Math, matter, monism, and dualism

Metaphysics & Epistemology
21

My view here is influenced by my experience as a computer programmer — a major concept in computing is the concept of emulation, where one computing environment can be embedded in another, and when done seamlessly enough there is no way to tell from within the inner computing environment that it is within an emulation. You can even arbitrarily nest emulated environments, with the only limitation being that the outermost environment must be implemented in terms of our world and must be subject to the physical constraints imposed by our world.

When we consider a mathematical universe, the same logic applies — a mathematical universe can be embedded in another mathematical universe can be embedded in another mathematical universe, ad infinitum, such that from an inner view in any given universe you have no way of telling if you are in the ‘outermost’ universe or not, or if there even is an ‘outermost’ universe.

A good example of this is that we can construct our own little mathematical universes within our own, such as Conway’s Game of Life, and given that Life is Turing-complete, you can even nest Life within Life, with the only real limits being practical ones imposed by the limitations of our universe. Within any Life universe, if properly implemented, there is no way of telling that it is embedded in another universe (e.g. there is no way of telling how many, if any, nested Life worlds are ‘above’ it).

22

I agree completely that an alien would ‘invent’ the same math as we humans.

Of course the cosmic programmer and intelligent design are the same thing, that was entirely my point.

If I am reading you correctly, you are bringing up the possibility that not all supposedly ‘possible’ universes are truly possible in the first place, which if there is a multiverse may constrain the set of truly possible universes in ways that may not be obvious to us at the present, but which we could potentially discover with further investigation in the future.

23

Don’t mean that. Not even sure what distinction would be between a possible universe and a truly possible one.

Somebody (I forget who, my search turned up crap) asked why the mathematics of our universe is interesting when the vast majority of mathematical structures are not interesting at all. Statistically, there are far more copies of you in uninteresting (random noise) universes than in ordered interesting ones. So you should be one of those uninteresting ones, but we believe otherwise. That’s a real problem with the idea of the universe supervening on mathematics.

24

What I meant was that there may be constraints on what universes can exist, if the multiverse hypothesis is true, that may not be obvious to us right now, that the set of universes that actually are instantiated may differ from the set one would expect if all the constants and mathematical structures of the universe are randomly selected.

Of course, the anthropic principle seeks to answer this by stating that in the vast majority of potential universes intelligent life (i.e. ourselves) could not exist in the first place to make note of them, which is why we are in an unusually interesting universe and not in one of far greater number of less interesting ones.

25

Whether that qualifies as philosophy, however, is a different matter, as I think philosophy does attempt to grapple with real questions, not just abstractions.

26

For some even pure math is plausibly instantiated “temporally” in what people do with marks and sounds. The “dance” is “beyond” ( more than ) any particular dancer but not all possible dancers. No numeral is a number, but the numeral is a numeral through playing a role. That role is the number, roughly speaking.

Crucially, this temporal instantiation is not “meaningless physicality,” for “meaningless physicality” is the shadow cast by the “purity” of “de-qualified meaning.”

27

Yeah, people will go to any length to avoid the suggestion of the reality of incorporeals.

28

I agree with you here, in a complicated way. Physicalism often manifests to me as a declaration that “the scientific image” is the “true” or “substrate” reality. Our scientific image is intensely mathematical.

Such physicalists probably do not want to say that “numerals” are the substrate, for then the substrate is “just marks and noises.” So instead the “meaning” of the math is the substrate. But this is tacitly a monological idealism. The “substrate” is “meaning” but “physical meaning.”

In some sense, “of course” something like “meaning” is the substrate, if you insist on having one. For if you call it “(generalized) water” then you mean the meaning of “(generalized) water,” whatever that is !

Because meaning is “tacitly presupposed,” there’s something fishy in physicalism. And in every monism. If “All is X,” then “X” is meaningless except for its emotional associations. To me emotional associations are “meaningful,” but does this kind of meaning fit with “physicalism” ? Which seems to want to erase just this kind of meaning as bias or mirage ?

29

This suggests that a different approach can only be explained in terms of bias.

Zoom out for a moment. I’m suggesting elsewhere that “consciousness is presence.” That is not exactly a scientistic move. It’s so “idealistic” that it’s not even idealism anymore, but ontological perspectivism, a updated monadology.

I also read Plato’s unwritten doctrine this way, in terms of the “fusion” of form and quality, one and dyad, being and nonbeing. I found a beautiful passage in Timaeus last night that’ll probably inspire an OP.

I really don’t know what you are making of my approach, except that you don’t like it. But how are you understanding it ? That would help me in this dialogue.

30

It wasn’t so much directed at you, but the dispute in ‘philosophy of mathematics’ over platonism, in favour of logicism, intuitionism, formalism etc. The SEP article on philosophy of maths notes that platonism has been deprecated because ‘the once highly praised faculty of rational intuition of ideas was regarded with suspicion.’ Likewise another article on the so-called ‘indispensability theory of mathematics’ says that ‘the (rationalist) philosophers claim that we have a special, non-sensory capacity for understanding mathematical truths, a rational insight arising from pure thought. But, the rationalist’s claims appear incompatible with an understanding of human beings as physical creatures whose capacities for learning are exhausted by our physical bodies.’ And another essay on the same topic: ‘Scientists tend to be empiricists; they imagine the universe to be made up of things we can touch and taste and so on; things we can learn about through observation and experiment. The idea of something (i.e. ‘Platonic reals’) existing “outside of space and time” makes empiricists nervous: It sounds embarrassingly like the way religious believers talk about God, and God was banished from respectable scientific discourse a long time ago.’

