Sadly, this is a common lie among modern as well as ancient philosophy. Natural philosophy since Descartes (Durant's "Father of the Age of Reason") has corrected this to:
"All these elements are yoked together by natural language — the distinctly human capacity to apply logic in the forming of judgements."
With this we can tie your otherwise excellent philosophical scholarship to the most current natural philosophy (i.e., science). We now know perfection is achieved by the hundreds of billions if not trillions of simple predications dynamically maintained between your ears and seen in all natural language. It is out of natural language that the perfect reason of even mice can be seen.
It is not the reasoning that is unique, it is the capacity to communicate reason with a uniquely human organ that can capture all of what reason in any mind (man or mouse) can compute.
See my "100 Billion Sources of Hate Between Your Ears" in this paper just published in the last two weeks. The most fundamental computation replicated dynamically trillions of times between your ears is the linguistic predication that every person proves they know in high school today and first seen clearly for what it was by DeSaussure. It's the orb.
Even a worm reasons. But their natural language is no where even close to what humans have uniquely evolved for communication among their meager reasoning brains. There are proofs in these papers.
Prove this stuff to yourself by becoming a mendaciologist and trying truths and lies in the media (it's free) www.truthcourt.net
Without Mendaciology there is no Ontology. The human brain proves that and why it is must be true. Descartes' "Method" is just on that point. "I think therefore I am." and 'here is how to properly communicate this reasoning you think among humans: necessarily by unique human communication of agreed on truths (and lies)..