A plausible resolution of the free will paradox?

The question is not so much, “Do we have free will?”, as, “What would free will even mean?" There does not seem to be a way to make the concept of free will coherent. If there is no way to render an idea sensible, then what sense would it make to ask if the idea is correct?

The paradox comes in because I believe we all assume that we have free will, and usually that others do too. And we blame and punish wrongdoers, i.e., criminals, as if they were free do not have committed their crimes. We try to convince others of some idea, or to persuade them to do something, all of which seems nonsensical if their behavior and their thoughts are determined. To complete the paradox, consider that no one can consistently maintain strict determinism, since they would make to make the tacit assumption that they were free to have arrived at that conclusion.

Consider this: you by a new Mac. It comes bundled with software and firmware, that is, an operating system along with a host of standard applications, but of course this all runs on a particular hardware architecture that is presumably identical to all other instances of that particular Mac model. Certain settings are peculiar to your machine, as you fire up the machine and choose preferences and various control panel settings. As time passes, and you begin to use your computer, you create files, and download and install certain additional programs. Very quickly your computer is like no other. The computer acquires what seems to be a “personality”. You yell at it such things as “Oh, come on, I didn’t say to do that”! and so forth, even though you know it is just a machine, doing what its hardware and software dictate it will do. To this, we can in principle add randomness, that is, such things as a power surge, or cosmic ray induced bit flips, and so on, which can cause it to deviate from a predictable path on occasion.

Now I want to make the analogy that the initial state of the machine is like our genetic makeup, with the aforementioned “preferences” added, while the installed software is analogous to what an organism learns and adapts to through experience. So, just as the hardware and installed software entirely determine what the machine will do (excepting the small input from random perturbations), so genetic makeup (“nature”) plus the build up of life experiences (“nurture”) entirely determine how an organism will behave. If you doubt this, please tell me what these other factors might conceivably be.

It does no good to say that there is some kind of “internal you” or “self”, that decides what to do, because we cannot imagine where that self has emerged from other that from experience plus genes. “Nature plus nurture” seem to be the only conceivable process that could have created a conscious self.

Some people have suggested that the existence of a spirit or soul might be injected here to leave room for escaping from the hardware plus software factors. I disagree, because the same problem emerges even then. As long as we postulate that that spirit or soul has a beginning (in some sense, not necessarily temporal), the determining factors would seem to shift to some kind of “supernatural hardware” plus experience (in the natural world plus in the postulated “super-nature” or transcendent realm).

So, what is the proposed “solution”, or “resolution”, I mentioned in the heading? It is, not unexpectedly, difficult to explain. I believe that it is that, to be able to render the concept of determinism coherent, we would have to be outside “the system” of existence we are all in. Only a being outside of that would have the intellectual basis to observe that we are all determined beings, without free will. Since we are all inside, and not outside, nobody can get outside to make the consistent observation that we are all determined. We are trapped, “within the system”, and all have to make (what is at least a consistent assumption) that we are possessed of free-will. But all of us knowing that, at some level of reality beyond the one we have access to, we all have to be determined. In other words, we have no choice but to consider all of human-kind to have free will.

This has perhaps some similarities to the Godelian idea that mathematical systems are either incomplete or inconsistent. Only here we have a concept, “free will”, which cannot really be defined in a coherent manner, but one that we must necessarily assume exists. This appears to be a consistent approach, in that by symmetry everyone can assume everyone else has free will, knowing that our understanding of what it means is fuzzy and incomplete. The opposite position, that everyone is determined, is not a symmetrically consistent ‘solution”, since the person maintaining it would seem be excluding himself or herself as a determined being (since he/she would not have been free to use reason to arrive at that position). This is all an odd state of affairs, to be sure, but we know going in that it has to be, since philosophers have struggled with it with limited success for a good chunk of recorded history.

The Story of the Blue Eyed Islanders

One of the most perplexing problems I have ever encountered is the infamous “Blue Eyed Islanders” puzzle. The perplexing aspect is a seeming paradox I will get to shortly, but the nominal solution involves straightforward induction, and is relatively easy to understand. It is possible that the story also has some applicability to more realistic human societeies.

The puzzle may be stated as follows:

There is a village where everyone has either blue eyes or brown eyes. Each person can see what eye color everyone else has, but each does not know the color of his or her own eyes. It is strictly forbidden for any islander to tell anyone else what color he/she has. If on a given day one happens to find out the color of ones own eyes, one must hurl oneself into the volcano at dawn the next day.One day an outsider comes to visit, a person who is known to always tell the truth. This person asserts for all to hear that “some of the people in this village have blue eyes”. Within a certain number of days, all in the village have killed themselves.The relatively easy parts of the puzzle are "why", and "when" does this happen?

Assume first that there is only one blue eyed person. He does not know that he has blue eyes until the fateful day of the outsider’s statement, but he does know that all of his fellow islanders have brown eyes. He thinks it is possible that he has brown eyes himself. But after the statement that there is at least one blue eyed person, he knows that it must be he himself, and the next day he commits “volcanacide”. If he were to see any other blue-eyed persons, he would not do himself in on the first dawn. So when the remaining brown eyed people see him do the deed, they all know that he saw all brown eyes, and thus they all have brown eyes. On the second dawn, they too jump into the fiery pit.

