On 14 May 2013, at 04:15, Pierz wrote:

On Tuesday, May 14, 2013 12:13:19 AM UTC+10, Bruno Marchal wrote:

On 13 May 2013, at 09:30, Pierz wrote:

> On Monday, May 13, 2013 2:49:32 AM UTC+10, Bruno Marchal wrote:

The inside view comes when we agree that knowledge obeys to S4, and we
recover S4 (S4Grz) by linking truth to belief.
In a sense, for a machine M1 much stronger than a machine M2, the
theology of M2 can be made mathematical. What M2 cannot do
"mathematically" is to lift that theology on herself, unless she bet
(cautiously) on some self-correctness principle, but that cannot be
done in any 3p method, and usually math is considered as 3p-science,
so that correctness is not a part of math, but on faith in some
reality made by the machine M2. Likewise, I decide to not look at such
machine as zombie, and that means I project a non mathematical thing
(my consciousness) on them. This too is not mathematical.
In fact some mathematicians understood already that the encompassing
notion of "mathematical truth", or even just "arithmetical truth" is
not accessible by mathematics. In practice, this is no problem because
we hardly need such an encompassing notion, but in "theology" we need
it for the inside views.

Well I'll need to read the magical island story to make any sense of that.

Computerland or Numberland are more magic than the Wonderland :)

A good book is Boolos 1979. A nice recreative introduction to G is
Smullyan's "Forever Undecided". In that last book it looks like it
concerns only people living in some fairy tale, with perfect liars and
truth-tellers inhabiting some magic island, but that fairy tale is
shown to be the case for ideally perfect machines thanks to the
"famous" diagonalization lemma of Gödel.

Cool. Thanks for those references. A fairy tale! I can cope with that :)

Nice. I will come back on this, soon or later on Russell's FOAR list.

I think you did a pretty good summary of the UDA(*). I am not sure
what you are missing. Feel free to try to point on an assumption which
would have been made implicitly, or if a step is not valid. UDA1-7 is
enough I think, as step 8 is more subtle, and can certainly be


Ha! Nothing on the net is safe!

Nope :)

     (I will reread it and answer some questions there asap)

I wrote that for my philosophy group quite some time ago (well, 2011 as you can see). Since then I have gotten my head around step 8. My agnosticism about the argument stems not so much from having found a concrete flaw as from a lack of confidence in our understanding of the nature of consciousness (a question about the comp assumption itself), as well as an uncertainty about your use of arithmetical realism. I know you insist that your version of AR is "weak", but I wonder if you're not conflating types of "being". To be sure, I can accept "7 is prime" as an independently "existing" fact, but of all the problems of philosophy, the nature of what being is is surely one of the trickiest.


Our minds just don't seem to be well equipped to grasp something so fundamental - perhaps even the whole notion of being and non-being is unintelligible when enquired into deeply enough. There are propositions about the states of being in the world ("the cat is dead"), and there are propositions about propositions - purely logical ones (forgive my lack of rigorous philosophical terms here. I'm not an academic philosopher

That's why you are clear and talk in an intelligible way. I am not an academic philosopher too. I am a biologist/psychologist/theologian who understood early that with comp, biology/psychology/theology admits mathematical (even arithmetical) foundations.

and I can't recall the technical way of defining this distinction). You've merged the two, making statements about the world a special kind of logical statement. You've argued in effect in the MGA that this move is the only elegant solution to the paradoxes that become apparent when the notion of physical supervenience is pushed far enough. But it is a pretty massive leap. I see the appeal of the solution - but I've also wondered if paradoxes like the one exposed by the MGA aren't actually better seen as refutations of the comp hypothesis itself.

That remains logically possible.

The comp hypothesis is in a sense a naive one - one notices that computers can perform 'thinking-like' operations, solving problems that we use thought for, so one makes the leap that perhaps the mind itself is a computer.

Well, the brain, or the body, or the environment, at some level. The mind is a too fuzzy term, even with comp. It can be the software (still machine or number like), or the consciousness, which is more in the limit of the UD* than in any particular computations.

This began as a natural hypothesis, before anyone saw the abyss that it inevitably and logically leads to. To my mind, the MGA is unnecessary. One can arrive at much the same point by imagining computations carried out with hoses and buckets ("Olympia") or spread out over continents and centuries, with partial results passed around from one weird hose and bucket computer to another by letters, pigeons, arrangements of stones or whatever. How on earth can such a computational system contain consciousness?

Leibniz asked the same question with a brain, when look in details, it is not different from buckets and stone and pigeons, ... Consciousness is "in platonia", even a bit above (truth). The computational system just makes it possible for the "divine consciousness" to forget its divine nature and to concentrate on the terrestrial duties.

You really are forced either to abandon comp or to embrace the idea that it's the logical relations themselves that "create" the consciousness.

OK. I find this nice, as I tend to consider matter and physics as hiding problem, or even create it, due to the incorrect conception of reality (WYSIWYG, instead of non-wysiwig).

