Category Archives: Logic

The Implicit “All”

12 Tuesday Nov 2019

Posted by in Critical Thinking, Logic

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One of the fundamental units in logical analysis is that function/operatori lovingly known as “the quantifier.” Most logic texts content themselves with just two: “all” and “some,” formally symbolized as “” and “” respectively. Thus, to say that, “All X is p,” one is asserting that every (or any) instance of X is also an instance of p, or is characterized by p, etc. Similarly, when someone says only that, “Some X is p,” the claim is made that, if one looks hard enough, one will find at least one instance where X is p. There are ways of precisifying (one of those $5.00 words philosophers love to use) the above statements, but there is hardly any need to do so here. It suffices to have a general idea. Two points I’ll mention in passing. First, in most formal contexts (substructural logics are an example of an exception), “all” and “some” are defined as being interchangeable using “not”: thus, “not-All X is not-p” is taken to mean “Some X is p,” and conversely. Secondly, these are not the only quantifiers possible: “many” and “most” are also examples. But these last two are difficult to formalize (to say the least) and by a polite convention among logicians they are generally ignored wholesale.Implicit All

As the title of this post states, I wish to talk about what I am calling the implicit “all”; uses of the “all” quantifier in which that quantifier is functioning but not explicitly stated. This happens quite often, in point of fact, and is not problematical in itself. Where problems do arise is when that usage is not merely implicit, but actively denied as a means of evading the consequences of what someone has actively stated or written. When this happens, we are faced not merely with a logical error, but an overt act of dishonesty. The dishonesty becomes not merely overt but blatant when, even after the implicit “all” is pointed out, the individual continues to deny it. Continue reading →

Nonsense on Stilts

06 Wednesday Nov 2019

Posted by in Logic, Metaphysics, Process Philosophy, Relationalism

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The Washington Post had an article in their science section a few days ago announcing “Scientists are baffled: What’s up with the universe?” It is a welcome relief to see mainstream reporting paying some attention to the massive problems that absolutely dog contemporary gravitational cosmology. One more frequently encounters a breathless declaration that this or that latest “discovery” “confirms” the Standard Model of Gravitational Cosmology (“SMGC”),i yet which then goes on to announce that we’ll need a “whole new physics” to make sense of this new data. (This article from The Guardian is slightly more balanced than many of the sources that later picked up the same story.) But the deeply problematic nature of SMGC is not really news, nor are the issues mentioned in the WaPo article even the most directly pressing matters. An extensive review of many of these problems may be found in the newsletters of the A(lternative) Cosmology Group. While a serious measure of background in mathematics and physics is required to read the listed and cited papers at any level of comprehension, a person with a basic background in these topics will be able to follow the newsletter discussions themselves and gain a modest acquaintance with the issues.Stilts

There are yet other issues that appear where SMGC intersects with micro-physics, in the realm of quantum mechanics. Part of the problem is that the mathematical bases of these two realms of inquiry – which, in the case of SMGC, is Einstein’s general theory of relativity (“GR”) – are built around radically different and largely incompatible kinds of mathematical structures: quantum mechanics, for all of its peculiarities, is linear in nature, while GR is fundamentally non-linear. This unification of the macro and the micro levels continues to defy serious scientific efforts, but the emphasis here is most definitely on “serious.” Unserious – because blatantly unscientific – efforts have given us the “string theory” nonsense which, while mathematically clever (at least by some accounts) is empirically vacuous, and as such devoid of any actual scientific content. Indeed, string-theory is so lacking in any basic scientific standing that not only is it empty of any actual empirical content, it lacks even the possibility of such content. Philosophers being disdained by the gate-keepers of SMGC – persons such as Brian Greene, Stephen Hawking, Neil DeGrasse Tyson, and Sean Carroll – one may also turn to the observations of scientists such as Lee Smolin and Peter Woit for confirmation of these statements. Continue reading →

A = B

10 Monday Jun 2019

Posted by in Logic, Mathematics, measurement, Philosophy of Logic

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Anyone who is reading this post – indeed, anyone who can read at all – has some minimal exposure to mathematical ideas, even if that exposure goes no further than elementary arithmetic and not, as I am only half-jokingly known to say, actual mathematics. (Well, since I’ve mentioned it: the thing I’m known to say is, “that’s not mathematics, that’s arithmetic.” This is always in response to someone who has protested something along the lines, “I’m no good at mathematics; I can’t even balance my checkbook.” The humorous, yet legitimately educative nature of MY statement always strikes me as obvious, yet I am constantly amazed by the numbers of people who get lost in the elementary rhetoric of my statement.)A equals B

