Combining Philosophers

Ideas for H.Putnam/P.Oppenheim, Friedrich Nietzsche and Peter van Inwagen

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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     From: Friedrich Nietzsche (Unpublished Notebooks 1885-86 [1886], 34[058])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
Counting needs unities, but that doesn't mean they exist; we borrowed it from the concept of 'I' [Nietzsche]
     Full Idea: We need unities in order to be able to count: we should not therefore assume that such unities exist. We have borrowed the concept of unity from our concept of 'I' - our oldest article of faith.
     From: Friedrich Nietzsche (Writings from Late Notebooks [1887], 14[79])
     A reaction: Personally I think that counting derives from patterns, and that all creatures can discern patterns in their environment, which means discriminating the parts of the pattern, which are therefore real and existing entities.
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.