Category Archives: Philosophy of Logic

Foolish Consistency?

18 Saturday Oct 2014

Posted by in Critical Thinking, Logic, Philosophy of Logic

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So I’ve previously floated some remarks about Emerson’s famous quote about a foolish consistency being the hobgoblin of a narrow mind. It seems reasonable that there might be something like a foolish consistency, but is that evident reasonableness actually validated in practice? And how might a person with a logical turn of mind validate, in turn, that reasonableness in theory? I’d like to explore this subject a bit by offering some informal remarks on formal logic, the thought being that there are actually reasons for learning the latter, yet intelligent things that can be discovered pursuing the former.

Formal logic, as it is traditionally taught and interpreted, holds that a formal contradiction is the End of Days. It is the thing that causes Jason Voorhees to drop his machete, Freddy Krueger to weep like a baby, and Michael Myers to pee himself hiding under his bed. It is the gate kicked open on the Pit of Hell, the black hole that swallows the universe, the Cubs winning the Series. OK, maybe not the “black hole” thing.

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Thinking about Thinking 3: Statistical modes

22 Friday Aug 2014

Posted by in Climate Change, Critical Thinking, Philosophy of Logic, Philosophy of Science

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Statistical thinking is one of the most important formal methods of engaging reality available to human beings. Sadly, it is also one of the more difficult, because human beings, in general, have absolutely no intuitive sense regarding probabilistic claims or statistical analyses. The people who do such things – even the ones that do them poorly – only reach such a stage of analysis after a significant amount of disciplined education. For the rest of us (and I must perforce include myself in this list) our statistical guesses only rise to the level of the merely appalling on those rare occasions that they are not completely idiotic. Quite usable texts can be had for the downloading (although the interested reader might consider supporting the Open Intro foundation), but one still requires no small measure of determination to “climb Mount Statistics” on one’s own. It is a challenge I’ve never completed at any substantive level, making this post more than a trifle daunting. However, even lacking any measure of expertise on the subject, there remain a few intelligent things that can be said, even by someone like me.

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Thinking about Thinking 2: Algebraic Reasoning

13 Wednesday Aug 2014

Posted by in Critical Thinking, General Philosophy, Philosophy of Logic

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“I’m never going to use that!” Variations of this war cry are frequently lodged in protest against that Torquemada-ish, 7th level of hell known as “high school algebra.” I am inclined to sympathize with this lament, but not for the reasons one might suppose. The problem, you see, lies not in the pragmatics – the usefulness (or lack thereof) of the subject – but rather in the pedagogical techniques and intentions with which it is presented. Algebra, as it is almost universally taught in secondary school, is little more than a peculiarly mangled arithmetic. Algebra as it ought to be taught is relational logic, it is algebraic reasoning.

So what does the above mean?

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Thinking About Thinking 1

29 Tuesday Jul 2014

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The study of philosophy – whether as an academic discipline, or the individually engaged pursuit of wisdom – has often been called “thinking about thinking.” This is a fairly vacuous description, not because it is wrong, but because it is so egregiously vague as to provide nothing beyond a comfortingly information-free verbalization that does not require us to attend to even a fourth word. 2500 years of written (which is to say, disregarding the purely oral traditions) speculative inquiry merits rather less of a trivialization in my book. Nevertheless, I did think it might be nice to spend a few posts thinking about good thinking from several useful perspectives, focusing, as it were, on the “logic” part of my mantra (Logic, Principles, Evidence, Facts.) This time out the gate, I want to talk a bit about “informal logic,” or that subject which is frequently found under the title of Critical Thinking.

The “critical” in “critical thinking” sometimes throws people off. This is not about being judgmental, or “you’re ugly and your mother dresses you funny” sorts of schoolyard pettiness. No, this is the criticism of the scientist and the art critic, the careful (but merciless!) evaluation of reason, BY reason. No cheap shots, but no free passes, either.

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(E)merging Traffic

25 Friday Jul 2014

Posted by in General Philosophy, Philosophy of Logic, Philosophy of Science

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      What does it mean to say that some thing, quality, relation, or constellation of combinations of any of the above (as well as whatever I might not have mentioned) is “emergent”? What does it mean for something to be genuinely new, for the universe to be genuinely creative?

      One obvious response falls out along the lines that, “Well, something is there now that wasn’t there before.” Despite its initial plausibility, I would suggest that such an account is badly off-base. For one thing, the reliance on a difference over time is quite naïve. The evolution of eukaryotic cells on the primordial Earth took place over time, and in a sense such nucleated cells “emerged” from an earlier situation where they did not exist. But this is a kind of “weak tea” emergence that is easily accounted for within ordinary evolutionary theory. No, when philosophers speak of emergence, they mean something radically new, seemingly unaccountable within the existing scheme of things. In a very real sense, they mean something genuinely creative.

