I have had an intuitive idea for a while that I am now trying to link to the actual mathematical theory treating this.

The idea comes from debating if a thing is “intrinsically real” or just “socially constructed” (which was originally taken to mean, “not actually real”), but it was questioning the premises behind the question, as follows.

If something is “just socially constructed”, it invites one to ask if it is therefore

a) not real

b) real, because the noumenal world is experienced as real by humans

c) or, the word “real” is confusing - we are talking about different kinds of “reality”, and we need to study their differences.

a and b can lead you further to ask:

  • If social constructions are not real, how do you update your understanding of the world to eliminate them and see only the objective world instead?

  • If social constructions are not real, how do you account for that they can have a causative effect on the objective world? - for example, someone’s belief, even if untrue, may cause them to build a sculpture, harm themselves or other people, or become physically ill.

In the next round of thinking, one may consider,

  • Removing the property “real” from things which are “socially constructed” does not seem to give us much understanding, because we have to find a way to account for what they are, even though they are not real (in other words, they may not be real, but they are still something, in some way). So what can be said about the way in which they exist?

Finally, I believe it can lead you to consider:

  • the actual problem is the word “real”. When you designate two things as “real” vs. “not real”, it’s possible this tells us more about what you think the word “real” means, and it may have diverse uses.

In the last case, “real” appears like an arbitrary predicate, like claiming “cherries are xmnkdhslpjay” - the question may be less about cherries than it is about xmnkdhslpjay, and we may wonder if this is an equative proposition between them, or if xmnkdhslpjay is defined, and receives its meaning, by virtue of that cherries are it.

Backtracking a bit; a key idea motivating the distinction between real and unreal appears to be the the relationship between mind and matter, or the mind and the world. When something is indeed real, like a “tree”, my best current guess is that people hold a mental model in their head, which corresponds well to some supposed thing, outside of it. Maybe we can ask someone to explain and define what a tree is, and we think it suffices to identify an example, perceived by the senses, of one - identifying a tree that exists.

This might be a naive first attempt at the question. I am not sure debates about what is not “real” - the kinds that evoked the question - are of the same form as assertions that unicorns are not real. Like above, “real” here has a much more specific meaning here, about a thing which was physically manifested in the known universe at a point in time.

I think debates about what concepts are real is a debate about what concepts are valid, and so the issue becomes complicated, because it might be a conflict between human psychological impulses both to reify language (to consider it self-justifying, in a way*), vs. their critical component to question words themselves, and be aware that sometimes a word has no real-world referent, like xmnkdhslpjay.

* I believe this is deeply evident and could be the topic of an entire study dedicated to it, about how humans are very un-adept at distinguishing between an assertive and a descriptive definition of something - all you have to do is turn on the news to see people disagreeing over what some thing is, without clearly separating the question of the thing, vs. the word just being a shortcut or nickname, for the thing.

Thus, the kinds of debates I am thinking about are really about:

  1. Is the thing you claim is a thing, actually a thing?
  2. Which thing should some word we are using refer to? (ie, Does “xmnkdhslpjay” refer to a bear with slippers, or a bear who likes wearing slippers?)

The second is trivial if examined this way, even though a hotly debated topic. The second is the bettered version of the true question - not if something is real, but to what extent is a thing a thing; when you refer to some thing, can we be sure you refer to something, anything?

One naive starting point (I just mean, where one begins before further realizations might disrupt the initial point of view) is the common idea that there is just the physical world - a morass of jiggling atoms - and that only the human mind segments and compartmentalizes it into separable things, for example, that two adjacent atoms have no idea what higher social categorization that they are a part of. Like the Ship of Theseus, it is implied that things are human projections onto the world, as is evident because it does not seem the identification of something is decomposable, and therefore, not ‘inherent’ or objective to that thing, the real thing it is (ie, atoms).

Two adjacent atoms do not ‘know’ that one is in white paint on a wall, one is an air molecule passing by, or that one is in the skin of your hand. At that scale, they are (believed to be) indistinguishable, actually.