So I see this as a kind of fault line in modern philosophy. There are contemporary Platonists - Godel and Penrose are often mentioned - but overall, I think Platonism conflicts with naturalism, in asserting the reality of intelligible objects. So my remark was directed at the tendency to avoid that suggestion.

That said, I’ve been studying the (maverick?) biologist Michael Levin, who is saying that he can derive empirical arguments for the reality of Platonic reals. See for instance this article which I’m still in the process of reading.

31

I get it. The philosophical positions that some take on science they also mistake for science. As a kid in highschool, I was good at science, and ( like so many today ) I understood it in terms of a “substrate” reality. Because, probably, my science teachers implicitly took it that way.

I don’t recall much talk about method or philosophy of science. I was given, implicitly, absolute “facts.” Elsewhere we disagreed about positivism, but for me positivism and empiricism “accounted for the subject” through a concern with perception and observation statements. So it was at least “seen” that human language somehow “articulates” sense experience, often but not always in quantitative terms. Empirical science, if empirical, is “responsible to” mundane perception. This “residue” of the “lifeworld” is much better than the naive leap to an “objective reality” that is “physical” and yet “only math.” Which is to say that “all is (dehydrated) water.” Yet this dehydrated water is intensely taken for granted, especially by young people who thirst for an absolute “truth,” however grimly amoral. Indeed, it is “heroic” to face this abyss and maybe even “die for Truth.”

I died for beauty, but was scarce
Adjusted in the tomb,
When one who died for truth was lain
In an adjoining room.

He questioned softly why I failed?
“For beauty,” I replied.”
And I for truth – the two are one;
We brethren are,” he said.

And so, as kinsmen met a-night,
We talked between the rooms,
Until the moss had reached our lips,
And covered up our names.

With this, another:

What are days for?
Days are where we live.
They come, they wake us
Time and time over.
They are to be happy in:
Where can we live but days?

Ah, solving that question
Brings the priest and the doctor
In their long coats
Running over the fields.

32

I would say that math is a necessity in manifestation, just like spacial extension and temporal extension. You can’t have either kind of extension without the presence of math. For when one becomes two (1 divides into 2 halves), all three are present; spatial extension, temporal extension and mathematical principle.

Or another way of looking at the same idea is that if you start with a whole, a one thing, a unity in an empty space. In order to become anything else it fractures, the symmetry is broken. That fracture, is mathematically constituted. How could it be otherwise?

Plus the explanations which are beyond our capacity to understand. We can’t really address this aspect of our world, because our explanations can only consist of what we can understand in this kind of universe. Also we can’t determine to what extent the reality is veiled (metaphorically) from us.

33

It is known that physical systems behave in a certain way. This behavior is predictable, so we can establish a set of laws, so-called laws of nature, that describe the behavior of physical systems. Math is about relations, structures, and rules between abstract entities. Math is, therefore, just a useful tool for formulating the behavior of nature in general. The domain to which math is applicable is much wider than what is used to describe the behavior of systems in nature. Math does not belong to a different realm, though. There is only one realm in which real things exist, whether monism, dualism, or pluralism is true. Abstract entities in general exist only as a form of experience in the mind of intelligent creatures, such as humans.

You cannot dismiss substance dualism that simply.

34

If math were not privileged, though, you would expect predictions made on little evidence justified primarily in mathematical terms to simply not hold.

Newton, for instance, justified his laws of gravitation on the basis of relatively limited observations of the parabolic paths of thrown objects here on Earth ─ which as we know were certainly flawed due to the effect of air resistance ─ and the observations of the oval paths of a limited number of celestial objects ─ frankly, a very scanty set of evidence that should not have been rationally used to back up proposals of sweeping physical laws.

There is no rational reason why we should expect mathematical laws formulated on such little basis to hold, especially if math were just a pragmatic human tool, a mere approximation of underlying reality.

Yet his laws hold up extremely well, and only break down in corner cases where general relativity, which superseded them, describes things better ─ and even though they have been superseded, in the vast majority of cases within the human experience they are effectively true.

I justify my position based on that substance dualism implies that something is privileged about human biology that causes an independent metaphysical realm of the ‘mind’ to arise, yet how does a separate metaphysical quantity come to be from what is essentially just the small bags of DNA, RNA, proteins, and lipids that comprise a human egg and sperm, which fundamentally are not really all that different from, say, those that comprise the egg and sperm of, say, a sea urchin? There are really no physical laws that apply differently to the development of humans and the development of sea urchins, yet humans are posited to have ‘minds’ while no one thinks of the same of sea urchins.

