Is The Number of Our Possible Thoughts Finite or Infinite?

- Frank J. Leavitt, Ph.D.
Chairman, The Centre for International Bioethics

Faculty of Health Sciences, Ben Gurion University of the Negev, Beer Sheva, Israel

Email: yeruham@bgumail.bgu.ac.il

Eubios Journal of Asian and International Bioethics 13 (2003), 48-49.


Darryl seems to think that his mental mapping project (EJAIB 12 (2002), 203-6) requires the assumption that the number of our possible thoughts is finite. I do not know if this assumption is really required. I shall first discuss the question of the finitude or infinitude of our possible thoughts. Then I'll raise the question whether the assumption of finitude is really necessary. Then I'll explain why I think the project is in any case infeasible.

If human beings have only existed for a finite period of time, then the number of thoughts, which humans think or have thought seems to be finite. But the interesting question is whether the number of possible thoughts is infinite or finite. The philosopher, Wittgenstein, wrote that what can be thought can be said. If he was right, then the question can be rephrased as asking whether the number of possible sentences in a given language is infinite or finite. The linguist, Noam Chomsky, used to say that we have finite linguistic "performance" but infinite "competence". But this is incorrect. Languages are made from a finite number of building blocks, which might be phonemes or letters or whatever. We'll discuss letters for simplicity. The same letter can of course appear as many times as you like in one sentence, so we should discuss letter-places. There will be a finite number of one letter-place sentences, a finite number of two letter-place sentences, and so on. So if you were to have infinitely many sentences, then there could be no finite limit to the number of letter-places in a sentence in your language. There would have to be sentences so long that some would take a hundred years to pronounce, some would take a thousand years, some a million and so on. But no human being can to our knowledge pronounce such long sentences. So we must conclude that the number of possible human sentences is finite. If we may assume that every thought can be represented by a sentence, it follows that the number of possible thoughts is finite.

Wittgenstein's doctrine that what can be thought can be said was a dogmatic assertion for which he did not, to my knowledge, ever give a proof. Some dogmas, of course, may be true. Is this dogma true? It surely happens that we sometimes, or maybe even often, have thoughts which we cannot readily put into words. Often we search around for a way of saying what we wanted to say. Sometimes the language is inadequate. So we might try another language. Surely Hebrew is better than English for Biblical spiritual thoughts, Japanese is superior for the nuances of Japanese spirituality, and English is unbeatable for discussing Shakespeare, baseball, and things like that. And sometimes no existing language will do, so we invent new words and ways of using words in existing languages. Such is how languages develop. Nowadays, Asia seems to be leading the culture of the world, including bioethics. But the language is International English. So Asians are remaking English to fit new needs, often by inserting Asian idiom, often by simply free creativity. English is already out of the hands of the Americans and British, and will eventually become something which today's Americans and British would not recognize. Sometimes, however, no language, even after modification, can express our thoughts. We use, instead, art, or facial expressions, or touch, or try to help a friend to have an experience similar to that which words fail. If thought is freed from the constraints of language, might not the number of possible human thoughts be infinite?

If thoughts are not all expressible by language, are they not all expressible by other physical means? We might even hypothesize that every thought may be represented by a different brain state. I am neither suggesting that thoughts are brain states, nor that thoughts are not brain states, but merely asking what might be learned from the hypotheses that there is a potential one-one correlation between thoughts and brain states.

I should think that if there is a finite limit to the number of different kinds of brain cell, and a finite limit to the size of a human cranium, then it ought to be provable, by an argument similar to the one about sentences, above, that the number of possible brain states is finite. So if thoughts and brain states can be correlated one-to-one, then it would seem to follow that the number of thoughts is finite.

But what proof have we that thoughts and brain states can be correlated one-to-one? It should be noted that people have not always believed that the brain is the main organ of thought, or even that it is an organ of thought at all. The Bible and other traditional Israeli spiritual books sometimes refer to our thoughts as being in our hearts, and our ethics or conscience as in our kidneys. There is a recent book called The Heart's Code, by Paul Pearsall. Dr Pearsall argues that much of our thought is in our hearts, rather than our brains. He relates astonishing tales about heart transplant recipients acquiring thoughts, memories and feelings from their donors. He tells about a little girl who received a heart transplant from a murdered little boy. The girl began to have nightmares and fantasies about the boy's murderer and the circumstances of the murder.. According to Dr Pearsall, the girl then lead the police to the arrest of the murderer.