A problem with this point of view is something like, it is clear humans are not at total liberty in recompartmentalizing the world around them - splitting them up, deciding what “things” there are, anyway, like the one cited by Foucault in the Order of Things, an unusual classification on animals. Intuitively, (but it could use more development), there obviously appears to be a world outside the human mind which acts with a logic of its own, like forces, laws of nature, predictable relationships, patterns, and so on.

Possibly, a simple property which reflects the claim that a thing is a thing, is coherence (or “cohesion”, “self-adherence”, “self-continuity”, or “contiguousness”.) Why does a table retain its form moment to moment? The atoms do not ‘know’ what they are, but there seems like there is a logical precondition on matter, on that set of atoms, that they are in a particular physical position in space, at certain energy levels, in certain chemical bonds, etc., and those preconditions seem to have a causal influence on the state of the atoms from moment to moment, over time. Therefore, the reason the table does not diffuse into a random vortex of atoms flying in each and every direction in 1 microsecond is because there are some sort of objective, logical conditions specifying some part of reality, there - information. So, beyond the human, social, cultural, conceptual recognition of objects as things, it seems unprovocative of there being some objective world out there, outside of human mental construction, and the “order” of the world we end up perceiving, in our minds, is a consequence of whatever original, internal logic there already is, a priori, in that external world. (For example, the properties of colors, various geometric relations, etc.)

It comes back to the original goal, of a mental model only serving to provide an accurate depiction of the real world - so, can we judge the validity of a concept, by assessing its predictive value, a classic idea in science? If we can delineate what we think (abstractly, virtually, as information) something is, the logical preconditions governing it, hopefully we can check how well we actually observe that thing in the world, check how our model performs, if it is on-track or off-.

This still does not wrap things up because the question is what the actual intrinsic, objective property of a “thing being a thing” is. In physical terms, what if it was energy - a tree circulates nutrients and sap within its own physically bounded self - described informationally, we might say there is a clear numerical property where the causal mechanisms of those self-same atoms (or subatomic particles, or whatever) results in marked non-arbitrariness: maybe, if it boils down to energy as powering all kinds of physical processes and systems, “things” (living and non-living) share energy diffusely within “themselves” (their bounded region), like a gas diffuses to fill a volume, evenly. We can choose what specific substance, property, object, or material as a specific lens we want to look under, to see what “forms” emerge as enclosed, separable “regions” regarding that property (like looking via an infrared camera). It may vary depending on what we are checking for the contiguity of. Some people say consciousness is characterized by closure, ie, I cannot access your consciousness with my own mind, and neither can you mine, so the result appears that, even if my self is an orchestration of many modular brain functions, they interoperate with such a high degree of constant blending, interactivity, mutual access and mutual responsiveness, that seeking only an objective, numerical boundary in some phenomenon, we might say that “energy”, “information”, or whatever the stuff consciousness is made of, has no objective, impossible-to-look-away from boundary within my “self”; hence, the supposed parts are not meaningfully distinguishable from each other, at least as flows of information; so it becomes natural to claim that as one thing. Whereas, clearly, the influence of my nervous system extends powerfully, evenly, and responsively throughout my limbs and whole body, then drops off sharply the second one checks at the layer of my skin, which forms a boundary: my brain is not able to significantly shoot off electrons (or whatever) out of my fingers into the enclosing space, to interact with the inner information of external objects, then in a continuum of real time continue exchanging information between my consciousness and the inner states of that object (unless you believe in telepathy). So, there is an objective, quantifiable boundary where there is clearly “coherence” between some property (a flow of electrons) - they take on interchangeability within that region (of my body) - and there is extremely low probability (for physical, logical reasons) that they would extend the area of their regular “migration” outside of that logically indicated area.

This is like the concept in physics and information called “entropy”, I think, but I haven’t studied it enough yet.

I also think this idea that most abstractly, the intrinsic mathematical coherence of some elements (whatever they represent, be they physical or virtual, just statistics or something purely mathematical, not just atoms) applies to mental concepts, as well.

If the human mind can somehow construct a world of concepts partially based on its own mental experiences (like colors and feelings and symbols and so on), one may hypothesize that good “concepts” have their own kind of cohesion - here, the “basis”, of what a mathematical function is checking for, could be based on something mental, yet still specifiable and describable as information, such as, how many other concepts is a given concept defined in terms of, and how intrinsically inseparable (given however the ontology / web of concepts is already structured, to begin with) are the concepts?

