Curt Doolittle

Category: Epistemology and Method

  • IGNORANCE OF MATHEMATICAL PHILOSOPHY – CONTINUED I’ve been working my way throug

    http://plato.stanford.edu/entries/naturalism-mathematics/LESS IGNORANCE OF MATHEMATICAL PHILOSOPHY – CONTINUED

    I’ve been working my way through this reading list and it turns out that plenty of people have written on the subject, but it’s not clear that they understand the underlying problem of correspondence (even if they use the term ‘external authority’). And the best author in the space is incorrect, and the matter apparently isnt settled.

    So, now it’s off to articulate the solution to this particular problem, even in mathematics. That will sort of anchor the legitimacy of my argument in favor of operational language in all disciplines.

    Sigh.

    Roman is pushing me to publish and not to spend time outside of Politics and Ethics. But my instinct tells me that my argument (calculation) seems to invite the solution to unifying the ‘logics’ and, as I’d hoped, eliminating platonism as well as obscurantism.

    If in fact, the innovations that I’m adding to political ethics are largely in the realm of requiring calculability and operational language, then it would seem to me that I should also ground operational language and calculability.

    Source date (UTC): 2014-01-08 04:16:00 UTC

  • ACADEMIC PHILOSOPHY – EVENTUALLY, IT WILL LOOK LIKE THE SCIENTIFIC METHOD Academ

    ACADEMIC PHILOSOPHY – EVENTUALLY, IT WILL LOOK LIKE THE SCIENTIFIC METHOD

    Academic philosophy is pretty much a zombie profession. It’s actually humorous to read how bad the papers are. Every few months I just grab a dozen or two and read through them.

    And the consequences speak for themselves: the funding for philosophy departments, and administration’s tendency to group them in with religion has led to the progressive decline of departments.

    Conversely, economics and psychology together have pretty much taken over the social sciences. And that was probably a deterministic outcome, when late in the 19th century the analytical movement made the choice to try to make philosophy into a science, it was a pretty sizable bet that failed. And it was followed by a flurry of attempts to justify socialism in an effort to stay relevant. That failed too.

    It’s not that the study of philosophy has no value, it’s that except for very notable exceptions (Dennett) where philosophers are trying to integrate ethics and the product of scientific investigation, it’s pretty barren – like the study of medieval and ancient literature.

    **And given what I’ve learned from my own work, I’d argue that we can, within at most two generations, solve the problem of the logic of the social sciences. And when we do, I suspect that philosophy will, in practice, look not very much different from the scientific method, with each of the logical systems we have developed: language, logic, math, physics, and economics (cooperation), merely specializations for isolating one property of the universe or another, so that we are capable of reducing it to analogy to experience and therefore understanding it.**

    Source date (UTC): 2014-01-07 17:37:00 UTC

  • WERE THE CONSERVATIVES RIGHT ALL ALONG? (interesting) We cannot, like mathematic

    WERE THE CONSERVATIVES RIGHT ALL ALONG?

    (interesting)

    We cannot, like mathematicians tried to do, define something into existence. We can define rules of deduction, but not define something into existence. Truth consists of correspondence and cause, not definition. Definitions are our choice. Truth is not. That is the entire purpose of ‘truth’ – that which we cannot choose.

    So, if instead of some artificial scheme, we understand that PROPERTY is nothing but what remains, after we suppress all possible DISCOUNTS, by every means possible. Then, does that mean that the conservatives were right all along?

    That, since discounts, as a spectrum, are suppressible by a spectrum of actions which include the organized threat of violence, ostracization, boycott, reduction of opportunity, and the consequential limits on consumption, then the conservatives, correctly value NORMATIVE CONFORMITY TO SUPPRESSION OF DISCOUNTS, and that the model of property articulated by rothbard, taken as it was from the low trust society he was familiar with,

    In effect, Rothbard’s ethics are an attempt to preserve ‘cheating’ as a viable means of profiting from others, whereas conservative, aristocratic, ‘high trust’ ethics are an effort to suppress ALL cheating. Rothbard masks this cheating by stating that competition will suppress such cheating. But empirically, and praxeologically, this is demonstrably and logically false. So what are we left with no possible conclusion that either he committed a significant error or, that Rothbard’s ethics are an attempt, intentionally, to preserve cheating: which is precisely what the left correctly argues – albeit in their amateurish terms.

    The formation of a government, which is a monopoly that suppresses violence and theft, and then by taxation, suppresses free riding on the government’s suppression of violence, then, as a consequence, because of its monopoly, only displaces free riding with rents.

    The formal question remains the same, which is that rule of law, or liberty, is a prohibition on discretionary compulsion, but is only possible by the prohibition of all discounts. And the only possible means of both suppressing discounts, and preventing the conversion of free riding into rents, is to rely on competition for the suppression of these discounts.

    That is, I think, the fundamental equilibrial analysis of political order.

    The sequence is:

    1) Suppression of discounts results in property rights.

    2) Property rights lead to the division of labor, and prosperity.

