To be honest, I think Russell's paradox is, well, over-hyped. It's not that hard to avoid, just don't allow the forming of arbitrary subsets of classes.
This isn't enough for a whole new post, but the main error you're committing is in the step of your reasoning where you argue that the entire universe could not be represented because representation requires differentiation. There are several components to this error:
- Representation does not require differentiation, only representiation of parts of a non-trivial system does. If we assume the surrounding context of the one-element set, every inhabitant of it can be represented with only one symbol and without being differentiated from one another. It's just not very interesting to do so.
- You're conflating the physical universe with a more general mathematical universe (which you have to assume exists to disprove my point from its premises, or simply to have a coherent physical theory). The physical universe is represented by one symbol all the time by physicists, usually in the form of a sentence like "Let X be spacetime…".
- Russell's paradox is only valid in regards to sets. In Von Neumann–Bernays–Gödel set theory, for instance, the "set of all sets" is not a set but a class, for which not all subsets can be taken. In such a context, it is not problematic whatsoever to assign to this universe a symbol, say U, and treat it just like a set, with only a slight number of additional restrictions of what can be done with it (namely not taking arbitrary subsets). The fact that ZFC is still used as the standard set theory, and not NBG or something better, is mostly due to institutional inertia. However, even in set theory using ZFC, the universe of sets is regularly signified by set theorists, though, depending on their metaphysics, if you were to press them they would say that they are using it as a shorthand. Lastly on that point, if we assume the existence of a class of all sets U, this class can still be differentiated from any other set or class X simply by the fact that X is contained within U but U is not contained within X. So simply because something contains everything that does not mean that it cannot be distinguished. It is also not clear how valid Russell's paradox remains if a paraconsistent logic is used, but I wouldn't hang my argument on that, it is perfectly plausible that no paraconsistent logic can be devised in which Russell's paradox could occur and which would still be rich enough to allow for the existence of the physical universe.
- It is not necessary to assume one final mathematical universe to treat the physical universe as a mathematical object, it can just be one node in an infinitely increasing network of connected nodes. Among category theorists, usually a framework of "Grothendieck Universes" U_i is assumed, where U_i contains all sets one size smaller and is in turn contained in U_{i + 1}. So U_0 contains all small sets, U_1 contains U_0 along with all small sets and all sets one size larger, which would appear as classes from the perspective of U_0, and so on. In fact, I do assume the existence of an "∞-category of ∞-categories", but only as shorthand for a pattern in such a hierarchy: there is an ∞-category of small ∞-categories, an ∞-category of next-larger ∞-categories and so on. In praxis however, one finds that very little changes as this size increases, the only thing to look out for is to not allow for constructions that would allow for something like Russell's paradox to occur.
I will also say that I don't find any of the variants of the Quine-Putnam indispensability argument addressed satisfactorily. Now, you are quite right in saying that I'm drawing from "string theory" (more precisely M-theory), which is not experimentally verified, which matters very little to me but does to you. What is experimentally verified (though not true) is the standard model however, as well as Einstein's relativity theory (whether special or general), which are gauge theories (to be completely precise, the standard model is actually a model of a gauge theory, namely Yang-Mills theory). What these gauge theories have in common is that they are invariant under the action of a symmetry group. In fact, the entire notion of a gauge theory, which is of fundamental importance in modern physics, whether M-theory or not, requires the notion of a symmetry group, one for every gauge theory (there might be some slight simplification here), so, again, symmetry groups have to be assumed to exist for gauge theory to make any sense.
On a more philosophical level, you are already assigning yourself to at least dualism when you write that "it seems possible we could one day have the rule which governs all reality. Is that not enough? Well, the universe is not just that rule, it’s that rule in motion, applying itself, or perhaps already applied infinitely, depending on your perspective, that’s what separates the rule written down from the universe itself." You now have two "substances": one, whatever the physical universe consists of, and one, the rule which governs how the first substance interacts, let's call it R. Now, there has to be some distinction between the "matter" of the universe and the rule governing its interactions, but to not be dualist those two would have to be brought together in some way, which can be done perfectly well if we assume the physical universe is a mathematical structure, because the axioms of one mathematical structure are themselves mathematical structures on a slightly higher level, and, while one one level distinct from the structure they regulate, they are fundamentally of the same substance. If meanwhile we do not make that assumption, we would need to introduce further logico-mathematical rules governing the consequences of the application of R in terms of logic/mathematics, otherwise the rule would be void and everything would be allowed since nothing could be deduced from it. Thus, you would have in fact a whole hierarchy of distinct substances: "matter"(/energy/whatever), the rule that governs the interactions of matter and rules governing the consequences of that rule as well as an open number of further rules giving coherence to those rules. It would be a nightmare!
So I'm not really sure this actually deals with what I'm saying.
"Representation does not require differentiation, only representiation of parts of a non-trivial system does." This is what I'm explaining in the first part, of course you can use "1" to represent things, the trouble is exactly that you can't do so in a precise way, that it's a necessarily incomplete representation. When physicists say "let x be space time" they're using math to describe the universe in a simplistic way, which, by the way, even to be useful means they're relating x to some other symbol. You're not just claiming that the universe is described by math, but that it /is/ math.
"Lastly on that point, if we assume the existence of a class of all sets U, this class can still be differentiated from any other set or class X simply by the fact that X is contained within U but U is not contained within X. So simply because something contains everything that does not mean that it cannot be distinguished."
My point is precisely that you have to come up with some new category like "class" which is not a set in order for this to work, it's a way of defining a new "everything" which does not contain "everything".
"Now, you are quite right in saying that I'm drawing from "string theory" (more precisely M-theory), which is not experimentally verified, which matters very little to me but does to you. What is experimentally verified (though not true) is the standard model however, as well as Einstein's relativity theory (whether special or general), which are gauge theories (to be completely precise, the standard model is actually a model of a gauge theory, namely Yang-Mills theory). ... symmetry groups have to be assumed to exist for gauge theory to make any sense."
I don't believe general relativity is "reality itself", I just think it's a description of reality, that it is the realist sort of idea that we have.
"On a more philosophical level, you are already assigning yourself to at least dualism when you write that "it seems possible we could one day have the rule which governs all reality. Is that not enough? Well, the universe is not just that rule, it’s that rule in motion, applying itself, or perhaps already applied infinitely, depending on your perspective, that’s what separates the rule written down from the universe itself." You now have two "substances": one, whatever the physical universe consists of, and one, the rule which governs how the first substance interacts, let's call it R. Now, there has to be some distinction between the "matter" of the universe and the rule governing its interactions, but to not be dualist those two would have to be brought together in some way, which can be done perfectly well if we assume the physical universe is a mathematical structure"
That was just for illustration, once we speak of "the rule in motion" that already contains the rule and its execution, and they need not be two separate things. The rule is just a description of it. In digital computers we need the rule to be symbolically expressed, but that's not the case for physics, or really analogue computers for that matter.
