/lit/ - Literature

>>20935268
Don't take it from me. Take it from Aristotle himself (through a secondhand account of one of this students). See pic-related. Amirthanayagam David also makes the convincing argument that Aristotle was perhaps reacting not to Plato but to his Pythagorean-like students.
>That Aristotle knew about the geometry of means is clear enough, but he must not have been familiar with the interpolation of means in the peculiar configuration of the indeterminate dyad, where means become extremes, which in turn beget means, which then in turn become extremes, while each pair of harmonic and arithmetic means serves as the extremes to the geometric mean in the middle. The notion of relativity embodied in this configuration, involving a process of equalising, and motion towards a fixed object, is more subtle and peculiar than that involved in a simple comparison, or even a static analysis expressed in terms of a mean and extremes. I claim it is this peculiar conception of the relative that Plato raised to the level of a principle, to stand in tandem with the absolute measure connoted by the unit.
>While the Academic metaphysicians may appear to have used these very same principles, right down to the letter of their formulation, it is clear that neither they nor Aristotle grasped their proper function. They have nothing to do with accounting for multiplicity in the universe, or with the generation of numbers. They have everything to do with the measurement of numbers. After Theaetetus, numbers are figured as square or rectangular; they can be compared not only in quantity, but in size, by the length of their square roots, just as after Euclid’s II.14, any rectilinear figures can be compared by the sides of their equivalent squares. While all numbers have either absolutely or relatively measurable rootlengths, not all lengths have countable squares. This is one of the odd new ways that arithmetic and geometry, number and magnitude, become interlinked after Theaetetus’ happy reformulation.
>It is therefore in this context, the context of measurement, that Plato is likely to have distinguished the absolute from the relative being-in itself from relative being. Aristotle alludes to just such a distinction, in a passage which once again exemplifies his peculiar mire: he wants to review the Academic theories on the generation of multiplicity based on certain contrary principles, including principles first conceived by Plato, but conceived in a context where in some cases they weren’t even contraries, and where they had had nothing to do with generating either multiplicity or numbers; he knows the language of Plato’s own articulation of these principles, but doesn’t have the mathematics to interpret the words. In this case, he may even foist his own innovations in usage back on to Plato’s original phrases, just to make sense of them.
link: (p25-61) https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/2b69b2ce561c611b2fc3cefb8e8bdaec.pdf

>>20935268
Don't take it from me. Take it from Aristotle himself (through a secondhand account of one of this students). See pic-related. Amirthanayagam David also makes the convincing argument that Aristotle was perhaps reacting not to Plato but to his Pythagorean-like students.
>That Aristotle knew about the geometry of means is clear enough, but he must not have been familiar with the interpolation of means in the peculiar configuration of the indeterminate dyad, where means become extremes, which in turn beget means, which then in turn become extremes, while each pair of harmonic and arithmetic means serves as the extremes to the geometric mean in the middle. The notion of relativity embodied in this configuration, involving a process of equalising, and motion towards a fixed object, is more subtle and peculiar than that involved in a simple comparison, or even a static analysis expressed in terms of a mean and extremes. I claim it is this peculiar conception of the relative that Plato raised to the level of a principle, to stand in tandem with the absolute measure connoted by the unit.
>While the Academic metaphysicians may appear to have used these very same principles, right down to the letter of their formulation, it is clear that neither they nor Aristotle grasped their proper function. They have nothing to do with accounting for multiplicity in the universe, or with the generation of numbers. They have everything to do with the measurement of numbers. After Theaetetus, numbers are figured as square or rectangular; they can be compared not only in quantity, but in size, by the length of their square roots, just as after Euclid’s II.14, any rectilinear figures can be compared by the sides of their equivalent squares. While all numbers have either absolutely or relatively measurable rootlengths, not all lengths have countable squares. This is one of the odd new ways that arithmetic and geometry, number and magnitude, become interlinked after Theaetetus’ happy reformulation.
>It is therefore in this context, the context of
measurement, that Plato is likely to have
distinguished the absolute from the relative being-in-itself from relative being. Aristotle alludes to just such a distinction, in a passage which once again exemplifies his peculiar mire: he wants to review the Academic theories on the generation of multiplicity based on certain contrary principles, including principles first conceived by Plato, but conceived in a context where in some cases they weren’t even contraries, and where they had had nothing to do with generating either multiplicity or numbers; he knows the language of Plato’s own articulation of these principles, but doesn’t have the mathematics to interpret the words. In this case, he may even foist his own innovations in usage back on to Plato’s original phrases, just to make sense of them.
Link: (p25-61) https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/2b69b2ce561c611b2fc3cefb8e8bdaec.pdf

>>20935268
Don't take it from me. Take it from Aristotle himself (through a secondhand account of one of this students). See pic-related. Amirthanayagam David also makes the convincing argument that Aristotle was perhaps reacting not to Plato but to his Pythagorean-like students.
>That Aristotle knew about the geometry of means is clear enough, but he must not have been familiar with the interpolation of means in the peculiar configuration of the indeterminate dyad, where means become extremes, which in turn beget means, which then in turn become extremes, while each pair of harmonic and arithmetic means serves as the extremes to the geometric mean in the middle. The notion of relativity embodied in this configuration, involving a process of equalising, and motion towards a fixed object, is more subtle and peculiar than that involved in a simple comparison, or even a static analysis expressed in terms of a mean and extremes. I claim it is this peculiar conception of the relative that Plato raised to the level of a principle, to stand in tandem with the absolute measure connoted by the unit.
>While the Academic metaphysicians may appear to have used these very same principles, right down to the letter of their formulation, it is clear that neither they nor Aristotle grasped their proper function. They have nothing to do with accounting for multiplicity in the universe, or with the generation of numbers. They have everything to do with the measurement of numbers. After Theaetetus, numbers are figured as square or rectangular; they can be compared not only in quantity, but in size, by the length of their square roots, just as after Euclid’s II.14, any rectilinear figures can be compared by the sides of their equivalent squares. While all numbers have either absolutely or relatively measurable rootlengths, not all lengths have countable squares. This is one of the odd new ways that arithmetic and geometry, number and magnitude, become interlinked after Theaetetus’ happy reformulation.
>It is therefore in this context, the context of measurement, that Plato is likely to have distinguished the absolute from the relative, being-in-itself from relative being. Aristotle alludes to just such a distinction, in a passage which once again exemplifies his peculiar mire: he wants to review the Academic theories on the generation
of multiplicity based on certain contrary principles, including principles first conceived by Plato, but conceived in a context where in some cases they weren’t even contraries, and where they had had nothing to do with generating either multiplicity or numbers; he knows the language of Plato’s own articulation of these principles, but doesn’t have the mathematics to interpret the words. In this case, he may even foist his own innovations in usage back on to Plato’s original phrases, just to make sense of them.
https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/2b69b2ce561c611b2fc3cefb8e8bdaec.pdf