Comments on: The caveats of logical thinking

By: The caveats of logical thinking (part II) « blog.elevenseconds

The caveats of logical thinking (part II) « blog.elevenseconds — Mon, 08 Mar 2010 19:51:05 +0000

[...] twentieth century, mathematicians realized that logic doesn’t actually get you that far. As described previously, logic is as strong as a set of axioms behind it. This is fine in a highly contrived world, like [...]

By: Rudolf Carnap

Rudolf Carnap — Tue, 17 Nov 2009 05:58:25 +0000

This quote amps up the pretension, but I think it’s perfect. Nietzsche’s opening lines from Beyond Good and Evil…

“Supposing truth is a woman – what then? Are there not grounds for the suspicion that all philosophers, insofar as they were dogmatists, have been very inexpert about women? That the gruesome seriousness, the clumsy obtrusiveness with which they have usually approached truth so far have been awkward and very improper methods for winning a woman’s heart?”

That kind of says it all

By: Rudolf Carnap

Rudolf Carnap — Tue, 17 Nov 2009 05:54:06 +0000

Suppose there is something wonderful and impractical to talk about. If a person starts off with, “let’s use logic to discuss” – oh, girls or Being or silence – how could s/he possibly have something worth saying?

By: me

me — Tue, 17 Nov 2009 02:35:57 +0000

Thank you Rudolf, I struggled to disagree with anything you said. In fact, I imagined folding your exploration into my metaphor by relaxing the definition of an “axiom”–that is, turning the rules of logic into axioms themselves, in a way analogous to noting the duality of program (the algorithm) and data of a van Neumann architecture as every program can be encoded as data.

You did, however, touch upon much more fundamental problems that people will encounter when they attempt to use logic as a common framework (and I guess such was my point; countless times I’ve heard my friends agree to “use logic to discuss” a particular point. Something had to be done about it, even if it is just a rant somewhere…)

By: Rudolf Carnap

Rudolf Carnap — Sat, 14 Nov 2009 15:50:08 +0000

While I think this is a good start in understanding others who try to apprehend the profound or the mysterious, it’s also deeply wrong. Or as Wolfgang Pauli might say, “It’s not even wrong.”

To further extend your logical system metaphor: it’s not just that different people start from different axioms. They can have different transformation rules altogether. If two “logical” thinkers disagree on whether A and B imply C, you can set yourself on a fool’s errand if you try to tease out the axiom that only one holds in his pocket. They might just be overlaying different rules.

Also – what are we talking about here, anyway? Human beings, right? What’s to say that the set of transformation rules and axioms that a person employs is constant among contexts? It’s plainly a different set employed when we talk about math and when we talk about love. (Perhaps there are some so consistent that they would use the same set, but what’s the use of worrying about people like that?)

But the thinness is this framing is put into relief when you consider the disagreements, or the disagree-ers. What’s the axiomatic base of religious vision? Or aesthetic revelation – or even aesthetic comparison? Logic is so weak when it comes to “meaning” in its human sense. Logic is no handrail down these staircases. Just walk slowly and with open eyes.