Extensional logic includes standard scientific and mathematical logic. In this sets and objects are determined by their members. Intensional Logic is the logic of informal everyday human reasoning, where the order and context of sets or objects affects how they are determined. As an example let us specify two sets: “creatures with hearts” and “creatures with kidneys”, extensionally these two sets refer to exactly the same group, thus the two specifications are identical. Intensionally however, it is obvious that the two statements have different meanings, since different aspects of reality have been highlighted by the words.

Extensional logic allows us to substitute equivalent objects, so if :

K = sqr(9) = 3 = (2+1)

we can substitute any of these in an equation for any other without a problem. Contrast that with:

26th June 2001 = my birthday = three days after my discharge from hospital =ten years after the day uncle Fred passed away

These dates are extensionally identical, but when I invite people to my party, I specify the date as 26th June, to specify the date as “three days after my discharge from hospital” would be to refer to the same date but to say something confusing. Intensional logic thus disallows substitution, due to the limited knowledge and frame of reference of persons. Extensional logic is beyond psychology, intensional logic is wrapped up in, and intertwined with, the subjective viewpoints of people.

The distinction between these two logics can become apparent in statistics and probability. Consider a person, Jack who is a member of three different groups (among many), white adults, working men, residents of the UK. Each of these groups can have an average expected age of death, which is different in each case. This doesn’t mean that Jack has three different expected death ages, he obviously has just one, but by referring to him intensionally as a member of each different group, one at a time the probability appears to change. This shows the context/viewpoint dependent nature of intensional logic.

For more information about this subject see:

“Once upon a number”, by John Allen Paulos