The Truth Machine

Try thinking of the world as a machine for the production of true statements (including, possibly, if it is true, the statement that the world is a machine for producing true statements...).

We almost need to believe something like this if we are to be motivated to pursue certain scientific projects - it is like the belief that it is possible to do science, to explore the logic of the machine ('God does not play dice').

If it was true, would it have to produce an explanation of why it was true? Only if it was a machine that could produce all the true statements, since this explanation would be one of them. If it produced only true statements, then this explanation need not be among them. Also, (algorithmic information theory?) it couldn't produce a list of which statements it could show to be true.

What kinds of things do we mean by something's being a machine? Being modellable in a Turing machine seems plausible, which means that it must have a series of discrete states, and a 'time' dimension (the number of operations carried out). After any finite number of steps, there would be some unproved theorems which it simply hadn't reached yet. In any finite amount of time, there would be knowable things which were not yet known. There would be things that would eventually be demonstrated which were not yet demonstrated. These could not (?) always be distinguished from the things which the machine formally could not demonstrate - 'not yet halted' and 'will not halt' won't always be distinguishable (because we would need a paradoxical algorithm to completely determine this).

The interesting thing is this, though: If the 'world' is not a Turing machine, we could never find this out. (It certainly wouldn't be a computable question.) And there would be a respect in which we could never 'find this out' because an outcome of the chaos would be that we would have no language in which to formulate the conclusion. The end of intelligibility is a kind of possible future state.

If the world looks like a Turing machine, that's partly because it's the only kind of world we can describe. Which means that as long as we can go on discovering and describing things, we will go on demonstrating that the world looks like a Turing machine - and, possibly, thinking that we can work out its whole logical structure, even while we know that this must be impossible.