  Two major areas of interest in the era of Large Language Models regard
questions of what do LLMs know, and if and how they may be able to reason (or
rather, approximately reason). Since to date these lines of work progressed
largely in parallel (with notable exceptions), we are interested in
investigating the intersection: probing for reasoning about the implicitly-held
knowledge. Suspecting the performance to be lacking in this area, we use a very
simple set-up of comparisons between cardinalities associated with elements of
various subjects (e.g. the number of legs a bird has versus the number of
wheels on a tricycle). We empirically demonstrate that although LLMs make
steady progress in knowledge acquisition and (pseudo)reasoning with each new
GPT release, their capabilities are limited to statistical inference only. It
is difficult to argue that pure statistical learning can cope with the
combinatorial explosion inherent in many commonsense reasoning tasks,
especially once arithmetical notions are involved. Further, we argue that
bigger is not always better and chasing purely statistical improvements is
flawed at the core, since it only exacerbates the dangerous conflation of the
production of correct answers with genuine reasoning ability.
