Possible Words

Consider the proposition P

(1) I am a man.

P(1) happens to be true.  I am in point of fact a man, cisgendered and all.  Consider, now, Q:

(2) I wear a bra.

Q(2) is not true.  I don’t happen to wear a bra.  Some men do, I’m sure, and I have no problem with that at all (in fact, good on them!) but I am not one of them.  Now, consider this statement:

~P -> Q

(3) If I were not a man, I would wear a bra.

I’m aware that man and woman are not the only two options, probably more aware of that fact than most, but let’s for the sake of argument assume that ~P is equivalent to R:

(4) I am a woman.

So (3) is equivalent to:

(5) If I were a woman, I would wear a bra.

Is (5) true?

In traditional logic, R -> Q is true just in case Q is true when R is true.  But there’s a problem: What I wrote above isn’t quite accurate.  ~P -> Q isn’t (3) If I were not a man, I would wear a bra.  ~P -> Q is this:

(6) If I am not a man, then I wear a bra.

The difference between (5) and (6) is a different of modality.  (6) is making binary yes/no, true/false distinctions about the world.  (5) is making hypothetical statements about the world.  We have no problem saying that (6) is true or not true according to traditional logic, but (5) throws a wrench in traditional logic.

For a statement like (5) you need modal logic: a logic that takes into account the hypothetical.

But there are problems with that, problems that impinge on the nature of magic in ways that logicians might not like, or even be aware of.

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2 Responses to “Possible Words”

  1. Greetings Patrick,

    I’m not familiar with Modal Logic, can you suggest a premier that will be useful in understanding your recent view on magic?

    A casual observer,
    Adonis

    • There’s a really good book on formal logic, but I can’t remember the name and a tour of my bookshelves didn’t turn it up. I think it’s got a black cover? Maybe?

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