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On the innateness of human concepts



Consider an algebra which defines a set of initially uninterpreted symbols. The algebra is employed by a system which is exposed to an unknown and unpredictable sequence of inputs. Depending on the input sequence, the symbols from the algebra are used to represent subsets of the input states with certain similarity properties. In this case, we may say that the system assigns "meanings" to the symbols; and the set of meanings that may be acquired by the symbols is undefined and open-ended.

Consider an algebra which defines a set of symbols. We fix the meanings of these symbols through some recursive definition. In this case, the set of meanings that may be acquired by the symbols is fixed.

The doctrine that the human conceptual repertoire is a closed combinatory system was an explicit tenet of Mediæval Catholic theology, and returned surprisingly in twentieth-century linguistics. One of its most enlightening discussions is due to Lewis Carrroll.

   




Mediæval theology

Anima enim facit novas compositiones, licet non faciat novas res.
(The soul makes new compositions – it cannot make new things.)

Bonaventura de Bagnoreggio: Commentarium in Tertium Librum Sententiarum, 37, 1, dub. 1. (1250-1252) [Quoted in: Umberto Eco: Il problema estetico in San Tommaso (1956).]

Aquinas does not refer to artistic production as "creation." His position is that man must have the humility to acknowledge that he does not bring forms into existence ex nihilo, since the forms which he produces are dependent upon a preexisting, concrete, and organic reality. In fact Aquinas suggests that they arise out of the preexisting reality, that they were already present there in potency.

Umberto Eco: Il problema estetico in San Tommaso (1956).

 




Lewis Carroll

        After a minute or two he began again. “If I’m not wearying you, I would like to tell you an idea of the future Life which has haunted me for years, like a sort of waking nightmare--I ca’n’t reason myself out of it.”       

        “Pray do,” Arthur and I replied, almost in a breath. Lady Muriel put aside the heap of music, and folded her hands together.

       “The one idea”, the Earl resumed, “that has seemed to me to overshadow all the rest, is that of Eternity -- involving, as it seems to do, the necessary exhaustion of all subjects of human interest. Take Pure Mathematics, for instance -- a Science independent of our present surroundings. I have studied it, myself, a little. Take the subject of circles and ellipses -- what we call ‘curves of the second degree’. In a future Life, it would only be a question of so many years (or hundreds of years, if you like) for a man to work out all their properties. Then he might go to curves of the third degree. Say that took ten times as long (you see we have unlimited time to deal with). I can hardly imagine his interest in the subject holding out even for those; and, though there is no limit to the degree of the curves he might study, yet surely the time, needed to exhaust all the novelty and interest of the subject, would be absolutely finite? And so of all other branches of Science. And, when I transport myself, in thought, through some thousands or millions of years, and fancy myself possessed of as much Science as one created reason can carry, I ask myself ‘What then? With nothing more to learn, can one rest content on knowledge, for the eternity yet to be lived through?’ It has been a very wearying thought to me. I have sometimes fancied one might, in that event, say ‘It is better not to be’, and pray for personal annihilation -- the Nirvana of the Buddhists.”

       “But that is only half the picture,” I said. “Besides working for oneself, may there not be the helping of others?”

       ”Surely, surely!” Lady Muriel exclaimed in a tone of relief, looking at her father with sparkling eyes.

       “Yes,” said the Earl, “so long as there were any others needing help. But, given ages and ages more, surely all created reasons would at length reach the same dead level of satiety. And then what is there to look forward to?”

       “I know that weary feeling,” said the young Doctor. “I have gone through it all, more than once. Now let me tell you how I have put it to myself. I have imagined a little child, playing with toys on his nursery-floor, and yet able to reason, and to look on, thirty years ahead. Might he not say to himself ‘By that time I shall have had enough of bricks and ninepins. How weary Life will be!’ Yet, if we look forward through those thirty years, we find him a great statesman, full of interests and joys far more intense than his baby-life could give -- joys wholly inconceivable to his baby-mind -- joys such as no baby-language could in the faintest degree describe. Now, may not our life, a million years hence, have the same relation, to our life now, that the man’s life has to the child’s? And, just as one might try, all in vain, to express to that child, in the language of bricks and ninepins, the meaning of ‘politics’, so perhaps all those descriptions of Heaven, with its music, and its feasts, and its streets of gold, may be only attempts to describe, in our words, things for which we really have no words at all. Don’t you think that in your picture of another life, you are in fact transplanting that child into political life, without making any allowance for his growing up?”

       “I think I understand you,” said the Earl. “The music of Heaven may be something beyond our powers of thought. Yet the music of Earth is sweet! Muriel, my child, sing us something before we go to bed!”


Lewis Carroll: Sylvie and Bruno Concluded, 1893. Chapter XVI: "Beyond These Voices".


 


Kazimir Malevich

If originally there was no consciousness, then today it doesn't exist either, and also there are no thoughts, where should they come from?

