Lessons from when Barbara exploded

The Port-Royal logicians devised a nifty aporetic barbara syllogism:

Who calls you an animal speaks the truth

Who calls you a jackass calls you an animal.

So who calls you a jackass speaks the truth.

Once you get the hang of it, you can prove anything is anything else it shares a genus with:

Whoever says black is a color speaks the truth

Whoever says black is white says it’s a color.

Whoever says black is white speaks the truth.

You can even prove anything is anything. Whoever says being is non-being says you have a word for it, right? Barbara has exploded.

The argument shows that any conclusion is only true so far as its terms are joined per se in a middle term and no further. There are at least two important corollaries to this:

1a.) Since the presence of a middle term allows for the truth of the conclusion only so far as some term joins the truth together per se, where no middle term is given (like in any hypothetical syllogism or even in the truth tables of modern logic, for example) the conclusions drawn are not even formally true.

1b.) Following this, there is something dissatisfying about the validity-soundness definition. Something can follow necessarily from premises without being formally true. If we insist on some account of validity, the best we can do is base it, as Aristotle does, on “what follows necessarily” (see chapter 1).

2.) The middle term of truths now called scientific is the result of a contrived environment (i.e. an experiment). I suppose this is better than nothing, but formally, it’s not an account of nature at all, but of nature-cum-art, with the two fused together in such a way as to cause an in-principle impossibility of determining how much each element is in play.

 

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6 Comments

  1. September 19, 2016 at 9:20 pm

    The arguments in question are both valid and sound, but do not prove what they appear to prove. That is, the one who calls you a jackasss speaks the truth insofar as he calls you an animal, and the one who says black is white speaks the truth insofar as he says that it is a color.

  2. September 20, 2016 at 7:17 am

    Let’s look at a more careful statement of the second argument, making use of the precision that the conventions of direct discourse make possible.

    All speakers who say, “Black is a color,” are speakers who speak the truth.
    All speakers who say, “Black is white,” are speakers who say, “Black is a color.”
    Therefore, all speakers who say, “Black is white,” are speakers who speak the truth.

    The argument as thus reformulated is absolutely valid in that, if both of the premises are (or were) true, the conclusion has to be (or would have to be) true. The most we can say is that the minor premise may be false, for it may be that not all speakers who say, “Black is white,” are speakers who say, “Black is a color.” Because the one statement and the other are not identical, it is possible for some speaker to enunciate either one without also enunciating the other.

    Further, given that one of the argument’s premises is false, it may be that the conclusion is false. On the other hand, the conclusion may yet be true; it may be the case that all speakers who say, “Black is white,” are speakers who speak the truth, though not, of course, when they say, “Black is white.”

    Precisely similar remarks can be brought to bear on the argument if we employ the conventions of indirect discourse in its statement, thus:

    All speakers who say that black is a color are speakers who speak the truth.
    All speakers who say that black is white are speakers who say that black is a color.
    Therefore, all speakers who say that black is white are speakers who speak the truth.

    Precisely similar remarks can be brought to bear on the first argument, the restatement making use of the conventions of indirect discourse in its statement, thus:

    All speakers who say, “You are an animal,” are speakers who speak the truth.
    All speakers who say, “You are a jackass,” are speakers who say, “You are an animal.”
    Therefore, all speakers who say, “You are a jackass,” are speakers who speak the truth.

    It seems to me that Barbara has not exploded; she is intact.

  3. Aron Wall said,

    September 20, 2016 at 8:51 am

    Possibly relevant (see the discussion as well):
    https://golem.ph.utexas.edu/category/2015/02/concepts_of_sameness_part_2.html

    • September 20, 2016 at 10:20 am

      The article has some sense of the problem here: what does one do with accidental predication? Does predication of the accidental count as truth? STA, for example, would say that the whole argument commits the fallacy of the accident since the minor is an accidental predication as opposed to a per se one. This is fine for STA since he doesn’t think that mere formal structures suffice to ensure truth of conclusions – one also needs what is now called “material logic” to ward off sophistical conclusions. But it’s just this subject-predicate nexus in human truth that gets overlooked or remains underappreciated in the three areas I describe at the end of the post.

      The Lesson from when Barbara exploded is the same one the ancients drew: There is no formal truth apart from material perseity. To separate them gives us a “truth” where every possible premise is true (and false). Who needs logic under such conditions?

  4. September 20, 2016 at 10:30 pm

    I believe the problem lies in an ambiguity in the major term. That is, we take “speaks the truth” to mean something like “speaks the truth with respect to what you are called in the subject term of this proposition”. So the syllogism slips in a fourth term:

    P1. Whoever calls you an animal speaks the truth with respect to what you are called in the subject term of P1.
    P2. Whoever calls you a jackass calls you an animal.
    C. Whoever calls you a jackass speaks the truth with respect to what you are called in the subject term of C.

    That is, the conclusion needs to say that the person calling you a jackass has spoken truly about you being a jackass. But that requires a reference to what is said in the conclusion, whereas P1 references what is said in P1.

    To fix the problem you would need the syllogism to say:

    P1. Whoever calls you an animal speaks the truth with respect to what you are called in the subject term of P1.
    P2. Whoever calls you a jackass calls you an animal.
    C. Whoever calls you a jackass speaks the truth with respect to what you are called in the subject term of P1.

    And this seems less objectionable, at least insofar as P2 tells us that by calling someone a jackass, one has called that person an animal, and so, by P1, has spoken truly about the person (that he is an animal). Of course, this is a far less juicy syllogism!

  5. a k a smith said,

    September 23, 2016 at 3:23 am

    You have to be vary careful with silly jizzums.


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