Systematicity & Related Phenomena
The ability to think certain thoughts (or certain to say certain things) is intrinsically connected to the ability to think certain other thoughts (or to say other things). Systematicity can also be characterised as a kind of mental symmetry.
A related point is that systematically related thoughts are not related to certain other thoughts. For example, "John loves Sally" is systematically related to "Sally loves John" but not to "two plus two equals four".
This property of cognitive systems is so closely linked to systematicity that is often overlooked. It has been called compositionality, but this term is confusing, because compositionality is normally used to refer to the compositional structure of mental states (see sidebar, "Constituent structure of mental representations" on this map).
The ability to make certain inferences is related to the ability to make certain others. For xample, an organism that can infer p from p & q can also infer q from p & q. This is also called systematicity of inference.
From a finite stock of resources, a person can think of an indefinite number of thoughts (for, say, an indefinite number of things) by combining atomic and molecular representations in various ways. This is also known as generativity.