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Logic, Principles, Evidence, Facts

13 Sunday Jul 2014

Posted by in Critical Thinking, Philosophy of Logic

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      There is a hierarchy of relational structures involved in any rational inquiry. No step or stage of this hierarchy may be legitimately skipped, although in various contexts certain of them may be relatively invisible. As might be guessed by the title of this entry, that hierarchy is the one that runs between logic, principles, evidence and facts. In essence, this is a “meta-relation” between that which is universal – logic, that which is general (in the sense of genera) – principles, that which is specific (in the sense of species) – evidence, and that which is particular – facts. Now, anyone familiar with the works of Peirce and Dewey (see for example, HERE, HERE and HERE) will not find what I have to say in this post especially surprising. Nevertheless, the basic ideas presented seem like ones that deserve a broader audience than just and only scholars in American Pragmatism. And I have long found this litany – logic, principles, evidence, facts – to be a useful one, such that I am inclined to repeat it often enough that having a citable explanation will be of value.

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Exempli Gratia: Misleading Authority

11 Friday Jul 2014

Posted by in Critical Thinking, Philosophy of Logic, Philosophy of Science

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     The recent publication in the peer-reviewed scientific literature of research showing that 97% of Climate Scientists are convinced that, not only is global warming very real, but the principal forcings in global warming are anthropogenic[1] in nature has created quite a stir amongst the denialists. Multiple independent lines of research have shown that the 97% figure is quite robust; the scientific data may be explored in detail at the authors’ of the original research own website, The Consensus Project. On the other hand, thorough-going debunkings of the attempts to dispute the 97% claim may be found HERE and HERE. More general discussions by actual Climate Scientists (not just John Conway) can be found HERE.

     My purpose here is somewhat different. In yet another sad attempt to dispute the real science behind the 97% consensus, one now sees the “Oregon Petition” once again being trotted out by denialists. This petition purports to show some 30,000+ “scientists” who dispute the scientific findings relating to AGW and the 97% consensus regarding those findings. What I wish to show here is how trivially easy it is to refute the Oregon Petition without making any appeals to a refined understanding of climate science or legitimate statistical techniques. All one really needs is a basic grasp as to the nature of science, and a casual grasp of the precepts of critical thinking.

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What Is Science?

09 Wednesday Jul 2014

Posted by in Philosophy of Logic, Philosophy of Science

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     Having floated the problem of legitimate authority the other day, it is worth considering some of the things that make an authority legitimate. And in that regard, few things in the world are supposed to occupy the role of legitimate authority to the extent that science does. So what is science, and what lends it the weight we justifiably give it?

     Well, the first and most important thing to recognize is that science is not a body of pronouncements nor a collection of “facts”; rather, it is a self-correcting method of inquiry. From the foregoing, we can see that, qua “method of inquiry,” science is essentially a process, not a product. And qua “self-correcting,” we can see that the process is one of constant test and re-examination where previous conclusions are themselves treated as only provisional and subjected to renewed critique and inquiry.

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On Whose Authority?

06 Sunday Jul 2014

Posted by in Critical Thinking, Philosophy of Logic

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One of the most widely recognized yet least well understood informal logical fallacies is the appeal to authority: the argumentum ad vericundiam. Most everyone understands that appealing to authority is, in some sense or other, an illegitimate move in any reasoned discussion. (If one doesn’t care a fig about reason, than any rhetorical move whatsoever becomes “legitimate,” which is to say, allowable provided you get away with it.) The problem here, though, is that if one could rigorously eschew all appeals to authority, not only would one avoid a particular fallacy, one would completely subvert the very possibility of reasoned discussion of any kind. Appeals to authority are not only constant, they are absolutely unavoidable in anything that might even barely resemble civilized existence. The problem, therefore, cannot be in the appeal to authority simply in itself, taken at face value.

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Mathematics and the Beautiful

05 Saturday Jul 2014

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Mathematicians are not driven by truth so much as by beauty. There is nothing exceptional about this claim, and it is only surprising to those who are not themselves mathematicians. The driving force of beauty in mathematical research has occasionally been documented; G. Hardy’s A Mathematician’s Apology being one example, Davis and Hersch’s The Mathematical Experience being another, more contemporary one. However, I thought I would mention another aspect of the connection between beauty and mathematics, one to which I can speak more directly and personally.

You see, many years ago my father gave me his slide rule.

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