I am looking for a view that would completely eliminate concrete objects by saying that being an abstract structure is enough for a world to be experienced by it's observers. If it is enough for a structure to be abstract for subjective experience to arise in it, it would be more parsimonious if no worlds were concrete (and the term "concrete" was meaningless in that sense).

Mathematical Universe Hypothesis is probably the closest; however, Tegmark didn't write anything about substances and abstract/concrete objects. His arguments are mostly from a scientific perspective. I've never seen modal realism being described in that way either.

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    Are observers with their subjective experiences supposed to be abstract too? How are causally inert abstractions supposed to account for causality and action? These questions plague Tegmark's framework as he was unable to answer them. Particulars are eliminated by treating them as placeholders in relational ontologies, where the relations are universals. But then universals can not be treated as abstracta, they must be causally efficacious, as in Platonism that motivated Tegmark.
    – Conifold
    Commented Apr 17, 2021 at 20:29
  • @Conifold Maybe some philosophers and posters on here should actually read Our Mathematical Universe sometime. Pigliucci's post was posted before his actual book released, and you claim he never said how abstract objects can experience. He does though. "Mathematical structure: set of abstract entities with relations". "At the bottom level reality is a mathematical structure". There are equivalent descriptions of the same mathematical structures. Some have more baggage. Every physical description, argues Tegmark, has an equivalent baggage-less, purely mathematical description.
    – J Kusin
    Commented Apr 17, 2021 at 22:25
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    @Conifold Forgive me but I think you still don't get it? Tegmark says "cause" and "act" are not fundamental. All Tegmark needs is to describe. Act and cause some later on in the theory. All you need are some abstract, quality-less entities like found in math, and some relationships between them That's his whole point. There are what we experience as cause and effect on this level of macroscopic reality, but both and more are wholly describable by a base ontology of static relationships between quality-less entities.
    – J Kusin
    Commented Apr 17, 2021 at 23:39
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    @Conifold "abstract structures...cannot act or cause". Are you not assuming cause and act are ontological? Again, to Tegmark, there is no ontological causes or acts so that argument doesn't even apply. Causes or acts are what we experience. Experience of causes and acts is wholly explainable by something more fundamental - abstract structures. I feel you are the first to assume some higher level ontology - namely causes, acts, effects, and Tegmark is being the less presumptive.
    – J Kusin
    Commented Apr 18, 2021 at 0:30
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    @Conifold "Are observers with their subjective experiences supposed to be abstract too? How are causally inert abstractions supposed to account for causality and action? These questions plague Tegmark's framework as he was unable to answer them" As I pointed out in this answer, those kinds of questions can be dealt with by postulating a variant of 'psychophysical laws' (and Tegmark does talk about 'laws' of consciousness) which dictate that abstract mathematical structures give rise to corresponding conscious experiences.
    – Hypnosifl
    Commented Apr 18, 2021 at 4:22

2 Answers 2


MUH does sound exactly like what you're looking for in your OP. Regarding your remaining concern:

Tegmark they didn't write anything about substances and abstract/concrete objects, his arguments are mostly from a scientific perspective.

First of all MUH is entirely math based thus it describes anything from a fully scientific perspective, not even mostly. For the concrete objects and substances, including much advanced self-awareness, from MUH's wikipedia says:

Mathematical existence equals physical existence, and all structures that exist mathematically exist physically as well. Observers, including humans, are "self-aware substructures (SASs)". In any mathematical structure complex enough to contain such substructures, they "will subjectively perceive themselves as existing in a physically 'real' world".

Of course these are just some sketches and rough ideas from MUH to address your concern, not remotely realizable yet. There's been some patterns suggested from neuroscience studies such as re-entrant signaling or strange loop, etc. Here's some explanation about our perceived "causality" from strange loop theory:

Hofstadter thinks our minds appear to us to determine the world by way of "downward causality", which refers to a situation where a cause-and-effect relationship in a system gets flipped upside-down. Hofstadter says this happens in the proof of Gödel's incompleteness theorem:

Merely from knowing the formula's meaning, one can infer its truth or falsity without any effort to derive it in the old-fashioned way, which requires one to trudge methodically "upwards" from the axioms. This is not just peculiar; it is astonishing. Normally, one cannot merely look at what a mathematical conjecture says and simply appeal to the content of that statement on its own to deduce whether the statement is true or false.

Hofstadter claims a similar "flipping around of causality" appears to happen in minds possessing self-consciousness. The mind perceives itself as the cause of certain feelings ("I" am the source of my desires), while according to popular scientific models, feelings and desires are strictly caused by the interactions of neurons.

Regarding your other concern:

I've never seen modal realism being described in that way either.

Again from the same reference above, it suggests:

Jürgen Schmidhuber argues that "Although Tegmark suggests that '... all mathematical structures are a priori given equal statistical weight,' there is no way of assigning equal non-vanishing probability to all (infinitely many) mathematical structures." Schmidhuber puts forward a more restricted ensemble which admits only universe representations describable by constructive mathematics, that is, computer programs; e.g., the Global Digital Mathematics Library and Digital Library of Mathematical Functions, linked open data representations of formalized fundamental theorems intended to serve as building blocks for additional mathematical results.

In response, Tegmark notes that a constructive mathematics formalized measure of free parameter variations of physical dimensions, constants, and laws over all universes has not yet been constructed for the string theory landscape either, so this should not be regarded as a "show-stopper".

