A theory is like a scheme someone draws up to help us see the principles of operation of a complicated machine, or to help us find our way through a town: it makes us see something which is otherwise obscured - and this may be accomplished at the cost of purposefully neglecting something else.
In order to lead him to admit that what he had was not trisection we should have to lead him to something new. Suppose we had a geometry allowing only the operation of bisection.
Full syllables can only be concatenated, an operation that does not require a pointer stack or equivalent apparatus necessary to implement true recursion.
Since language combines words into hierarchical tree structures, it is necessary for the language faculty to include, at a minimum, an operation for combining items.
All of these are ‘computational’ in Fodor’s original, generic sense (that is, they contain symbols that have both semantic and causal properties), and all of them are syntactic (rather than connectionist or associationist) in that at least some of their operation depends on the internal relations among the elements in their representations.
It is probable, that one operation and principle of the mind depends on another; which, again, may be resolved into one more general and universal: and how far these researches may possibly be carried, it will be difficult for us, before, or even after, a careful trial, exactly to determine. This is certain, that attempts of this kind are every day made even by those who philosophize the most negligently: and nothing can be more requisite than to enter upon the enterprize with thorough care and attention; that, if it lie within the compass of human understanding, it may at last be happily achieved; if not, it may, however, be rejected with some confidence and security.
Propositions of this kind are discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe.
We are apt to imagine that we could discover these effects by the mere operation of our reason, without experience.
But to convince us that all the laws of nature, and all the operations of bodies without exception, are known only by experience, the following reflections may, perhaps, suffice. Were any object presented to us, and were we required to pronounce concerning the effect, which will result from it, without consulting past observation; after what manner, I beseech you, must the mind proceed in this operation?
And as the first imagination or invention of a particular effect, in all natural operations, is arbitrary, where we consult not experience; so must we also esteem the supposed tie or connexion between the cause and effect, which binds them together, and renders it impossible that any other effect could result from the operation of that cause.