"Representation does not require differentiation, only representiation of parts of a non-trivial system does." This is what I'm explaining in the first part, of course you can use "1" to represent things, the trouble is exactly that you can't do so in a precise way, that it's a necessarily incomplete representation.
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No, it's a complete representation of a trivial structure, but that's a side point.
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When physicists say "let x be space time" they're using math to describe the universe in a simplistic way, which, by the way, even to be useful means they're relating x to some other symbol.
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Yes, and that symbol describes the physical universe, allowing us to symbolically describe its relations to other mathematical structures. The point is, the physical universe can be described through a symbol, and in order to accurately depict the physics of this universe, symbolically, it is necessary to relate it to other mathematical objects, again described by symbols, and for that description to make sense, those other objects have again to be real.
Yes, but not all of math is the physical universe. It is simply one object among many.
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My point is precisely that you have to come up with some new category like "class" which is not a set in order for this to work…
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Yes.
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…it's a way of defining a new "everything" which does not contain "everything".
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No. The class of all sets contains itself, that's the thing. You just can't take arbitrary sub-sets of it. You can form the "class of all sets that don't contain themselves", for instance, and it doesn't contain itself because it's not a set.
Edit: actually, I have to clarify this: there are two senses of containment in regards to sets/classes: membership as an element ∈ and membership as a subset/subclass (of which I can't quickly write the symbol). The class of all sets contains itself as a subclass, but not an element. But it isn't really necessary for it to contain itself as an element to be a "universe". The universe doesn't have to be a box in the universe, basically, it just have to consist of everything that exists. Though, again, I actually go with, basically, an ascending hierarchy of universes anyway.
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I don't believe general relativity is "reality itself", I just think it's a description of reality, that it is the realist sort of idea that we have.
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Of course relativity theory is a description of reality, the question is, is it an accurate description? Because if it is, it uses symbols that refer to non-physical entities, so if it is accurate, those have to refer to something real as well.
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That was just for illustration, once we speak of "the rule in motion" that already contains the rule and its execution, and they need not be two separate things
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Yes they do, because if "the rule of" motion were simply all of motion in existence, there would be no use in defining "motion" at all, because no non-tautological rule existed that distinguished it from anything else. For there to even be a concept of motion, an underlying commonality has to exist that structures all of motion. But this "law of motion" is completely indifferent to any actual motion taking place: it could be applied to any fictional objects in any starting position and would yield paths for them. Thus, for it to structure all motion, it has to be independent of any actual motion.
To summarize my first comment again, you were arguing against mathematicism on the basis that representation, or at least exact representation, requires differentiation and the totality of the universe cannot be represented in this way based on Russell's paradox. I replied that
- Since I distinguish the physical universe from the mathematical universe, the question of whether one complete mathematical universe exists or can be described is independent from that of whether the physical universe is a mathematical structure.
- Russell's paradox only applies to sets and can easily be circumvented by either distinguishing between sets and classes, or, better, using an infinite hierarchy of ascendingly large mathematical "universes".
- The Quine-Putnam indispensability argument has not been addressed satisfactorily.
- A description of the laws of nature that treats them as of a separate substance is (at least) dualist.
To this I have added now in response to your reply that one which treats the laws of nature as the same as nature cannot account for there being any regularity within nature at all. Only (at least) mathematicism allows them to be both different enough so they can explain one another while being of fundamentally the same substance.
To also reply to your second comment:
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That science begins from categories and concepts doesn't really matter as abstraction is required for all thought, communication and meaning. This is an anthropic principle thing, I don't think you can extrapolate to the universe necessarily.
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Here I don't see how you're addressing my points. You basically said there are a lot of things that are coherent, so simply using coherence as a criterion of reality would leave us with too many structures. I said no, there just are many structures in the physical universe already, many more mathematical structures can exist, but only some of them are complex enough to allow the physical universe to exist, but also, these structures generate one another, so this is not a satisfactory starting point either, so that, having excluded matter, physics, and mathematics as not sufficiently fundamental (because, again, mathematics itself contains layers of elementarity) we have to repeat the question with Hegel: "with what does science have to begin?"
"Yes, and that symbol describes the physical universe, allowing us to symbolically describe its relations to other mathematical structures. The point is, the physical universe can be described through a symbol, and in order to accurately depict the physics of this universe, symbolically, it is necessary to relate it to other mathematical objects, again described by symbols, and for that description to make sense, those other objects have again to be real."
Yes you can form descriptions, but, as I've said many times, that's not the same as the universe itself, you cannot symbolically represent the universe in its entirety. Symbols may refer to real objects, but what makes those real objects differentiated is only human abstraction. Or abstraction created by some other observer.
"Yes they do, because if "the rule of" motion were simply all of motion in existence, there would be no use in defining "motion" at all, because no non-tautological rule existed that distinguished it from anything else. "
That is the whole point in what I'm saying, once you get to the level of everything that exists, the ability to distinguish things goes away.
"To this I have added now in response to your reply that one which treats the laws of nature as the same as nature cannot account for there being any regularity within nature at all. Only (at least) mathematicism allows them to be both different enough so they can explain one another while being of fundamentally the same substance."
One what? The probably is exactly this, as I'm not saying what substance the universe is made out of as a matter of /logical necessity/ but mathematicism does. To me, how we describe the universe must be fundamentally contingent due to human fallibility. The claims of physics are always contingent claims, even if they are really sticking their neck out in terms of credibility. Human kind could not go from the ancient cosmologies to the present ones without an openness to either on some level.
"…you cannot symbolically represent the universe in its entirety"
And I have said, with arguments that I don't really feel like have been answered, that it can, both the physical and the mathematical universe, which you would have to distinguish if only to prove they are the same, and that this is done all the time. Your only counterarguments to this were:
- a structure that includes everything loses distinction.
- Russell's paradox.
I have said repeatedly that
- the physical universe has to be distinguished from the mathematical universe and so does not necessarily contain everything.
- Russell's paradox would only apply to the "set of all sets", which the physical universe is not anyway (a set is, basically, a bracketed collection so there is no way in which the physical universe is a set), and can easily be dispersed with in several ways.
- A thing that contains everything can still be distinguished from other things, for instance by the fact that they don't contain everything.
Trying to guess what you mean when you say that you cannot symbolically represent the universe in its entirety, because I genuinely don't understand how you can even say that given that it's done all the time, I guess the idea is that a symbolic reference to the physical universe does not contain references to every thing in it. But this is true of every symbol that ever referred to anything. When I say "this vase" and point to a vase, the word(s) do not contain a reference to every particle in that vase, but that doesn't mean the utterance doesn't describe that vase.
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"To this I have added now in response to your reply that one which treats the laws of nature as the same as nature cannot account for there being any regularity within nature at all. Only (at least) mathematicism allows them to be both different enough so they can explain one another while being of fundamentally the same substance."
