## Intensional philosophy

16 September, 2008 at 9:49 pm (philosophy) ()

This is a pretty significant paradigm shift for me. It may or may not be of personal interest to you.

## Of intensionality and extensionality

First, an example from the field of set theory. If I take some set, like the set of people who read this blog, I can mean at least two things with it. The first meaning is the set of people who currently are reading this blog, or are currently readers of this blog in some other sense. I could in theory name them and list them, like so: {Tommi, ksym, Phil, Fred, …}. This is the extension of the set. On the other hand, I can mean any people who are readers now or who might be readers some day or who could potentially be readers. In this case the actual list would be largely irrelevant; the way the set is defined is what matters, not the contents it may or may not have.

A more philosophically interesting example: I have two tables in my room/apartment. Assume, for a moment, some ontological theory that ascribes existence to single material objects only, not classes of them (like “tables”). Now, consider, can I meaningfully refer to the two tables as, well, two tables, as I have been doing here? For a mathematician, the answer is “of course”. If I have two entities, I can certainly define a set to which those two belong (assuming the entities are not built so as to resist this). That: The extension of the set is what matters, the intension is irrelevant and in this case not even distinct. But a philosopher would think about the intension: By what means can I refer to the two tables, if they are ontologically only arbitrary physical objects? Certainly not as I have been doing, because given the ontology here, “table” is not very meaningful (at least obviously).

So, in closing: In math, intensionality is a means to an end or a red herring; the extensional is what matters. In philosophy, the intensional is the interesting parts, and the extensional may or may not matter. Philosophy is about the why of the world, or segments thereof, while math (and physics and other hard sciences) about the what and how.

As a disclaimer, the parts about philosophy apply most to ontology and metaphysics and ethics by Kant, and maybe to other stuff I am less familiar with. Also: Almost all distinctions are fuzzy around the edges.

## What this means to me

This realisation has been fundamental in that now I no longer see significant parts of philosophy as trivial, which is useful for being motivated to actually study it.

Furthermore, I will need to re-evaluate my interest in philosophy. It requires learning a new way to think, which is generally fun and useful. Can I learn to think philosophically? Maybe. Do I want to? Maybe.

## In case I am utterly wrong

In case I am misrepresenting large portions of philosophy or mathematics, please do inform me. I will presumably argue against such a claim, which will force me to sharpen my thoughts on the subject, which is useful. Or I may admit to being wrong.

## In case you know something about the subject matter

I would be interested in any literature concerning this subject. Very interested. So, if you know any, I would much appreciate you sharing the information.