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
Hi Brian,
Let’s try to step through this together. I am with you in thinking there is
something fundamentally and structurally wrong with this argument in regards
to Y.
Here’s my gut reaction. It goes to Ayn Rand’s clarification that something
can not both be and not be. Thus you can not both do and not do. The argument
asserts that DOING something that CAN NOT BE DONE is wrong. However you can
never DO what CAN NOT BE DONE and the question whether DOING it is right or
wrong can not even be asked because you have to have DONE IT in order ask
whether what’s been DONE is right or wrong. Something that HAS BEEN DONE can
not be something that CAN NOT BE DONE.
It may end up that this entire argument is fallacious due to the equivocation
of doing with attempting. All right, to the argument step by step.
Let’s start with the first two statements:
(1) To do something that cannot be done without something wrong being done
would itself be wrong.
So given the presumption that to do something wrong is wrong this is obvious
right? If I can’t open a particular door, a door that can not be opened,
without also killing someone, an act accepted as being wrong, then the fact
that the door can not be opened is irrelevant to the question of right or wrong
because the death that results would make it wrong in and of itself. This is
really no more than a trivial statement that doing something wrong is wrong.
It looks like here doing something that can’t be done is the red herring.
But (2) what cannot be done at all cannot be done either with or without
something wrong being done.
Again trivial, you can not do something that can not be done. The doing or
not of something wrong seems to be the red herring here.
So how are we doing here? Is this entire paradox a meaningless red herring
altogether?
Looking forward to your perspective.
Professor Homunculus sez:
Vince, those were pretty much my thoughts, too. But knowing me, I think I am probably missing something. I was hoping someone who has dealt with this paradox from a “professional” point-of-view would fill me in on what I was missing.
I think the key lies in that conclusion that what is wrong is “forbidden” (not just wrong). I’m not sure about that, though. What I am pretty sure about is that something that has gotten as much attention from brainiacs as much as deontic logic has, probably has some deeper meaning behind it. That’s not a definite, but usually things I find trivial, that did not originate from trivial minds (like, say, “Survivor”) has something that I can learn from.
My pragmatic interest in this is that one of the things that I believe, but do not have a good logical proof for (by proof, I mean formal proof) is that if something is impossible, or cannot be done without creating a bigger wrong than if it is not done at all, then it is wrong to ask someone to do it.
Aside from politics and empire-building, my interest in this is pedagogical. I’m trying to figure out an iron-clad argument against unfunded and impossible-to-fulfill mandates like “No Child Left Behind.” Even the name is bullcrap. No society will ever exist without leaving some member of it behind, and children are usually first.
Of course the common-sense argument is iron-clad against this atrocity, but common sense is not really within the purview of most people. Not that formal logic is, but I guess I need it to make myself feel better. You know the old saw – “When everyone is crazy, the sane man seems insane,” or something like that. Sometimes I need the comfort of math to prop up my war-weary soul.
Does it even make sense to talk about doing things in terms of impossibility?
The true paradox of this entire discussion is you can not prove impossibility.
Or is it a paradox at all? Couldn’t an argument asking you to consider a
premise that can not be proved in the first place be considered a red herring
itself?
I think you have two choices to resolve your dilemma:
1. calculate the probability of failure for a given policy goal
and create an argument that shows pursuing such a minimal chance
of success is morally wrong
2. prove the argument that led to the pursuit of a policy is
not valid and/or not sound. This would allow you to conclude the
pursuit is not only wrong but also insane.
It’s a daunting task for sure because the creators of such
arguments are trained at concealing fallacies to promote their
causes.
Vince
“but usually things I find trivial, that did not originate from trivial minds (like, say, “Survivor”) has something that I can learn from.”
Don’t discount yourself. One of the reasons I left academic philosophy
is the de facto acceptance of espousals made by proven experts to be
worthy of consideration.
The other was the shift to linguistic gaming which allows the use of
words to change meaning and be considered proof.