One what?
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The laws of nature can explain how nature unfolds while nature can be a particular embodiment of the laws of nature.
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The probably is exactly this, as I'm not saying what substance the universe is made out of as a matter of /logical necessity/ but mathematicism does.
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Again, there is no logical necessity in this. It's just an article of faith, a fundamentally religious impulse to deny the intelligibility of the universe, which wouldn't be problematic if it wasn't done in the name of science. Also, I'm underlining again that I'm not arguing for mathematicism, as mathematicism is itself not foundational, I'm arguing for Hegelianism.
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To me, how we describe the universe must be fundamentally contingent due to human fallibility.
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No, because the processes of the universe have an inherent structure to them that is mirrored in our mind. This is necessary for anything we think to be applicable to the universe whatsoever, but implies that the structure of our thinking can be used to understand the structure of our universe, which is what Hegel understood. Even apart from that however, it is just standard practice to assume that our understanding of the universe approximates it more closely through the science. Moving from physicalism to mathematicism is only a continuation of this process.
Goo would be matter. Of course matter decomposes into fields, but the real question is, why does the universe follow any rationally comprehensible pattern at all? The answer has to be that it itself is subject to a structure, but that structure cannot be physical because it literally governs the laws of physics, so it has to be logico-mathematical because logic and mathematics are literally the structure of our thought that we can use to reason from empirical data, which ensures that our reasoning is sound i.e. corresponds to real developments. If this wouldn't be the case, we could not predict anything whatsoever. I've gone through this in "Why the Physical Universe is a Mathematical Structure" and "The Incoherence of Metaphysical Materialism", but, to sharpen the point, it does not suffice to say "the universe is made out of X" because that doesn't address what the laws of physics are made out of, unless one includes that too, in which case one is already in the domain of mathematics. Hegel knew that already, that's why he says in the introduction to SoL that the question of what the universe is made out of pales in comparison to that what truth is.
Apologies for typos, typed on phone. Third section ("This resonance...") best captures what I am trying to say, I think, especially when I got to the idea of an emergent structure enabling that structure to dominante its surroundings, resulting in a selective pressure in the struggle to exist that favors orderly, lawful activities - without any "law" ever forcing itself on the situation.
Let us take it as a given that the universe exists without an imposed set of divine or platonic rules and is not math. I will tell a story that I think is conceivable and will explain what I mean when I say the universe is made of goo.
Let us start with no universe and no reality and nothing at all. There is no sense of what is and is not possible. Nothing is defined. But because nothing is defined, nothing is prohibited. Thus, nothing can stop impossible things from happening, like the beginning of a universe. Now, we have a universe, but it has no laws. A newly born reality begins to tug and pull on itself in every direction. Most of this does not amount to much, but some tendrils of reality resonate with themselves and begin to spontaneously develop order. If you put paint on a speaker; the vibrations will resonate the paint and long tendrils of paint can begin to grow off the speaker. There is no natural law which orders this, it is spontaneous self-assembly because of a resonance which leads to structure. If reality pushes and pulls into everything which is possible, it would begin building structure in this same way. Structure takes root because it is sustainable. The chaotic frenzy lurches and crashes in every direction, but never amounts to much, but within this sea of chaos, structure is crystallized. This would be akin to how crystals actually form, in the ordinary sense. These structures are self-reinforcing and expansive, they grow and absorb and grow and with it structure comes to be imposed on the playing field as a whole. It is goo. It is a good that crystallizes itself into a patterned skeleton because that is the only way for one moment to be sustained into the next. And when we look to reality - it is orbits, generations, cycles, phase alignment, and matter itself is now understood as vibrations in fields.
This resonance is how coherent, logical structures emerge without there ever being a commanding law. Solar systems follow patterns, stars follow patterns, your life will follow patterbs - but there is no law of solar system, no law of stars, and no law of biological reproduction. Consciousness is matter and motion, it follows patterns, in fact it relies on patterns in order to sustain its existence - the atoms at weavelengths, your breathe every few seconds, you sleep every day - these patterns are what allow reality to summit and conquer itself, whether by natural forces unintentionally lighting a star or by humanity intentionally damming a river - and thus outcompetes and imposes itself over the nonsense and the random and the chaotic. This is not driven by math but it settles upon math, the pure formalizations you can cook up in the mind do not exist anywhere but the mind, but the success of patterns and routine haunts reality like a ghost, they inevitably creep into a situation, and can then be discerned by scientific study.
I think this is why Quantum Mechanics is the way that it is and is so befuddling. People expect reality to be lawful all the way down but scientists have drilled to rock bottom and discovered the raw chaos and churning seas of possibility which underly concrete existence. What we see instead is that reality is loose at the joints and built on shifting sands, it can be pinned down, crystallized into descrete forms, quanta, but it is squishy, you can never get it to reveal everything, and as soon as you release the pressure, it pushes itself back out into a state of indeterminancy and possibility.
This is also why I am skeptical of inflation theories. They're trying to treat time and space as well defined categories prior to the deposition of matter. That would certainly also explain why everything was so smoothly distributed in the beginning as well - you can't unevenly distibute mass within a universe which has yet to be divided into distinct locations.
This sounds very Zizekian to me. Regardless, the point you're overlooking is that the selection that would let more orderly structures dominate others is if there was a context that would advantage orderly structures against disorderly ones — and a context that would allow for the notion of orderliness itself to make sense. This is actually akin to how crystals form, because they don't just form in isolation, or in every condition whatsoever. So you can't get around this by appealing to some notion of evolution from a primordial chaos because for that evolution to occur at all there has to be a structure that advantages some forms of existence over others.
In the earlier comment you have responded to, I was stuck in the weeds of asking why there is something rather than nothing (or to put it into Hegel speak - How do we not end up with pure being or pure nothing, and total indeterminancy, but rather, how do we end up in process of becoming, embodied by determinate things?).
But we know there is something rather than nothing, so we can take that as a given and look at how something became something. I am much happier with the resulting explanation I have given in the other comment just now, jumping off from what we empirically know about the development of the universe, life, and consciousness.
Zizek is Hegelian and I am Marxist so that sounds about right to be hearing him.
We know the universe starts from as simple of a state as it possibly could - no meaningful distinctions in where matter is allocated and no meaningful distinctions in the temperature of that matter. In fact the matter itself has to deposit out of this blanket uniformity, we do not even start with a distinction of having parts of reality which are matter and parts which are not. We can even see that there are temperatures, above which, there does not appear to be any difference between 3 of the 4 fundamental forces. All of this indicates a state of absolute unity which dissolved itself as soon as it meaningfully embodied any notion of time and space.
Reality collapsed out of pure unity and draws distinctions within itself. You are posing that this can only happen because of a logical structure, but to have logical structure, reality must first draw distinctions between things (this is the context you refer to as being necessary, forms of meaning only arise through contrast).
