Intuition in Mathematics and Physics: A Whiteheadian Approach

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This is just a quick shout-out to my friend and colleague, Ronny Desmet, for putting together the papers that were presented at the 2015 International Whitehead conference in the new book, Intuition in Mathematics and Physics: A Whiteheadian Approach, in which yours truly is a contributor. Intuition Mathematics

The articles within are from Section IV, Track 2 of the conference. The table of contents is not yet available at Amazon, so the contributions are as follows:

  1. Integral Philosophy – An Essay on Speculative Philosophy – Ronald Preston Phipps
  2. Reflection on Intuition, Physics, and Speculative Philosophy – Timothy E. Eastman
  3. Whitehead on Intuition – Implications for Science and Civilization – Farzad Mahootian
  4. Whitehead’s Notion of Intuitive Recognition – Ronny Desmet
  5. The Beauty of the Two-Color Sphere Problem – Ronny Desmet
  6. The Complementary Faces of Mathematical Beauty – Jean Paul van Bendegam and Ronny Desmet
  7. Creating a New Mathematics – Aran Gare
  8. Whitehead, Intuition, and Radical Empiricism – Gary Herstein
  9. What Does a Particle Know? Information and Entaglement – Robert J. Valenza
  10. A Neurobiological Basis of Intuition – Jesse Bettinger

Arrow’s Paradox of Voting

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Kenneth Arrow is a well known economist, logician, statistician, and political theorist. While his scholarly contributions are numerous, his best known was his first, published as a part of his dissertation. This is the above titled “paradox of voting,” which is also referred to has his “impossibility theorem.” This latter is evidently the technically correct title. However, I learned about it as the paradox of voting, and that’s the title I’ll stick with here. For one thing, calling it his “paradox of voting” makes it more clear at the outset what the theorem is about, and suggests what is really at stake. Details of the impossibility theorem are readily found for no more effort than looking, so my intention here is to provide a non-technical gloss of the topic. Still, enough of what I say here is about basic logic (and not merely political screed) that I am satisfied that this topic falls within my basic parameters for this blog.

Kenneth Arrow

Kenneth Arrow

The stakes here could scarcely be any higher, as they effect the very foundation of our nominally democratic system. Because of how our voting and electoral system is set up, we have a “winner take all” format that can (and often enough, does) allow a person to be elected even thought that person did not receive a majority of the votes. Once you have more than two candidates (or more than two parties) involved in any particular election, it is no longer possible to representatively distribute preferences in the election. This is the somewhat fancy way of saying things. The simpler way of saying it is that the more widely detested candidate can win. Continue reading

The Qualities of Quantities

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An oddity about philosophers, and especially logicians, is that when they talk about “quantity” they are not talking about numbers, or numerical counts. Rather, they are talking about the ways things can be gathered together (or singled out) using words like “all” or “some.” These ideas are called “quantifiers.” I want to do three things (briefly, as always) here: say a little about the “basic” quantifiers (“all” and “some”), say a little about how they get dropped from common discourse and argument – whether from laziness or deliberate obfuscation – leading to much gratuitous confusion. Finally, I want to say something about quantifiers that typically do not make it onto philosophers’ or logicians’ lists, yet are at least as common in ordinary discourse and argument as the “principal” two are. My purpose here (as always) is not to lead you onto the path of righteous proof making, but simply alert the reader to the importance of these operators so that they might not slip by quite so stealthily in the future.abacus_logo1

The second greatest sin in logic is to allow things to pass implicitly; the greatest sin is to block the road of inquiry, which is one of the things that happens when concepts are allowed to pass implicitly. Allowing things to remain implicit means that vague statements are permitted, by innuendo, to become concrete, thus leading us astray (blocking inquiry) from the directly stated vagueness. Sometimes things really are ambiguous, and they must be allowed to stay that way until real data, rather than jumping at conclusions, enables us to clear up the ambiguity. That, or recognize that the ambiguity is not – or, at least, not yet – cleared. Continue reading

