Principle of contradiction denies the
existence of contradictions, that is, the existence of combinations
of contradictories. What then are these contradictories one might
ask? Contradictories themselves are a kind of opposites, Wolff answers. Opposites,
on the other hand, are such things that cannot exist at the same
time, in the same situation (for instance, complete blackness and
complete whiteness cannot exist in the same surface). Contradictories
are then opposites, one of which must exist in a situation.
It is a well-known fact that when one
modal notion (e.g. possibility) is defined, the rest of the
modalities can be defined from that beginning. Thus, impossibility is
contradictory of possibility: what is not possible, is impossible,
and vice versa, and things must be either possible or impossible.
More importantly, when the opposite of
something is impossible, this something itself must be necessary.
That is, when some situation or thing has no capacity of
ever becoming actual, it's opposite must undoubtedly have the power
to actualise itself in every situation. For instance, a figure with
three sides, but not three angles would be something impossible and
could not ever be actualised, thus, if we do have an actual figure
with three sides, it must be actualised with three angles. Generally, all such combinations or propositions describing them are necessary,
if the predicate could be deduced from the definition of the subject.
Now, there is a special case of
necessary propositions, that is, propositions describing the
existence of something necessary. Here it is not any feature of the
thing that is necessary, but the very entity is supposed to be such
that its non-existence would be impossible. In other words, the
actualisation of the haecceitas of such an entity would be necessary.
Because this haecceitas or individual essence would contain at least
implicitly all the predicates of the thing, it could not really have
any other predicates. In other words, it could not change into
anything else, but would eternally be what it is.
Wolff leaves it open for now, whether
there are any concrete necessary individuals – this is a task left
for other branches of metaphysics. Then again, Wolff does find
examples of more abstract necessary entities. In Wolffian ontological
scheme, what is absolutely possible is defined by its
non-contradictoriness, and thus, one cannot change what is possible.
If something is then possible, it is necessary possible. Then again,
essences or coherent combinations of essential predicates correspond
to certain possibilities. These abstract combinations or lists of
predicates are then necessary, which means merely that it must be
possible that some things satisfy these combinations of predicates.
Wolff also points out that there are
actually two different concepts of necessity. Firstly, one can speak
of necessity plain and simple or absolute necessity – this is
essentially what we have considered now. Then again, there is also
hypothetical necessity, that is, necessity under some assumption.
Wolff's example of hypothetical necessity is the relationship between
a feature of a thing determining what other features the thing has:
for instance, if a certain figure has three straight lines as its
sides, then it is necessary on this condition of its trianglehood
that it also has three angles.
This mathematical example is a good
point to move to consider how mathematics is presented in Wolff's
ontology, which will be the topic of my next post.
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