[lit-ideas] Re: Practical Logic

  • From: Robert Paul <rpaul@xxxxxxxx>
  • To: lit-ideas@xxxxxxxxxxxxx
  • Date: Wed, 26 Dec 2007 21:04:29 -0800

John lists some areas of study and fields of inquiry and remarks

What these studies have in common is not the rejection of modus ponens (if p then q, p is true, therefore q) or the definition of validity specific to logic. It is, rather, the recognition that in most practical situations (including most forms of scholarly research), the proposition "if p then q" is itself problematic. "p" is one observation, "q" another. In the best cases, the observations are measurements, using widely accepted and replicable methods. More often, they are "eye-witness" testimony, subject to all the distortions to which the human senses and brain are prone. They may be nothing more than uncritical assimilation of incoming information to existing categories.

To say that the conditional 'if p then q' is 'problematic' because the determination of p requires (?) that one make one observation and the determination of q requires that one make another tells us nothing about the conditional. The conditional—usually the first step in modus-ponens—is completely general and is moreover indifferent to the actual truth or falsity of whatever propositions are substituted for 'p' and 'q' respectively. (That is why it's called a conditional, one might imagine.) It is also indifferent to how their truth or falsity is determined, and is thus independent of any epistemological questions; the the fallibility of human sensory mechanisms and the uncritical assumptions people make about what happened and how, if it happened, to 'classify' it are completely irrelevant to any role that modus ponens may play in determining what follows from what.

One might think that the following would show I'm mistaken about this. 'If you build a baseball diamond in the middle of a cornfield, people will flock to see games played on it,' would seem to be falsified by the diamond's being built and nobody's showing up. True. But this is to treat the 'if p then q' premise in modus ponens as making an empirical claim analogous to 'if water is heated to a certain point, it will boil.' An instance in which (Popper aside) water is heated to that point yet fails to boil (at sea level) appears to falsify this.

But in modus ponens, no hypothesis or empirical claim is being advanced.
Imagine a meta-if (IF) standing behind the whole schemata. IF says,
'If p, then q, and p, then q.' It doesn't address the truth or falsity of the conditional, the conjoined premise (or the conclusion) but merely says that if the conjoined premises were true, the conclusion would have to be true also. If you don't see this, then logic will take you by the throat and force you to, as the tortoise said.

Looking for a real-world case in which the conditional is asserted along with the antecedent, yet the hoped for event doesn't happen, or the unwanted event does, will falsify the hypothesis, or claim that given this there will be that. In modus ponens, the truth of the conditional is assumed, not discovered.

John elucidates his suggestion further.

as general systems theorists point out…in practical terms, what we call knowledge can be divided into three zones: (A) a small zone in which mechanical theories work, and modus ponens can be invoked with little risk of contradiction; (B) a somewhat larger zone in which statistical inference works, and modus ponens can be modified to read "if p then q with probability x"; and (C) most of what we claim to know, where relations are complex and the best we can do is parse the evidence within a limited domain and reach conclusions that only in rare cases survive the lawyer's test of "beyond a reasonable doubt," where we lack formalized procedures for deciding what a reasonable doubt is and fall back, for better or worse, on familiar heuristics--in other words, the dispositions that Bourdieu calls a habitus.

I hope I addressed some of this above. Let me say a bit more. Logic is not a 'mechanical theory.' It is the general theory of inference, and its intramural skirmishes and notational crochets shouldn't be intimidating. What it means to invoke modus ponens and thereby be caught in a contradiction, I really don't know. A girlfriend of mine once said, 'Don't try any of that logic stuff on me!' whereupon I disclaimed any intention to use that nasty scheme, said it must have been an accident, and shouldn't we have another drink? But as far as running into actual contradictions by using modus ponens goes I'm lost. In (B) john says that there's a zone in which statistical inference works, but not modus ponens in some pure sense. The conditional can be 'modified to read "if p then q with probability x."' This is ambiguous. Does it mean e.g.

a) If the pressure reaches n psi, the probability that the boiler will burst is m—?

or does it mean e.g.

b) That the boiler will burst when the pressure reaches n, has a probability m—?

These seem to me different because I take (b) as saying that there is a probability of m that (b) is true; that is, the probability ranges over the entire statement whereas in (a) it's restricted to the probability of a particular event's happening. Perhaps this ia a distinction without a difference. However, again we seem caught up in the epistemological problems that might arise in determining whether the conditional and the antecedent were true; and this is no concern of logic. I might say, as some have already said here, that in order to settle questions about such things one already has to be able to see what follows from what, and this logic, not epistemology can help you with.

c) If p, then q has a probability of n.
   p
   So, q has a probability of n.

Well, it walks like modus ponens, and it sounds like modus ponens…

John asks

Why does one care about this stuff? So long as we are safe in ivory towers and can focus our attention on the students who will be our successors, we can choose to behave as if all knowledge were (A) or (B) and reject (C) as beyond the pale. If we see ourselves and our students as people who want to make a difference outside the ivory tower's walls, we need to equip ourselves and them to approach (C) with greater sophistication than "Not (A), not (B), therefore nonsense" provides.

Now, putting on my flameproof suit....

I'll admit that my eyebrows were singed by the reference to ivory towers, and I was blown clean over by the implication that those safe in them are concerned with transmitting a useless formalism to students who will in their turn repeat this inbred process &c. This I take not only as an insult but what may be worse, a clear misunderstanding of what logic is and what logic does and why logic underlies all of one's attempts to discover not only how the world works but how to think about human problems of the deepest sort. Logic is not epistemology. But no epistemology without logic.

And if one is happy with a generation of Americans who cannot see that what a politician claims does not follow from what that politician offers as reasons for claiming it, then we can keep logic safe within the ivory tower under a glass case, safe from the speech of the people.

Robert Paul,

not really flaming anybody, just giving somebody the hot foot, as the Sunday comics taught him to do; a kid at heart, really




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