On Mon, May 13, 2019 at 6:06 PM Bruce Kellett <[email protected]> wrote:
> On Tue, May 14, 2019 at 1:50 AM Jason Resch <[email protected]> wrote: > >> On Mon, May 13, 2019 at 7:45 AM Bruce Kellett <[email protected]> >> wrote: >> >>> >>> I am not sure I have the time to delve into Muller's paper to find out >>> his reasons. He is clearly misguided, because there are many viable >>> cosmological theories that do not have a beginning of time (such as eternal >>> inflation and related ideas) -- even if time is universally defined, which >>> is very doubtful. >>> >> >> To be clear, his result does not rule out inflation, he finds only that >> observers can expect that there we will find a beginning in history where >> if we try to penetrate more deeply into what happened before, it devolves >> into a multitude of indistinguishable possibilities. >> > > So he is not proposing an absolute beginning to time after all! > > ...... > I don't want to go down the rabbit hole of what is meant by "absolute beginning", but I will leave you with these excerpts from the paper I referenced, if they help: In particular, we will see that our theory predicts (under the assumption > just mentioned) that observers should indeed expect to see two facts which > are features of our physics as we know it: first, the fact that the > observer seems to be part of an external world that evolves in time (a > “universe”), and second, that this external world seems to have had an > absolute beginning in the past (the “Big Bang”). If she continues computing backwards to retrodict earlier and earlier > states of her universe, she will typically find simpler and more “compact” > states, with measures of entropy or algorithmic complexity decreasing — > simply because she is looking at earlier and earlier stages of an unfolding > computation43. At some point, Abby will necessarily arrive at the state > that corresponds to the initial state of the graph machine’s computation > (right after the machine U has read the prefix q), where simplicity and > compactness are maximal. At this point, two cases are possible: either > Abby’s method of computing backwards will cease to work; or Abby will > retrodict a fictitious sequence of “states before the initial state”, > typically with increasing complexity backwards in time [100]. In both cases, Abby will identify a singular state in the past, where the > universe was particularly “small” and “simple” in the algorithmic sense. If > Abby reconstructs the previous history of her universe (the computational > process giving rise to her asymptotic measure µ), she will see that > complexity unfolded after this stage in a way that resembles an abstract > computation according to simple probabilistic laws. Thus, she may call this > initial state the “Big Bang”, and hypothesize that time had its beginning > in this moment. This is a striking consistency with our actual physical > observations. We will discuss further details of this in Section 11. > > No they didn't. Zeh's ideas of decoherence go some distance, but Everett >>> is totally irrelevant to this. >>> >> >> Do you think something more than decoherence is needed to get there? >> > > Yes. You need to reduce the superposition to a mixture. > > .... > What will this require in your opinion, new postulates, or simply a better understanding of the existing postulates? > > >> You seem to be using the old scholastic notion of nominalism. >>> "In more recent usage, 'nominalism' is often employed as a label for any >>> repudiation of abstract entities, whether universals or particulars, and >>> thus embraces the rejection of such things as propositions, sets, and >>> numbers." (Oxford Companion to Philosophy, OUP, 2005) >>> >> >> But then what is arithmetical truth? We have no label for it. It cannot >> be derived from or defined by labels. >> > > What is truth? (Pontus Pilate). Arithmetical statements are true if they > are theorems derived from the axioms. > This is false. In every consistent system of axioms there are statements that are true but cannot be derived from the axioms. In other words truth =/= proof, truth is always greater that what can be proved. > "Snow is white" (Brent) is true because it corresponds with the facts. > These are different notions of truth. > > ..... > > >> >>> We might discover some of their properties, but we can never know the >>> "thing" in itself. Theoretical entities are generally dealt with by >>> nominalism, as above. >>> >> >> Most scientists would say quarks are real, because they are part of >> successful theories which have explanatory power. >> > > That is the semantic part of scientific realism -- the entities in our > most successful theories correspond to elements of reality. That is just to > acknowledge that the ontology is theory dependent -- not mind independent. > So quarks may or may not be real -- we will probably never know. > > So what is wrong with the theory that the integers are real? (arithmetic is successful, after all) > > Calabi-Yau manifolds are mathematical constructs, depending on the >>> definitions of topological manifolds. They are certainly theoretical items >>> that have no mind-independent existence. >>> >> >> Most string theorists would guess that Calabi-Yau manifolds are real, >> because they are part of successful theories which have explanatory power. >> > > Most stirring theorist are hooked on a failed theory. String theory is not > a successful theory, and it has no explanatory power. > > >> The more you keep pushing this, the closer you get to seeing there is >> some truth to the Quine Putnam indispensability argument. You can't remove >> mathematical objects and numbers from our scientific theories. >> > > Why would I want to? Mathematics is useful for describing the results of > our observations and experiments. It is a convenient language. Do you think > that English sentences are part of a mind-independent reality? > Because arithmetical realism explains more while assuming less. > > > What separates the existent from the non-existent? >>>>>> >>>>>> >>>>>> It might be that at a certain level of description it becomes >>>>>> impossible to adequately represent the world other than mathematically. >>>>>> ... >>>>>> So yeah, you might think, if we eventually did have a one-to-one >>>>>> mapping, what could be the grounds for denying that reality was >>>>>> mathematical? I'm not really sure. I suppose I'm very skeptical of >>>>>> anything >>>>>> in