http://reflectionsontime-pmer.blogspot.com/

http://reflectionsontime-pmer.blogspot.com/

Moving Blog

I'm moving the blog to TowardsRationalExplanationExistence.blogspot.com because I don't want to give the impression that I think I have all the answers.

Maximality, uniqueness, and reliability

What is a definition of logical inevitability that is better than

(1)  T® á$T

?

We want T to be reliable in the sense of Kaplan []. T is reliable if

(2) from kT infer káT

where k means “knowing”. The paradigmatic example is a speaker speaking “I am here now.” I don’t know if (2) is the best interpretation of reliable.   

What can it mean for a logical system to “know” something? This is the structure the system is “aware” of. And this is the image of implication within the system, given all of T as axioms. Let k_T be what T knows. Then (1) gives

(3) T k_T á$T

There are arguments elsewhere that this relational existence is sufficient for actual existence. A big question is the one of the uniqueness of T. There had better be a maximal T, where

(4) T is maximal if for all theories S such that S® á$S, S Ì T.

If there is no maximal T, then there would be many things that have an equal right to exist. In this case a reinterpretation of (1) would be called for.

Maximality results usually proceed…

Time and Physical Probability

Probably the things most useful to identify in T are those which correspond to time and physical probability.

Hawking and Stenger

Hawking and M... 's idea is that the gravitational potential energy exactly cancels out the positive energy of the gravitating masses. In terms of energy, it is the same as having nothingness. The problem with this kind of approach is that the notion of energy is given significance only by theories of physics. So we can always ask: why should such-and-such a theory be the correct one out of so many possibilities?

Also, to argue that zero total energy (or stress-energy or whatever) is equivalent to the energy of nothingness assumes a background physical theory. Once again we would want to know why that theory obtains.

Stenger has said nothingness is unstable. By "unstable" one means nothingness is likely to decay into a state of somethingness as time goes along. But this assumes both time and the background physical theory defining what it is that is unstable. So it suffers from the same problem.

Hawking's Book

I read much of The Grand Design. It did not reveal how to get the existence of the universe.

Summary with Reliable T

I take a theory T in the sense of 1^st-order logic to be such that T ® the existence of T is logically inevitable. This might take the form T ® ƒ$T. But this isn’t quite what we want, since it leaves the question of T’s existence undetermined.

Supposing existence is really just relational existence, what can be said about the relationship between T and ƒ$T?

Interpret necessarily true not in the sense that it is true in every possible world, but more in the sense that “I am here now” where “I” refers to the speaker.

The relationship in question is the one that happens between the theory T and what it proves, ƒ$T, or necessarily there exists T.

ƒ$T is to T like “I am here now” is to its speaker. In some sense, it is already true.

We know there is necessarily the possibility of such a T.

Hence, T exists, logically inevitability.

T is, and does not merely represent the physical universe.

If we found evidence T is our universe, then

we would have a rational explanation for existence.

The main problem I see, which not everybody will see as a problem, is that even if we grant all these suppositions, there is no way to account for qualia. By the hypothesis, physical reality is ultimately mathematical structure. But I do not see how one could account for the experience of greenness, for example, with just mathematical structure.