Category: Epistemology and Method

VERY CLOSE TO PUTTING ANOTHER STAKE IN POSTMODERNISM: MATHEMATICAL PLATONISM AS ‘FRAUD’.

(Excerpt From A Very Very Very long thread)

Hopefully some people will begin to gasp the difference between morality and property in Propertarianism as I’ve defined them, versus the way Rothbard defined morality and property in libertarianism.

I think that I should probably write 2500 words on how Rothbard’s argument was sufficient for socialism, but insufficient for Postmodernism. That way I don’t have to attack rothbard as hard as I do now.

The necessity of operational language is something that I understood was necessary in politics and law. But it was only over the past year or two that I understood that it is necessary for avoiding fraud.

I still cannot solve the point of demarcation between literature and it’s appeals for empathy, or Heidegger’s confusing mixture of literature and reason, at the expense of causality. I think I know where it is. But I’ll have to work on it.

-Curt

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From: William

@Curt Doolittle says: “So I would argue, why not just admit that these are utilities and contrivances, not operational truths, and just go on your merry way?”

I don’t have the vocabulary to express what I think in response to the above. But, I will try to give a stab to convey my thoughts.

First, it appears to me that you are using “utilities”, ” contrivances”, etc in a derogatory meaning, but “operational” in a favorable meaning. This is similar to attaching a derogatory meaning to “liberal”. I will leave it at this without going into it any further.

Second, I have a book “A Course In Constructive Algebra” by Ray Mines, Fred Richman and Wim Ruitenburg. The authors don’t accept the principle of excluded middle and they require elements of sets to be constructable. I have no problem reading it and following the proofs. I realize that I am working in a different context. It is just as good as if I worked in the context of ZFC with allowing excluded middle. In other words, I am not converted over to their method and give up standard ZFC. I do both.

Third, I have no qualms about working out a problem in Newtonian physics (like calculating the moment of inertia of a spinning top). I don’t know if you would say I am doing “operational truths” because the operations are constructive, or if you would say I an not doing “operational truths” because the result is not true because Newtonian physics is not true.

Fourth, I suspect that in the 21th century there are still philosophers who support the framework of mathematicians who do standard ZFC theorem proving. That is, those mathematicians have not been abandoned by philosophers who try to justify, explain, etc what the mathematicians are doing. And there are other philosophers who support other different views, who have mathematicians following them to provide their ground to stand on. If these philosophers can’t agree among themselves, why do you want the mathematicians to choose just one of them. Are mathematicians a better judge of the various philosophical views than the philosophers themselves?

Fifth, I believe mathematicians would not have any qualms switching among the various mathematical foundations. Would a “utilitarian” philosopher be ok with writing a paper in the “platonic” viewpoint, and vice versa?

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From: Curt Doolittle

@William Hale

RE “Second”, “Fourth”, “Fifth”

I think we are still talking past each other. I’m fully appreciative of using multiple methodologies to solve problems. I’m fully appreciative of the fact that mathematicians, like a general staff, run theories – and that surprisingly often, some particular formula describes a useful natural process. The question is, do you understand that point of demarcation, or not. And do you claim that the standard of truth in deduction is equal to the standard of truth in construction. That the two standards are marginally indifferent is different from the two standards being identical. They aren’t. So then, there are statements that are necessarily true. And statements that are deductively true. IF we can claim there are many types of infinities but some are larger or smaller. Then perhaps we can claim their are many truths, but that some are more authoritative than others. if you claim that .999… is operationally equal to one, that is different from whether .999.. is deductively equal to one, or equal by fiat. But in a conflict over which statement is a more authoritative truth, the operational must be. Because it can be nothing else. And even this is not important to me. What is important is that the Russell/Cantor debate led to platonism. And platonism was adopted by postmodernists. Yet the more parsimonious answer was readily available.

RE: “Third”

I would say that newtonian physics is sufficiently precise for the calculations where it is sufficiently precise. This is all that needs to be said. Just like all scientific theories are open to revision, so are all formulae. Why mathematicians feel that they need to create Platonistic standards of truth when the matter is one of precision is … as far as I can tell… an artifact of the language of the Greeks, Bacon and Newton – religious language. Appeals to divine authority.