Also, how does one take into account the fact that said proposed metaphysical quantity can be directly internally impacted by the physical, ranging from things such as my prior example of psychoactive drugs, neurological diseases and injuries, genes that we can demonstrate the existence of, and so on?

35

Not sure how ‘exist’ is being used here. I mean, you use it below in the same post “… in the vast majority of potential universes intelligent life could not exist in the first place …”
That’s a relational usage: life being contained by the universe to which it relates. But that usage would be a category error when speaking of a universe existing since there isn’t a larger container (in time say) that contains it.
Secondly, which ‘multiverse hypothesis’ are we talking about here? Tegmark only counted to 4, but Greene listed at least 9: [quilted, inflationary, brane, cyclic, landscape, quantum, holographic, simulated, and ultimate]

It doesn’t necessarily follow. It needs more than that.
Yes, anthropic principle says that only the rare universes with observers get observed, but that does not imply that the ones with observers are necessarily interesting. Most (more by inexpressible orders of magnitude) of mathematical structures with intelligent observers like say us are not interesting mathematical structures, despite the beliefs of said observers. That’s the problem I’m talking about. Sean Carroll wrote a paper about this problem, saying that certain theories cannot be simultaneously believed and justified. This MUH hypothesis seems to in that category, something distressing to me since I’m otherwise all over it.

36

That is an interesting implied definition of ‘exist’, because by it, if one does not believe in there being any kind of parent universe to ours, one would say that one could not state that our universe exists, which is a basically absurd position.

(Of course our universe exists — if it didn’t exist we couldn’t exist. Unless you are seriously going to argue that we don’t exist either… where then how could we be here discussing this?)

Any of them — I’m currently noncommital towards any particular multiverse hypothesis. (I frankly should do more reading on them.)

Can these mathematically less-interesting universes harbor intelligent life that can act as observers though?

37

Why would no parent universe mean we can’t say the universe exists?

That is enough for the universe to exist. No external container required.

38

Nature behaves in a certain way, and this behavior can be explained mathematically. That is all.

39

The matter is that nature behaves in a fashion consistent with math in the first place. If math were merely a human invention there should be no reason for nature to be consistent with it.

40

Given a non-relational definition of ‘exist’, it doesn’t seem absurd at all to me since an absolute definition of the word seems to be a mere mental construct without any metaphysical distinction. I mean, imagine two identical universes, except one exists and the other doesn’t. What test could an observer in that universe perform to determine which one he was in? Yes, the question presumes a denial of the principle that existence precedes predication. A unicorn is horny. That’s predication without supposed existence, so I ignore the principle.

Did a whole topic on this if you’re interested.

That kind of follows. Objective existence is typically hereditary. If X relates to Y (like we do to our universe), then both presumably share the same objective ontology. But so what? There not being a test for non-relational existence, my lack of it would be undetectable.

As you might tell, I abandoned realism some time back since it creats far more problems than it solves.

Well, we’re trying to leverage weak anthropic principle here, so only some of the multiverse types help with that.

Quilted: Kind of like Tegmark type I: The universe is infinite, so if there’s one of you, there’s infinitely many more, separated by some computable average distance. This doesn’t much help the anthropic thing.

Inflationary and Landscape: Combined, this is Tegmark type II

Inflationary posits multiple bubbles where inflation epoch ceased. Landscape suggests that each of these bubble universes might have different settings of the constants, which is critical to anthropic reasoning that seeks to explain observation of optimal settings. But it’s still all the same QM rules, and neither inflationary nor landscape helps explain that.
Landscape

Brane: From string theory

Cyclic: Doesn’t help since presumably the same rules happen over and over.

Quantum: MWI: Doesn’t help. This is Tegmark type III

Holographic: I fail to see how this is a multiverse

Simulation: This is by design, so doesn’t count. It’s the same as positing a god.

Ultimate: Tegmark type IV: all other mathematical structures, notably anything where QM doesn’t apply. This must also be taken into account to ground anthropic reasoning.

Yes, that’s the whole point. If they ‘exist’ as you put it, then there’s probably a lot (oodles of orders of magnitude) more of them than there are observers in interesting ordered universes like the one we believe ourselves to be part of. So the odds of our beliefs being correct become zero.

Per Carroll, “the theories that predict [such consciousnesses] are cognitively unstable: they cannot simultaneously be true and justifiably believed.”
MUH, without modifications, is a theory that makes such predictions.
Tegmark seems to simply deny that MUH predicts them, but without justifying the assertion. Maybe it’s justified somewhere. My search didn’t get that far.

That was using a relational definition of ‘exists’, ‘to be containted by X’, kind of like I exist in this universe. A universe not contained by something not part of it lacks this kind of relation, and hence does not meaningfully exist in that sense. Of course there’s several alternate definitions of ‘exist’ that one can choose, many of which are still relations.

For instance, many believe that the universe ‘started’, that it didn’t exist, and then at some point came into being. That’s a suggestion of it being contained (by time), and so that usage is consistent with the ‘contained by’ definition of ‘exists’. Of course that naive view was pretty much demolished over a century ago. Time is part of the universe, probably not the other way around.

1 Like