philosophy that purports to explain the difference between abstract >>>>>> maths and maths that's substantiated. Because in the end, what could >>>>>> possibly explain that difference in terms of? Like, I reject the >>>>>> question >>>>>> 'What breathes fire into the equations?' Because anything you say is just >>>>>> gonna be figurative, right? Because you'd say, 'Well, there's the >>>>>> abstract >>>>>> maths and then the actual universe is a sort of substructure of all the >>>>>> possible structure there could be. So what's the difference between the >>>>>> uninstantiated structure and the instantiated structure?' Well, the >>>>>> philosopher will say there's a primitive instantiation relation or >>>>>> something--you could invent some metaphysical language to talk about it, >>>>>> but to me that's no different from saying that some of the maths has >>>>>> pixie >>>>>> dust in it. It's not going to do any work. Because what could it possibly >>>>>> connect to that would have any meaning? If you ask questions in science >>>>>> like 'What causes an earthquake?' you appeal to conceptual resources and >>>>>> those are non-empty because they're tied to observation. But maths--pure >>>>>> maths isn't tied to observation. If the theory of everything id a >>>>>> mathematical theory, how would you test it? It would have to have some >>>>>> content that has to do with something other than mathematics. -- James >>>>>> Ladyman, when asked "Does that mean the physical world is made of math?" >>>>>> >>>>>> >>>>> That sounds confused. But if anything, Ladyman is arguing for >>>>> scientific realism >>>>> >>>> >>>> He's saying any attempt to draw a boundary between "instantiated >>>> possibility" and "uninstantiated possibility", or between "physical >>>> structure" and "mathematical structure" is doomed to be ad hoc. >>>> >>> >>> He has a very good point, then. The problem with identifying "things" in >>> terms of their relations to other things, as Muller seems to do, is that >>> you make things into mathematical structures, and that is what Ladyman is >>> rejecting as ad hoc. This is a straight rejection of such ideas as >>> Tegmark's 'Mathematical (or Computable) Universe Hypothesis'. The universe >>> has its inherent physical structure, which is part of the 'ding an such', >>> which is not identified with any 'mathematical structure'. >>> >> >> You think there is no mathematical structure that can be identical to our >> physical universe with?! This is very surprising to me, why would this not >> be the case? >> > > We must be careful not to identify the map with the territory. > Mathematical models are descriptions, not the reality itself. > A sufficiently accurate map eventually becomes indistinguishable from the territory. Maybe we have been living in the map all along. > > ...... > > > That does not follow. The sets of axioms that we can employ is effective >>> unlimited, but all invented. >>> >> >> I know, I said as much. But arithmetical truth does not come from the >> axioms we invent. That was my point. >> > > It does, you know. There is no other explanation that makes sense. > Arithmetical realism does not make sense. > > Please read the opening paragraph of this page: https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems I admit the result is shocking. It was shocking to the mathematicians of Godel's day when he published it, which is why: "Gödel is referred to as the discoverer of the most significant mathematical truth in the century (on the occasion of his Honorary Doctor degree from Harvard University in 1952 – [W87] p. XXIII). ..... > > > Why do you think arithmetical or mathematical realism does not qualify as >> an external mind-independent reality? >> >> The answer of "*No*" to my question "*Is it possible that the physical >> universe could be explained from something more primitive?*" signals a >> quasi-religious belief. There is little point in trying to debate any >> further on this question while you hold so firmly to this belief. >> > > Your belief in arithmetical realism is also a quasi-religious belief. > I accept that. But I have provided reasons in support of that belief. The only justification I have received from you suggests that you reject it because you don't like it. > One has to start somewhere. Numbers are a poor starting point . > I think they are an excellent starting point. It is much easier, conceptually for me to accept 2+2=4 is true, has always been and always will be true, and needs no reason to be true, rather than the alternative, which is to accept the physical universe as we see it exists on its own, independently of anything else or any other reason. For what reason would such a physical universe exist, why does it have this form, was it caused by something else, is there more beyond it? Arithmetical realism provides a simple, elegant answer to these questions, and moreover answers many more questions than assuming the physical universe at the start. > Believing that there is something mind-independent to explain is better -- > as long as one explores what this might mean, rather than assuming the > answer from the start. > > We both assume something mind independent. You think it is the physical universe, I think it is the integers. My assumption of the integers not only explains why we have an objective field of mathematics, but with Mechanism, it explains the emergence of the appearance of the physical universe (without having to assume the physical universe). So I get to explain two things with one assumption. Since you start with physicalism, and deny the objective existence of arithmetical truth, you are confronted with the problem of explaining where arithmetical truth comes from. You say it comes from axioms but since Godel this has been known to be false. Your assumption can explain the physical universe, but not the objective nature of arithmetical truth. Further, I don't see any hope for how you can ever hope to explain why the physical universe has the laws that it does. Why is it quantum mechanical, why are the laws so simple compared to the total information state of the universe, do altogether other universes exist? There is hope of getting answers to these questions starting from the assumption of the integers, but there is not if your starting assumption is the physical universe itself. Jason -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CA%2BBCJUhis0JFN8X_RaT_hkQMhBECwbTCO4x-bUFu4vKhKXDidg%40mail.gmail.com.
