[1005a]
[1]
and
the principles adduced by other thinkers fall entirely under these as
genera.It is clear,
then, from these considerations also, that it pertains to a single
science to study Being qua Being; for all
things are either contraries or derived from contraries, and the first
principles of the contraries are Unity and Plurality. And these belong
to one science, whether they have reference to one common notion or
not. Probably the truth is that they have not; but nevertheless even
if the term "one" is used in various senses, the others will be
related to the primary sense (and similarly with the
contraries)—even if Being or Unity is not a universal and
the same in all cases, or is not separable from particulars (as it
presumably is not; the unity is in some cases one of reference and in
others one of succession). For this very reason it is not the function
of the geometrician to inquire what is Contrariety or Completeness or
Being or Unity or Identity or Otherness, but to proceed from the
assumption of them.Clearly, then, it pertains to one
science to study Being qua Being, and the
attributes inherent in it qua Being; and the
same science investigates, besides the concepts mentioned above,
Priority and Posteriority, Genus and Species, Whole and Part, and all
other such concepts.We must pronounce whether it pertains
to the same science
[20]
to study
both the so-called axioms in mathematics and substance, or to
different sciences. It is obvious that the investigation of these
axioms too pertains to one science, namely the science of the
philosopher; for they apply to all existing things, and not to a
particular class separate and distinct from the rest. Moreover all
thinkers employ them—because they are axioms of Being qua Being, and every genus possesses
Being—but
employ them only in so far as their purposes require; i.e., so far as
the genus extends about which they are carrying out their proofs.
Hence since these axioms apply to all things qua Being (for this is what is common to them), it is the
function of him who studies Being qua Being to
investigate them as well.For this reason no one who is pursuing a particular
inquiry—neither a geometrician nor an
arithmetician—attempts to state whether they are true or
false; but some of the physicists did so, quite naturally; for they
alone professed to investigate nature as a whole, and Being.But inasmuch as there is a more
ultimate type of thinker than the natural philosopher (for nature is
only a genus of Being), the investigation of these axioms too will
belong to the universal thinker who studies the primary reality.
Aristotle. Aristotle in 23 Volumes, Vols.17, 18, translated by Hugh Tredennick. Cambridge, MA, Harvard University Press; London, William Heinemann Ltd. 1933, 1989.
The Annenberg CPB/Project provided support for entering this text.
Purchase a copy of this text (not necessarily the same edition) from Amazon.com
This work is licensed under a
Creative Commons Attribution-ShareAlike 3.0 United States License.
An XML version of this text is available for download, with the additional restriction that you offer Perseus any modifications you make. Perseus provides credit for all accepted changes, storing new additions in a versioning system.