We do not start with distinctions between things, so we do not start with logic
In the process of reality drawing distinctions within itself, what we can see is that ideology is a complex order which erupts from less complex premises - quite literally. As a species, we can see how we exist within a complexity gradient. When you have two jugs of milk and coffee, each substance is not very complex or dynamic. They just sit on table. And when you combine these, the end result of complete mixing is not very complex or dynamic either, you just have one big jug of averaged color. However, in the interum, as the fluids mix, white and brown tendrils swirl, vortices appear, and, through this contrast and active transition, the system is able to produce a dynamic, visual complexity. This is much akin to how we subsist off the sun and our planet, making poetry and equations and computers - we are ultimately just generating poop, trash, and body heat. The structure in our thought is more complex then the premises which birth it. It is not necessarily true, then, that the ability for such structure to arise in our thought is merely imported into our minds from the mainframe of the universe.
"We know the universe starts from as simple of a state as it possibly could - no meaningful distinctions in where matter is allocated and no meaningful distinctions in the temperature of that matter. In fact the matter itself has to deposit out of this blanket uniformity, we do not even start with a distinction of having parts of reality which are matter and parts which are not. We can even see that there are temperatures, above which, there does not appear to be any difference between 3 of the 4 fundamental forces. All of this indicates a state of absolute unity which dissolved itself as soon as it meaningfully embodied any notion of time and space. "
Well, not really. We don't even know that the universe ever "started" — I'd place more stock on eternal inflation than the Big Bang Theory, though I don't have any strong committments there. More importantly though, at the time of the Big Bang, all laws of mathematics and logic already held — that's why we can say anything meaningful about it whatsoever. That's actually one of those conflations Zizekians like to make, of physical and mathematical/logical necessity: the laws of physics are way more peculiar than those of matematics.
"We do not start with distinctions between things, so we do not start with logic."
That's very anti-Hegelian.
"The structure in our thought is more complex then the premises which birth it. It is not necessarily true, then, that the ability for such structure to arise in our thought is merely imported into our minds from the mainframe of the universe. "
Again, for our thought to be able to say anything about reality it has to correspond to structures in reality, otherwise the structure of our internal logic would not map onto reality, so no predictions could make would correspond to real events and there would not be any way to change our models to improve them. The workings of the universe would simply be incomprehensible to us.
The trouble with Prähauser’s reasoning that we should, for example, embrace M-theory/string theory because of its mathematical coherence, is simply that there are a lot of things which are logically coherent.
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This is indeed true, but there are far fewer things that are both coherent and complex enough to allow for something like the physical universe to exist. In fact, with the rise of M-theory, for the first time we can approximately locate our position within the larger mathematical universe (or multiverse, it does not matter for the point). We are over the four-dimensional sphere in a super-cohesive ∞-topos. It's amazing! In any case, it should be noted that there are also just many things, period. The (physical) universe has shown itself to be pretty big, possibly infinite, and we are (almost) literally a needle in a haystack.
Also, you will note that I did not argue for mathematicsm as such, because, as I said, more complex mathematical structures can be generated from simpler ones, whereupon I said that this forces us to ask again "with what does science have to begin?" and then develop it again from that notion. Even harder than finding things that can generate the physical universe is finding one notion and generating all others from that, but once we have that, we can simply follow the dialectical flow of notions and find that it leads us to the physical universe towards the end, among other things, which is what Hegel did (though it could be argued he starts with two notions, being and nothing).
That's what the beginning of science has to be made with, and that can actually answer the question of "why does anything exist? (And why isn't it all just one thing?)"
That science begins from categories and concepts doesn't really matter as abstraction is required for all thought, communication and meaning. This is an anthropic principle thing, I don't think you can extrapolate to the universe necessarily.
Does your version of materialism make any claims about the physical nature of matter, or is "matter" just a stand-in for substance monism? If you care about the nature of matter, then you need to rely on modern physics, which doesn't necessarily lead to mathematicalism but at least displaces the role of matter as ontological fundament. If you don't care about what physics says matter is, what sort of properties does your one substance have that make it more like Matter than Idea, as opposed to a Spinozist position than doesn't privilege either of the two attributes of extension or thought?
I would say it both makes claims about physical nature and is a substance monism, for the simple reason that the claims about physical nature are just like any of the other claims about reality, contingent and subject to overcoming through science. The substance monism is more a matter of faith about the relation of thought to reality, but one which is useful for approaching thought and abstraction as not necessarily structuring of the world, while at the same time, as not being totally disconnected from it.
Of course you can make claims about the nature of matter, if you wanted to. But I'm asking if it DEPENDS on any claims about the the physical constitution of matter in general, or really on any physical claims about the universe at all. For example, in what sense can forces said to be material? Light is not typically considered matter, but surely you are allowing for its reality, so perhaps you mean something different by matter. Etc.
I don't think materialism, in its most general sense, necessarily requires matter to be a certain way, but it should be connected to a certain epistemology about what is real, the type that focuses on and leads towards phenomena like light and atoms and such
If you're not reducing everything to matter (eg. light), and you don't care if matter has itself been reduced to immaterial terms as Prähauser points out, this seems more like a limited physical reductionism where objects are real as long as they are composed of matter (even if we can't or don't describe that composition), and processes are real as long as they can be reduced (again, only in theory) to physical laws of motion. Given the fact that these reductions are extremely hypothetical (eg. no one has a mechanistic description of the brain or an economy as a process), it seems like we should have a more capacious definition of which objects and processes are "real" that accepts the way that "real objects" are constructed by scientific discourse, even if "reality itself", whatever that means, is not.
I did read it, that's why I'm here. You kept referring to "real objects" (a "given real-concrete totality" which occur in "the real") as opposed to the "object of knowledge". What these real objects are is unclear to me (you allow atoms, brains, and nations?), and the distinction between the real object and the object of knowledge seems rather dualistic and dogmatic, especially insofar as not-very-concrete totalities like nations are constructed to an important extent by our discourse about them.
Materialism, as a statement, only entails that reality exists prior to and independent of the particular manners in which it is disclosed to itself. The underlying content of reality precedes and exceeds the disclosed form.
This cuts the line between materialism and divine idealism (reality is downwind of God's plan), as well as cutting a line between materialism and the disputed platonism (reality is downwind of mathematical forms).
This also leads to Marx, and his statement that social consciousness is a result of social being. As another example - more relevant to this debate - Humanity is a particular form of matter in motion through which the universe understands itself, because as expressions of the universe we are able to look around us and look within us and understand what is happening, but the universe also existed before humanity. Reality existed independent and prior to how it came to disclose itself in consciousness.
To be honest, I think Russell's paradox is, well, over-hyped. It's not that hard to avoid, just don't allow the forming of arbitrary subsets of classes.
