Curt Doolittle

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  • HISTORY OF MATHEMATICS? Need a mathematical historian. Boole onward, through Hil

    HISTORY OF MATHEMATICS?

    Need a mathematical historian. Boole onward, through Hilbert and Broewer.

    When Boole, Frege, Peano Russell, Hilbert et al, developed boolean algebra and set theory, cumulating in ZFC+AC, theory did they understand WHY their solution worked, but was now disconnected from reality, correspondence, and truth?

    I can’t find anything but it’s got to be there. It looks like it starts with Frege? How did they categorize the problem?

    Is this one of those things like property rights, that we didn’t understand the cause, but talk about incessantly?

    Or is the reason that boolean (binary), and sets, solve the problem of precision in context?

    Someone smarter than I am had to solve this already….. But if not Broewer, who?

    Source date (UTC): 2014-01-04 16:27:00 UTC

  • POLITICS: LEADERS VERSUS JUDGES: WHY? Does one want a leader or a judge? What is

    POLITICS: LEADERS VERSUS JUDGES: WHY?

    Does one want a leader or a judge? What is the difference between a leader and a judge? Why is it that some people desire leaders, and some people desire judges? Why is it that nearly all people desire leaders and so few people desire judges?

    Leaders enact change, judges resolve differences. Why should a group with leaders implement political change? Why should not any individual appeal to judges for the restitution of property?

    Aristocracy relies upon judges.

    Source date (UTC): 2014-01-04 03:19:00 UTC

  • Does The Separation Between Mathematical Truth And Mathematical Proof Necessarily Imply A Platonist View Of Mathematics?

    Here is the debate as I understand it:

    (And forgive me if I mix language from multiple domains please.)

    The Intuitionists argue that all mathematics can be stated operationally, and as such, for all intents and purposes, all mathematical symbols other than the glyphs we use to name the natural numbers, are nothing more than names for functions (sets of operations).

    However, the intuitionist (‘recursive’) solution causes a problem in that the excluded middle is impermissible – but without it, much of mathematics because much more difficult, and harder to prove. So with that constraint on the excluded middle, the higher truth requirement of computational and constructivist, intuitionist logic has been deemed not useful for departmental mathematicians.

    So under the ZFC+AC and ‘spontaneous platonic imaginary’ creation of sets, we obtain the ability to do mathematics that include both double negation and the excluded middle. 

    This ‘trick’ separates Pure math in one discipline and  Scientific math, Computational mathematics, and philosophical realism into different discipline, each with different standards of truth. In fact, technically speaking, mathematics is absent truth (correspondence) and relies entirely on proof. ie: there are no true statements in pure mathematics.

    IF ANYONE  KNOWS —>> It does not appear that Brouwer or any of his followers understood why their method failed and the set method succeeded.  But even if they failed, I am trying to figure out if the Formalists understood their ‘hack’ and why it worked. 

    And lastly, if anyone at all understood how Intuitionist, constructivist, and computational logic could be improved to solve the problem of retaining correspondence (truth) while also retaining the excluded middle (even if it was burdensome). 

    Someone smarter than I am has got to have addressed this problem already although for the life of me I can’t find anyone who has.

    https://www.quora.com/Does-the-separation-between-mathematical-truth-and-mathematical-proof-necessarily-imply-a-Platonist-view-of-mathematics

  • Does The Separation Between Mathematical Truth And Mathematical Proof Necessarily Imply A Platonist View Of Mathematics?

    Here is the debate as I understand it:

    (And forgive me if I mix language from multiple domains please.)

    The Intuitionists argue that all mathematics can be stated operationally, and as such, for all intents and purposes, all mathematical symbols other than the glyphs we use to name the natural numbers, are nothing more than names for functions (sets of operations).

    However, the intuitionist (‘recursive’) solution causes a problem in that the excluded middle is impermissible – but without it, much of mathematics because much more difficult, and harder to prove. So with that constraint on the excluded middle, the higher truth requirement of computational and constructivist, intuitionist logic has been deemed not useful for departmental mathematicians.

    So under the ZFC+AC and ‘spontaneous platonic imaginary’ creation of sets, we obtain the ability to do mathematics that include both double negation and the excluded middle. 

    This ‘trick’ separates Pure math in one discipline and  Scientific math, Computational mathematics, and philosophical realism into different discipline, each with different standards of truth. In fact, technically speaking, mathematics is absent truth (correspondence) and relies entirely on proof. ie: there are no true statements in pure mathematics.

