Tom I often find your informed opinion on things very helpful but in this case what you say does not make sense to me and I contrast it with the cautious optimism in Weinberg's talk.
I think Weinberg was using a very pragmatic idea of a ToE when he referred to "how nature is". Talking about a predictive theory that appears good to arbitrary high energy.
The commonsense view of science as a process and a community---not as an ultimate.
A theory is a ToE if it acts like a ToE and most of the community accepts it provisionally as such.
And he was saying that string may be irrelevant. String may not turn out to be "how nature is". He suggested an alternative line he is currently pursuing based on asymsafe qg and quantum field theory.
Therefore I think your references to string theory (ST) in your quote may be irrelevant and distracting. Maybe I will take them out and look at the bare bones skeleton of the argument, minus the flesh of that example.
My conclusion is that something like a ToE cannot exist in a physical sense:
a) you can only "prove", support or disprove a theory in a very restricted sense = in certain regimes
b) a ToE should be able to tell you why
it is the ToE
c) in a certain sense the discussions regarding duality show that there may be not one fundamental theory but only certain dual descriptions of something we like to call "reality" - whatever that means;
look at QFT: what are the fundamental entities of a "quantum ontology"? state vectors in Fock space and field operators - or path integrals and "trajectories in field configuration space"
d) any mathematical approach to a ToE is not able to prove why this approach must be mathematical at all
==end of excerpt==
Let me think a bit about this
d) is right of course. physical theories are mathematical. the fact that math works to describe regularity in nature is a mystery. but we do not have to address that. A ToE is just a physical theory that works predictively to arbitrary high energy, it does not have to explain all the mysteries.
Like "why does existence exist?" That is a good question but ToE does not have to address it.
c) does not have to worry us. There can be alternative equivalent formulations of the regularities in nature. Sometimes we eventually find that one is better. Sometimes we find a more general mathematics that comprehends both. It is OK. There can still be a ToE even if it comes in several equivalent formulations.
b) pragmatically, I do not see why any physical theory has to explain why it is an adequate theory. If something works and acts like a ToE then it is a ToE.
It does not have to contain a "theory of theories". Science is a communal process governed in part by tradition---and the tradition says that a theory is accepted provisionally until and if a better one is found. That is as good as it gets, in the tradition. All acceptance by the community is provisional. No acceptance is ultimate. So b) is no problem.
a) What you say here is absolutely right, except that we do not know in advance the ultimate limit that we can probe empirically.
Clever ways of testing a model may be invented which surprise us and which go beyond the domain of verifiability that we would have expected.
Pragmatically, the meaning of infinity is "way beyond what anybody expected".
If an theory predicts accurately way beyond what anybody ever thought we would be able to test, because of some clever ways to test that people think up, then it will be acting like a ToE. Predictive out to arbitrarily high energies. It's possible that humans will get such a theory. I don't think that on purely logical grounds you can deny us the possibility.
But I like your argument and think that it is one worth making.