Thursday, April 28, 2005

Formal Systems and the Absolute

Many people seem to take as absolute, concepts that I think are inherently relational. I guess that's because I'm inclined to think that only physical reality, or what "is", is absolute. So other concepts we come up with, like "could", or "should", must be constructed in relation to some purely formal system. I can't make sense of them otherwise. A few examples:

1) Normativity. I find absolute oughts (and value) to be entirely incomprehensible, and discuss here how to understand them in a relational sense.

2) Modality. I just recently wrote about why I find absolute modality incomprehensible. (I would really appreciate some more criticism or other feedback there, since I'm feeling a bit perplexed about the whole topic.) I present a relational alternative here.

3) Maths and Logic. (The ultimate in formal systems.) We posit some axioms, and see what follows. But the laws of logic aren't themselves true or false -- rather, they are (useful, but in a sense 'arbitrary') rules that describe ways to manipulate symbols. We could adopt different rules if that would suit our purposes better, and indeed that's what various "alternative logics" are for. It just seems a mistake to think that there is one true logic, any more than there is one true geometry.

What do you think? Can these concepts be 'absolutized'? Can you think of any others that might be added to the list? Does anyone else get a headache thinking about this stuff?


  1. Are you interested in going non-cognitivist about these things? Allan Gibbard and some bright kids at Michigan are trying to make this work for all sorts of things beyond normativity. Your talk about how the "laws of logic aren't themselves true or false" suggests that you might like noncognitivism about that domain. Maybe rather than making assertions, we're expressing adherence to a rule governing what statements we'll permit.

  2. Neil, that sounds very interesting! I think I might prefer to just avoiding talking about the truth of a framework altogether (as it seems to me a category error). But insofar as someone wants to call a framework "true", I'd agree that this is best interpreted as adherence to it.

    But I do want things to be true within a system. I'm not non-cognitivist about morality, for example, as you can see if you follow the links in the post. (I guess I am about normativity though.) I see morality as a particular normative framework, so once we get inside it, it is objectively true that we morally ought to do such-and-such. Just like it's objectively true that (P & ~P) is classically impossible.

    It's just talk of 'ought' or 'impossible' simpliciter that I want to avoid.


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