It is easy to see that if there were two blue-eyed persons, say Sam and Sara, each would think it possible that the other blue eyed person is the only one. But Sam sees that when Sara does not jump into the volcano upon the first dawn, he knows that he also has blue eyes, and on the second dawn Sam jumps in, and so does Sara, for exactly the same reasoning with regard to Sam. All the rest would jump in the third day, since they then deduce that they all have brown eyes, since evidently only Sam and Sara had the blue eyes the outsider noticed.

From induction, it follows that for a village population of N people, with X blue-eyed people and N-X brown eyed people, all of the blue eyed people will hurl themselves into the volcano X days after the outsider’s assertion. On day X+1, the brown eyed people will follow.The paradox is that every individual person in the village already knew, before the outsider’s visit, that there were some people in the village that have blue eyes (assuming that there was more than 1). They simply could see them, because if you were a blue, you’d see X-1 blues, if you were a brown, you’d see X blues. So what did the outsider tell them that they did not already know? That is, what specific new information did the outsider give them that led to the mass suicide of the village?

To illustrate this more concretely: What if there were 1000 villagers, 400 (say) with blue eyes. Before the outsiders visit and his unfortunate faux pas, each native knew that there were at least 399 blue eyed people on the island. Doesn’t it seem absurd that the statement that there is at least one would cause all 400 of the blue eyed people to hurl themselves to their doom on the 400th dawn, and the rest of the browns would follow on the 401st dawn? Thus, in this example, it would take over a year for the village society to cease to exist.

It seems that if one accepts logical induction, as surely one must, this surprising outcome must occur. The situation was stable before the outsiders made his observation, but the observation rendered that society unstable, and it rather quickly became extinct. It makes one wonder about possible applicability to more realistic human societies: could it be that some of the seemingly arbitrary taboos that have been put in place in various closed civilizations could somehow serve to stabilize them? In the example above, the particular taboo seems silly and unrealistic (and have they no mirrors or reflecting surfaces?). And even if an arbitrary taboo does bring about stability, we must also ask whether it involves a morally acceptable restriction, and if it is the only way that such stability could be achieved.

Perhaps the morale to this story is that there should be no taboos, but rather that human societies should be based on universal morality, that in turn is based on game theoretic reasoning such as is involved in the “prisoners dilemma” (this is really a sort of a generalized “golden rule”, wherein each person respects the rights of others to “live and let live”). But that is another tale, hopefully to come in a later blog.

Resolution of the "Unexpected Hanging Paradox"

The Unexpected Hanging Paradox:

Here is a short version of a paradox that has intrigued me since I was in college: A condemned prisoner is told by the warden on a Sunday evening that he will be executed at noon on one of the upcoming weekdays, i.e., M-Tu-W-Th or F, but he will not know in advance which day it is until the time comes. The day of his hanging will be a “surprise”. The prisoner reasons that if Thursday noon passes and he has not yet been hung, then he can rule out Friday since that is the only day left and then he would know what day he was to die, in violation of the conditions specified by the warden. But having crossed Friday off the list, he quickly realizes that he can cross Thursday off too, since once Wednesday noon is past Thursday is the only day left (since he has already eliminated Friday). Going on this way, he realizes that he can eliminate all 5 weekdays, one by one, and he is happy to realize that he cannot therefore be hung (let’s say that he strongly believes the warden to be a truthful man). But here is the (sad) paradox…the executioner comes to his cell on (say) that Wednesday, and informs him that he is now to be hung. His last thoughts before dying are that the warden indeed spoke the truth: that he, the prisoner, was indeed going to be hung, and he was certainly surprised by it too. Where did his reasoning go wrong? It seemed so logical that he could not be hung if the warden was telling the truth……and yet, in the end, the warden did tell the truth. Seemingly, a paradox!

The Resolution:

Here is my understanding of the resolution of the paradox (and I think I follow, essentially, Martin Gardner’s explanation from his book with the paradox as the title). The prisoners’ reasoning goes wrong on the very first step. He cannot rule out Friday even if Thursday noon has come and gone. In somewhat formal logic terms, I see it as follows. Let the wardens statement to the prisoner be written as C =A + B, where A = “you will be hung”, and B = “you will not know in advance of the day of the deed”. First, suppose A = true. That would mean that B = false, and hence C = A + B = false. Next, suppose instead that B = true. Then this would mean that either A or “not A” can be true; if A is true, then C = A + B is true, and if instead "not A" is true, then C = A + B is false. This makes sense because even if he doesn’t know the day of the hanging, then he could still either be hung or not hung. Thus, considering all of the above possibilities, we see that C can be true or false. It could just as well turn out to be true as it could turn out to be false. So, if it turns out after the fact that C is true, this does not really entail a contradiction. What the prisoner should have realized is that the warden’s statement could turn out to be true or false, and since he could not be sure ahead of time what the truth value was, he could not logically deduce the outcome from it.