Models and Interpretations

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A number of years ago I got into a discussion with an acquaintance about what kind of symbol system tells us “the truth” about the world. This is not how my interlocutor expressed the problem; she simply insisted that mathematics gives us the truth. I tried many different approaches to get her to understand that what she was saying made absolutely no sense, because the first thing that must happen (once any collection of symbols is at hand) in order to talk about truth was that those symbols have to be interpreted, and such interpretation is not given in advance. Thus, I have a modest background in some advanced forms of mathematics (mainly formal logic, abstract algebra, and a touch of differential geometry), and I understand that simply having a bunch of squiggles in front of you is not enough to adjudicate whether those squiggles say anything at all, much less anything that is true. Meanings must be assigned to those squiggles such that they hang together to form some kind of model, and that model then must be associated with the world in some form such that the model can be interpreted as making claims about the world which then can be interpreted as to its truth content. And here, “world” can mean either the world of concrete experience or a purely abstract “world” which is itself something of a mathematical construct. Also, my choice of the term “truth content” rather than “truth value” is not an innocent one: I wish to leave open the possibility that truth evaluations can be more complex and multi-dimensional than the mere assignment of values.Three Mesas

It became very clear that while I understood my acquaintance’s position, she in no way understood mine. This was because while I was repeatedly able to paraphrase – that is, interpret – her argument, when asked to do the same for mine she was unable to do anything other than repeat her own position, which addressed none of the points I had made. In later years, she was known to crow a bit about how she “won” the argument. To be fair, in retrospect I realize that there were a number of ways I could have made my own position clearer, as it was burdened by a much greater degree of philosophical nuance than the position she was presenting. And I confess that I do not think quickly on my feet; indeed, I’ve only ever suggested that, given time, I can think thoroughly. (One of the reasons I went into philosophy is because a line like, “Herstein! If we don’t get this metaphysical principle out the door by end of business today, our competition is going to crucify us!” is not something one is ever likely to hear from one’s department head.) Continue reading

Fiat Justitia Ruat Caelum

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“Let justice be done, though the heavens fall!”

(This is the third in a series of posts relating to the contemporary political scene in the United States. I’d originally intended there only be two posts in this series, but addressing issues at the progressive side of politics needed more comment. I’ve had plenty to say about the authoritarian character of conservatives.)

The above phrase was much favored by the philosopher Immanuel Kant and, it would seem, those people I previously described as “cry baby” progressives. There is a certain thrilling nobility to the sentiment; or, at least, that’s how it might first appear to people driven by ideology and indifferent to consequences. This is made evident by the regular as clockwork whining by such progressives (because they didn’t get everything they wanted, the instant they wanted it, exactly the way they wanted it) about what the cry-babies pejoratively refer to as “lesser-of-two-evils-ism.” I’ve seen some people – I believe the Green party candidate Jill Stein is one, but I didn’t save the URL and wouldn’t dignify it with a link if I had saved it – claim something to the effect that this oogity-boogity “lesser-of-two-evils-ism” is “anti-democratic” (regardless of the fact that it won far more votes than the alternative of Fiat Justitia Ruat Caelum. Evidently, for these cry-babies, not getting everything they wanted, the instant they wanted it, exactly the way they wanted it, is “anti-democratic.”) So it would seem that these cry-baby progressives would rather burn the world to a cinder, because obviously that always makes things better. Just look at how Shrub … er, I mean, Bush Jr. … advanced progressive causes with his programs. (And who cares about the upwards of one million – that’s 1,000,000 – Iraqis who died to justify our infantile self-righteousness.) Because, after all … Fiat Justitia Ruat Caelum.Votaire Perfect