In any event, even such minimal exposure is typically enough to satisfy most people, even most mathematicians (I suspect), that they have a pretty good handle on what that equals sign (“=”) means as it is expressed in, say, the title of this little essay. Clearly I wouldn’t be writing about it if such an impression was even remotely true. For one thing, how do we read “A = B”? Does it say, “A equals B”, or does it say “A is B”, and is there a difference between those two? Spoiler: yes. Yes to both questions, depending on how crudely one is using one’s language, which makes the fact that “equals” does not equal “is” an especially problematic conflation of terms. “Is” tends to mean “identity” in such a context, which is tricky enough in its own right (I wrote an MA thesis on the subject). The reading of “=” as “equals” helps to emphasize a somewhat more functional approach to matters, though it is still more rigid and “substantive” than such formal notions as “equivalence” and “isomorphism.” topics I’ll likely blog about in the future because I can already hear the math-phobes screaming in horror. For now, I want to focus on the logical issues of “equals,” as a formal relation. Thus, the word “equality” may also find a use here, but that use should not be mistaken for the political, economic, cultural, &/or social senses of the term. (On the other hand, I do not preclude in advance that what I say here will have no bearing on those uses, either.) Obviously, the starting point for the primary discussion is with the work of Alfred North Whitehead. Continue reading →

Measure is The Measure of All Things

29 Saturday Dec 2018

Posted by in General Philosophy, Logic, measurement

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The online journal Eidos, A Journal for the Philosophy of Culture has just published a focus issue (#4 (6)/2018) on the topic of “Philosophy and Technology,” in which yours truly has an item. The title of my contribution is the same as this blog post, and it, along with all the other articles, is free for the download. It is a “discussion paper”, which means it is permitted a bit more leeway when it comes to scholarly standards of argument and citation. At some 6,000 words it is a good 4+ times larger than my longest blog posts, but it is free and possibly even interesting; at the very least it is at the same general level of readability of my regular blog posts, so folk who are interested can download it HERE.Robot

The entire journal may be accessed from the Eidos link above, and is well worth checking out, both for this current issue (table of contents reproduced below) and for the back issues that can be accessed through the link to the archives. As mentioned, this issue is about philosophy and technology approached, as one might guess from the journal’s title, from the general position and environment of questions of culture. Some folks might be surprised at such a choice of philosophical topics, as technology might not seem on the surface to have much to do with “the true, the beautiful, and the good,” the supposedly “core” topics of philosophy. But a couple of sentences from Marcin Rychter’s opening editorial struck me as quite appropriate here:

A simple conclusion seems inevitable: we can neither understand ourselves nor our times without deeply thinking about technology. A stronger claim seems plausible: technology should be the main topic of contemporary philosophy of culture.

Continue reading →

Whitehead’s Quantum of Explanation: Thinking with Auxier and Herstein

21 Wednesday Nov 2018

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A review of Randy and my book, “The Quantum of Explanation,” from a fellow traveler in the process philosophy field:

Footnotes2Plato

“Our central idea is that concrete existence explains the abstract aspects of experience and not vice-versa.”
-Auxier and Herstein

“So long as necessity is taken to be the guarantor of rationality, the conception of rationality advocated will be as useless to science as it is to practical life.”
-Auxier and Herstein

Those looking for a proper review of their book should read George Lucas’ in NDPR. My thoughts are somewhat self-referential, as I am trying to sort through the intellectual earthquake unleashed within my mind as a result of reading this text.

Auxier and Herstein’s book has been on my radar for several years. I first read small sections of the unpublished manuscript in late 2016 as I was finishing my dissertation. The book was published last year…

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Objects and Relations

19 Monday Nov 2018

Posted by in Logic, Process Philosophy, Relationalism

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Let’s get (a little) mathematical. If you’re still reading, good for you!

