MATHEMATICAL PLATONISM IN THE BROADER INTELLECTUAL CONTEXT, AND THE CURRENT STAT

MATHEMATICAL PLATONISM IN THE BROADER INTELLECTUAL CONTEXT, AND THE CURRENT STATE OF DEVELOPMENT IN MATHEMATICS (the study of measurement using constant relations via positional naming)

(continuing discussion)

Converting statements of mathematical platonism:

If we say: “Can we say a subset…?” rather than “All is/are…” we eliminate a great deal of mathematical platonism, that requires us to use terminological special pleading.

This eliminates the cultism (fictionalism) of mathematical platonism and ensures that the speaker knows of what he speaks, rather than simply performing operations he does not understand, but is still capable of constructing proofs of possibility.

In other words, there is a difference between an idiot savant who masters pattern recognition and the individual who explains why the patterns can exist in the first place.

As the intuitionists discovered, (and authors of proof software have taken advantage of), a proof must be falsified, and the two dimensions of doing so are via negativa (application tests), and via positiva (construction from operations)

Unfortunately it seems that Wolfram is trying to cast operationalism as a separate science, rather than restoring mathematics to operations AND deductions, and it seems theoreticians are still describing symmetries (lie groups), it appears we are stuck with fictionalisms in each sub discipline rather than the rather obvious: that by free association we can either identify or search for patterns, and by a competition between construction and deduction we can test them, in any number of dimensions. And that our topography is largely little more than puzzles, while the problem of N-dimensional permutations producing consistent intermediary symmetries whose change in state is measurable, and lends prediction to heretofore unimaginable outcomes of n-dimensional high causal density is the holy grail of mathematics at which point we will be able to produce semantic intelligences rather than mere computations and algorithms.

This is a perhaps more articulate explanation of the pseudoscience and pseudo-rationalism of the 20th (and now 21st century) that Hayek chastened us would be remembered in history as a second age of ‘mysticism’.

Unfortunately, the great wars interfered wth the second enlightenment and the second industrial revolution, and gave the common man economic and political influence by which to distribute that new mysticism (Boaz/marx/freud/cantor/frankfurt school/postmodernism) when poincare, hayek, popper, brouwer, bridgman, and mises all failed to complete the operational revolution.

(I’m doing my best to pick up the pieces.)

Cheers.

Curt Doolittle

The Propertarian Institute

Kiev, Ukraine