    3) Property (capital) and prosperity lead to greater opportunity for discounts.

    4) The cost of suppressing discounts increases demand for specialized suppression.

    5) The specialized suppressing discounts leads to free riding (fee avoidance)

    6) The specialized suppression of free riding (taxation) leads to opportunity for rent seeking.

    7) Opportunity for rent seeking leads to bureaucracy.

    8) Bureaucracy leads to subjugation and expropriation.

    9) Expropriation leads to circumvention (Religiosity, black markets, tax evasion, nullification, secession and revolt and revolution)

    10 (fragmentation)

    The only solution is rule of law: no state, merely laws, and judges who resolve disputes. Governments must be local and under direct democracy. Everything else provided competing firms.

    CHEERS

    Source date (UTC): 2014-01-07 06:54:00 UTC

  • THOUGHTS ON TRUTH THE TWO QUESTIONS OF MATHEMATICAL PHILOSOPHY –“If you ask a p

    https://www.dpmms.cam.ac.uk/~wtg10/philosophy.htmlMORE THOUGHTS ON TRUTH

    THE TWO QUESTIONS OF MATHEMATICAL PHILOSOPHY

    –“If you ask a philosopher what the main problems are in the philosophy of mathematics, then the following two are likely to come up: what is the status of mathematical truth, and what is the nature of mathematical objects? That is, what gives mathematical statements their aura of infallibility, and what on earth are these statements about ?” —

    ON THE PAPER

    Nothing new or interesting. I still can’t figure out if the problem of what mathematicians consider ‘arbitrary precision’ is one that they are conscious of or not. (Correspondence and utility in context. )

    What I can tell you is that mathematicians do not define truth, that philosophers do. Conversely, the craft of math requires a language for the production of proofs that humans can manipulate symbolically. Just like we need language that humans can speak and use, not language which would be more ‘true’.

    However, if at some point we want to test whether our mathematics or our language is in fact ‘true’ – in that whatever content we construct corresponds to reality – we must be able to express it in operational language. If we cannot, then it is not in fact ‘true’. I can tell a story about a fantasy world with a certain form of gravity. I can write a proof using certain assumptions. However, these cannot correspond to reality, and therefore, can be consistent with their definitions (internally consistent) but they cannot ever be ‘true’ (correspondent).

    This is important otherwise truth has no meaning, and reality is indistinguishable from dream.

    More later.

    Source date (UTC): 2014-01-06 16:54:00 UTC

  • IN THIS STRANGE LITTLE BIT OF LANGUAGE, BROUWER PROVIDES THE ANSWER TO PLATONIST

    IN THIS STRANGE LITTLE BIT OF LANGUAGE, BROUWER PROVIDES THE ANSWER TO PLATONISTS.

    (emphasis mine)

    “…mathematics is an essentially languageless activity of the mind having its ***origin in the perception of a move of time.*** This perception of a move of time may be described as the falling apart of a life moment into two distinct things, one of which gives way to the other, but is retained by memory. If the twoity thus born is divested of all quality, it passes into the empty form of the common substratum of all twoities.” — Brouwer.

    Genius.

    NELSON’S CRITIQUE

    –“Since the advent of digital computers, attention has turned from effective methods — functions computable in principle – to feasible algorithms and programs. There is strong evidence that polynomial time functions provide the correct formalization of the intuitive notion of a feasible computation, and unlike the situation for recursive functions there is a purely syntactical characterization of polynomial time functions. I am convinced that intuitionism reformulated in this context will become a powerful practical method for constructing and verifying feasible algorithms, and that Kleene’s realization predicate will provide an incisive tool for

    analyzing problems concerning interactive programs.”– Nelson.

    https://web.math.princeton.edu/~nelson/papers/int.pdf

    CURT: These are different contracts, for utility not different truths.

    As far as I can tell, if it is not computable it is questionable. But I need to learn more.

    Source date (UTC): 2014-01-04 18:00:00 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

  • 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

  • ON CERTAINTY “Thou cannot be sufficiently certain of anything that you can use a

    ON CERTAINTY

    “Thou cannot be sufficiently certain of anything that you can use argument to demand my agreement. Thou canst only seek to obtain my consent by eliminating the possibility or desirability of my position in contrast to yours.”

    Source date (UTC): 2014-01-03 13:22:00 UTC

  • One of those interesting problems with ideation is that in intellectual discours

    One of those interesting problems with ideation is that in intellectual discourse we use the names of thinkers, their books (usually one idea), their quotes, and the inherited terminology from their works and the discussions of their works. Most of which, in philosophy, are reduced to ‘isms’.

    The problem of innovative argument then, can be solved as did all those philosophers who invent terms. Or it can be solved by altering the properties of those terms. Or it can be solved by rearranging the relationships of those terms. But in general, we are asked by convention to use extant terms.

    This does assist in comprehension, and accessibility and the effort to test any new theory. However, it also runs up against paradigmatic investment.

    Source date (UTC): 2014-01-03 11:06:00 UTC