RE: “First”

I am raising a moral objection. Correct? Is then moral context not relevant? 🙂 But that said, I think that when one makes a truth claim about something that is in fact, utilitarian, it is… either immoral, ignorant, or dishonest.

In other words, do we get to act selfishly when it suits us?

WHY

What if all political language (law, regulation) was stated operationally, so that it was not open to interpretation? How would that change civic discourse?

Utterances are actions and all actions have consequences. Or, are we not responsible for our actions?

The basic argument is that, when making truth claims, scientific statements, stated operationally, are moral, and non scientific statements are immoral. It is very hard to commit fraud by operational argument. It is very easy to commit fraud by platonic argument. In fact – that is the entire purpose of it.

For example, money laundering. Money laundering is the process of removing causation. If mathematicians remove causality from their language, it is laundering as well (information loss). If I cannot launder money because it causes externalities, why can I launder causality in mathematics if it causes externalities?

Everything isn’t relative. 🙂 Truth is accurate description of causal relations. Everything else is ‘contrivance’. And the only reason for developing alternative forms is to say ‘we can get away with it’ and to raise it to the same level of legitimacy as truth. The same way that politicians use the word ‘law’ to give legitimacy to ‘command’. There is but one LAW of human cooperation. The rest is commands and punishments. And non-operational language, platonic language, meant to provide legitimacy, is in fact, a violation of that single law: theft. It is fraud by omission. Obtaining convenience and legitimacy by use of language that avoids causal relations. Mathematical platonism if argued as a truth claim, where that truth claim is also stated as equivalent to operational truth, is in fact, fraud.

This is, in fact, the source of the argument for postmodern thought: mathematics.

We may not HOLD each other accountable for our actions. But our actions have consequences that we are RESPONSIBLE for, whether we hold our selves accountable, or others hold us accountable for them. I am holding (or anticipating holding) mathematicians responsible for the consequences of their actions. (this is the theory I am testing via argument to make sure that I understand it.)

And operational language is the only truth. Everything else is an allegory to it. We can speak truthfully to the best of our knowledge. We can write theories that are testable. But we can make no truth claim that is not operationally stated. Because platonism is the laundry of causal relations.

Mathematics has reinvented mysticism – appeals to platonism to justify arguments. I don’t care about math as a discipline. It’s not terribly important. I care about society. i care about the fact that in democracy, debates have consequences. And the moral commons is an asset we must protect like any other asset from the privatization of wins and the socialization of losses.

So when I say, operationally .999… cannot exist, and even if it could could not equal 1, because it never CAN equal one. That is a true statement. Or, given that the the correct term is ‘substitution’, that .999.. in any context we can imagine, can be substituted for 1. Or if you were to say that … is a a notation for that which we cannot operationally state because of the limits of our number system. Or if you were to say that because in all real world applications, precision is contextually dependent, and infinity allows us to represent contextual precision. Or if you say you say deductively, they are equivalent, if not equal. Or if you say that in practice, the fields of irrational numbers tell us what geometric calculations will be problematic or easy. Or if you say that in practice, fields of (rings of) complex numbers, actually do represent combinations of charges we observe at the subatomic level. (there are still more I can think of). Then all of those are valid statements. They are true statements. But under no conditions are platonic arguments ‘true’. That is a terribly deceptive game that is the source of moral ‘relevance’ in our society.

Mathematical ‘truth’, not stated operationally, is a contrivance, which we use to give status and legitimacy to pragmatic utilitarian actions just as governments give legitimacy to commands by calling them laws. In practice this does not affect our calculations due to the marginal indifference of contextual precision. Symbolic substitution, at marginally indifferent precision does not affect our calculations as well.

There is absolutely no reason that mathematical language must be stated platonically other than status seeking, and legitimacy seeking.

If questioned, it is quite alright to say, ‘we do these things because, in our craft it is easier’ that is different from saying, ‘we do these things because they are true’. The first is a pleading for understanding given the high cost of operational language. The second is an act of fraud.

– cheers. 🙂

(PS: I suspect that I may have given you the vocabulary to express your thoughts.) 🙂