I’ve learned much about logic in the week and a half since my previous post here. In that little missive, I wrote about a Peter Kreeft essay that I had trouble making sense of. Kreeft argued that symbolic logic “has serious social, moral, and even sexual implications, and it is one of the unrecognized indirect causes of ‘the culture of death’,” but I hardly recognized in his description the logic I used in undergraduate studies and in work with computers.
After some correspondence with philosophically educated friends, I can say that the first question that would pop into a mathematician’s mind — why not simply symbolize Aristotelian logic in a modern form? — is beside the point. The issue is the difference between the interpretations that tend to accompany the systems. They metaphysical concerns of logicians in the time of Aquinas were indeed different from those of many modern logicians, just as Kreeft says. And at a certain level, this is very important. I’m just not convinced that this level is the level of everyday use, or, if it is, then I suspect the effects are so diffuse that we should counteract them, not by rejecting a useful tool, but rather by robust metaphysical arguments and a sort of logical multilingualism.
But enough rehashing of my own position. What I’d really like to do is point readers to some resources I’ve had recommended to me and found helpful:
- The Internet Encyclopedia of Philosophy’s article on Aristotelian logic is fairly friendly to non-philosophers. (“It is hard to capture in modern English the underlying metaphysical force in Aristotle’s categorical statements.”)
- Reader “HT,” along with another friend, recommended an essay by Peter Geach called “A History of the Corruptions of Logic,” which is a rollicking good read.
- Martin Cothran is offering a more in-depth defense of traditional logic in a series of blog posts.
- There’s an example-laden defense of term logic in Fred Sommers’s introduction to George Englebretsen’s Something to Reckon With, though I’ve only been able to get my hands on an excerpt.
I’d like to close by recommending that any reader not acquainted with one or both of the logics try them out. In addition to the general benefits of logical thinking, symbolic logic will improve your SQL, and Aristotelian logic will unlock a wealth of Celarant- and Darii-based humor in old books and poems.
December 19th, 2012 | 2:04 pm
Thanks, Mr. Brafford, for taking my Geach tip and passing it on. Looking quickly at the Martin Cothran post you mention does not inspire confidence in his understanding. He repeats the (more-or-less commonly heard) neothomist canard that modern logic entails a different (and inferior) metaphysics. It does not. The considerations driving the creation of modern logic were not metaphysical. Lukasiewicz formalized Aristotelian (non-modal) syllogistic in a modern axiomatic formal system, so the resources of modern logic don’t fall down in expressing Aristotle’s formalism. Cothran makes some sweeping and misleading comments about Wittgenstein and other modern figures; actually Wittgenstein’s later philosophy moved away from a reliance on Principia-type formalisms, and the scope of what he considered “logic” (or “logical grammar”) was greatly expanded to the mapping of large tracts of human conceptual space. Anscombe certainly regarded her knowledge of Frege, Wittgenstein and Russell as no impediment to her development of Aristotle on a variety of topics.
December 19th, 2012 | 3:44 pm
Note also in this hooplaw over the syllogism that the scholastics made increasing use of consequences/conditionals as one of the basic engines of the argument.
December 19th, 2012 | 3:44 pm
“Two Logics: The Conflict Between Classical and Neo-Analytic Philosophy” by Henry Veatch is the best take on this from a classical/Thomistic stance: http://tinyurl.com/twologics
Great post, great idea about the poems, etc.
December 19th, 2012 | 5:45 pm
Additional note: I meant to say the later Wittgenstein very much understood himself to be investigating *essence*. He was concerned with what he called the “grammar” of concepts, and he famously stated “essence is expressed by grammar”. See Anscombe’s “The question of linguistic idealism” paper, probably the most important single paper written about Wittgenstein. So, in a sense he wasn’t all that far from the scholastics, though he didn’t take on any of the largely incomprehensible lingo or baggage about “abstracting” essences from experience.
December 20th, 2012 | 12:43 pm
HT says that I “repeat the neothomist canard that modern logic entails a different (and inferior) metaphysics.”
First of all, my argument is not that modern logic entails a different metaphysics (than the traditional Aristotelian one), but that a different metaphysics entails modern logic. So I think he has my point (and that of Thomists generally speaking, I think) precisely backward.
I am not arguing that modern symbolic logic forces one to accept, say, logical positivism (even though I do think it is logically positivist logic). I assume that there are at least some neohomist computer programmers out there, for example, who would find modern logic quite useful in their profession, but who would not be so philosophically naive as to think that it is an adequate representation of human thought.
HT follows up this assertion, as if to bolster it, by saying that “considerations driving the creation of modern logic were not metaphysical.” Whether or not this is true (I don’t think it is), it confuses the motivations that brought something about with the nature of the thing itself. There could have been no conscious intent at all among the developers of modern logic to create a generally nominalist or more specifically logical positivist logic, but it does not follow from this that the system is not inherently nominalist or positivistic in its basic assumptions (conscious or not), its structure, and its purposes, which it clearly is.
One thing that should make us suspicious of dismissive assertions like HT’s that metaphysics is irrelevant to the differences between the two systems is not only the fact that Maritain and Veatch showed quite convincingly that there was, but that Bertrand Russell himself (one of the authors of the Principia Mathematica) thought it did.
Part of the problem with having a debate on this issue with some analytic philosophers is that they seem to think that merely labeling something “neothomist” makes neothomist arguments magically go away–or at least makes the necessity of actually addressing their arguments unnecessary.
I am in the process of giving my reasons for thinking that metaphysics matters here. I would love to hear HT do something more than wave a dismissive hand and give his reasons for thinking it isn’t so.
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