The human brain does not start out as an efficient reasoning machine, plausible or deductive. This is something which we require years to learn, and a person who is an expert in one field of knowledge may do only rather poor plausible reasoning in another. What is happening in the brain during this learning process?
Education could be defined as the process of becoming aware of more and more propositions, and of more and more logical relationships between them. Then it seems natural to conjecture that a small child reasons on a lattice of very open structure: large parts of it are not interconnected at all. For example, the association of historical events with a time sequence is not automatic; the writer has had the experience of seeing a child, who knew about ancient Egypt and had studied pictures of the treasures from the tomb of Tutankhamen, nevertheless coming home from school with a puzzled expression and asking: ‘Was Abraham Lincoln the first person?’
It had been explained to him that the Egyptian artifacts were over 3000 years old, and that Abraham Lincoln was alive 120 years ago; but the meaning of those statements had not registered in his mind. This makes us wonder whether there may be primitive cultures in which the adults have no conception of time as something extending beyond their own lives. If so, that fact might not have been discovered by anthropologists, just because it was so unexpected that they would not have raised the question.
As learning proceeds, the lattice develops more and more points (propositions) and interconnecting lines (relations of comparability), some of which will need to be modified for consistency in the light of later knowledge. By developing a lattice with denser and denser structure, one is making his scale of plausibilities more rigidly defined.
No adult ever comes anywhere near to the degree of education where he would perceive relationships between all possible propositions, but he can approach this condition with some narrow field of specialization. Within this field, there would be a ‘quasi-universal comparability’, and his plausible reasoning within this field would approximate that given by the Laplace–Bayes theory.
A brain might develop several isolated regions where the lattice was locally quite dense; for example, one might be very well-informed about both biochemistry and musicology. Then for reasoning within each separate region, the Laplace–Bayes theory would be well-approximated, but there would still be no way of relating different regions to each other.
Then what would be the limiting case as the lattice becomes everywhere dense with truly universal comparability? Evidently, the lattice would then collapse into a line, and some unique association of all plausibilities with real numbers would then be possible. Thus, the Laplace–Bayes theory does not describe the inductive reasoning of actual human brains; it describes the ideal limiting case of an ‘infinitely educated’ brain. No wonder that we fail to see how to use it in all problems!
This speculation may easily turn out to be nothing but science fiction; yet we feel that it must contain at least a little bit of truth. As in all really fundamental questions, we must leave the final decision to the future.
David Udell comments on David Udell’s Shortform