Mad Men Series #5: Martin Gardner on mathematics as reality and the mystery of free will

By | July 24, 2010

A few days after the death of Martin Gardner this past May 22, 2010, a friend handed me the text of a very interesting interview that he did with “Skeptic” magazine. Most likely Michael Shermer, the editor, was the interviewer. In this interview Gardner discussed of number of fascinating issues and questions in science, philosophy, and religion. The interview gives us a picture of a lively, probing intellect, which Gardner unquestionably was. Although I often disagreed with some of his views, I always felt that reading and listening to what Gardner had to say taught me a lot. So my criticism of a couple of ideas brought out by this interview should not be read as implying that I did not respect and admire Gardner’s work.

What Mr. Gardner says concerning the possibility of an afterlife and the “mystery” of free will reminds me that even very intelligent persons can go off on the wrong track. Even a genius can sometimes affirm ideas, which in other contexts we might associate with the assertions of mad men. This overstates the issue, of course, but I’m impressed by the ease with which critics admit crazy ideas as respectable just because respected scientists, mathematicians, and philosophers affirm them. In this context, I propose inclusion of the following two sets of ideas in my mad man series.

Mathematics, Reality, and Possible After-Life

First, Gardner on the possibility of an afterlife based on the possibilities suggested by string theory in physics:

“ can defend immortality on the grounds that everything that constitutes our selves or our identity is a mathematical pattern. If superstring theory turns out to be true, they you can ask what are superstrings made up of, and they aren’t made of anything! If all matter is pure mathematics, then you can imagine that an all powerful deity who knew the pattern could reconstruct you. .”

The proposition that “everything that constitutes our selves or our identity is a mathematical pattern” is simply fantastic. Doesn’t it simply ignore biological reality, that is, the fact that first and foremost, human beings are biological beings? Regardless of where the highly theoretical work of string theorists seems to point, the facts are that physical, chemical, and biological reality is not just a mathematical pattern. To say that much of physical reality can be analyzed in terms of mathematical patterns is not to demonstrate that physical reality reduces to a mathematical pattern. This is simply a leap in reasoning, a fallacy, that too many mathematical physicists (e.g. string theorists) and metaphysically inclined mathematicians make. Gardner should have been more cautious in his philosophical inference.

The other part of Gardner’s statement, that one can ask “what superstrings are made up of” and answers that, since they’re not made of anything, “all matter is pure mathematics,” is simply some very hasty generalizations that don’t stand up to scrutiny. First, with regard to a highly mathematized physical theory like string theory, our intuitive concepts and ordinary language probably are not applicable. It is far from clear what is meant by asking what “superstrings are made of” or to see the equation of a constitutive ‘nothing’ with pure mathematics. These are simply metaphysical inferences that would need a lot of clarification before we could draw such inferences as Gardner is inclined to make: His conclusion that “matter is pure mathematics,” strikes me as just a piece of confused mystical metaphysics. Again it is surprising that Gardner would make such a careless move.

Surely such hasty and careless inferences regarding mathematics and physics cannot offer any support for the idea that a person, once having physically expired, can somehow be reconstituted. There is no support here for the idea of an afterlife.

Mystery of Free Will

Now let me turn to the other set of ideas, those concerning free will, that Mr. Gardner discussed in the interview:

M.G. “…there is the problem of human free will that makes prediction extremely difficult. On this question of free will, as a member of a group called the mysterians, I believe that we have no idea whether free will exists or how it works. .. “

Skeptic: You don’t believe free will is at the quantum level like some physicists do?

M.G. “ It doesn’t help if it is at the quantum level. That just makes it a random event, as if there is some kind of a roulette wheel in the brain. That doesn’t give you a choice. There are certain things I regards as ultimate mysteries. Free will is one of those. . . . Free will is bound up in the mysteries of time about which we can never understand, at least at this stage of our evolutionary history. . . ….. Mysterians believe that at this point in our evolutionary history there are mysteries that cannot be resolved, like free will. Noam Chomsky, for example, is a mysterian. He is on record saying that we don’t have the mental capacity to understand the nature of free will. . .”

Gardner claims that free will is a profound mystery beyond our power to resolve at this stage of our evolutionary history. This raises a number of issues which would take up more time and space than I have in this brief article. But I shall bring up a few outstanding problems and what I see as fallacies in this line of reasoning. It is commendable that Mr. Gardner gives short shrift to the idea that quantum physics somehow enables us to have free will. As Daniel Dennett has ably stated, this is wrong turn based on a misconception of what the free will problem amounts to; and would only show that some action is random. This does not show that humans are capable of what is normally understood by “free will.”

But Gardner’s statement that “we have no idea whether free will exists or how it works” assumes that free will is a mysterious entity which functions (works) in some way. This is surely a very questionable, likely confused, assumption. At the very least, this assumption needs to be examined and evaluated, not simply accepted as clear and unquestioned. It is the basis for much of the mystery of free will which Gardner then mentions as beyond our capacity to understand; hence, the embrace of the view of persons who call themselves “Mysterians.” (Daniel Dennett, in one of his books dealing the with free will issue, refers to the ‘mysterians.’ But I thought he was just applying a derogatory term to some of his opponents, like John Searle. Now I see that there is a group who go under that label.)

Admittedly, there are some puzzles and questions as to how our ability to make choices and engage in actions of our choosing (act ‘freely’ in this sense) is consistent with causal, scientific explanations (physics, biology, physiology, genetics, evolutionary psychology) of our conduct. But these puzzles do not demonstrate that we are incapable of free action or what traditionally has been called “free will.”
As Dennett has argued well, in this books Elbow Room and Freedom Evolves, nothing brought out by any of the relevant sciences show that what we ordinarily call free choice or free action are paradoxes or impossible in the context of scientific explanation.

The mystery that impresses Gardner only arises because people assume that free will is a faculty or power that operates outside the scope of the physical-biological functions that comprise the physical human person. It is much like the mystery that arises when one assumes that the soul and the mind are entities which are not accounted for by the natural sciences as they apply to human beings. Yes, if we assume the presence of such entities as the soul and the mind, which are not part of the human brain, nervous system, sense faculties, and such — then you have a great mystery. The same is true regarding the very questionable assumption that free will is an entity operating independently of a person’s physical nature. But there is no reason whatsoever to make that assumption. A number of clear-headed philosophers, like Daniel Dennett, have shown that our capacity for free action — what is ordinarily called “free will’ – is compatible with all that the sciences have to say regarding human behavior. The so-called, mysterians, despite counting among themselves brilliant people like Gardner and Noam Chomsky, have simply followed a very confused path on this question.

There are many mysteries, some even profound mysteries, which science has not yet solved and which we might not be capable of resolving at this stage of our evolutionary history. But the puzzle of free will is not one of them.

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