The only reason I dwelled upon so long on history in the previous section is to show you the forced adoption of logic and related formalisms as theories of thinking. I will argue below that logic was created as a science of demonstrative statements rather than thinking.
We can start by asking the question, why create formalisms at all? To give an example from a different domain, consider the science of harmony and counterpoint in music. Today, you can take a class in these topics, and learn about the basic principles and rules by which ``good music'' is made. There are well formed rules for constructing chords, which are ultimately collections of pitches that sound nice when played together. In fact, more than being nice, you can predict the psychological effect of particular chords on the listener (happy, sad, tension creating etc.) The surprising fact for me was to learn that a lot of such rules were not known during the lives of great composers like Bach and Mozart. In fact, analysts later constructed these rules by finding the regularities in the compositions of such geniuses. This allowed mediocre non-geniuses like me to study and learn the basic principles.
Socrates was one of the best virtuoso of argument making. He believed that the nature of things could be discovered by argument instead of empirical observation. Looking at the dialogues by Plato, one can't help but think that he almost succeeded. Aristotle later layed the rules for ``dialectic'' and ``rhetoric'' which formed the foundations of logic. These fields captured the regularities in the verbal demonstrations of geniuses like Socrates. They were put down so that mediocre non-geniuses could learn the principles and not get stuck, or be misled by arguments. Thus logic was invented as a science for the means of persuasion. It assumed the existence of two intelligent parties arguing on some topic. It layed down the rules which encapsulated the minimum intersection between people with different views that could be used for persuasion. Meaning of symbols were agreed upon the participants using their common concepts. So there is no focus on where those concepts actually come from. And finally, it did not say anything about what went on in the heads of the speakers.
Even in Leibniz's dream I quoted in the previous section, one can see the same picture. He says ``If controversies were to arise, there would be no more need of disputation between two philosophers than between two accountants.'' Logic is intended as a way to resolve disputes between two already intelligent participants. Again, the meaning of the symbols are taken for granted, because they exist in the heads of the participants. And nothing is said about what goes on in the heads of the participants, other than maybe the expectation that a small portion of it, namely deductive argumentation, might be simulated by mechanical calculation.
I do not mean to imply that classical AI is founded on mathematical logic. I do mean that they share some basic principles, namely
To illustrate the power of these principles in guiding an AI researcher's thinking, consider this quote from Lenat:
``First, we criticized the current expert systems for merely containing opaque tokens and pushing them around. Yet our example of having more general, flexible knowledge was nothing more than having more (and more general) tokens and pushing them around! Yes, all we're doing is pushing tokens around, but that's all that cognition is.''[Lenat and Guha, 1990]
Saying that a particular theory was not intended for a particular application is certainly not a proof for its inadequacy. But it makes one think whether we are stretching too far. After all, the physical symbol system hypothesis believes in an explanation of what goes on in our brains, within a formalism intended as a theory of statements those brains can generate. A formalism that just concerns itself with the minimum common ground that those brains can use to resolve disputes. In the following section I will try to describe a theory of thinking that relaxes some of these bonds, and gets its inspiration from cognitive science.