force inherent in distance’ to handle multiplicity via abstract patterns and symbols.
• Under conditions of remoteness, ‘every assemblage’ becomes a multitude and ‘every multitude’ falls into patterns of the same validity ‘and no more significance’ than a mathematically drawn curve among random points (Leibniz).
• If a ‘mathematical web’ can be woven around any universe with several objects, then the universe’s mathematical treatability carries ‘no great philosophic significance.’

Source Quotes

When, moreover, the same analytical geometry proved “conversely that numerical truths . . . can be fully represented spatially,” a physical science had been evolved which required no principles for its completion beyond those of pure mathematics, and in this science man could move, risk himself into space and be certain that he would not encounter anything but himself, nothing that could not be reduced to patterns present in him. Now the phenomena could be saved only in so far as they could be reduced to a mathematical order, and this mathematical operation does not serve to prepare man’s mind for the revelation of true being by directing it to the ideal measures that appear in the sensually given data, but serves, on the contrary, to reduce these data to the measure of the human mind, which, given enough distance, being sufficiently remote and uninvolved, can look upon and handle the multitude and variety of the concrete in accordance with its own patterns and symbols. These are no longer ideal forms disclosed to the eye of the mind, but are the results of removing the eyes of the mind, no less than the eyes of the body, from the phenomena, of reducing all appearances through the force inherent in distance.

Now the phenomena could be saved only in so far as they could be reduced to a mathematical order, and this mathematical operation does not serve to prepare man’s mind for the revelation of true being by directing it to the ideal measures that appear in the sensually given data, but serves, on the contrary, to reduce these data to the measure of the human mind, which, given enough distance, being sufficiently remote and uninvolved, can look upon and handle the multitude and variety of the concrete in accordance with its own patterns and symbols. These are no longer ideal forms disclosed to the eye of the mind, but are the results of removing the eyes of the mind, no less than the eyes of the body, from the phenomena, of reducing all appearances through the force inherent in distance. Under this condition of remoteness, every assemblage of things is transformed into a mere multitude, and every multitude, no matter how disordered, incoherent, and confused, will fall into certain patterns and configurations possessing the same validity and no more significance than the mathematical curve, which, as Leibniz once remarked, can always be found between points thrown at random on a piece of paper.

These are no longer ideal forms disclosed to the eye of the mind, but are the results of removing the eyes of the mind, no less than the eyes of the body, from the phenomena, of reducing all appearances through the force inherent in distance. Under this condition of remoteness, every assemblage of things is transformed into a mere multitude, and every multitude, no matter how disordered, incoherent, and confused, will fall into certain patterns and configurations possessing the same validity and no more significance than the mathematical curve, which, as Leibniz once remarked, can always be found between points thrown at random on a piece of paper. For if “it can be shown that a mathematical web of some kind can be woven about any universe containing several objects . . . then the fact that our universe lends itself to mathematical treatment is not a fact of any great philosophic significance.”

Under this condition of remoteness, every assemblage of things is transformed into a mere multitude, and every multitude, no matter how disordered, incoherent, and confused, will fall into certain patterns and configurations possessing the same validity and no more significance than the mathematical curve, which, as Leibniz once remarked, can always be found between points thrown at random on a piece of paper. For if “it can be shown that a mathematical web of some kind can be woven about any universe containing several objects . . . then the fact that our universe lends itself to mathematical treatment is not a fact of any great philosophic significance.” It certainly is neither a demonstration of an inherent and inherently beautiful order of nature nor does it offer a confirmation of the human mind, of its capacity to surpass the senses in perceptivity or of its adequateness as an organ for the reception of truth.

Key Concepts

• Now the phenomena could be saved only in so far as they could be reduced to a mathematical order,
• serves, on the contrary, to reduce these data to the measure of the human mind, which, given enough distance, being sufficiently remote and uninvolved, can look upon and handle the multitude and variety of the concrete in accordance with its own patterns and symbols.
• These are no longer ideal forms disclosed to the eye of the mind, but are the results of removing the eyes of the mind, no less than the eyes of the body, from the phenomena, of reducing all appearances through the force inherent in distance.
• Under this condition of remoteness, every assemblage of things is transformed into a mere multitude, and every multitude, no matter how disordered, incoherent, and confused, will fall into certain patterns and configurations possessing the same validity and no more significance than the mathematical curve, which, as Leibniz once remarked, can always be found between points thrown at random on a piece of paper.
• For if “it can be shown that a mathematical web of some kind can be woven about any universe containing several objects . . . then the fact that our universe lends itself to mathematical treatment is not a fact of any great philosophic significance.”

Context

Section 36, lines 5191–5253; Arendt argues that mathematical reduction arises from methodological distance, making pattern-imposition ubiquitous and philosophically deflationary.