It stretches comp to the breaking point and throws one back on the whole problem of consciousness yet again. I see the appeal in your mathematical formalism, but it still leaves many strange unanswered questions, like where time comes from for instance.

Subjective time comes from the third hypostases (the first person, S4Grz1). Physical time is more mysterious and difficult to derive. It might be just a local indexical gauge of some sort. Physicist have not solved that problem either.

Maybe computationalism is just wrong.

Absolutely. Even if true, it is unbelievable, from a purely rational standpoint. But there are also strong evidences for it, and few evidences for an alternative theory.

It seems a digital substitution *should* work, but do we know really enough to make that claim - or bet?

The next generation will not wait to know, they will accept copies, just to have a higher probability to see the next soccer cup or something.

Our understanding of the brain is still in its infancy and the philosophy of mind still flounders about in a logical quagmire (I've read the deeply unsatisfactory texts).

But we don't need to understand the brain to copy it. We can't really understand completely our own brain, and that's why I insist on the act of faith or theological aspect of comp.

There are data from studies of psychedelics that are still *way* too confronting and radical for the mainstream to even dare to talk about because of the fear of being labelled a mystic and having one's reputation as a serious scientist trashed.

In my case some other people did a good job, without mentioning psychedelic. In a sense it makes me free to aboard such talk. But then, with salvia, I have got a better understanding that many people are not ready, neither for salvia, nor comp, nor QM or GR actually ...

What's appealing about your theory Bruno is that it does provide some kind of framework within which those data could make sense - I know you've talked about Someone-Who-Isn't-You's salvia experiences as fitting or supporting comp, and have argued for greater openness to the phenomenological evidence of psychedelics.

Yes. It is of course quite double edged today. Then salvia go quite farer than comp. I am overwhelmed by the data on consciousness and "reality" ....

But the weakness of the arithmetical ontology is its permissiveness. I have grave doubts about your claims of testability. You've admitted that the mathematical problems of deriving physics from arithmetic are "hard".

We got already the quantum shape, but we have no hamiltonian, nor anything looking like a physical constant. It is works for the infinity of future generations.

I think that is surely an understatement! The maths involves far too many infinities.

But that's not really a problem. On the contrary, those infinities are needed for having reasonable measure, and the modal logics can cope with the constraints for the certainty case, from which we can derive the logic they obey. The self-referential logics does bring a lot of information, and notably that justifiable/non-justifiable distinction, and the negative (neo-platonist) aspect of the theology.

On the face of it, it seems to me that pure arithmetic would permit all self-consistent physics and any specific set of physical laws would be a local condition so to speak (mathematically, not spatially "local" of course).

Not really. That's an advanatge of comp: the physics is unique and the same for all machines, but it is complex and has possible cluster of multiverse (multi-multi-verse, intermediate realities between heaven and earth, etc.).

There's also the question of measuring infinite sets - a problem raised by Deutsch in "The Beginning of Infinity" when critiquing ideas similar to yours. I've asked about this before but you assured me Deutsch was wrong and you were right - alas my maths was not up to disputing the point. But I still wonder how it's possible to measure the proportion of infinite sets of computations. If I have some function f(), then I can also imagine some function f1() where f1() = f() +1 -1. Then of course I get f2() = f1() +1 -1, f3() =... etc up to f()inf, all equivalent to f(). So deriving a proportional measure seems impossible, since every function can be calculated in an infinite number of (admittedly more or less efficient or inefficient) ways.

But infinities makes measure theory more easy. And the self- referential constraints put a lot of order there. But of course, this leads to very hard mathematical questions (one of which has been solved by Vandenbussche).

Phew. So, in a word I find appeal in your ideas, but despite recognizing the force of the argument, I remain agnostic on the initial assumption of comp

I am too. That's why I am not a philosopher, but a scientist. A scientist does not defend that a theory is true. Only that it is testable, and then he can love it for its elegance, but true? Nobody knows, especially for comp, we just can't know (but we can be deluded in believing we know, like after surviving, apparently, with a digital body).

and am as inclined to see the UDA as an argument *against* comp as to see it as an inevitable conclusion.

Without QM Everett, I would have thought so. But the MW looks like a confirmation of the most startling consequence of comp, that we are multiple. It does not make comp true, but it makes it quite plausible with the current knowledge.

Truth is bigger than us, (a proposition I know you agree with), and Truth I suspect is bigger than mathematics, bigger even than arithmetical truth which incompleteness shows is beyond the reach of formulation. In these deep realms we are over our heads in mystery and I'm suspicious of any reduction to rationality.

Well, here rationality forces us to see the limit of that reduction, like if the left brain can see the grandeur and depth, and the necessity, of the right brain. This really gives sense, informally and formally, to Plato. Even if false, all this can help to open our mind, and have fun. Then comp gives a sense of modesty, which I like very much, notably it reminds us that we are linked to something that we cannot reduce in any 3p manner, so it looks more like a vaccine against reductionism (notably of numbers and machines) than a reductionism. I certainly love comp. But, like salvia, this does not mean I believe they are true. Just very interesting, quite mind blowing, and, as far as I can know, rather plausible.



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