Combining Philosophers

Ideas for H.Putnam/P.Oppenheim, Friedrich Nietzsche and Alexander Baumgarten

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3 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
Numbers enable us to manage the world - to the limits of counting [Nietzsche]
     Full Idea: Numbers are our major means of making the world manageable. We comprehend as far as we can count, i.e. as far as a constancy can be perceived.
     From: Friedrich Nietzsche (Unpublished Notebooks 1885-86 [1886], 34[058])
     A reaction: I don't agree with 'major', but it is a nice thought. The intermediate concept is a 'unit', which means identifying something as a 'thing', which is how we seem to grasp the world. So to what extent do we comprehend the infinite. Enter Cantor…
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
We need 'unities' for reckoning, but that does not mean they exist [Nietzsche]
     Full Idea: We need 'unities' in order to be able to reckon: that does not mean we must suppose that such unities exist.
     From: Friedrich Nietzsche (The Will to Power (notebooks) [1888], §635)
     A reaction: True. I takes this thought to be important in the Psychology of Metaphysics (an unfashionable branch).
6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
Logic and maths refer to fictitious entities which we have created [Nietzsche]
     Full Idea: Logic (like geometry and arithmetic) applies only to fictitious entities that we have created.
     From: Friedrich Nietzsche (The Will to Power (notebooks) [1888], §516)
     A reaction: This finds Nietzsche on the relativist wing of logical empiricism. The thing is, fictitious entities can have a close relationship with truth, as in a great novel. I believe in necessary logical truth, but there are many ways of slicing it.