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I am Dumb, but Dummies Lie

One of the most interesting and challenging logical phenomena discovered in the 20th century was the rigorous study of the relationship, for a certain class of statements, between what the statement asserted, and what the statement said about itself asserting what it did.  

I know it sounds like a bit of tongue twister, or something far too post-modern.

But hang with me, here.

Assertion is only one concept that could be used here, whatever sentences can be used to do could be also be studied.

Raymond Smullyan popularized a good deal of the formal logic, which started by by the great logician Kurt Godel, in 1931.

A simple toy example is the statement, said by someone who either neither lies or always lies, a knight or knave, is the statement:

"if I am a knight, then the next US President will be black.".  

If a Knight says this, the sentence is true and since the antecedent is true, the consequent must be true.

If a Knave says this, the sentence is false, which can only be if the antecedent is true and consequent is false.  But, this cannot happen since the speaker is a knave.

Basically, in this toy world of knights and knaves, whenever the sentence "If, I am a knight, then P" is asserted we can conclude the speaker is a knight and P is true.

But what does this matter for to our world?  Where people are neither knights or knaves?

The Godel/Smullyan model of relating the truth content of the statement to manner in which it was asserted gives us useful insights.

For example, consider what Robin Hanson said about Byran Caplan recently on the relationship between being irrational and the consequences of being wrong.

Hanson notes that

"Caplan says that people tend to be irrational on questions where there are no direct material costs of being wrong.

But there are no direct material costs to Caplan of being wrong on most if not all of the questions he addresses in this book.

Even if he is utterly mistaken, he will continue to receive his salary for the rest of his tenured existence.

Admittedly, this is only a "tendency," but considering the fact that Caplan has gone to the trouble of writing a book on this topic, he probably has a big emotional investment in his answer."

His considered conclusion?

"Bryan says he is not claiming to be infallible and that experts are better than amateurs, but those are beside the point. 

The issue is simple: does Bryan in fact have much lower confidence in his political opinions, vs. his other opinions?  If so, he is consistent; if not, not."

This is the right conclusion - we should all have lower confidences about beliefs that if wrong don't immediately whack us in the pocket book.

But the Caplan thesis is even odder, as I pointed out on Hanson's blog, which he agreed with.

Let Y, version of Caplan's thesis be, "I hold irrational beliefs about X, when there are no material costs to being wrong about X."

Suppose that there are no material costs about being wrong about Y.

Then, if Caplan's thesis, Y, is true, then Caplan is irrational about Y.

Is this a valid argument?

Is this a sound argument? (Valid, with true premises?)

I think so, and I believe that Hanson does too, because his response was:

"Michael, substituting "tend to be" for "am" sounds valid and sound."

If Hanson is right, it makes for a wild conclusion:  

If Caplan's thesis is correct but they are no material costs being wrong about it, we ought to distrust as irrational anyone who puts forth this true view!

And you thought Diogenes had it difficult!

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Full post as published by Misleading Advertising Law on September 10, 2009 (boomark / email).