This isn't enough for a whole new post, but the main error you're committing is in the step of your reasoning where you argue that the entire universe could not be represented because representation requires differentiation. There are several components to this error:
- Representation does not require differentiation, only representiation of parts of a non-trivial system does. If we assume the surrounding context of the one-element set, every inhabitant of it can be represented with only one symbol and without being differentiated from one another. It's just not very interesting to do so.
- You're conflating the physical universe with a more general mathematical universe (which you have to assume exists to disprove my point from its premises, or simply to have a coherent physical theory). The physical universe is represented by one symbol all the time by physicists, usually in the form of a sentence like "Let X be spacetime…".
- Russell's paradox is only valid in regards to sets. In Von Neumann–Bernays–Gödel set theory, for instance, the "set of all sets" is not a set but a class, for which not all subsets can be taken. In such a context, it is not problematic whatsoever to assign to this universe a symbol, say U, and treat it just like a set, with only a slight number of additional restrictions of what can be done with it (namely not taking arbitrary subsets). The fact that ZFC is still used as the standard set theory, and not NBG or something better, is mostly due to institutional inertia. However, even in set theory using ZFC, the universe of sets is regularly signified by set theorists, though, depending on their metaphysics, if you were to press them they would say that they are using it as a shorthand. Lastly on that point, if we assume the existence of a class of all sets U, this class can still be differentiated from any other set or class X simply by the fact that X is contained within U but U is not contained within X. So simply because something contains everything that does not mean that it cannot be distinguished. It is also not clear how valid Russell's paradox remains if a paraconsistent logic is used, but I wouldn't hang my argument on that, it is perfectly plausible that no paraconsistent logic can be devised in which Russell's paradox could occur and which would still be rich enough to allow for the existence of the physical universe.
- It is not necessary to assume one final mathematical universe to treat the physical universe as a mathematical object, it can just be one node in an infinitely increasing network of connected nodes. Among category theorists, usually a framework of "Grothendieck Universes" U_i is assumed, where U_i contains all sets one size smaller and is in turn contained in U_{i + 1}. So U_0 contains all small sets, U_1 contains U_0 along with all small sets and all sets one size larger, which would appear as classes from the perspective of U_0, and so on. In fact, I do assume the existence of an "∞-category of ∞-categories", but only as shorthand for a pattern in such a hierarchy: there is an ∞-category of small ∞-categories, an ∞-category of next-larger ∞-categories and so on. In praxis however, one finds that very little changes as this size increases, the only thing to look out for is to not allow for constructions that would allow for something like Russell's paradox to occur.
I will also say that I don't find any of the variants of the Quine-Putnam indispensability argument addressed satisfactorily. Now, you are quite right in saying that I'm drawing from "string theory" (more precisely M-theory), which is not experimentally verified, which matters very little to me but does to you. What is experimentally verified (though not true) is the standard model however, as well as Einstein's relativity theory (whether special or general), which are gauge theories (to be completely precise, the standard model is actually a model of a gauge theory, namely Yang-Mills theory). What these gauge theories have in common is that they are invariant under the action of a symmetry group. In fact, the entire notion of a gauge theory, which is of fundamental importance in modern physics, whether M-theory or not, requires the notion of a symmetry group, one for every gauge theory (there might be some slight simplification here), so, again, symmetry groups have to be assumed to exist for gauge theory to make any sense.
On a more philosophical level, you are already assigning yourself to at least dualism when you write that "it seems possible we could one day have the rule which governs all reality. Is that not enough? Well, the universe is not just that rule, it’s that rule in motion, applying itself, or perhaps already applied infinitely, depending on your perspective, that’s what separates the rule written down from the universe itself." You now have two "substances": one, whatever the physical universe consists of, and one, the rule which governs how the first substance interacts, let's call it R. Now, there has to be some distinction between the "matter" of the universe and the rule governing its interactions, but to not be dualist those two would have to be brought together in some way, which can be done perfectly well if we assume the physical universe is a mathematical structure, because the axioms of one mathematical structure are themselves mathematical structures on a slightly higher level, and, while one one level distinct from the structure they regulate, they are fundamentally of the same substance. If meanwhile we do not make that assumption, we would need to introduce further logico-mathematical rules governing the consequences of the application of R in terms of logic/mathematics, otherwise the rule would be void and everything would be allowed since nothing could be deduced from it. Thus, you would have in fact a whole hierarchy of distinct substances: "matter"(/energy/whatever), the rule that governs the interactions of matter and rules governing the consequences of that rule as well as an open number of further rules giving coherence to those rules. It would be a nightmare!
So I'm not really sure this actually deals with what I'm saying.
"Representation does not require differentiation, only representiation of parts of a non-trivial system does." This is what I'm explaining in the first part, of course you can use "1" to represent things, the trouble is exactly that you can't do so in a precise way, that it's a necessarily incomplete representation. When physicists say "let x be space time" they're using math to describe the universe in a simplistic way, which, by the way, even to be useful means they're relating x to some other symbol. You're not just claiming that the universe is described by math, but that it /is/ math.
"Lastly on that point, if we assume the existence of a class of all sets U, this class can still be differentiated from any other set or class X simply by the fact that X is contained within U but U is not contained within X. So simply because something contains everything that does not mean that it cannot be distinguished."
My point is precisely that you have to come up with some new category like "class" which is not a set in order for this to work, it's a way of defining a new "everything" which does not contain "everything".
"Now, you are quite right in saying that I'm drawing from "string theory" (more precisely M-theory), which is not experimentally verified, which matters very little to me but does to you. What is experimentally verified (though not true) is the standard model however, as well as Einstein's relativity theory (whether special or general), which are gauge theories (to be completely precise, the standard model is actually a model of a gauge theory, namely Yang-Mills theory). ... symmetry groups have to be assumed to exist for gauge theory to make any sense."
I don't believe general relativity is "reality itself", I just think it's a description of reality, that it is the realist sort of idea that we have.
"On a more philosophical level, you are already assigning yourself to at least dualism when you write that "it seems possible we could one day have the rule which governs all reality. Is that not enough? Well, the universe is not just that rule, it’s that rule in motion, applying itself, or perhaps already applied infinitely, depending on your perspective, that’s what separates the rule written down from the universe itself." You now have two "substances": one, whatever the physical universe consists of, and one, the rule which governs how the first substance interacts, let's call it R. Now, there has to be some distinction between the "matter" of the universe and the rule governing its interactions, but to not be dualist those two would have to be brought together in some way, which can be done perfectly well if we assume the physical universe is a mathematical structure"
That was just for illustration, once we speak of "the rule in motion" that already contains the rule and its execution, and they need not be two separate things. The rule is just a description of it. In digital computers we need the rule to be symbolically expressed, but that's not the case for physics, or really analogue computers for that matter.
#+begin_center
"Representation does not require differentiation, only representiation of parts of a non-trivial system does." This is what I'm explaining in the first part, of course you can use "1" to represent things, the trouble is exactly that you can't do so in a precise way, that it's a necessarily incomplete representation.
