Heckscher-Ohlin and the ‘principle of explosion’

17 March, 2016 at 12:14 | Posted in Theory of Science & Methodology | 4 Comments

The other day yours truly had a post up on the Heckscher-Ohlin theorem, arguing that since the assumptions on which the theorem build are empirically false, one might, from a methodological point of view, wonder

how we are supposed to evaluate tests of a theorem building on known to be false assumptions. What is the point of such tests? What can those tests possibly teach us? From falsehoods anything logically follows.

Some people have had troubles with the last sentence — from falsehoods anything whatsoever follows.

But that’s really nothing very deep or controversial. What I’m referring to — without going into the intricacies of distinguishing between ‘false,’ ‘inconsistent’ and ‘self-contradictory’ statements — is the well-known ‘principle of explosion,’ according to which if both a statement and its negation are considered true, any statement whatsoever can be inferred.

poppWhilst tautologies, purely existential statements and other nonfalsifiable statements assert, as it were, too little about the class of possible basic statements, self-contradictory statements assert too much. From a self-contradictory statement, any statement whatsoever can be validly deduced. Consequently, the class of its potential falsifiers is identical with that of all possible basic statements: it is falsified by any statement whatsoever.

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  1. Professor, I’m one of those people who had trouble with that last sentence. I hear what you’re saying but, really, should you not go into the intricacies of distinguishing between ‘false,’ ‘inconsistent’ and ‘self-contradictory’?

    A false statement is a statement that can be, and has been, shown to be wrong. E.g. “Lars P. Syll is a famous footballer”. A self-contradictory statement is just that, self-contradictory, which means that, necessarily, one part of it will always be true and one false. E.g. “The famous footballer Lars P. Syll has never played football in his life”.

    If your last sentence should have been read “from self-contradictory statements, anything can follow”, you’re perfectly right. But, It was not at all obvious that this is how should have been read.

  2. Recommended reading: Popper’s Conjectures and refutations (1965, pages 317-319)🙂

    • Thank you. I’m not sure I have the same edition, can you give me the title of the essay that you refer to and, perhaps, a couple of sentences from the relevant pages?

  3. Bertrand Russell was once challenged to prove from the falsehood, 2 = 1, that he was the Pope. Russell replied, “The Pope and I and two, therefore the Pope and I are one. I am the Pope. ”🙂


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