| | Matt,
You were right about Godel's Incompleteness Theorem. Godel's Incompleteness Theorem attempts to discredit the practice of deducing knowledge, rationalistic-style, from a set of axioms. The 2 relevant questions to ask are:
1) Did it work (did he really do this)?
and
2) Does it matter (are there epistemic implications)?
Notice how the critical notion here is whether axioms are that FROM WHICH knowledge is acquired (ie. deduced FROM axioms) or that BY WHICH knowledge is acquired (ie. experience, when collected and examined against the background context of axioms, leads to incorrigable knowledge). This also brings up notions such as "analytical" and "a priori."
The interesting thing (perhaps even an "open secret"?) about the concepts "analytical" and "a priori" is that they are agent-relative (agent = a thinker; a thinking agent).
A thinking agent such as myself does not wrestle with the conundrum of reconciling how both the Morning Star and the Evening Star are both the self-same star: the planet Venus.
Another way to say this is that the fact that these 2 different observations (of a star in the sky) have always and only been observations of the self-same star in different contexts (at different times), has already been integrated into my growing body of personal knowledge. HOWEVER, for the initial observers (initially researching these "two" stars), ADDITIONAL EXPERIENCE leading to the formation of synthetic, a posteriori statements was required to GAIN THE KNOWLEDGE of "self-sameness" or "identity" between these 2 different observations in the sky.
So, it appears that experience of the world is an "a priori" (pardon the pun) necessity before a thinking agent can have knowledge of any kind.
But once that knowledge exists (in their mind) - ie. they have discovered and validated varius relations between identities (of entities) - many things (indeed, ALL known facts!) which were previously a posteriori (for that thinking agent) BECOME a priori for that thinking agent (ie. new knowledge is no longer needed to state that "a thing is what it is" - in relation to other known things - and also, that "it has exhibited the behavior that it has" - again, in relation to other known things).
So Godel's Incompleteness knocks down a straw-man (as human knowledge is not something that is deduced, rationalistic-style from axioms, in the first place). However, an explanation is in order to shed light on Godel-type proofs (to explain why sentences such as "This sentence doesn't exist" are still so problematic to "some" thinkers).
The short explanation is that the "stumped thinkers" have always and only examined these sentences in an "agent-free" context. But sentences are not meant to be examined as such (sentences are statements OF agents ABOUT existence). Think about this once.
Think about yourself (a thinking agent) actually reading the sentence: "This sentence doesn't exist." Do you have a "problem" knowing whether or not the sentence is true or false? No, you have no problem with this. Therefore, incompleteness is totally irrelevant to your growing body of knowledge (you DO know the things that you know, and you WILL know much more - if you keep your eyes open and your axioms in mind).
Devastating recap: Godel is a precision-junkie who "forgot" about accuracy as it applies to human knowledge.
Thanks for spotting (and conveying) the connection, Matt!
Ed
(Edited by Ed Thompson on 7/28, 9:36am)
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The most intractable problem for contemporary philosophers to overcome is to learn how and when to sacrifice precision for accuracy (when the goal is to think well, nothing is more vital than accuracy).