#+end_center
No, it's a complete representation of a trivial structure, but that's a side point.
#+begin_quote
When physicists say "let x be space time" they're using math to describe the universe in a simplistic way, which, by the way, even to be useful means they're relating x to some other symbol.
#+end_quote
Yes, and that symbol describes the physical universe, allowing us to symbolically describe its relations to other mathematical structures. The point is, the physical universe can be described through a symbol, and in order to accurately depict the physics of this universe, symbolically, it is necessary to relate it to other mathematical objects, again described by symbols, and for that description to make sense, those other objects have again to be real.
Yes, but not all of math is the physical universe. It is simply one object among many.
#+begin_quote
My point is precisely that you have to come up with some new category like "class" which is not a set in order for this to work…
#+end_quote
Yes.
#+begin_quote
…it's a way of defining a new "everything" which does not contain "everything".
#+end_quote
No. The class of all sets contains itself, that's the thing. You just can't take arbitrary sub-sets of it. You can form the "class of all sets that don't contain themselves", for instance, and it doesn't contain itself because it's not a set.
Edit: actually, I have to clarify this: there are two senses of containment in regards to sets/classes: membership as an element ∈ and membership as a subset/subclass (of which I can't quickly write the symbol). The class of all sets contains itself as a subclass, but not an element. But it isn't really necessary for it to contain itself as an element to be a "universe". The universe doesn't have to be a box in the universe, basically, it just have to consist of everything that exists. Though, again, I actually go with, basically, an ascending hierarchy of universes anyway.
#+begin_quote
I don't believe general relativity is "reality itself", I just think it's a description of reality, that it is the realist sort of idea that we have.
#+end_quote
Of course relativity theory is a description of reality, the question is, is it an accurate description? Because if it is, it uses symbols that refer to non-physical entities, so if it is accurate, those have to refer to something real as well.
#+begin_quote
That was just for illustration, once we speak of "the rule in motion" that already contains the rule and its execution, and they need not be two separate things
#+end_quote
Yes they do, because if "the rule of" motion were simply all of motion in existence, there would be no use in defining "motion" at all, because no non-tautological rule existed that distinguished it from anything else. For there to even be a concept of motion, an underlying commonality has to exist that structures all of motion. But this "law of motion" is completely indifferent to any actual motion taking place: it could be applied to any fictional objects in any starting position and would yield paths for them. Thus, for it to structure all motion, it has to be independent of any actual motion.
To summarize my first comment again, you were arguing against mathematicism on the basis that representation, or at least exact representation, requires differentiation and the totality of the universe cannot be represented in this way based on Russell's paradox. I replied that
- Since I distinguish the physical universe from the mathematical universe, the question of whether one complete mathematical universe exists or can be described is independent from that of whether the physical universe is a mathematical structure.
- Russell's paradox only applies to sets and can easily be circumvented by either distinguishing between sets and classes, or, better, using an infinite hierarchy of ascendingly large mathematical "universes".
- The Quine-Putnam indispensability argument has not been addressed satisfactorily.
- A description of the laws of nature that treats them as of a separate substance is (at least) dualist.
To this I have added now in response to your reply that one which treats the laws of nature as the same as nature cannot account for there being any regularity within nature at all. Only (at least) mathematicism allows them to be both different enough so they can explain one another while being of fundamentally the same substance.
To also reply to your second comment:
#+begin_quote
That science begins from categories and concepts doesn't really matter as abstraction is required for all thought, communication and meaning. This is an anthropic principle thing, I don't think you can extrapolate to the universe necessarily.
#+end_quote
Here I don't see how you're addressing my points. You basically said there are a lot of things that are coherent, so simply using coherence as a criterion of reality would leave us with too many structures. I said no, there just are many structures in the physical universe already, many more mathematical structures can exist, but only some of them are complex enough to allow the physical universe to exist, but also, these structures generate one another, so this is not a satisfactory starting point either, so that, having excluded matter, physics, and mathematics as not sufficiently fundamental (because, again, mathematics itself contains layers of elementarity) we have to repeat the question with Hegel: "with what does science have to begin?"
"Yes, and that symbol describes the physical universe, allowing us to symbolically describe its relations to other mathematical structures. The point is, the physical universe can be described through a symbol, and in order to accurately depict the physics of this universe, symbolically, it is necessary to relate it to other mathematical objects, again described by symbols, and for that description to make sense, those other objects have again to be real."
Yes you can form descriptions, but, as I've said many times, that's not the same as the universe itself, you cannot symbolically represent the universe in its entirety. Symbols may refer to real objects, but what makes those real objects differentiated is only human abstraction. Or abstraction created by some other observer.
"Yes they do, because if "the rule of" motion were simply all of motion in existence, there would be no use in defining "motion" at all, because no non-tautological rule existed that distinguished it from anything else. "
That is the whole point in what I'm saying, once you get to the level of everything that exists, the ability to distinguish things goes away.
"To this I have added now in response to your reply that one which treats the laws of nature as the same as nature cannot account for there being any regularity within nature at all. Only (at least) mathematicism allows them to be both different enough so they can explain one another while being of fundamentally the same substance."
One what? The probably is exactly this, as I'm not saying what substance the universe is made out of as a matter of /logical necessity/ but mathematicism does. To me, how we describe the universe must be fundamentally contingent due to human fallibility. The claims of physics are always contingent claims, even if they are really sticking their neck out in terms of credibility. Human kind could not go from the ancient cosmologies to the present ones without an openness to either on some level.
"…you cannot symbolically represent the universe in its entirety"
And I have said, with arguments that I don't really feel like have been answered, that it can, both the physical and the mathematical universe, which you would have to distinguish if only to prove they are the same, and that this is done all the time. Your only counterarguments to this were:
- a structure that includes everything loses distinction.
- Russell's paradox.
I have said repeatedly that
- the physical universe has to be distinguished from the mathematical universe and so does not necessarily contain everything.
- Russell's paradox would only apply to the "set of all sets", which the physical universe is not anyway (a set is, basically, a bracketed collection so there is no way in which the physical universe is a set), and can easily be dispersed with in several ways.
- A thing that contains everything can still be distinguished from other things, for instance by the fact that they don't contain everything.
Trying to guess what you mean when you say that you cannot symbolically represent the universe in its entirety, because I genuinely don't understand how you can even say that given that it's done all the time, I guess the idea is that a symbolic reference to the physical universe does not contain references to every thing in it. But this is true of every symbol that ever referred to anything. When I say "this vase" and point to a vase, the word(s) do not contain a reference to every particle in that vase, but that doesn't mean the utterance doesn't describe that vase.
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"To this I have added now in response to your reply that one which treats the laws of nature as the same as nature cannot account for there being any regularity within nature at all. Only (at least) mathematicism allows them to be both different enough so they can explain one another while being of fundamentally the same substance."
