Author: Curt Doolittle

  • 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

  • The Necessary Properties of Economic Cooperation

    (draft of the correction of a priorism in economics, politics and ethics.) (important) Exchanges are unique. Every one. Marginalism alone renders all exchanges unique – even before we consider the uneven distribution of resources and ability, and the vagaries of nature, and the shifting wants and signals of human beings. As such, each exchange is unique, and even aggregate measures of inputs, operations and outputs in similar exchanges are dependent upon Patterns of Sustainable Specialization and Trade; which while sticky, are no guarantee of future exchanges under similar conditions. Constancy is an illusion. Businesses continuously adjust to conditions. So, no relations are constant in economics, even if in the aggregate, in short time periods, they appear so. If no relations are constant in economics, that means that we cannot organize production on the assumption of constant relations. This criticism stands alone, even prior to either the problem of calculation without money and prices, or the problem of incentives independent of rewards. However, we cannot organize any form of production under the assumption of constant relations without the incentives of multitudinous individuals to produce. This is the correct criticism of the socialist method of production. 1) calculation 2) inconstancy of relations 3) impossibility of organization 4) impossibility of incentives. The reason capitalists and executives of all kinds cost more than labor and are rewarded more than labor, is because labor has little to no value in production; and what value it has in production, constantly decreases with mechanization. So, the problem remains how to organize labor whether human, computational or mechanical. And while we might argue that middle management has very little value in the organization of labor, organizing the production of goods using labor, using prices and payments as rules, limits and incentives, is the highest contribution to the value of the goods, since the alignment of incentives – what we call ‘execution’ : organizing humans into production – is the art. And that is the scarcity that the market rewards. THE PROBLEM OF THE A PRIORI ARGUMENT If there are no constant relations in economics, but mathematics is the logic of constant relations, and further we attempt to use mathematics to justify intervention in the market for goods and services, then doing is logically impossible. The logical of constant relations, entirely dependent upon constant categories, cannot be used to describe economic conditions and apply them to the future. All we can do with mathematics is mine the recent data for descriptions of what has happened in the existing patterns of sustainable specialization and trade. So, if the socialist method of production was impossible, and measurement of the economy at all but the aggregate level is impossible, and measurement at the aggregate level does not capture changes in human, social and moral capital, then it becomes very difficult to suggest that governments can do much except (a) limited trade policy, (b) limited industrial policy, and (c) limited education and health policy (d) defend the rule of law and the common law (e) provide a means for the resolution of disputes. Thus, the prior generations argued that we must both not supplant the market means of dynamically organizing unique instances of production, nor interfere with it, and that we may only rely upon deduction and guesswork, and simply leave the market alone. However, this is either mistaken – or it is ill said. We can deduce almost nothing of consequence from human action. First, we can however, TEST any set of statements to determine whether they are rational and what incentives that they produce. But we cannot deduce much of anything at all – we can only test statements and hypotheses to determine likely human action. Second, when we understand that the problem of production is not labor, nor resources, but ORGANIZING production, what we can do is increasingly expand the means by which groups can cooperate on disparate means. The most effective way to assist groups in cooperating on means, even if they have disparate or even irreconcilable ends, which we cannot choose between because of the inability to forecast into a kaleidic future, other than value inferences we obtain from existing patterns of specialization and trade, is to suppress all risks OTHER than those of forecasting. Namely, the suppression of ‘discounts’. Then more discounts we suppress, the more human action that must be pressed into the market for goods and services, entirely upon the price, quality and distribution of those goods in time. (And independent of schemes.) So, if we understand that the production we organize, is the ability for others to frictionlessly organize production, in a world of constant invention and change, it is not entirely true that we can take little action. It is not the production of goods and services that we assist in producing with our governments, but it is the rules by which we dynamically organize production by the suppression of all discounts, everywhere, such than the only possible actions that remain, are to take risks on one’s forecast of the future within one’s patterns of specialization and trade. RATHER THAN THE A PRIORI ERROR – WE STATE THIS INSTEAD: Economics then, consists of: The near universal human ability to test rationality of incentives. The near universal human desire to seek discounts. The use of organized violence to suppress all discounts. The resulting pressure of all human action into the market. The construction of institutions to suppress discounting. The use of empirical measures to gain short term insight into the patterns of trade. The use of such information to inform participants in the ongoing adjustment of such patterns. Institutions required are: 1) Articulated Property Rights and Obligations. 2) The common law. 3) An independent Judiciary. 4) Universal standing so that any individual can seek restitution from any other individual for taking discounts, no matter what the accused’s function in society. 5) A body of people with the ability to construct contracts on behalf of larger groups, to produce goods that the market cannot organize to produce because of arbitrariness of the choices, or the openness of such contractual investments to free riding, privatization, and socialization or other discounts. 6) A means for the collection of dividends and choosing between the expenditure on further investments and distribution of proceeds to shareholders. We do not need much government. What government we do need, need not be a monopoly. What investments we need need not be decided by majority rule – a monopoly. And those services and goods we need, need not be provided by a monopoly bureaucracy. Even if it may be true that the INITIAL CONSTRUCTION of property rights requires the imposition of a monopoly of those rights, and a total prohibition on discounts, that is the limit of such a monopoly. Which is why corporations of separate interests in creating such a system is superior to monopoly of interests in creating such a system, since no member of such a polycentric order would tolerate the usurpation of his rights by another. Such a government is a government of unbreakable rules which we call ‘laws’, not a government of people with capacity for decision making, or coercion, or the ability to make laws. And our defense against that monopoly government and all forms of abuse, is the training of a near-priesthood called judges who adjudicate differences according to private property rights, and the voluntary agreements that we enter into, and the prohibitions against free riding on the goods produced by those agreements we chose NOT to enter into. And to construct as such, that those judges possess only the incentives to use those laws in the fulfillment of their roles. We can reduce all of this to the simple assertion, that no man can know the future sufficiently to force others to obey his direction on the use of their minds, bodies, time and property. However, it is quite possible for each of us to judge incentives and for men with training to judge whether property rights were respected or not. That is all we need.