But how much “justice” can really be on the agenda when one is prepared to let the world be reduced to rubble on no other account than that it failed to provide perfect justice instantly, right here, right now? Cry-baby progressives often talk about “revolution,” but they seldom if ever talk about hard work. (The overwhelming majority of progressives who do talk about hard work, about incremental change, and about such things as the long bend in the “arc of the universe,” strangely never find themselves welcomed to the cry-babies’ club meetings.) The condemnatory language with which certain progressives use the “lesser-of-two-evils-ism” terminology is intended to hide from you the fact that the alternative is the GREATER-of-two-evils. But these cry-baby progressives do not want to deal with this fact; rather they want to dazzle you with fantastical promises that amount to winning the lottery in a single stroke without even purchasing a ticket. “We must reject the system!” is their rallying cry, raised in voices loud enough to drown out anyone wondering how they plan to replace that system, especially when any effort to make that system better is just too hard to contemplate. Justice never comes without hard work, and hard work only ever makes things a little bit better at a time. But these folks do not want “a little bit” – they want it all, and they want it now. Continue reading

Cry Babies

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This is the promised follow up to my “American Fascist” post. I began writing this a long time ago, but was never happy with it. So what appears now is a massive rewrite in the context of contemporary events.It ought to go without saying that the persons I am being critical of in this post form a small (albeit, vocal) minority of American Progressives.Crying-baby-white-background

Contemporary events are informed by, and created from, past events. And the past events that need to be resolutely, uncompromisingly, born in mind here, all have in common the FACT that fascism only ever came to power because those on the political left was so divided and busily bickering amongst themselves that their infantilism and ideology prevented them from presenting a unified front against an enemy that was unimaginably worse than their own childish, internecine grievances. Among our contemporary grievances is the rather presumptuous coronation of Hillary Clinton as the Democratic nominee by major news outlets, before the final round of voting actually made her so. (Fantasies of Sanders “flipping” superdelegates at the convention were always nonsense on stilts; the results from New Jersey and California make them even more so.) This premature declaration has generated a considerable amount of complaint from the political left, including questions of whether it might have skewed the vote in California. Still, great deal of that complaint has taken on the air of the sort of cry-baby-ism we often see from persons with politically progressive leanings. And that is a problem. Continue reading

American Fascist: The Reality Show

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So, Herr Drumpf is the presumptive Republican presidential nominee, and the concern about fascism coming to America has itself taken on yet another layer of poignancy. Concerns are being raised by individuals as diverse as neo-con and Iraq war cheerleader Robert Kagan, and leading expert on the structural characteristics of fascist movements, Robert O. Paxton. It is Paxton’s work on the subject that most interests me here. While this post can be viewed as a follow up to my earlier one (hence the recycled picture), this post can also be viewed as the first of a two part series on aspects of those structural characteristic Paxton so carefully analyzed, and how they are visibly playing themselves out this election cycle. My argument here will be a fairly informal one – I’ll not be providing detailed endnotes or extensive quotations (although, such quotes as do appear will have their location in the Kindle text provided). This is because the details I’ll be offering from Paxton’s work are entirely uncontroversial readings of his arguments. Besides which, Paxton’s book is readily available, eminently readable, and an essential book for any citizen caught up in contemporary events.Fascists

My concern here is to remind folks not only of some of the essential characteristics that go into making a fascist movement – and fascism is always a movement, a populist one at that, and not a party or a collection of policies – and consider some of the ways the Trump phenomenon differs from other post WWII forms of conservative extremism, ways that actually push it closer to fascism. The movements I’ll be describing will be European ones, and most of what I’ll have to say about these European forms of conservative extremism will be based on chapter 7 of The Anatomy of Fascism. First, however, it will be useful to remind ourselves about the nature of fascism itself. Continue reading

