Wednesday, 31 August 2011

Consequences

All systems of knowledge are, in one way or another, axiomatic. No matter how thorough our logic is, we ultimately begin with a premise and make the assumption that it is true. Everything else unfolds from that, whether by syllogism or dialectic or whatever. If the rules of logic hold true, then they only hold true for the consequences of a premise. And that's logic 101. It's also part of the basic argument that John Lennox uses about rationalists and faith.

We always start with an axiom or a premise and infer its consequences. It's great technique to use those inferences to determine whether the axiom is true. In the more complicated questions, the logic can be quite convoluted. Not everything is just a matter of "David is unmarried. Is he also a bachelor?" When it comes to questions of God, both theists and atheists have appealed to nature to support their arguments, and in both cases there is an interpretative element to the logic that's based around some axiom. Ultimately, I think axioms are inescapable. We need to postulate them in order to understand the world, and we need to test them to make sure we aren't being deceived, but we can't do without them.

I'm also interested in the consequences for another reason. If we have an axiom that holds reasonably true (albeit beyond proof either way) then we should take time to figure out what that means for our daily lives and then do it. I don't think there's enough of this going on, and I think that's because we're happy not to have to do that work. And that, I think, is the point of any philosophy that matters.
"The philosophers have only interpreted the world, in various ways; the point is to change it."
Marx, Theses on Feuerbach

5 comments:

Anglican Parish of Yarraville said...
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Absurd Project 0 said...

Re: all systems of knowledge are axiomatic. I guess you could say so, but Heidegger, John Searle and Rodney Brooks (and probably Polanyi and others) would want to say that there's a lot of practice knowledge that is encoded in gestures, shortcuts, stances, presumptions, readings. This is not undescribable, but it is encoded so densely that unpacking it is not tenable.
(I left a better post but with a wrong account. Can you resurrect it? I am working on a mac and the ctrl for ctrl-c is in a different spot, so that comment was gone forever.)

Absurd Project 0 said...

Found it!

Have you seen Rodney Brooks paper 'A plan is just away of avoiding figuring out what to do next' ? There is a link of the Subsumption Architecture / Rodney Brooks page on wikipedia.

He is something of a Heideggerian and suggests that the way our minds work is not really rational / representational. We don;t have a model of the world for any meaningful value of the word 'model.' We have a morass of shortcuts for dealing with the world. For another mathsy example, if you decompose a Mcullough-Pitts neural network, you don't get axioms - you get a system of simultaneous equations that serve to hook one set of inputs to matching outputs reliably, but the meaning is all coded in the network so as to be unmeaningful to humans. Brooks also has a paper 'reasoning without representation.' John Searle has the construct of the background, which Hubert Dreyfus uses a lot as speaking of Heidegger's understanding.

I was surprised in my reading of 'Orthodoxy' (first time!) to see Chesterton say 'We shall explain reason by unreason' - but he was meaning the higher but equally opaque meaningfulness of purpose.

Andrew Smith said...

Sure, I get that. When we gather information about the world around us we're relying on cause and effect to figure out basic laws of interaction, especially between consciousness and the world "out there."

Surely even that method of acquiring rules derives from an axiom about the self, about the I. It's an axiom that there is an integrated self that interacts (somehow) with the world (Kant's synthetic unity of apperception, right?). And maybe Brooks is challenging that axiom, but it's an axiom nonetheless and it's the basis for a system of knowledge, at least in a Cartesian sense.

Absurd Project 0 said...

I guess it depends how you load the word system. Does a dog have a system of knowledge? It certainly has knowledge, but I think it would be a stretch to attribute axioms. A dog probably has its own categories of experience, and synthetical unity of apperception, but it doesn't have any words about them. It just has them. I think that ultimately all axiomatic systems (maths being one, philosophical accounts in the analytic tradition being another) are just lucky if they apply usefully enough to reality enough to survive as memes.

But I think your post is really about pragmatism (of which my knowledge comes entirely from the guys at Partially Examined Life). You are saying that the things you know (to the extent that they're important structures of knowledge) should be fitting you to the world. Which I agree with entirely.