I spend a fair amount of time reading various logic texts. Most of that time, these days, is spent on texts that are shared with a “Creative Commons” license, and are thus freely downloadable. This is for two reasons: first, I am deeply offended by contemporary text book prices. For example, Hurley’s logic book (you can look that up on your own) is around $100.00 for the more recent editions. Not as bad as Calculus text books, but certainly extreme when one considers that the material presented can be had for free from other sources. So, despite the overwhelming improbability of it ever occurring, I can’t stop myself from thinking about the scam inherent in textbook pricing, and thinking how I, as a would-be teacher, might better serve my students w/o bankrupting them.Venn diagram

The second reason is that I just really like the subject, and want to keep my nose in the books on this subject at all times. Like playing the cello, if you stop practicing, you lose whatever mastery you may once have possessed. (The cello analogy is in reference to the great Pablo Casals and the possibly apocryphal response(s) he gave to why he always practiced so diligently.) Since I am otherwise utterly penurious, my choice of texts to “practice” with are limited to what I can download for free. With respect to topics within mathematics, including formal logic, the range of materials is actually enormous, and the quality exceptionally good. One of these books is the Open Logic Text by the Open Logic Group (“OL”), licensed under Creative Commons international attribution 4.0. (I believe I have fulfilled my legal obligations in the forgoing; full .PDF HERE.) I very much approve of this text, and almost anyone but me would never have even the slightest critique to offer regarding its exceptionally comprehensive coverage of the topic in a readily understandable fashion. But I do have one criticism, one that pretty much no one but a Whiteheadian would ever think to make. And that is about their too sanguine opening about the centrality of sets, and their uncritical acceptance of an intransigently object structured thinking. Continue reading →

Feeling The Possible

26 Wednesday Sep 2018

Posted by in Logic

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Possibility and the possible have long been treated as the bastard third cousins of philosophy. This is true even though there are entire areas and sub-disciplines of formal logic that are nominally dedicated to studying those topics. The problem is that the approaches taken to the nature of the possible (and I will be using that term and “possibility” as more or less interchangeable cognates) as parasitic upon the ideas of “necessity.” In formal terms, possibility and necessity are supposed to stand on equal footing. But in approach and intention, that almost never occurs. This is discouraging, to say the least, since our sense, our feeling, of possibility is a very real aspect of our feeling of reality overall, whereas our only notions of necessity are the abstract, or even recondite, mathematical constructions we make of a thing we can have no experience of whatsoever. Car speeding

Thus, necessity and possibility are traditionally represented with a box and a diamond, respectively. When attached to a sentence, schematically represented by “p” or “r”, then merely asserting “p” becomes the stronger claim of “necessarily p”, or “p is necessarily true,” represented by “□p.” Similarly then, “possibly r,” or “r is possibly true” is schematized as “◊r.” Either can then be treated as a shorthand form for the other using a variation of DeMorgan’s rules: “□p = ~◊~p”, and “◊r = ~□~r,” where “~◊~p” reads as “not-possibly not-p” and “~□~r” reads as “not-necessarily not-r.” This is all very handy for when you are doing formal logic, but a little thought might well lead one to doubt that any so mechanical and reductive formulation is capable of actually representing reality. Is necessity real at all? And even if it is, why would it be nothing more than a truth-functional inversion of possibility? Meanwhile, there is nothing mechanical about possibility itself, even as we mechanize – for purposes of convenience – what we end up saying about the possible. Right there is the rub: the reality and what we say about that reality are not the same at all. And while I cannot escape the use of words to do so, it is to the experience of the possible that I now wish to turn. Continue reading →

Shut Up and Calculate

06 Tuesday Mar 2018

Posted by in Logic, Philosophy of Science

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Neil DeGrasse Tyson shares with Stephen Hawing a commitment to demonstrating that lots of schooling will never, by itself, equate to an education (a distinction I’ve explored in a variety of places.) For example, in a bromide from a few years back, Tyson not only dismissed philosophy as being of no value, but insisted that bright students should stay away from it as it is nothing more than a distraction.i Stephen Hawking, for his part, has maintained a long running snark-fest directed at philosophers, notable mainly in that Hawking’s petulance is only exceeded by his ignorance, and the indefensibility of his “arguments”. One must scare quote the word “arguments” in the preceding because neither Tyson nor Hawking have an actual argument, only ex cathedra pronouncements that are to be accepted without question, and in the complete absence of anything like logic, principles, evidence, or facts.Adding Machine