Luck is Not a Method; Hope is Not a Plan

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Having taught a variety of philosophy courses in my less than traditional career, one of the ideas I am most committed to conveying to my students is that it is not good enough – not by a long shot – to simply be “right.” Quite the contrary: it is better to be mistaken for good reasons than to be “right” by accident. After all, even a broken clock is “right” twice a day, but that doesn’t make it a reliable timepiece. It takes a real commitment to inquiry and logic to be mistaken based on genuinely substantive reasons. And the most important difference is, of course, that if you are mistaken, but on the grounds of solid reasons, then that mistake can be rectified by finding and correcting the mistake in those reasons. Because if you are mistaken on the grounds of good reasons, then it is necessarily the case that the mistake is somewhere in those reasons.craps2

This can be a tricky notion for younger persons to accept. (It is an especially tricky notion for narcissistic sociopaths of any age to accept. Consider, for example, Donald Trump … ) The notion that “being right” is the only thing that counts, regardless of how one achieves that particular form of “right”, is arguably a driving factor behind a great deal of plagiarism. But conclusions that are achieved in fashions that are not methodologically sound are not “conclusions” of any kind, they are dogmatically asserted bullet-points, as cognitively vacuous as mere barnyard noises. Not only do such things fail to advance inquiry, they actively impede inquiry. Continue reading

Games People Play

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So, what is it that makes something true? (Trust me, this ties in with this post’s title.) If I say that “X is the case,” and it, indeed, turns out that X IS the case, then my saying so was true. Or, rather, the thing I said was true, and my saying it was said truly. (Actually, my saying it was said truly, because I truly said it, regardless of whether what I said was actually true.) But what establishes the connection(s) between my saying it is the case, and its actually being the case? Well, presumably it is reality that makes that establishment; but how is that reality, how is that establishment, established in experience such that the truth-saying and the truth-being converge in a truth making?Chess

Because even as (and insofar) as “the truth is out there,” our having, getting, finding, or whatever, that truth involves a substantial amount of making. If you take the idea of truth seriously, then you must take seriously the fact that we have to go out and make that truth apparent through significant and substantive inquiry. Where this is going (and it will go fast) is that the maker that connects the truth as said with the truth as found, looks a lot like a successful “strategy” in a “game.” This is a formal, logical concept, which brings scientific inquiry into a dirty-dance with that part of formal logic known as model-theory. (Somewhere, somebody has sheet music on this stuff … ) Continue reading

Just Giving it Away

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I notice on social media that various conservatives are becoming increasingly irate at being reminded of the fact that things like roads, police, fire protection, are essentially socialist programs which they are not only happy to use without thought, but view as their well-deserved entitlements. Jim Wright, over at Stonekettle Station, set off something of a firestorm on Twitter for pointing out that, “Calling universal healthcare and public education free stuff is the same as calling a Navy aircraft carrier a free ship.” The conservative outrage, apparently, stems from the “fact” that things like roads, police, and fire departments, are the sorts of things that government is “supposed” to provide. What the self-righteous conservative objects to is all of that other stuff, like public education and healthcare, that socialists propose to just “give away.”

Gift

It is very hard to give a measured response to such immeasurable ignorance and hypocrisy. It really is not all that long ago that fire, police, and roads were the sorts of things that governments did NOT bother to provide. Part of the devastation of the Great Fire of London in 1666 was that there was no uniform, government provided and enforced system of fire protection and suppression. The introduction of the “King’s Highway” (“high,” because the road was built up above the surrounding ground, so that when it rained the road would not turn into an impassable quagmire) was something of a revolutionary approach to transportation. The idea of an actual police force didn’t really come into being in the European world until the 19th Century. In earlier times such tasks were handled by local thugs and warlords whose only claim to “law” was that there was no one around who might challenge their arbitrary decisions and actions. So why are these things suddenly just and only the sorts of things that government is supposed to provide? Specifically, if fire and police protection, roads, water and sewage, are the sort of things government is supposed to provide, then why are things like healthcare, education, minimal standards of living, access to basic resources such as information and community, examples of things that those nasty-evil socialists want to just “give away”? Continue reading

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