A truly scientific attitude can neither reject any idea, no matter how farfetched, until it is disproved, nor accept any idea, no matter how reasonable, until it is proved. So I shall remain open-mindedly skeptical about Dr Pearsall's book. But even if many of our thoughts are in our hearts and kidneys or elsewhere in our bodies, restrictions of kinds of cell and size of organ would probably lead us to the conclusion that the number of possible human thoughts is nonetheless finite.

Let us consider, however, an argument based on ideas of some of the great philosophers. The conclusion of the argument will be that our thoughts are not in our bodies, but our bodies are in our thoughts. For indeed, we have no conception of a physical body. So we have no good reason to believe that physical bodies exist. The full argument is in the philosophy of George Berkeley, and has been elaborated by his great successors such as David Hume and Bertrand Russell and A.J. Ayer and other Logical Positivists of the 20th Century. But here it is in brief. We can have no idea of anything other than sense perceptions. But the senses only perceive colour, sound, taste, smell, and tactile sensations. All of these are subjective, depending upon the state of the perceiver, the medium, and the distance and perspective from which the object is perceived. A tower might seem tall to someone close to it, and small to someone far. You might enjoy a dry red wine, and I might think it is unpleasantly sour. A surface might feel smooth to you and rough to me, or a weight might be heavy to one person, and light to another. The conclusion is that all we can know are subjective impressions in our own minds.

Some people think that physical objects cause these subjective impressions by reflecting light, or vibrating the air to make sound waves, or influencing our tactile sense through contact with the skin. But we have never had any experience of these so-called "physical objects". We have only experienced our subjective impressions. Indeed, nobody has ever experienced electrons, but only the colours of the subjective impression of a picture. Nobody has ever experienced a brain but only the subjective impressions which we call "seeing a brain" or "touching a brain". The same can be said of hearts and kidneys. And not having had experience of physical bodies, we have no idea what we are talking about when we try to talk about them. Our thoughts are not in our bodies. Our bodies are in our thoughts.

This being the case, the question of whether our thoughts are infinite or finite becomes unmanageable. If our thoughts are not in our bodies, we do not know where they are, if indeed they are anywhere at all. Are they in our souls, or in the mind of God? Is there a different soul for each of us, or do we all share in one universal soul? And not knowing the home or source of our thoughts, the question of their cardinality, finite or infinite, becomes totally unmanageable. There seems no way to prove it one way or the other. So our conclusion seems to be that we have no way of knowing if possible human thoughts are infinite or finite.

I am not sure, however, that the assumption of finitude is necessary to what Darryl wants to do. For the sake of the argument, let us assume per impossible that my arguments above are wrong, and that the number of possible human thoughts is finite. This would mean that although we cannot think all of an infinite set of thoughts, we can think any of them. Let us now assume that we have an algorithm, or a finite set of algorithms, which will allow us to get to any member of this infinite set of thoughts. The kind of algorithm which I have in mind can be simply illustrated by the operation of "+2", i.e. the addition of 2. If we start with zero, the first even number, we can use this operation to get to any member of the infinite set of even numbers. Given our per impossible assumption above, this means that although we cannot think of every even number, we can think of any one of them. Wouldn't a finite set of algorithms, which would allow us to get to any - but of course never to all -- of an infinite set of thoughts, be exactly what Darryl means by a mental map?

A problem with the above idea of approaching the project by means of algorithms is that a finite set of algorithms which is supposed to generate an infinite set of ideas, seems suspiciously similar to a finite set of axioms which is supposed to generate an infinite set of mathematical theorems. As everyone knows, Kurt Gdel proved in 1931 that given any axiom system in which the language of simple arithmetic can be formulated, there will be truths of simple arithmetic which the system cannot generate. Or to put it in other words, there will be statements of simple arithmetic for which the axiom system can give us no basis for deciding whether they are true or false. I do not know if the same proof would apply to a finite set of algorithms which is supposed to generate all possible human ideas. But the question would have to be investigated if we wanted to take the idea of mental mapping seriously.

But for a reason unconnected with infinitude, Darryl's project isn't feasible anyway. The reason is intellectual and artistic creativity.

Even if the number of possible human thoughts is finite, it is impossible to "map" them, because we have no way of knowing what acts of genius or prophesy will occur in the future. Could human thoughts have been "mapped" before Einstein published his theory of relativity? Or before Shakespeare wrote his plays? Or before the Bible was written? There are also countless archeological artifacts whose meaning and use are unknown or only matters for speculation, ancient societies whose cultures, religions and philosophies can only be guessed at. Is it not presumptuous and lacking in scientific humility to suggest that we could even begin to "map" human ideas?


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