Kazimir Malevich: "Aus dem Buch der Ungegenständlichkeit." (1924) German translation by Gabriele Leupold in: Boris Groys, Aage Hansen-Löve & Anne von der Heiden (eds.): Am Nullpunkt. Positionen der russischen Avantgarde. Frankfurt am Main: Suhrkamp Verlag, 2005, pp. 545-599. [p. 588]

 

 



Fodor & Chomsky

In "The Language of Thought" (1975), Jerrold Fodor observes that the models of modern cognitive science, inspired by "symbolic A.I.", analyse the mind as a consistent computational system that performs calculations on mathematically well-defined "representations". This implies that all concepts that a person's cognition can ever employ are generated by a pre-established algebra of elementary concepts and operations: the "language of thought" of this person. A person's conceptual repertoire is therefore completely innate.

In the preface of his book (p. ix), Fodor emphasizes that its major claim has the structure of a logical implication ("If our psychology is, in general, right, then the nature of the mind must be roughly this ..."), and he mentions the possibility that its premiss is false: "It may, after all, turn out that the whole information-processing approach to psychology is somehow a bad idea". One could therefore surmise that Fodor's book is a "tongue-in-cheek reductio ad absurdum" (Scha, 1992); and in a live discussion with Seymour Papert and others, Fodor admitted this in so many words (cf. Piatelli-Palmarini 1980, p. 269).

Whenever his interlocutors are less fearless than Papert and Putnam, however, Fodor tends to reiterate the innateness of our conceptual repertoire (e.g. Fodor, 1981). Noam Chomsky (1988, pp. 134, 190-191) admitted that the idea is "so surprising as to seem outrageous", but nevertheless endorsed it as an incontrovertible research result.

Quotes

Fodor's position that we can only learn or conceive of what we already know, since any concept that we form must be assembled from concepts and relations that we already possess, has the flavor of the well-known proposition that "all books are already contained in the alphabet." As the reciprocal of this proposition is equally true, we may deduce that "the set of all books is equal to the alphabet," namely, "there exist 26 books" and "the alphabet is an infinite set." Applied to biology, Fodor's theorem leads to even more startling conclusions, one of which peremptorily dispells all further reflection on this subject. The first is that Darwinian mechanisms are incapable of producing the sequence of forms leading to species like Homo Sapiens: from this follows the proposition that "all species and their subsequent forms are contained in the primitive protogenetic alphabet," with conclusions analogous to those of the preceding example. The second conclusion is that species like Homo Sapiens do not in fact exist; I will call it Fodor's cogito ergo non sum.

Cellérier (1980), pp. 86/87


Then, applying Fodor's theory to the history of mathematics would be tantamount to saying that nothing has ever been invented, that everything is always contained in the previous state, and that, consequently, mathematics in its totality is predetermined and innate. (...) For my part, I have a difficult time believing that Cantor's theories or today's theories of categories are already preformed in bacteria or viruses; something must have developed . . .

Jean Piaget, in Piatelli-Palmarini (1980), p. 150.


Fodor has not pursued his train of thought until its final conclusion. If we accept that our conceptual repertoire is innate, Fodor's reasoning can be applied in exactly the same way to the biological evolution of this genetic conceptual repertoire. And then it follows that dead matter already possesses the same set of concepts! This improved version of Fodor's reasoning was in fact put forth in all seriousness by the unorthodox Jesuit paleonthologist Pierre Teilhard de Chardin, in the visionary Darwinist eschatology of his book "Le Phénomène Humain."

Scha (1992)


Seymour Papert:
"I would like to ask Fodor why he wrote a book that was so difficult (...), if all he wanted to say was the tautology that you can't build from nothing?"
Jerrold Fodor: " (...) the reason that I pursued my line of argument, despite the fact that I find it embarrassingly trivial, the way Papert puts it, is that (...) it seems to me to have ramifications of a very great importance, so great, as a matter of fact, that (...) I am inclined to think that the argument has to be wrong, that a nativism pushed to that point becomes unsupportable, that something important must have been left aside. What I think it shows is really not so much an a priori argument for nativism as that there must be some notion of learning that is so incredibly different from the one we have imagined that we don't even know what it would be like as things now stand."

In: Piatelli-Palmarini (1980), pp. 268/269. (Italics in the original.)

References

Guy Cellérier: "Some Clarifications on Innatism and Constructivism." In: Piatelli-Palmarini (1980), pp. 83-87.

Noam Chomsky: Language and Problems of Knowledge. The Managua Lectures. Cambridge, MA: The MIT Press, 1988, pp. 134, 190-191.

Jerrold A. Fodor: The Language of Thought. New York: T.Y. Crowell, 1975.

Jerrold A. Fodor: "The Present Status of the Innateness Controversy." In: Representations. Philosophical Essays on the Foundations of Cognitive Science. Cambridge, MA: The MIT Press, 1981, pp. 257-316.

Massimo Piatelli-Palmarini: Language and Learning. The Debate between Jean Piaget and Noam Chomsky. Cambridge, MA: Harvard University Press, 1980.

Remko Scha:
"Virtual Grammars and Creative Algorithms." Gramma/TTT 1, 1 (1992), pp. 57-77.

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