I am a student of mathematics, that afirmation of the question I propose seems plausible to me. But I remember that some days ago, I was talking to a friend and he said that such terms are not exactly consequences of a quantitative method. Is that feasible?

I don't remember perfectly if he said that one is not consequence of another or if it was about somethings that don't need to be quantified. But I would like to know about my initial question.

Note: I have no idea of what tags should be used for this question - any edit is welcome.

  • Your friend is right - but this seems more of a language usage question. 'More or less' is a qualified affirmation. Of course one could consider it as meaning neither more nor less in some implicit measure left understood. But that seems rather excessive. – Mozibur Ullah May 22 '13 at 14:47
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    I'm reminded of some of the paradoxes in Alice in Wonderland -- Alice simultaneously growing bigger and smaller (bigger than she is, smaller than she was...) – Joseph Weissman May 22 '13 at 14:55
  • Is a tooth ache more painful than a sore-throat, or less painful? Most of us would give the same answer. How would one measure or quantify them? – prash May 22 '13 at 21:28
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    Do you mean whether there is in principle some quantitative method, whether you actually have some quantiative method, or whether you can map your state onto (some subset of) the reals? – Rex Kerr May 22 '13 at 22:05

No, a preorder relation - aka weak preference relation - or, equivalently, a strict ordering plus an equivalence relation suffice to talk about "more" or "less". Not all such relations can be represented by a "value function" and even if they can the value function is only ordinal and such a representation is still considered qualitative even though it involves real numbers. (The term "value function" comes from normative economics, where also sometimes "utility" is used, though the later is often reserved for values undr risk; I don't know how mathematicians would call it. It 's just a function v: D→ℝ from some domain of objects D to the reals such that v(a)≥v(b) ⇔ a≽b)

For quantitative method, you likely want to measure intensities of "more" and "less" directly and compare distances such measures, which under normal circumstances would correspond to a cardinal utility function. That's all a bit vague and fuzzy; a fellow mathematician who knows some measure theory could give you more details and representation theorems.

Or did I misunderstand your question?

  • +1 But I think that with measure theory, you're quite a bit off. – user3164 May 22 '13 at 18:06
  • AFAIK measure theory is the domain in which these kind of issues are investigated (and much more, of course). But I'm not a mathematician. – Eric '3ToedSloth' May 22 '13 at 19:28
  • @Eric'3ToedSloth' Sorry my naïvety: But doesn't that count as a quantitative method? (It's an honest question. Although I employed the term quantitative method in the title, I'm don't have a rigorous definition for it, but I was probably thinking that quantitative method = something mathematical). – Red Banana Jan 4 '14 at 1:51

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