When you are talking about machine cognition you are talking philosophy, and are building up on what other philosophers have done in this area. One of which is Bertrand Russell which funded type theory, and Gilbert Ryle which described category mistake as “a property is ascribed to a thing that could not possibly have that property”.

Cognition is a term from psychology, not statistics, if we are applying type theory, cognition would be a (none-pure) function term which take the atom term stimulus and maps them to another atom term behavior and involves states of types including knowledge, memory, attention, emotions, etc. In cognitive this is notated with S → R where S stands for stimulus, and R stands for response.

Attributing cognition to machine learning algorithms superficially takes this S → R function and replaces all state variables of cognition with weight matrices, at that point you are no longer talking about cognition. The S → R mapping of machine learning algorithms are most glaringly (apart from randomness) pure functions, during the S → R mapping of prompt to output nothing is stored in the long term memory of the algorithm, the attention is not shifted, the perception is not altered, no new knowledge is added, etc. Machine learning algorithms are simply just computing, and not learning.