One what?
#+end_quote
The laws of nature can explain how nature unfolds while nature can be a particular embodiment of the laws of nature.
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The probably is exactly this, as I'm not saying what substance the universe is made out of as a matter of /logical necessity/ but mathematicism does.
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Again, there is no logical necessity in this. It's just an article of faith, a fundamentally religious impulse to deny the intelligibility of the universe, which wouldn't be problematic if it wasn't done in the name of science. Also, I'm underlining again that I'm not arguing for mathematicism, as mathematicism is itself not foundational, I'm arguing for Hegelianism.
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To me, how we describe the universe must be fundamentally contingent due to human fallibility.
#+end_quote
No, because the processes of the universe have an inherent structure to them that is mirrored in our mind. This is necessary for anything we think to be applicable to the universe whatsoever, but implies that the structure of our thinking can be used to understand the structure of our universe, which is what Hegel understood. Even apart from that however, it is just standard practice to assume that our understanding of the universe approximates it more closely through the science. Moving from physicalism to mathematicism is only a continuation of this process.
But the universe is made of goo, not math
Goo would be matter. Of course matter decomposes into fields, but the real question is, why does the universe follow any rationally comprehensible pattern at all? The answer has to be that it itself is subject to a structure, but that structure cannot be physical because it literally governs the laws of physics, so it has to be logico-mathematical because logic and mathematics are literally the structure of our thought that we can use to reason from empirical data, which ensures that our reasoning is sound i.e. corresponds to real developments. If this wouldn't be the case, we could not predict anything whatsoever. I've gone through this in "Why the Physical Universe is a Mathematical Structure" and "The Incoherence of Metaphysical Materialism", but, to sharpen the point, it does not suffice to say "the universe is made out of X" because that doesn't address what the laws of physics are made out of, unless one includes that too, in which case one is already in the domain of mathematics. Hegel knew that already, that's why he says in the introduction to SoL that the question of what the universe is made out of pales in comparison to that what truth is.
Apologies for typos, typed on phone. Third section ("This resonance...") best captures what I am trying to say, I think, especially when I got to the idea of an emergent structure enabling that structure to dominante its surroundings, resulting in a selective pressure in the struggle to exist that favors orderly, lawful activities - without any "law" ever forcing itself on the situation.
Let us take it as a given that the universe exists without an imposed set of divine or platonic rules and is not math. I will tell a story that I think is conceivable and will explain what I mean when I say the universe is made of goo.
Let us start with no universe and no reality and nothing at all. There is no sense of what is and is not possible. Nothing is defined. But because nothing is defined, nothing is prohibited. Thus, nothing can stop impossible things from happening, like the beginning of a universe. Now, we have a universe, but it has no laws. A newly born reality begins to tug and pull on itself in every direction. Most of this does not amount to much, but some tendrils of reality resonate with themselves and begin to spontaneously develop order. If you put paint on a speaker; the vibrations will resonate the paint and long tendrils of paint can begin to grow off the speaker. There is no natural law which orders this, it is spontaneous self-assembly because of a resonance which leads to structure. If reality pushes and pulls into everything which is possible, it would begin building structure in this same way. Structure takes root because it is sustainable. The chaotic frenzy lurches and crashes in every direction, but never amounts to much, but within this sea of chaos, structure is crystallized. This would be akin to how crystals actually form, in the ordinary sense. These structures are self-reinforcing and expansive, they grow and absorb and grow and with it structure comes to be imposed on the playing field as a whole. It is goo. It is a good that crystallizes itself into a patterned skeleton because that is the only way for one moment to be sustained into the next. And when we look to reality - it is orbits, generations, cycles, phase alignment, and matter itself is now understood as vibrations in fields.
This resonance is how coherent, logical structures emerge without there ever being a commanding law. Solar systems follow patterns, stars follow patterns, your life will follow patterbs - but there is no law of solar system, no law of stars, and no law of biological reproduction. Consciousness is matter and motion, it follows patterns, in fact it relies on patterns in order to sustain its existence - the atoms at weavelengths, your breathe every few seconds, you sleep every day - these patterns are what allow reality to summit and conquer itself, whether by natural forces unintentionally lighting a star or by humanity intentionally damming a river - and thus outcompetes and imposes itself over the nonsense and the random and the chaotic. This is not driven by math but it settles upon math, the pure formalizations you can cook up in the mind do not exist anywhere but the mind, but the success of patterns and routine haunts reality like a ghost, they inevitably creep into a situation, and can then be discerned by scientific study.
I think this is why Quantum Mechanics is the way that it is and is so befuddling. People expect reality to be lawful all the way down but scientists have drilled to rock bottom and discovered the raw chaos and churning seas of possibility which underly concrete existence. What we see instead is that reality is loose at the joints and built on shifting sands, it can be pinned down, crystallized into descrete forms, quanta, but it is squishy, you can never get it to reveal everything, and as soon as you release the pressure, it pushes itself back out into a state of indeterminancy and possibility.
This is also why I am skeptical of inflation theories. They're trying to treat time and space as well defined categories prior to the deposition of matter. That would certainly also explain why everything was so smoothly distributed in the beginning as well - you can't unevenly distibute mass within a universe which has yet to be divided into distinct locations.
This sounds very Zizekian to me. Regardless, the point you're overlooking is that the selection that would let more orderly structures dominate others is if there was a context that would advantage orderly structures against disorderly ones — and a context that would allow for the notion of orderliness itself to make sense. This is actually akin to how crystals form, because they don't just form in isolation, or in every condition whatsoever. So you can't get around this by appealing to some notion of evolution from a primordial chaos because for that evolution to occur at all there has to be a structure that advantages some forms of existence over others.
In the earlier comment you have responded to, I was stuck in the weeds of asking why there is something rather than nothing (or to put it into Hegel speak - How do we not end up with pure being or pure nothing, and total indeterminancy, but rather, how do we end up in process of becoming, embodied by determinate things?).
But we know there is something rather than nothing, so we can take that as a given and look at how something became something. I am much happier with the resulting explanation I have given in the other comment just now, jumping off from what we empirically know about the development of the universe, life, and consciousness.
Zizek is Hegelian and I am Marxist so that sounds about right to be hearing him.
We know the universe starts from as simple of a state as it possibly could - no meaningful distinctions in where matter is allocated and no meaningful distinctions in the temperature of that matter. In fact the matter itself has to deposit out of this blanket uniformity, we do not even start with a distinction of having parts of reality which are matter and parts which are not. We can even see that there are temperatures, above which, there does not appear to be any difference between 3 of the 4 fundamental forces. All of this indicates a state of absolute unity which dissolved itself as soon as it meaningfully embodied any notion of time and space.
Reality collapsed out of pure unity and draws distinctions within itself. You are posing that this can only happen because of a logical structure, but to have logical structure, reality must first draw distinctions between things (this is the context you refer to as being necessary, forms of meaning only arise through contrast).
