Discreteness is that feature by which syntactical elements retain their identity under the various syntactical operations.
Generativity, as I am using the term, implies that the syntactical operations of the language allow the speakers to generate an indefinite number of new sentences.
The vast number of logical possibilities for constructing erroneous derivations using Merge are kept in check by several principles of economy, which dictate, for example, that certain operations are to be executed later rather than earlier in a derivation, that local relations among elements are to be preferred to longer-distance ones, or that simple operations are to be preferred to more complex ones.
The theory still posits that the derivation of every sentence involves a sequence of abstract syntactic trees, related by movement operations or their equivalent.
For example, in the version of Chomsky (1995), a sentence like John saw Mary has a tree with six levels of embedding, four traces (the result of four movement operations), and five alternative derivations that need to be compared to ensure that one of the economy requirements has been satisfied (Johnson
Insofar as their desired effects on linguistic structures are clear at all, those effects must be explicitly stipulated, and would have to be spelled out as complicated conditions on operations in any explicit implementation.
Part III And finally, as it is not enough, before commencing to rebuild the house in which we live, that it be pulled down, and materials and builders provided, or that we engage in the work ourselves, according to a plan which we have beforehand carefully drawn out, but as it is likewise necessary that we be furnished with some other house in which we may live commodiously during the operations, so that I might not remain irresolute in my actions, while my reason compelled me to suspend my judgement, and that I might not be prevented from living thenceforward in the greatest possible felicity, I formed a provisory code of morals, composed of three or four maxims, with which I am desirous to make you acquainted.
Beliefs are a kind of information, thinking a kind of computation, and emotions, motives, and desires are a kind of feedback mechanism in which an agent senses the difference between a current state and goal state and executes operations designed to reduce the difference.
That sense—in which a system’s state transitions map onto logical relationships, or, as Fodor often puts it, the components of the system have both causal and semantic properties—says nothing about binary digits, program counters, register operations, stored programs, or any of the other particulars of the machines that process our email or compute our taxes and which are improbable characterizations of a human brain.
The beauty of Fodor’s original formulation is that it embraces a variety of systems that we might call ‘computational’, including ones that perform parallel computation, analogue computation (as in slide rules and adding machines), and fuzzy computation (in which graded physical variables represent the degree to which something is true, or the probability that something is true, and the physical transitions are designed to mirror operations in probability theory or fuzzy logic rather than in classical logic).