– The relationship between formal systems and human thought shows the insight of the Neo-platonic account of soul as “what returns to itself by a complete return”. From Russell through Godel and Turing it was clear that the formal system will always be at odds with itself if one allows self reference, which humans do every time they are aware that they know something.
– There is a sort of recollection theory in the fact that no perfectly random sequence can encode anything, since the code thus demands redundancies and so things already known. To know anything (i.e. to receive something encoded in sound waves, light, nerve stimulation, etc.) requires already knowing something (i.e. what allows for redundancies in the encoding). One can account for this by saying that human beings have a definite organic structure, but only if one sees this organic structure as possessing knowledge before it receives any nerve stimulation. While Plato could have distinguished between the before of time and of causality (which would make the baggage of reincarnation and pre-existence unnecessary) his general point is simply to locate the thinking part of man in something pre-existing physical cognition, and it seems that he’s done so.
-A friend published an argument that started with Feynmann’s saying many times that it is incomprehensible how energy can be measured in so many different ways, and that all the units in which it is measured are like so many currencies that can be exchanged for each other according to pre-set rules and within certain definite limits. So taken, energy itself seems to require nothing more than the rules for exchange, no longer requiring any non-formal reality.
-James Gleik related a story of a woman who brought a message into a telegraph station and asked for it to be sent. The operator dutifully tapped out the message and asked for the fee, but the woman responded that he obviously hadn’t sent it since she could see it right in front of him. But if he did in fact send the message, then what is a message? Not the ink and paper, since it was sent through the control of a circuit; but not the circuit either, because it could have been sent an indefinite number of ways. So on the one hand something is necessary to send the message in; but on another hand anything will do. This is exactly what Aristotle wants to call matter – in one sense it is essential (you need something) but in another sense all there is is form (since anything will do). This might serve as either a criticism or a modification of Wheeler’s “it from bit” idea, or the idea that there simply is no such thing as non-formal physical reality. This is true so far as one can encode into anything, and so “what one encodes into” can never have a definite description. But such a thing is still intrinsically necessary to the information.
-If a formal system cannot account for self-reference, this seems to prove the real possibility of a complete knowledge that (unlike our own) can be had apart from a formal system. But I think one can argue from such real possibility to the real existence of the same, and so of a separated soul or angel or divinity. Some analytic philosopher might work it out, but the bones are this: if a separated intellect is really possible, then the truths that it knows are really possible. But at least some of these truths are necessary, so a necessary truth of a separate intellect is possible. But necessary things by definition either exist or are impossible, and we’ve shown that a necessary truth of a separate intellect is not impossible, therefore etc.