  • The Necessary Properties of Economic Cooperation

    (draft of the correction of a priorism in economics, politics and ethics.) (important) Exchanges are unique. Every one. Marginalism alone renders all exchanges unique – even before we consider the uneven distribution of resources and ability, and the vagaries of nature, and the shifting wants and signals of human beings. As such, each exchange is unique, and even aggregate measures of inputs, operations and outputs in similar exchanges are dependent upon Patterns of Sustainable Specialization and Trade; which while sticky, are no guarantee of future exchanges under similar conditions. Constancy is an illusion. Businesses continuously adjust to conditions. So, no relations are constant in economics, even if in the aggregate, in short time periods, they appear so. If no relations are constant in economics, that means that we cannot organize production on the assumption of constant relations. This criticism stands alone, even prior to either the problem of calculation without money and prices, or the problem of incentives independent of rewards. However, we cannot organize any form of production under the assumption of constant relations without the incentives of multitudinous individuals to produce. This is the correct criticism of the socialist method of production. 1) calculation 2) inconstancy of relations 3) impossibility of organization 4) impossibility of incentives. The reason capitalists and executives of all kinds cost more than labor and are rewarded more than labor, is because labor has little to no value in production; and what value it has in production, constantly decreases with mechanization. So, the problem remains how to organize labor whether human, computational or mechanical. And while we might argue that middle management has very little value in the organization of labor, organizing the production of goods using labor, using prices and payments as rules, limits and incentives, is the highest contribution to the value of the goods, since the alignment of incentives – what we call ‘execution’ : organizing humans into production – is the art. And that is the scarcity that the market rewards. THE PROBLEM OF THE A PRIORI ARGUMENT If there are no constant relations in economics, but mathematics is the logic of constant relations, and further we attempt to use mathematics to justify intervention in the market for goods and services, then doing is logically impossible. The logical of constant relations, entirely dependent upon constant categories, cannot be used to describe economic conditions and apply them to the future. All we can do with mathematics is mine the recent data for descriptions of what has happened in the existing patterns of sustainable specialization and trade. So, if the socialist method of production was impossible, and measurement of the economy at all but the aggregate level is impossible, and measurement at the aggregate level does not capture changes in human, social and moral capital, then it becomes very difficult to suggest that governments can do much except (a) limited trade policy, (b) limited industrial policy, and (c) limited education and health policy (d) defend the rule of law and the common law (e) provide a means for the resolution of disputes. Thus, the prior generations argued that we must both not supplant the market means of dynamically organizing unique instances of production, nor interfere with it, and that we may only rely upon deduction and guesswork, and simply leave the market alone. However, this is either mistaken – or it is ill said. We can deduce almost nothing of consequence from human action. First, we can however, TEST any set of statements to determine whether they are rational and what incentives that they produce. But we cannot deduce much of anything at all – we can only test statements and hypotheses to determine likely human action. Second, when we understand that the problem of production is not labor, nor resources, but ORGANIZING production, what we can do is increasingly expand the means by which groups can cooperate on disparate means. The most effective way to assist groups in cooperating on means, even if they have disparate or even irreconcilable ends, which we cannot choose between because of the inability to forecast into a kaleidic future, other than value inferences we obtain from existing patterns of specialization and trade, is to suppress all risks OTHER than those of forecasting. Namely, the suppression of ‘discounts’. Then more discounts we suppress, the more human action that must be pressed into the market for goods and services, entirely upon the price, quality and distribution of those goods in time. (And independent of schemes.) So, if we understand that the production we organize, is the ability for others to frictionlessly organize production, in a world of constant invention and change, it is not entirely true that we can take little action. It is not the production of goods and services that we assist in producing with our governments, but it is the rules by which we dynamically organize production by the suppression of all discounts, everywhere, such than the only possible actions that remain, are to take risks on one’s forecast of the future within one’s patterns of specialization and trade. RATHER THAN THE A PRIORI ERROR – WE STATE THIS INSTEAD: Economics then, consists of: The near universal human ability to test rationality of incentives. The near universal human desire to seek discounts. The use of organized violence to suppress all discounts. The resulting pressure of all human action into the market. The construction of institutions to suppress discounting. The use of empirical measures to gain short term insight into the patterns of trade. The use of such information to inform participants in the ongoing adjustment of such patterns. Institutions required are: 1) Articulated Property Rights and Obligations. 2) The common law. 3) An independent Judiciary. 4) Universal standing so that any individual can seek restitution from any other individual for taking discounts, no matter what the accused’s function in society. 5) A body of people with the ability to construct contracts on behalf of larger groups, to produce goods that the market cannot organize to produce because of arbitrariness of the choices, or the openness of such contractual investments to free riding, privatization, and socialization or other discounts. 6) A means for the collection of dividends and choosing between the expenditure on further investments and distribution of proceeds to shareholders. We do not need much government. What government we do need, need not be a monopoly. What investments we need need not be decided by majority rule – a monopoly. And those services and goods we need, need not be provided by a monopoly bureaucracy. Even if it may be true that the INITIAL CONSTRUCTION of property rights requires the imposition of a monopoly of those rights, and a total prohibition on discounts, that is the limit of such a monopoly. Which is why corporations of separate interests in creating such a system is superior to monopoly of interests in creating such a system, since no member of such a polycentric order would tolerate the usurpation of his rights by another. Such a government is a government of unbreakable rules which we call ‘laws’, not a government of people with capacity for decision making, or coercion, or the ability to make laws. And our defense against that monopoly government and all forms of abuse, is the training of a near-priesthood called judges who adjudicate differences according to private property rights, and the voluntary agreements that we enter into, and the prohibitions against free riding on the goods produced by those agreements we chose NOT to enter into. And to construct as such, that those judges possess only the incentives to use those laws in the fulfillment of their roles. We can reduce all of this to the simple assertion, that no man can know the future sufficiently to force others to obey his direction on the use of their minds, bodies, time and property. However, it is quite possible for each of us to judge incentives and for men with training to judge whether property rights were respected or not. That is all we need.