We do not start with distinctions between things, so we do not start with logic
In the process of reality drawing distinctions within itself, what we can see is that ideology is a complex order which erupts from less complex premises - quite literally. As a species, we can see how we exist within a complexity gradient. When you have two jugs of milk and coffee, each substance is not very complex or dynamic. They just sit on table. And when you combine these, the end result of complete mixing is not very complex or dynamic either, you just have one big jug of averaged color. However, in the interum, as the fluids mix, white and brown tendrils swirl, vortices appear, and, through this contrast and active transition, the system is able to produce a dynamic, visual complexity. This is much akin to how we subsist off the sun and our planet, making poetry and equations and computers - we are ultimately just generating poop, trash, and body heat. The structure in our thought is more complex then the premises which birth it. It is not necessarily true, then, that the ability for such structure to arise in our thought is merely imported into our minds from the mainframe of the universe.
"We know the universe starts from as simple of a state as it possibly could - no meaningful distinctions in where matter is allocated and no meaningful distinctions in the temperature of that matter. In fact the matter itself has to deposit out of this blanket uniformity, we do not even start with a distinction of having parts of reality which are matter and parts which are not. We can even see that there are temperatures, above which, there does not appear to be any difference between 3 of the 4 fundamental forces. All of this indicates a state of absolute unity which dissolved itself as soon as it meaningfully embodied any notion of time and space. "
Well, not really. We don't even know that the universe ever "started" — I'd place more stock on eternal inflation than the Big Bang Theory, though I don't have any strong committments there. More importantly though, at the time of the Big Bang, all laws of mathematics and logic already held — that's why we can say anything meaningful about it whatsoever. That's actually one of those conflations Zizekians like to make, of physical and mathematical/logical necessity: the laws of physics are way more peculiar than those of matematics.
"We do not start with distinctions between things, so we do not start with logic."
That's very anti-Hegelian.
"The structure in our thought is more complex then the premises which birth it. It is not necessarily true, then, that the ability for such structure to arise in our thought is merely imported into our minds from the mainframe of the universe. "
Again, for our thought to be able to say anything about reality it has to correspond to structures in reality, otherwise the structure of our internal logic would not map onto reality, so no predictions could make would correspond to real events and there would not be any way to change our models to improve them. The workings of the universe would simply be incomprehensible to us.
One last thing, you write:
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The trouble with Prähauser’s reasoning that we should, for example, embrace M-theory/string theory because of its mathematical coherence, is simply that there are a lot of things which are logically coherent.
#+end_quote
This is indeed true, but there are far fewer things that are both coherent and complex enough to allow for something like the physical universe to exist. In fact, with the rise of M-theory, for the first time we can approximately locate our position within the larger mathematical universe (or multiverse, it does not matter for the point). We are over the four-dimensional sphere in a super-cohesive ∞-topos. It's amazing! In any case, it should be noted that there are also just many things, period. The (physical) universe has shown itself to be pretty big, possibly infinite, and we are (almost) literally a needle in a haystack.
Also, you will note that I did not argue for mathematicsm as such, because, as I said, more complex mathematical structures can be generated from simpler ones, whereupon I said that this forces us to ask again "with what does science have to begin?" and then develop it again from that notion. Even harder than finding things that can generate the physical universe is finding one notion and generating all others from that, but once we have that, we can simply follow the dialectical flow of notions and find that it leads us to the physical universe towards the end, among other things, which is what Hegel did (though it could be argued he starts with two notions, being and nothing).
That's what the beginning of science has to be made with, and that can actually answer the question of "why does anything exist? (And why isn't it all just one thing?)"
That science begins from categories and concepts doesn't really matter as abstraction is required for all thought, communication and meaning. This is an anthropic principle thing, I don't think you can extrapolate to the universe necessarily.
Does your version of materialism make any claims about the physical nature of matter, or is "matter" just a stand-in for substance monism? If you care about the nature of matter, then you need to rely on modern physics, which doesn't necessarily lead to mathematicalism but at least displaces the role of matter as ontological fundament. If you don't care about what physics says matter is, what sort of properties does your one substance have that make it more like Matter than Idea, as opposed to a Spinozist position than doesn't privilege either of the two attributes of extension or thought?
I would say it both makes claims about physical nature and is a substance monism, for the simple reason that the claims about physical nature are just like any of the other claims about reality, contingent and subject to overcoming through science. The substance monism is more a matter of faith about the relation of thought to reality, but one which is useful for approaching thought and abstraction as not necessarily structuring of the world, while at the same time, as not being totally disconnected from it.
Of course you can make claims about the nature of matter, if you wanted to. But I'm asking if it DEPENDS on any claims about the the physical constitution of matter in general, or really on any physical claims about the universe at all. For example, in what sense can forces said to be material? Light is not typically considered matter, but surely you are allowing for its reality, so perhaps you mean something different by matter. Etc.
I don't think materialism, in its most general sense, necessarily requires matter to be a certain way, but it should be connected to a certain epistemology about what is real, the type that focuses on and leads towards phenomena like light and atoms and such
If you're not reducing everything to matter (eg. light), and you don't care if matter has itself been reduced to immaterial terms as Prähauser points out, this seems more like a limited physical reductionism where objects are real as long as they are composed of matter (even if we can't or don't describe that composition), and processes are real as long as they can be reduced (again, only in theory) to physical laws of motion. Given the fact that these reductions are extremely hypothetical (eg. no one has a mechanistic description of the brain or an economy as a process), it seems like we should have a more capacious definition of which objects and processes are "real" that accepts the way that "real objects" are constructed by scientific discourse, even if "reality itself", whatever that means, is not.
Did you read my essay on Materialism, I think it goes into pretty good depth on what qualifies as realness https://cosmonautmag.com/2024/07/what-is-materialism/
I did read it, that's why I'm here. You kept referring to "real objects" (a "given real-concrete totality" which occur in "the real") as opposed to the "object of knowledge". What these real objects are is unclear to me (you allow atoms, brains, and nations?), and the distinction between the real object and the object of knowledge seems rather dualistic and dogmatic, especially insofar as not-very-concrete totalities like nations are constructed to an important extent by our discourse about them.
Materialism, as a statement, only entails that reality exists prior to and independent of the particular manners in which it is disclosed to itself. The underlying content of reality precedes and exceeds the disclosed form.
This cuts the line between materialism and divine idealism (reality is downwind of God's plan), as well as cutting a line between materialism and the disputed platonism (reality is downwind of mathematical forms).
This also leads to Marx, and his statement that social consciousness is a result of social being. As another example - more relevant to this debate - Humanity is a particular form of matter in motion through which the universe understands itself, because as expressions of the universe we are able to look around us and look within us and understand what is happening, but the universe also existed before humanity. Reality existed independent and prior to how it came to disclose itself in consciousness.