Category: Commentary, Critique, and Response

Tom Radcliffe

—“The claims about Hilbert, Brouwer, and Bridgeman are all bizarre.”—

They are only bizarre if you don’t understand the category of problems that western civilization was facing in the wake of cantorial sets, relativity and quantum theory, and the attempt by the analytic movement to find closure in the logics and raise it to a peerage with mathematics, the evolution of computational logic, economics made possible by fiat money, and the transformation of empirical to arbitrary law. All of these systems of reasoning changed from operational (or what we call classical) to arbitrary(descriptive or verbal), reversing descartes-newton-leibnitz restoration of mathematics to a foundation in geometry (classical), and the consequential effect it had on idealism and supernaturalism. We tend not to study various techniques of decidability – I do.

—“Hilbert was a formalist, Brouwer the father of intuitionism, which is the most significant anti-formalist, constructivist, approach to mathematical truth in the 20th century. Brouwer and Hilbert were literally on opposite sides of one of the most fundamental mathematical questions: what does it mean for an existential claim in mathematics to be true?”–

All of these men were frustrated with the re-platonization of mathematics by Cantor and Bohr in particular, and the affect on physics, as were Mises and Hayek in economics, and each took steps to restore mathematics to what we would call today classical foundations.

But while mathematics retains rather absurd vocabulary, vapid mathematical platonism, nonsense terms like multiple infinities (rather than production of pairs at different rates), and while neither the quantum nor relativity have been unstuck from descriptive and returned to causal (the classical), and while, in my understanding even the framing of mathematics in pure mathematics is has diverged from causality to the point where the importance of symmetries and fields has been reduced to puzzles rather than problems of changes, and while we seem unable to develop the next generation of mathematics (although it seems a few like Wolfram understand it’s need), the fact of the matter is, that despite the abandonment of realism(classicalism) and restoration of platonism, and despite the fact that mathematical platonism is a contagion to all subsequent fields, the practical reality is that mathematics is practiced as an archaic craft with archaic prose, and operationalization is less important *within* the fields than it is by contagion outside the field.

Even worse, economics follows the same theme by measuring the national equivalent of income statements while conveniently ignoring balance sheets (accounting for changes in genetic, institutional, cultural, normative, capital).

Unfortunately, computer science arrived late (blame Babbage), and both mathematics and logic, and Popper and Kuhn and the others failed to complete the falsificationary process, and discover that the scientific method (which does exist it turns out) applies to producing evidence that one can testify to in output, not what actions one takes.

And unfortunately, epistemologically, the means by which we obtain an idea(hypothesis) to test (falsify) is immaterial – whether deductive or freely associated tells us nothing.

So while we end with Strawson and company the project was not completed. Had the project of the 20th been completed, we might have reformed all the fields completely, producing a universally commensurable grammar and vocabulary across all the sciences, both hard and soft.

My particular contribution is this completing this deplatonization, and the contagion that follows upstream from it – especially to the economics, law, the social and psychological sciences. Where unlike mathematics, whose one categorical referent (positional name) is not open to undetectable error, there exist hundreds or thousands of referents (terms), in much more complex grammars (possible operations), that without commensurability across fields, and without deplatonization (or projection, or in the case of postmodernism – outright deceit), we cannot *produce a system of law that prohibits use of deceit in matters public*.

In other words, we cannot apply the same rigor that we use in physical science publication to speech, legislation, regulation, and findings of the court, and thereby repair the industrialization of lying by pseudoscience and sophism made possible in the twentieth century – equal in damage to the industrialization of lying by monotheism in the ancient world.

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—“It would be very weird if anyone praised both of them for reforming their fields, when they were doing so from diametrically opposed viewpoints. “—

Of course they were coming from different viewpoints. Just as physicists today are frustrated by the relativity vs quantum conflict (both descriptive not causal). Yet we have physicists trying to solve the problem from many different angles. And at least we can give name to the problem.

Of these different men, only Bridgman was successful in affecting the writing of publications in the physical science.

—“Nor was Hilbert more than one of many influences on mathematical physics, although his book with Courant was important. But in no sense did he reform the field or criticise its set basis. He mostly bitched about how damned sloppy we are with those precious formalisms, because his grasp of physics was that of an outsider who was trying to solve a different problem than the ones physicists care about.

—“Bridgeman is a footnote in the history of 20th century physics. His codification of the work of Eddington, Einstein, and others had far more influence in the social sciences than in physics,”—

And it is the social sciences that are the least reformed. So where the reformation was most important – and it has still failed.

—“where pure operationalism is needlessly restrictive, although it is a useful and powerful tool when things get hairy. “—

This is because again, operationalism is falsificationary.

—“And what is the “Bohr-Einstein and Copenhagen consensus”? It can’t be related to the Copenhagen Interpretation, for obvious reasons.”—

It’s that einstein and bohr produced descriptions not causalities and justified them, without providing the classical (constructive) definition. See hilbert’s criticism of Einstein upon publication.

—“I’m genuinely at a loss as to what it might be referring to. If anything is “reforming” physics today it is the Bayesian revolution, and if anyone “completed” Descarte’s algebraization of geometry it was Clifford. “—

Yes on the bayesian revolution. That doesn’t change the original question of why all these people saw similar problems in similar fields.

For example, why don’t we teach mathematics in operational prose – it would lose most of the frication in learning it.

—-“So all these claims read like they were written by someone who knows nothing about the history of modern science, but is both desperate to impose their own agenda on it, and hopeful that if they throw enough big names around they will impress the ignorant sufficiently to get by. Which I guess works. Maybe I should do more of it.”—

These claims read like someone who worked on solving the problem in social science – first in economics, then in law, then in psychology and sociology.

Which is a far harder problem than you would imagine, or someone would have done it before I did.

Although, in hindsight you can see that had Babbage not gotten lost in his gears, and a Turing come earlier, then Hayek would have solved the problem (I think). Chomsky was channeling Turing, and cognitive science (if it still exists in that form) has reduced our understanding to Turings.

So you are welcome to dance with me on these subjects if you wish but it’s extremely unlikely that I err.

And the reason for these chit chats is like practicing any sport, and that is to continuously improve my technique in communicating the great intellectual failure of the twentieth century that terminate Germany’s second scientific revolution, and as a consequence, resulted in a twentieth that advanced rapidly in technology, and slowly in physical science because of that technology, but that failed to progress much beyond the 1930’s, and failed entirely in the social sciences – reversing the gains of the century before.

All because of a single error: re-platonization.

Cheers