"Art is a lie that tells the truth" -- Pablo Picasso

[mdsimpson92]

Isn't it anti-realist to call mathematics normative? Sure the discipline and practice are normative, but it's not like there are competing theories of addition where 2 + 2 = cats. I think I'm a mathematical realist. Probably because I don't know much about math.

I don't think so, and the philosopher that was promoting this would also disagree. Normative facts deal with the "ought" so 2 and 2 ought to equal 4. It does not describe but prescribe. Though I have heard the idea that math is (in Quine's words) quasi-empirical.

[tinythinker]

Random interjection.

From The Cloister Walk by Kathleen Norris:

• One day, in fourth grade, I had an epiphany about the nature of numbers, a peculiar taste of otherness...
  
  In exasperation at some muddle I'd made with a math problem on the board, an experience which always terrified me, she [the teacher] grabbed the chalk, solved the problem, and said in a sarcastic voice, "You see, it's simple, as simple as two plus two always equals four."
  
  And without thinking, I said, "That can't be." Suddenly I was sure that two plus two could not always be four. And of course, it isn't. In Boolean algebra, two plus two can be zero, in base three, two plus two is eleven. I had stumbled into set theory, a truth about numbers I had no language for. As this was the early 1950s, my teacher had no language for it either, and she and the class had a good laugh over my ridiculous remark. I staggered away from my epiphany and went back to my seat, feeling certain of the truth of what I'd seen but also terribly confused. Briefly, number had seemed more interesting than I was lead to believe. But if two plus two was always four, then numbers were too literal, too boring, to be worth much attention. I wrote math off right then and there, and, ended up with a classic case of math anxiety.
  
  In a way though, this experience had a positive side, as the beginning of my formation as a poet. Whenever definitions were given as absolutes, as always, I would have that familiar tingle--that can't be true--and soon learned that I could focus on the fuzzy boundaries, where definitions gave way to metaphor.

This chapter goes into a brilliant yet brief analysis of poetry, metaphor, liturgy, and theology, but that's the part that rang out to me for this context.

[fleetmouse]

Normative facts deal with the "ought" so 2 and 2 ought to equal 4.

Why ought they equal 4 rather than 9 or blue? Custom?

[fleetmouse]

And without thinking, I said, "That can't be." Suddenly I was sure that two plus two could not always be four. And of course, it isn't. In Boolean algebra, two plus two can be zero, in base three, two plus two is eleven.

Yeah but that's a translation problem. It's no more surprising than the fact that the same sound can mean something different in a different language. If we couldn't translate consistently between binary and decimal our spreadsheets wouldn't work.

That does sound like an interesting book.

[tinythinker]

And without thinking, I said, "That can't be." Suddenly I was sure that two plus two could not always be four. And of course, it isn't. In Boolean algebra, two plus two can be zero, in base three, two plus two is eleven.

Yeah but that's a translation problem. It's no more surprising than the fact that the same sound can mean something different in a different language. If we couldn't translate consistently between binary and decimal our spreadsheets wouldn't work.

And the perceived distinction between description and prescription can't be pursued as a translation problem? These other forms of math require an unconventional view that can seem counterintuitive, contradictory, or mutually exclusive to those of us not well versed in set theory. What is the nature of the boundary between what we think "is" and we believe "ought" (to be)?

[fleetmouse]

And the perceived distinction between description and prescription can't be pursued as a translation problem?

No, because those are two functionally distinct concepts, not synonyms, or words for the same thing in different languages. I don't see how you'd "translate" between them without losing information - grinding away the distinctions between them.

These other forms of math require an unconventional view that can seem counterintuitive, contradictory, or mutually exclusive to those of us not well versed in set theory.

It probably feels natural to anyone who has any degree of programming experience, and that would be lots of us.

[mdsimpson92]

Normative facts deal with the "ought" so 2 and 2 ought to equal 4.

Why ought they equal 4 rather than 9 or blue? Custom?

Perhaps I would say that it is self-evident. But that isn't satisfactory isn't it. But then again, I guess if one were to continually ask "why" over and over again you would just end up in an infinite regress. Dangerous thought, given that you could apply that to all forms of knowledge.

Immature translation: JUST ACCEPT IT!! OTHERWISE EVERYTHING YOU KNOW AND LOVE WILL COME INTO QUESTION.

That being said we could go back to Zhuangzi and the relativity of knowledge.

[tinythinker]

And the perceived distinction between description and prescription can't be pursued as a translation problem?

No, because those are two functionally distinct concepts, not synonyms, or words for the same thing in different languages. I don't see how you'd "translate" between them without losing information - grinding away the distinctions between them.

So there is no dialectical potential at all? Many people come to a point, for example, where they simultaneously perceive the idea that there is a God and that there is no God as being true. Naturally, this tension can (and in many cases does) lead to a reformulation of perspective in which that dichotomy and the assumptions behind it are no longer useful, that is, where one sees that these assumptions no longer adequately frame the issue. This makes the old dichotomy and the thinking behind it obsolete, at least to these people. It doesn't so much grind away at the distinctions as it transcends them. I am not insisting I have a way to move forward here regarding ought/is, but it seems like it could be possible. It was at least worth throwing out to see what it might inspire

[fleetmouse]

Perhaps I would say that it is self-evident. But that isn't satisfactory isn't it.

Sure it's satisfactory, but what is this "it" that is self evident? That sounds descriptive.

I don't think you end up in an infinite regress if you recognize that some things are necessarily true.

[fleetmouse]

So there is no dialectical potential at all? Many people come to a point, for example, where they simultaneously perceive the idea that there is a God and that there is no God as being true. Naturally, this tension can (and in many cases does) lead to a reformulation of perspective in which that dichotomy and the assumptions behind it are no longer useful, that is, where one sees that these assumptions no longer adequately frame the issue. This makes the old dichotomy and the thinking behind it obsolete, at least to these people. It doesn't so much grind away at the distinctions as it transcends them. I am not insisting I have a way to move forward here regarding ought/is, but it seems like it could be possible. It was at least worth throwing out to see what it might inspire

OK, I see what you're getting at and I agree. For many subjects it's difficult to draw a clear distinction between how we see things and how we think they ought to be seen... once we can communicate, perception becomes a practice, not just a reflex or capacity, and there are "best practices" taught implicitly and explicitly in any social group. And as I was saying to md here, even the ability to make distinctions presupposes a kind of valuation.

So from that perspective, sure, we can and should transcend is/ought and "go meta" (if you know what I mean), at the very least as a form of self aware self criticism.

But it's very, very difficult for me to contemplate the stubbornness of numbers and math and not see our understanding as descriptive of something "real". I think I'd be more likely to accept that our models of atoms and molecules are completely wrong and just models (they probably are), than to see math as fictional and just a practice.