In the Ilahiyyat Avicenna develops and employs a number of recondite metaphysical distinctions; he focuses especially on the way in which the absolutely universal notion of being (mawjud, ens) can be intensionally
amplified and extensionally contracted by various sorts of notional transformations.
We can better adjust to realities when we recognize our tendency to intensionally
identify and give words more importance than the structures and realities we use them to represent.
They are neither extensionally nor intensionally
They are extensionally equivalent but intensionally
very different--something not captured in either the Hohfeld-Corbin approach or in later versions of Realism.
In a relation of x = y + z, y is intensionally
defined as x - z.
From my perspective, sameness of intension is determined by a definition of intensional equivalence that specifies when two descriptions are to be considered intensionally
The crucial difference lies in the fact that they are not conceived as completed infinite sets, but as intensionally
determined, infinitely proceeding sequences.
It should be stressed again at this point that, contra Dayal, I take the view that generics, in principle, do not refer extensionally to existing members of a kind but instead always refer intensionally
, pointing to the name of the kind.
, however, the relationship of "containment" has been seen as holding in the opposite direction.
These two concerns may become inextricable when classes are defined intensionally
(when the possession of a given set of properties strictly implies class membership), but they do not when class membership is primitive.
Again, we have identified a very significant body of connections between three intensionally
quite different similarity relations.
Most Prolog implementations provide built-in features, such as the setof predicate, for building a set intensionally
rather than extensionally; this means that a set is defined as the collection of all elements satisfying a given a property, instead of explicitly enumerating all elements belonging to the set.