Don Page has argued that "At the ultimate level, there can be only one world and, if mathematical structures are broad enough to include all possible worlds or at least our own, there must be one unique mathematical structure that describes ultimate reality. So I think it is logical nonsense to talk of Level 4 in the sense of the co-existence of all mathematical structures." This means there can only be one mathematical corpus. Tegmark responds that "this is less inconsistent with Level IV than it may sound, since many mathematical structures decompose into unrelated substructures, and separate ones can be unified."

  • I now realize that MUH is indeed what I was describing. I think MUH is directed towards people interested in science more than ontology. It doesn't hint towards eliminating concrete objects, which to me is the most powerful argument. Tegmark gave an argument from analogy, which I personally found weak. Eliminating concrete objects is more of a consequence of MUH that people might not even realize exists and what it means for the ontology. Modal Realism, for example, was proposed by a philosopher, described purely in those terms, and gained much more feedback and traction among philosophers. Commented Apr 18, 2021 at 7:19
  • There is, for example, a problem of transworld personal identity in extended modal realism, MUH doesn't seem to say anything about that Commented Apr 18, 2021 at 7:43
  • @nikishev. Seems you want ante rem OSR holding that structures (cannot be math objects simultaneously!) exist objectively, independently of, and metaphysically prior to, any systems that exemplify them, which MUH is inline. (rep.routledge.com/articles/thematic/…). But the ante rem realist must account for how one obtains knowledge of structures, so construed, and for how statements about ante rem structures play a role in scientific theories of the physical world. Michael Resnik, Stewart Shapiro,Edward N. Zalta hold such views. Commented Apr 19, 2021 at 2:23
  • @nikishev... so such view mainly needs to worry about and explain how such a non-spatial-temporal-causal eternal platonic form world can derive concrete physical objects. As for its modal realism if possible worlds really exist per Tagmark ( I don't think so personally if ante rem OSR is true, there should be just one such ontic world including possible derived concrete objects), Tegmark seems just assign more probability weights to simple math structures to account for how each structure possibly distributed across PWs... Commented Apr 19, 2021 at 2:42
  • thank you, the ante rem OSR is very helpful. So what I am looking for would be a view that it is more ontologically parsimonous if platonic form worlds are enough for their observers to have subjective experience, and concreteness isn't needed. I also tend to think that the structures and worlds are not mathematical, but logical structures, but I didn't really look into that. Commented Apr 19, 2021 at 12:01

Tegmark really does go as far as claiming reality is ontologically only a set of abstract entities with relations between them. These entities have no intrinsic qualities. He believes physics and eventually biology and neuroscience will eventually have equivalent "baggageless" descriptions of reality and subjective experience that will live purely in the abstract, like math. Relations between abstract entities provide interesting qualities, not the entities themselves.

Thus there is no ontological flow of time nor "redness" nor "pain". These are subjective experiences wholly capturable by a timeless, experience-less mathematical structure. Structure within the mathematical landscape can have experiences, obviously we do. But that is not the deep ontology.

  • One argument against MUH might be the violation of classical philosophical principle of sufficient reason (co-dependent origination in eastern philosophies using the metaphor of Indra's infinite net). If MUH is true to derive and explain our contingent physical world in a causally closed fashion, and since MUH is nothing but a purely axiomatic deductive system, then there's no sufficient reason to account for the axioms of MUH. Its axioms just become a modern synonym of the classical necessary "first cause" which lies transcendentally beyond our contingent world. Do u have any defense here? Commented Apr 18, 2021 at 1:15
  • @DoubleKnot 1) The original PSR is indefensible for many reasons. Only weakened forms of it still work. philosophy.stackexchange.com/questions/1701/…. 2) The MUH does not claim causality is fundamental so a deeper theory can recreate the subjective experience of causality/reasons. 3) Also I'm not sure how the MUH feels about quantum mechanics beyond the MWI. If it is compatible with ontologically random interpretations too, then the PSR is dead that way too.
    – J Kusin
    Commented Apr 18, 2021 at 1:29
  • Since MUH is still deductive math which critically relies on inference rules (essentially application of classical syllogism), so I tend to keep classical logic (ie, weak causality if u insist strong one is dead). There may be other principle(s) need to be discarded such as locality of causality as hinted by quantum entanglement, Newton's spooky distant action may come back to life... Commented Apr 18, 2021 at 4:06
  • In that section of the book tegmark was arguing for ontic structural realism, where the reality is math and everything above is "baggage". However you can be an ontic structural realism and still believe that this mathematical structure is actual, and others are only possible and do not exist. I now realize that MUH is indeed what I was describing, however still, the argument from abstract being "enough" to cause subjective experience seems to me very powerfull, but Tegmark, if I recall correctly, only argued for MUH by using an analogy with how there are many other planets, universes, etc. Commented Apr 18, 2021 at 7:09
  • @nikishev. " the argument from abstract being "enough" to cause subjective experience seems to me very powerfull, but Tegmark, if I recall correctly, only argued for MUH by using an analogy with how there are many other planets, universes" - Tegmark definitely has chapters (10-11) on subjective experience and its power. Every sensation from feeling time flow to pain to thinking you exist "right now" he is confident can not only be expressed in a baggageless way, it is only the mathematical relations/structure too.
    – J Kusin
    Commented Apr 18, 2021 at 17:23

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