Thus, for example, Hawking vapidly legislates in his recent book, The Grand Design, that, “philosophy is dead. Philosophy has not kept up with modern developments in science, particularly physics. Scientists have become the bearers of the torch of discovery in our quest for knowledge.” What Hawking is, in fact, asserting here is that philosophy is only philosophy when it is doing physics. So when it fails to do physics (and actually does philosophy – a subject Hawking knows absolutely nothing about, and imagines himself virtuous for his willful lack of education) then this can only be because philosophy is dead. He declares (in Black Holes and Baby Universes), without a particle of evidence to support his claim that,

There is a subspecies called philosophers of science who ought to be better equipped. But many of them are failed physicists who found it too hard to invent new theories and so took to writing about the philosophy of physics instead. They are still arguing about the scientific theories of the early years of this century, like relativity and quantum mechanics.

and then goes on to pule that, “Maybe I’m being harsh on philosophers, but they have not been very kind to me.”ii This is the sort of childishness one might expect from a 3rd grader, not from a man who held the Lucasian Chair at Cambridge University. In its way, however, it is perfectly representative of an attitude that has consumed much of physics, in which any attempts to ask deeper questions about the issues of contemporary physics are met with the dismissive command to just, “shut up and calculate.” Continue reading →

Self-Identity

27 Tuesday Feb 2018

Posted by in Logic, Mathematics, Metaphysics, Ontology, Process Philosophy, Relationalism

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I was not an especially “outward looking” or alert youth, working rather to shut the world out rather than invest painful consideration into something that was already almost unbearably painful. But occasionally my habits of thinking would turn themselves outward, to chew on a puzzle that had managed to break through my protective shell and demand my attention. This happened twice that I can recall in high school: the first time, after an especially depressing episode I realized I needed to make a study of reading people – perhaps, more importantly, I realized that I could learn this, and I began picking up clues effectively and rapidly. The second, and first genuinely philosophical moment, was when I “discovered” the “problem of evil” as it related to the born-again Christianity I’d been emotionally bullied into accepting by various members of my family – personal responsibility is a joke, of course, in any world dominated by an omniscient and omnipotent creator god. This began my “angry atheist” phase, which went on for another decade (until I’d actually read a substantial bit of philosophy.)Acropolis1

The third “break through” (second genuinely philosophical one) happened when I was in the army. I was stationed some 18 kliks from what was (at the time) the East German border, in the Central German highlands, as an electronics tech in an Improved HAWK anti-aircraft missile battery. Every year, each such unit chose a squad of people to be sent to NAMFI, Crete, to spend a few days training, culminating in firing a live bird at a drone target. As it happened (then, at least), the entire trip involved several days both before and after the actual training which were free time for the troops to explore the island or, as several of us chose to do, take the ferry from Souda bay to the Piraeus and Athens. So it came to pass that I climbed the steps up the hill of the Acropolis. Except, that’s not quite right. Nobody actually walked on those steps, and it wasn’t out of respect for their antiquity. Continue reading →

Making Sense

12 Monday Feb 2018

Posted by in General Philosophy, Inquiry, Logic, Metaphysics, Philosophy of Science, Process Philosophy, Whitehead

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Whitehead set out to make sense of things. After witnessing all of his attempts to point out how Einstein’s general theory of relativity failed to make the sense it claimed to make (and still fails to do so, but the model centrists won’t permit empirical evidence to get in the way of their clever mathematics), he arguably decided that he needed to step back from epistemology and philosophy of science, to present a more logically primary argument, in the metaphysical form of his “philosophy of organism.” Whitehead centered his argument on what I and Randy Auxier named “the quantum of explanation,” a logical (rather than ontological) center, around which Whitehead constructed his subtle and complex system of making sense. It has been suggested that Whitehead’s magnum opus, Process and Reality, is one of the five most difficulty works in the Western philosophical canon. I’m not inclined to argue with such a sentiment, since the most that could be credibly argued is that it might be knocked back to sixth place. For my part, I’m not sure what work could manage that feat.No Sense

One of the points that Randy and I tried to emphasize was that the process of “making sense” was itself a rather complex process, in which the most active word in the proceeding is process: this is not an object you hold, but an activity you engage in. So despite my habitual focus upon contemporary science &/or concerns, this is actually as classic an issue as you can find in the Western philosophical canon. (And I just don’t have the expertise to speak with even casual ignorance about the Eastern canon, a source of inestimable insight and subtlety. I am, however, inclined – ignorant as I am – to suspect that what I have to say here can find its analogs in that tradition.) Continue reading →