In a old and nice little essay on Platonism and the Ockham´s razor, Oswaldo Chateaubriand begins to pave a possible road for a renewed Platonism that would fill the holes which made philosophers so impatiently give up on such a theory about reality as a whole. He disparages against the Ockham razor, which is an absolute principle that favors desert landscapes against all sort of speculation. It has set the stage for confining mathematics to a physical non-place, devoid of any inherent connection to concrete things. In particular, it makes mathematisation something outside the sphere of what there is - to mathematize is to drift away, as the razor inspired projects like Hartry Field´s fictionalism. The razor keeps speculation to a minimum and exiles the products of a mathematizing effort.
My interest in negation and the reality of inconsistencies has driven me towards Platonist territories. The essay came back to my mind: why philosophers are so impatient against an overall view of reality just because there are some flimsy arguments against it? I remembered discussing with Meillassoux about mathematisation. He´s all for it, even though he has reservations against most mathematical doctrines. The problem with mathematisation, I said, had to do with measurement. Measurement is crucial and yet is laden with arbitrary choices from the user - it cannot be good enough to attain absulutes for reasons that go back to the old Wittgensteinian arguments in his Bemerkungen über die Grundlagen der Mathematik: why would I use a wooden ruler instead of a rubber one? Meillassoux didn´t answer quite to the contentment of the Wittgensteinian suspicion in the book. Mathematics is filled with our practices and in particular nothing can be mathematized without having been part of the process triggered by someone doing mathematics. God can only determine something mathematical by doing mathematics. But the issue of the measurement is dramatic only if we place it as the sole point of contact between abstracta and a physical world. If things are less clear-cut and abstracta are somehow part of the physical furniture, then mathematisation could be such that there is room for both a wooden ruler measured physical item and a rubber ruler measured physical item.
My interest in negation and the reality of inconsistencies has driven me towards Platonist territories. The essay came back to my mind: why philosophers are so impatient against an overall view of reality just because there are some flimsy arguments against it? I remembered discussing with Meillassoux about mathematisation. He´s all for it, even though he has reservations against most mathematical doctrines. The problem with mathematisation, I said, had to do with measurement. Measurement is crucial and yet is laden with arbitrary choices from the user - it cannot be good enough to attain absulutes for reasons that go back to the old Wittgensteinian arguments in his Bemerkungen über die Grundlagen der Mathematik: why would I use a wooden ruler instead of a rubber one? Meillassoux didn´t answer quite to the contentment of the Wittgensteinian suspicion in the book. Mathematics is filled with our practices and in particular nothing can be mathematized without having been part of the process triggered by someone doing mathematics. God can only determine something mathematical by doing mathematics. But the issue of the measurement is dramatic only if we place it as the sole point of contact between abstracta and a physical world. If things are less clear-cut and abstracta are somehow part of the physical furniture, then mathematisation could be such that there is room for both a wooden ruler measured physical item and a rubber ruler measured physical item.
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