The basis of Aristotle’s logic

Aristotle’s whole system of logic starts from two premises:

Logic is the direction of the act of reason

The direction of reason is from what is more universal in predication to what is less so.

Aristotle says the major premise everywhere, and at the slightest provocation; the minor is from St. Thomas, and Aristotle simply assumes it everywhere. The conclusion is that logic is the right order from what is more universal to what is less so. This is why Aristotle starts his logic with a study of most universal things (the Categories) Then shows all the ways that one universal thing can relate to another (On Interpretation) and then goes on to speak of arguments as the motion from what is major (or most universal) to what is minor (least universal) through a term of middle universality. The middle only has a middle universality when we speak in a way that follows what is called “the first figure syllogism” and so Aristotle rightly insists that this is the pre-eminent tool for ordering reason, and that all other tools of reasoning are correct so far as they can be reduced to it. Aristotle insists that this is even true of non-categorical reasoning, as Yvan Pellitier proves here (download “PelletierStrategy.pdf”). This is not to say it is the only way that reason can go from one thign to another: there is an ocean of dialectical tools that are used to bring us to the point where we can actually form a valid universal.

We more tend to look at terms like checkers that can be arranged in certain correct ways, and in doing so we can reach conclusions that cannot be reached by the mere categorical method. This is all fine, but it is not logic in the same sense of the term, and it is not clear how we can make one thing called logic relate to the other thing called logic.

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11 Comments

  1. Brandon said,

    February 23, 2010 at 3:10 pm

    I’m not so sure that it’s difficult to see how the two are related; our usual way of looking at it has all the features of dialectic, and the fact that it simply traces inferences regardless of whether they involve movement from the more to the less universal is one of the signs that we tend to be Platonists of a sort: what we call logic just is (a form of) dialectic. Our oddity is due chiefly to the fact that we think it so important to go by way of symbols (our checkers on the checkerboard) — we introduce the imagination as an intermediary. It often makes sense to do so, for the same reason it makes sense to convert mathematical word problems into equations; but this indicates the weakness of our intellects, which require a crutch, a way to help us keep track of things. Since we tend to make use of the symbols so extensively, and symbols are arbitrarily assigned, that makes us inclined to miss the movement from the more universal to the less universal, taken as such; and thus our addiction to symbolic reasoning leads us overlook the importance of demonstration as something other than dialectic. When we do that it’s effectively a conflation of logic and grammar — we confuse the grammatical rules for our symbols with logical principles because we’ve set up the grammatical rules to mimic the latter under certain conditions (much as the grammar of any language will mimic logical principles to some extent). But when we don’t make such a conflation, I don’t think there’s any real problem in linking the two — what we call logic is the liberal art of making systems of symbols that facilitate certain kinds of dialectical reasoning.

    Or were you thinking of some other problem here? I’m not wholly clear why you think it’s difficult to link the one to the other.

    • February 23, 2010 at 3:29 pm

      Brandon, as I read this post and your comment, it becomes clearer to me that there’s a lot about logic, dialectic, and demonstration that I simply don’t yet appreciate. What would be a good book on this topic? I’ve worked through a good bit of Peter Kreeft’s Socratic Logic; is there anything else I should look at?

      • February 23, 2010 at 4:14 pm

        Read the Pellitier article! Lots!

      • February 23, 2010 at 6:56 pm

        Lots, huh? Having taken this advice previously, I’ve finally managed to get through the first book of the Physics. Where’s that royal road to learning I keep hearing about? :-)

        I’ve downloaded it, and we shall see.

    • February 23, 2010 at 4:13 pm

      That’s a good explanation, and I think we really are or were disagreeing.

      I agree that symbol use is dialectical, that dialectics is a response to the weakness of our intellect, and that the solution to linking the two would be in finding the link between dialectics and demonstration. After that, things get very murky for me, and I have a hard time matching up logical symbol use to it relevant part of dialectic, and then in turn subordinating that part to demonstration correctly. I’m not saying it can’t be done, I’m just saying the links are murky.

      • Brandon said,

        February 23, 2010 at 4:48 pm

        I think that’s fair enough. I think part of the problem is the sheer complexity of dialectic. One notices this — just how much dialectic covers, and indeed must cover — even in medieval treatises on the Topics. There are a lot of different loci communes, maximal propositions, each of which could have a treatise of its own for full discussion; and all of what is now called logic fits entirely into what in the Middle Ages would have been a Treatise on Consequences in the logica moderna, which would have been an expanded inquiry into particular points relevant to dialectic (especially its conditional character, that something follows given something else).

  2. Brandon said,

    February 23, 2010 at 4:30 pm

    Robin Smith’s article at the SEP is a pretty good start for the general background. But views of the matter in the medieval period are influenced by the tendency to see logic as dividing up in correspondence with the ‘nine books of the Organon’, namely, the Isagoge of Porphyry and then the eight Aristotelian books that were seen as dividing up the major sections of logic.

    Categories (most universal terms)
    De Interpretatione (composition of terms into propositions)
    Prior Analytics (the syllogism, understood as the formal structure of inferences suitable for demonstration)
    Posterior Analytics (demonstration as such, or the matter that the form makes into actual demonstrations)
    Topics (dialectical inferences)
    Sophistical Refutations (sophistical inferences)
    Rhetoric (persuasive or plausible inferences)
    Poetics (imaginative associations)

    Demonstration is valid reasoning from the premises that are per se, universal, and necessary and it results in conclusions that are certain; it’s the pinnacle of the Aristotelian view of logic. Probable inferences fall under dialectics as opposed to analytics (although, confusingly, ‘dialectic’ is sometimes used as a synonym for logic in general, depending on the author); it creates assent that is conditional or leave some room for doubt. Demonstration yields knowledge (scientia); dialectic yields reasonable belief or opinion. Rhetoric insofar as it is a logical discipline yields suspicion (as in, “I suspect that the answer is such-and-such”); demonstration and dialectic deal with truth itself, the one with certainty and the other with probability, but rhetoric deals with verisimilitude, appearance of truth. Poetics, insofar as it is a logical discipline, deals with how imaginative representation creates a sort of attraction or repulsion that affects how we reason and act. And sophistics, of course, deals with errors of reasoning.

    I don’t know of any books that cover this as such (perhaps James might). I’d recommend reading Aquinas’s Proemium to his commentary on the Posterior Analytics; it’s short, but it lays out one of the clearest explanations of the above scheme.

    • February 23, 2010 at 6:58 pm

      Thank you! I’ve read Porphyry; I guess I’ll just have to continue.

  3. Frango Nabrasa said,

    March 20, 2010 at 8:12 am

    What is said above about the basis of Aristotle’s logic needs supplementation, to say the least.

    http://ndpr.nd.edu/review.cfm?id=18787

    • March 20, 2010 at 8:20 am

      A 200 word blog post about a 2300 year old subject on a text that has been read by billions of persons and is at the foundation of all Western thought needs to be supplemented? No way! That’s impossible! :-)

  4. November 3, 2011 at 8:31 pm

    The better logic system is to define logic as that which is not illogical. And, to define that which is illogical as that which involves a logical contradiction, such as attempting to assert that (A) and (not A) can exist at and in the same time and in the same place. Any attempt to base an argument, statement, proof, or action on a logical contradiction is illegal sophistry.


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