    IF ANYONE  KNOWS —>> It does not appear that Brouwer or any of his followers understood why their method failed and the set method succeeded.  But even if they failed, I am trying to figure out if the Formalists understood their ‘hack’ and why it worked. 

    And lastly, if anyone at all understood how Intuitionist, constructivist, and computational logic could be improved to solve the problem of retaining correspondence (truth) while also retaining the excluded middle (even if it was burdensome). 

    Someone smarter than I am has got to have addressed this problem already although for the life of me I can’t find anyone who has.

    https://www.quora.com/Does-the-separation-between-mathematical-truth-and-mathematical-proof-necessarily-imply-a-Platonist-view-of-mathematics

  • CAN I GET HELP WITH HISTORY OF MATHEMATICAL PHILOSOPHY? (edited) (request for he

    CAN I GET HELP WITH HISTORY OF MATHEMATICAL PHILOSOPHY?

    (edited) (request for help) (foundations of mathematics)

    Need a mathematical historian. Someone very well versed in teaching theory.

    I am going to say this badly because I don’t know the correct way to ask it:

    0) the classical construction of mathematics is an operational and (identity, counting and measurement) and analog one. It is the practical uniting of counting, measurement, geometry, and algebraic logic (deduction).

    1) The ZFC+AC argument (the set argument) converts the practice of math from one of dimensions (space and analog) to one of sets (binary). This allows the excluded middle. It is a very artful way of solving the problem, by simply returning to the very basics of the origination of counting. But the set solution is achieved by removing scale and therefore contextual utility from the calculation, leaving us with no means of external reference for choice of precision. I see this solution as useful, but a fabrication.. a ‘trick’. Whereas, one could just say ‘precision of N’, and increase or decrease that precision as needed. (Although this approach would require tagging variables or numbers I think, or maybe prevent us from reducing ratios including real numbers.) The solution to the problem of scale and context (analog representation) by converting to binary (set membership) representation is actually very interesting one. The question is, was it knowingly made, or what this solution achieved without understanding that the problem of context and scale was solved by effectively reducing math from analog (related to the real world scale) and binary (independent of real world scale). I can’t figure it out from the literature.

    2) The constructivist argument relies on a binary proof. (“Russian Recursive Mathematics”) This method disallows the excluded middle. (and double negation). It is a higher standard of proof. However, I don’t understand why we could not construct a syntax for the explicit preservation of scale (correspondence with whatever context we have in mind) and thereby retain correspondence as well as the excluded middle. (I am not sure about double negation. I haven’t thought it through yet.)

    3) Computational mathematics is both operational and binary.

    But why aren’t these three methods a spectrum – just like description, deduction, induction, abduction, guessing and intuitive choice? I mean, at the early end of the spectrum (0, 1) we require deduction, and at the later end of the spectrum (2,3) we require computability. The reason we have a problem with (1) and (2) is because they give upon correspondence (context). And with that we lose the use of context for determining the precision of a calculation.

    Deduction in context is always easier because we have information with which to make a choice (precision). But outside of context we cannot use external information, so we must rely on a binary choice (or decidability). Deduction is a very different problem from computation.

    Or, can we say then, that the foundations of mathematics have been wrongly divorced from correspondence and context by cantor through ZFC? When we could just say that binary is a universal substitute for arbitrary precision? I mean, that’s the functional equivalent of it?

    I need a frame of reference within the language of mathematics to talk about this issue and I don’t know how to get to it. I don’t even know how to ask this question any better than this?

    Was the solution to the foundations of math, culminating in ZFC+AC, understood as providing a solution to creating independence from the problem of correspondence and scale at the expense of ‘truth’ while retaining ‘proof’ and internal consistency?

    Or stated this way: Did mathematical philosophers understand that they were divorcing ‘departmental mathematics’ from physics (cause and correspondence) and logic (truth) by adopting ZFC+AC, thereby creating a study of pure relations independent of context?

    I have worked through both sides of the debate to the best of my ability.

    Why can the reason that sets work – reduction to binary in order to escape the burden of retaining context – simply be stated openly? I mean, if all it does is render scale infinitely variable, then that explains why ZFC works, and all these platonic devices are necessary: they create deducibility and computability. And it’s not ‘wrong’ per se, in the sense that it doesn’t produce correct calculations independent of context, or rather, independent of SCALE and therefore independent of correspondence. But it does sort of render mathematics platonic and almost magical rather than computational and rational.

