THE IMMORALITY AND UN-NECESSITY OF MATHEMATICAL PLATONISM (I’m getting closer. F

THE IMMORALITY AND UN-NECESSITY OF MATHEMATICAL PLATONISM

(I’m getting closer. From a post elsewhere. And, yes. ‘unnecessity’ is a word. Really. I checked.) 🙂

My argument, is that of mathematics can be stated operationally, and non-platonically, without negative externality, and that mathematicians have tragically produced the new mysticism in postmodernism for purely utilitarian and self interested reasons.

Can we create a “standard of truth”? In other words, can two or more of the theories of truth be organized such that one is more narrowly constrained and more parsimonious than the other? I think that correspondence theory of truth is pretty much the accepted practice, while deflationary and formal theories are adaptations to the needs of particular problems. That And that pluralistic theory attempts to compensate for these differences.

We can measure truth on two axis. The first is completeness of correspondence: it’s parsimony and explanatory power. And the second is the presence and severity of negative externalities. That means that a utilitarian standard of truth is a convenience and a necessary standard of truth is not. And it means that a necessary standard of truth that produces negative externalities is unavoidable and moral and a pragmatic standard of truth is both avoidable and immoral. Morality being a higher standard than disciplinary utility.

If you read the background on intuitionist mathematics, then that’s enough. And I don’t have to repeat it here. I think that ‘defining truth’ independent of correspondence is a non sequitur, and is conveniently circular use of the term ‘truth’. Internal consistency is not equal to external correspondence. Nor is it immune from criticism. I think if you read, even just the wiki article on the different forms of truth, including the difference between Formal (linguistic) and Substantive (correspondence) theories of truth, then that’s enough, and I don’t need to repeat it here. I think it’s not difficult to grasp that the different theories of truth have different standards – certainly intuitionist has a higher standard than classical. I think it’s not difficult to grasp that math has a lower standard than science. I think that it’s not difficult to grasp that the standards in classical mathematics are utilitarian. And I think it’s not difficult to grasp that utilitarian actions, if they produce externalities, allow us to criticize that utility. And to demand change if necessary. For example: free speech is one thing, but shouting fire in a theater is another. And while justifying and spreading postmodernism, is less immediate, it is more consequential.

I have not taken it on myself to play Wittgenstein’s game. I am not sure I am up to it. But I believe I can attack the mathematician’s justification of the logic of sets well enough to put the blame for postmodernism on the people within the discipline. And I can denounce their motives. I may be wrong. But I think I can do it. At least. I can do it well enough.

MARGINAL INDIFFERENCE is the only criteria for performative truth that I know of that is universally applicable in all circumstances.

This set of criteria satisfies the requirements of even the PLURALIST theory of truth. It allows us to use correspondence, marginal indifference, and externalities as the criteria of truth, without the need to resort to the ‘religion’ and ‘theology’ of platonism, and the external consequences of teaching generations of students a new theology that is dependent upon magic.