Sunday, April 03, 2011

on inconceivability and impossibility.

I take it that for any proposition p, p might be inconceivable in at least two senses.  The first sense we might call inconceivable simpliciter because p is seen to be necessarily false for either logical or metaphysical reasons. Consider, for instance, that something is both red and not reda.  I take it that the reason why something is both red and not red is inconceivable is because we simply see (with the mind’s eye, so to speak) that it is impossible in itself, and something that is impossible per se is (or can be?) ipso facto inconceivable.  Thus, that something is both red and not red is inconceivable simpliciter not because of a lack of cognitive ability on our part.  On the contrary: that something is red and not red is inconceivable simpliciter because we have the cognitive ability to see its impossibility.

Similarly, the same can be said for some metaphysical statements.  That something can be both red and green all overb does not assert a contradiction, and hence it is logically possiblec.  Nonetheless, that something can be both red and green all over is impossible. Even though it is not contradictory per se, we see (with the mind’s eye, so to speak) that it is impossible per se. Thus, that something can be both red and green all over is impossible (though not logically so) and hence it is (or can be?) ipso facto inconceivable.  And further, as before, that something is both red and green all over is inconceivable simpliciter not because of a lack of cognitive ability on our part.  On the contrary: that something is both red and green all over is inconceivable simpliciter because we have the cognitive ability to see its impossibility.

In sum, a proposition p may inconceivable in at least one sense: a proposition p might be inconceivable simpliciter for logical or metaphysical reasons; namely, that it asserts a logical or metaphysical impossibility.

But, a proposition p might be inconceivable simply because we lack the cognitive equipment to see its possibility. We might call this sense of inconceivability lack inconceivability. A putative candidate for lack inconceivability might be that there is a color that is not red, blue, or yellow, nor some combination thereof.  I say that this proposition is merely lack inconceivable because it does not violate a law of logic nor does it seem metaphysically impossible (for it violates no law of logic nor do I see its metaphysical impossibility), but rather because I simply cannot imagine what it such a color would look like.  The only colors I can think of (conceive of) are those colors that are red, yellow, and blue, or some combination thereof.  But, it seems to me, to group the proposition that there is a color that is not red, blue, or yellow nor some combination thereof in the same class with something can be both red and not red and something can be red and green all over seems wholly unwarranted: I can see the impossibility of the latter two; the former is indeed inconceivable to me, but I just do not see its impossibility.

In sum, a proposition p is inconceivable simpliciter just in case we see the impossibility of p.  On the other hand, a proposition p is merely lack inconceivable if we cannot think of p but yet do not see its utter impossibility.

Now, with which kind of inconceivability should we tag the following proposition?

There is some hotel with an actually infinite number of rooms and guests such that if you were to add one more guest to it then there would be the same number of guests before the guest arrived as there was after the guest arrived.

I take it that this (unwieldy) proposition is inconceivable.  But is it inconceivable simpliciter? Not by my lights: it does not violate a law of logic, nor do I see its per se metaphysical impossibility.  (It may be metaphysically impossible, though, but I do not see its metaphysical impossibility.)

At best it seems lack inconceivable:  I simply cannot comprehend it.  But, the mere fact that it is lack inconceivable is not enough for us to think it is inconceivable simpliciter. As such, we are not warranted in saying that it is impossible; it could be impossible, but we do not seem to be in a position to know. 

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  a If you want to be fussy, add at the same time.                                                b If you want to be fussy, add at the same time.                                                c For you naysayers:  that two contraries are true of same subject is indeed logically impossible, but that red and green are contraries is not a tautology. You could stipulate that red and green are contraries, but good luck proving that they are with the mere use of tautologies and the rules governing logical syntax. 

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2 Comments:

Blogger loudogg said...

I just read this! This is exactly what I was trying to communicate in my comment on your last blog. I think you nail it.

I haven't read the PDF you emailed me yet.

8:37 AM  
Blogger Derek said...

Hey Louis! Thanks so much for your comments! And thank you for inspiring me to think about this stuff.

10:47 AM  

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