Short of time, haven't got what I wrote with me here but:
There was an explanation of what Godel did in a book "Mathematics. The Science Of Patterns". I followed it carefully. I found that he was both wrong and right. My comment about making a 'category error' by juxtaposing 'axiom' and 'theorem' resulted from looking carefully at what was going on.
Aparantly Paul Cohen has gone beyong Godel; whatever he did I don't know the details. But so far as the fallacy? of Godel is concerned; I may be wrong or the book may mis-represent Godel; but when I have the piece of paper I wrote the argument on I can demonstrate it- it's short and simple but no time to re-discover it now.
I know what an axiom and what a theorem is, thanks to a book "Godel, Escher, Bach. An Eternal Golden Braid".
Alex: you use your senses to understand measuring sticks and so on. I didn't say reality comes from senses: I say reality comes from comparing and matching patterns. Reality is in the past. The future is optional. Correct matches of patterns constitutes true knowledge.
The fact of matching pattern A and pattern B; even if these do not match in reality; the fact that YOU MADE THE MATCH A TO B
that FACT is part of REALITY. It may be a real mistake, but it is real that you Y matched A and B! So anyone who thinks they can know reality is not an idiot. The question is, knowing that reality is that you made a match; was it a correct match? It is said, as you judge, so you are judged. Curioser and curioser.
Thus Dick is wrong: the moment you match two patterns, rightly or wrongly: the fact of THE MATCH ITSELF is REALITY and is known.
"Mind" is a verb; there is no such thing as mind.
"Mind the step, keep it in mind, etc." all show that 'mind" refers to "paying attention".
"Paying attention" involves being alert to matching patterns.
To regard 'mind' as an object like 'brain' is known as a 'category error'.
So someone says, and their arguments looked good to me.
Knowledge is relationships.
Reductive fallacy: just because activated cells might be a necessary condition of verbalised thought does not mean it IS verbalised thought.
A novel is not a pattern of electronics in a computer. That C is a condition of A doesn't reduce to C being A.