Here's my take on it.

Agnosticism is illogical and refutes itself. Agnosticism and agnostics characterize God as unknowable, ineffable, incomprehensible to all attempts to understand him. This doctrine is self-refuting. The agnostic is making a knowledge claim about what he/she claims is unknowable. How do agnostics know that God is unknowable if he is unknowable ? How do they even know that God's existence cannot be disproved if God is unknowable, or that God even exists if he is unknowable ? To claim any attribute for God is knowledge and claims to know this unknowable God possesses certain attributes. That's a logical contradiction, and any being containing two incompatible attributes cannot possibly exist. So one need not resort to agnosticism. He/she would be justified in not believing in that God if the concept of it contradicts itself in any way. One is justified in accepting and adopting the atheist position.

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So if you apply the Goedel incompleteness theorem to human thought, what do you get?

You can't apply a theorem about formal axiomatic systems to all of human thought because it doesn't satisfy the hypotheses—it's probably a category mistake as well.

So you don't think human thought could even in theory be axiomatized?

Penrose in The Emperor's New Mind was trying to do something of the sort as I remember.

So you don't think human thought could even in theory be axiomatized?

The term human thought encompasses many things that would be extremely hard to fit into a formal system. Within a formal system the statements must be true or false, but many thoughts, perhaps most, are not assertions and do not bear a truth value. Others might be both true and false—true for one individual and false for another. People lie and that means they speak falsely while knowing the truth, yet both would have to be considered a 'thought.' In other words the system would necessarily be inconsistent.

If you view thoughts as a representation of an underlying physical system, and you assume that system is functioning in a classically deterministic way, then human thinking could be translated into the actions of a physical system.  And because of the finite speed of light, the inputs into that physical system are finite, and perhaps it can be axiomatized in a finite way, as in "we assume that atom 1 is in position P(1), atom 2 in P(2), etc." at time T.  I'm not sure what's involved in the axiomatizing, but no actual contradictions would be "derived", e.g. you don't derive that atom 1 isn't in position P(1) AND in position P(2).  Although you might arrive at a physical system that represents an inconsistent thought. 

That view equates human thought with the physical state of human brains—a reductionist view I'm not sure evidence warrants. I doubt that we will ever be able to mind read by charting all the synapses.

In any case logic disappears from view completely. What would it mean to say that a particular state of a brain represented a true thought?

I doubt that we will ever be able to mind read by charting all the synapses.

In other words, humans couldn't specify their own Goedel true-but-unprovable sentence, assuming we have one?  

We don't know that we'll ever be able to specify that function exactly. 

Thought is certainly a function of the human brain, which also has many other functions as well. It does not follow that you can read thoughts directly from the state of the brain.

Open up the hard drive of any computer and read off what is there:  you find a long sequence of 0's and 1's, but unless you know how the computer is structured and what programs are used, the sequence is without meaning.

Each human brain is organized in many different ways depending on what experience its owner has had in forming his memories and thoughts.

First, is thought THE function, or A function, of the human brain.

We know too little about the brain to say it has but one function.

Second, to say function is to say evolution has a purpose.

Instead, say the brain is capable of thought.

I mean, the gist of Penrose's argument in The Emperor's New Mind was that if human thought does not involve a quantum element, if it is classically deterministic, he could derive a contradiction, in a handwaving way, via Goedel's incompleteness theorem. 

Give me the exact reference. Throughout his book Penrose mentions Gödel's incompleteness theorem many times. His discussions are informal and speculative and this is an area where precision is necessary.

The part where he's most explicit about his argument (as I remember) is where he has the human inventor of a robot arguing with the robot, and in time the robot breaks down because of the argument :)  Starts fizzing or something :)




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