  • TAXONOMIC SCHEME I was designing game engines back in the early 80’s using the s

    http://www.theatlantic.com/technology/archive/2014/01/how-netflix-reverse-engineered-hollywood/282679/NETFLIX’S TAXONOMIC SCHEME

    I was designing game engines back in the early 80’s using the same technology as were others. Obvious games like NetHack (80’s), Diablo (90’s), Borderlands (00’s) and so called ‘loot games’ use similar techniques.

    The insight that this provides is ‘serendipity’ : which is why loot games and netflix and an antique mall are interesting: the chance of finding something different.

    This goes against the apple-era inspired argument for simplicity. Simplicity is good when you want to lower access costs. But when you want to reward the user for exploring, then favoring complexity and serendipity are smarter than simplicity.

    Like the opposite sex, If it is easily understood, it’s boring.


    Source date (UTC): 2014-01-03 18:20:00 UTC

  • Curt Doolittle shared a photo

    Curt Doolittle shared a photo.


    Source date (UTC): 2014-01-03 16:52:00 UTC

  • Untitled

    http://t.co/Yb1X7XNAip


    Source date (UTC): 2014-01-03 16:49:00 UTC

  • Am I just arguing for a higher and stricter standard of truth? I think so. Opera

    Am I just arguing for a higher and stricter standard of truth? I think so.

    Operationalism in cooperation

    Operationalism in science (causality)

    Operationalism in mathematics (relations)

    Operationalism in numbers (identities)

    Operationalism in logic (words)


    Source date (UTC): 2014-01-03 16:06:00 UTC

  • 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

  • “Information is that which is sufficient to cause a change in state.”

    “Information is that which is sufficient to cause a change in state.”


    Source date (UTC): 2014-01-03 13:23:00 UTC