First there is a basic notion of TIME which is taken as primitive (and perhaps related to the TIME hypothesis of Russell Standish, I don't know) and which is just the (first order logic) notion of successive natural numbers. This TIME is fixed and lives atemporally in Platonia, and constitutes the core skeleton of arithmetical truth.
The parameter time of the physicist is a mystery for me, and I don't get it by comp, and perhaps it is not necessary, because even physicist doubt it exist (at least the relativist physicists). It would be just a type of "other universe" like in David Deutsch's conception of time (see its FOR book).
The Heraclitean Brouwerian Bergsonian sort of subjective duration time is what appear automatically with comp once the first person is defined modal-logically, and it is given by the modal logic S4Grz and S4Grz1 (see perhaps my SANE paper). I talk about this one to Stephen some time ago.
I would like to say more but I have not the time (paraphrasing a recent joke by Charles on the FOR LIST:)
I promise to Brian to explain what is the observer in comp, but I need to explain at least a minimal amount of modal logic, and this without technics, I will try asap, but then I can explain what is S4Grz and modal time).
Grz is for Grzegorczyk, a big polish logician.
Goldblatt (see ref in my thesis) has made also a startling modal analysis of Minkowsky space time through an old greek Diodorean modality, which I wish to extract in the arithmetical frame imposed by comp, but I don't even smell it (alas).
Le 10-mai-05, à 16:04, danny mayes a écrit :
You've probably already addressed this recently, but given the number of posts and my work load I have not been able to read the much of the list recently. What does comp make of time? Is it merely some measure of the relationships among bitstrings in platonia?
Bruno Marchal wrote:
Le 09-mai-05, à 19:39, Brent Meeker a écrit :
In what sense does "the program" exist if not as physical tokens? Is it
that you've thought of the concept? The same "program", i.e. bit-string,
different things on different computers. So how can the program instantiate
reality independent of the compu
By the magic of Church thesis, going from one computer to another is just like
making a change of basis in some space. All result in Algorithmic information theory
are independent of the choice of computer modulo some constant. The same
for recursion theory (abstract computer or generalized computer theory) even without constant.