    In that sense, we get to logically state WHY these methods work and when and when not they are applicable. The excluded middle is a problem of scale (analog, and correspondent values).

    In the end, the set method is useful because is just SO MUCH LESS BURDENSOME, but that’s all.

    But still, teaching people operational mathematics, and higher criteria of proof under constructive math, and then explicitly stating that we can move to sets at the expense of correspondence in order to obtain the ability to practice double negation and the excluded middle is not a problem, it’s a tool not a truth.

    I don’t need to solve this problem for my work. But since math is the gold standard, and contains this particularly burdensome problem, if I can describe the consequences in mathematics of non-operational language leading to platonism, I can explain why non-operational language in ethics, likewise leads to platonism.

    Source date (UTC): 2014-01-03 16:05:00 UTC

  • I don’t know what Arnold Kling is doing these days. How would data look differen

    I don’t know what Arnold Kling is doing these days.

    How would data look differently to economists if all accounting software, everywhere, reported sales data from A to B, whenever it was posted, to an independent database using a (large) generic chart of accounts, so that we could measure PSST at that level, rather than the macro level?

    Policy is enacted upon what can be measured.

    I suspect that we would just see even more intervention. On the other hand, the impact of all the intervention would be more visible. And that our counter -arguments would be much better.

    household data is nonsense. Macro data is all but useless. PSST is actionable.

    Source date (UTC): 2014-01-02 11:04:00 UTC

  • If a man must pay for a child at great personal cost to himself, and a woman and

    If a man must pay for a child at great personal cost to himself, and a woman and the child have a right to the standard of living prior to divorce, and he cannot export this expense to the state, then why does a woman have the right to export the cost of her single motherhood to the state?

    A man cannot chose whether or not he is to father a child. Women are no longer economic victims, but have both saturated their distribution in the economy, and forced men out of the economy such that more women are both voters and workers than are men. So we cannot say that women are disadvantaged. Just the opposite. It is true that men dominate the upper margins, but men dominate nowhere else in society.

    This is an inequality of justice. A double standard. Given the dissolution of the family, and our emphasis on individualism, it is only jus that men export their children’s cost to the state just as women export their children’s cost to the state. No?

    I don’t really see any moral case for child or spousal support. There isnt any evidence that it’s necessary. It is disproportionally more punitive to men, who have shorter working careers, and endure disproportionate economic risk.

    I mean, if we have universal socialized health coverage, why not universal socialized child coverage. Why not a minimum guaranteed income?

    In that world, men can contribute to a household or not, but they carry their productivity with them. So any woman whose nest he shares, gains from his productivity, but loses at his departure. His income is a luxury. A perk. A benefit, not a necessity.

    The point of my argument is that property rights in a world where the individual, not the family, is the rule, and where all costs are highly socialized, will be one in which it will be increasingly difficult for us to treat evolutionary norms and morals dependent upon previous economic political and social means of production and reproduction, as criteria for predicting human behavior.

    I wouldn’t mind a world where women could not become vampires on males, and where all rights were in fact, equal.

    I also realize that this is the only way to restore male-female relations. But I suspect it is too late. And that the more likely development will be a caste system like we see in the northeast, with white/jewish/asian elites and mixed and brown everyone else – with token representatives of those groups permitted into the upper castes as a means of preserving the illusion of meritocracy.

    Source date (UTC): 2013-12-30 15:13:00 UTC

  • Question: Is feeling = doing? Or is feeling != doing? (Where doing=acting)

    Question: Is feeling = doing? Or is feeling != doing? (Where doing=acting)

    Source date (UTC): 2013-12-28 18:05:00 UTC

  • ON PRAXEOLOGY AS ADVOCACY OR SCIENCE Why would we suppose that a science of huma

    ON PRAXEOLOGY AS ADVOCACY OR SCIENCE

    Why would we suppose that a science of human action would advocate liberty? Or, would the science of human action, not advocate liberty, but simply EXPLAIN all possible human incentives, and the means of cooperation possible within those, whether those incentives produced liberty or not?

    (Riddle on that one a bit.)

    Source date (UTC): 2013-12-27 14:53:00 UTC

  • Question. Is Praxeology a science, by which I mean a methodology for the purpose

    Question.

    Is Praxeology a science, by which I mean a methodology for the purpose of extending and testing our reason and perception by reducing that which we cannot sense or perceive to analogies to experience. Or is Praxeology a form of logic, like mathematics, or reason? And, is praxeology complete?

    Source date (UTC): 2013-12-23 20:39:00 UTC