Hintikka’s Paradox comes from Deontic Logic, a form of Modal Logic. I first read about it in Raymond Smullyan’s “Alice in Puzzleland’ (a brilliant book about logic, and Alice in Wonderland, that is [...]]]> I’ve got lots more to post about bases, but right now I’m faced with a paradox – Hintikka’s Paradox, to be precise. 

Hintikka’s Paradox comes from Deontic Logic, a form of Modal Logic. I first read about it in Raymond Smullyan’s “Alice in Puzzleland’ (a brilliant book about logic, and Alice in Wonderland, that is worth looking into.)

In the introduction to “… Puzzleland,” Smullyan describes Hintikaka’s Paradox this way:

“Is it proper to call morally wrong something a person cannot do? Hintikka has a notorious arguent designed to show it is wrong to try to do something impossible. There is now a large literature on this strange question…”

I’ve yet to encounter much of that literature, and boy, I have looked. I probably wouldn’t have understood most of it, anyway. 

But it boils down to this, Hintikka’s Paradox implies that, “What is not possible is positively forbidden.” 

It’s important not to approach this from a “common sense” frame of mind. Common sense is usually neither, and is often a disadvantage when approaching counter-intuitive material. So try to keep an open mind. 

As far as I can tell, the logic of the argument goes something like this:

What cannot be done without something wrong being done, would itself be wrong to do.

(1) To do something that cannot be done without something wrong being done would itself be wrong. But (2) what cannot be done at all cannot be done either with or without something wrong being done.

 So, if x is impossible and y is wrong, I can neither do both x and y, nor do x but not y.

But, (by 1) if y is wrong and doing x but not y is impossible, it is wrong to do x. “

Hence (3) if it is impossible to do x, it is wrong to do it.” 

From – Encyclopedia of Philosophy, Vol. 4, Ppg 509-514

OK, I can follow the argument. 

Here’s my question – Why do they have to addend ‘y’ to the argument to make the point? I mean, to me, in a “common sense”  way (always wrong to do), I would think* that I could just as equally say, “If x is impossible and y is not wrong, I can neither do both x and y, nor do x but not y. The “But, (by 1) part is not not applicable, thus the conclusion of above (“if it is impossible to do x, it is wrong to do it” ) cannot be drawn.

In my simple mind, it seems as though they are throwing in a red-herring (something that is not logical, but appears so, in order to muddle the argument). Sort of like saying, “If Joe is a guy, and Max is a communist spy, then Joe and Max cannot both be “good guys.” But if Max is a communist spy, and Joe existing without Max is impossible, then Joe must be a communist spy.”

Of course I am aware that my comparison is wrong. I just don’t understand (yet) why it is wrong. My not understanding is due to my incompetence, I know, and not to any flaw in Hintikka’s logic. I’d just love to be able to understand the logic. 

The reason for my interest in this paradox, is that if I can understand it better, I think I can use it for a philosophical quandary I am in. It relates to politics. (See kids, I am always trying to use math or logic to get more meaning out of life. Feel free to play along at home.)

I am not a logician. But if someone out there reading this is a logician, or understands the paradox, could you please explain it to me in a comment? Remember, neither I nor most of my readers are logicians, so take it easy on the jargon, K?

*By the way, whenever most people, including myself, use the phrase, “I would think,” or “You would think,” you can be fairly sure that they will follow it by saying something that is wrong to think. I’m probably guilty of it in thinking “y” is a red-herring.

If you have some mature, fermented thoughts on this, please let me know. Remember, I’m looking for clarity, not more common-sense muddling. If your not a logician, or something like it, please ask your logician uncle Raymond, or someone, and have him/her take a look at it. 

All the best, 

Brian