Intensional and extensional definitions
Of the many arcane and esoteric distinctions that professional logicians make, there’s one that I think is quite valuable outside of philosophical logic. It’s a distinction that can help us dissolve many of the merely verbal disputes that we get into — and awareness of the distinction can help us to be more careful with our language so as to pre-emptively avoid such disputes.
It’s the distinction between between the intension and extension of a word or phrase. The intension of a term is its meaning. The extension is what the term designates.
So for example, you and I might agree about what the term “truth” means — its intension, while disagreeing about which statements are true — its extension.
Another example is the word “planet”.
Here’s one intension for “planet”, from the International Astronomical Union:
In the Solar System, a “planet” is a celestial body which:
1. is in orbit around the Sun
2. has sufficient mass to be round
3. has cleared its path of orbit
Let’s call that intension planetIAU.
The extension of planetIAU would be these 8 objects:
The astrologers, on the other hand, might define “planet” differently. One astrological intension would be
A “planet” is any wandering star — a celestial object which moves relative to the fixed stars over the course of a year
We could call this planetastrology. The extension of planetastrology, according to Wikipedia, is these even objects:
Noam Chomsky uses the sentence “do submarines swim” as an example of the kind of semantically underspecified nonsense question that humans are often getting into arguments about. There is no answer other than “it depends what you mean by submarine.”
It’s interesting to notice what happens when people unknowingly conflate the intension and extension of a term — it leads to muddled and intractable-seeming disputes that might easily be resolved.