That is an idea I have been considering for a while. Anyone has the power to assertively construct any concept, such as, “A blanddar is when you cook peas with really loud music on.” But I believe a point of contention between humans, governing concepts, is at what point does the collocation of distinct concepts merit fusing completely into a single thing, with a degree of finality, a conceptual polyp, and will not any longer be presented as the apposition of a few things, which have more coherence as things, in themselves?

A really interesting example is the concept of a “species”, in biology. For all I know, Stephen Jay Gould worked out or suggested the current working definition, which focuses on reproductive compatibility: a “species” hitherto shall be regarded as that set of organisms that can (successfully) reproduce with one another. But we have to ask the same questions as before:

  • Did humans intuitively perceive there was some thing called a “species”, but their model was inadequate and they had yet to identify good, inner logical criteria which had the strongest causal effect (known so far) on predicting what they sensed was a natural thing in the world (a coherent pattern whereby lions often look like lions and act similar, gazelles usually look similar - more similar to each other than they do to other animals in general - there is a naturally arising coherence boundary in the natural variation and distribution of how those certain animals look)?
  • Should we ignore any past false claims of what a “species” apparently was, and take the new definition apodictically (as assertively defined), without linking it to anything other than what it says: it is a stand-in or nickname for “animals which can reproduce”, so there’s no ability to evaluate if the term (“species”) is right or wrong, rather if in the real world, to what extent does the thing - classes of entities separated by who then can (“effectively”) interbreed with them - have natural coherence, does it lead to a grouping where the differences between this or that thing become, in purely numerical terms, much larger?

The latter is not a discrete yes / no, we can imagine ‘coherence’ has its own varieties and internal ‘species’, mathematically speaking. Perhaps it is an inherently relational concept, in which the coherence something exhibits has to be taken relatively rather than as an absolute magnitude - imagine a mathematical space of many overlapping circles which each have evenly distributed points within them - we could say that there are many regions of coherence of different levels, but to try to find a coherence on the space that maximizes the global/overall coherence, we maybe hope to find the single top-ranking coherence of them all - the function or relation itself, we will use, in light of which, some measure of “intrinsic and maximal non-arbitrary separability” is maximized.

If “interreproductivity” does happen to lead to a very high degree of coherence, why? We can imagine the reason would not be arbitrary. For example, maybe the information encoded in species’ DNA just so happens to determine both similar characteristics and likelihood of successful (incl. non-pathological or morbid) reproduction. Thus, the “definition” seems perhaps less arbitrary than a blandarr, because it is a form which manifests itself in observed reality on its own - the difference between an observed concept, which is undeniable or unavoidable, vs., a constructed concept, which only persists because people believe it is a thing, but may not be ‘rediscovered’ later or elsewhere, because it is not a model with a lot of semantic coherence, respectively because it is not a model of a real-world thing with any intrinsic coherence (yes, I am thinking about “gender identity”.) (Also, a constructed concept can have semantic coherence without it corresponding to an objectively coherent thing.)

If we try to update our concept of a “species” to a thing with objective, internal self-coherence, it can change our cultural idea of what a “species” is. A lot of cultural assertions are made about humans as a class of entities with fundamentally equivalent properties - including the rhetoric of the political philosophy of the founding of the U.S.A. But if a former notion of “species” is a constructed concept - (mentally asserted and kept alive, a cluster of elements falsely believed to have intrinsically necessary mutual/inter-coherence to one another, because of a false belief it creates about the “real world”, which is undermined when we look for objective properties of the world that have objective mutual coherence, in physicals, causal, energetic, or informational terms, or any other), we must update our understanding of the world, if possible, to distinguish between the fossilized, socially constructed concept of a “species” - which still exists in the world, on the noumenal plane, and we cannot avoid - and the thing defined by Stephen Jay Gould, whose referent does not matter, which can can refer to as simply “X”. It could imply a number of things about humans commonly asserted are not automatically true, should not just be assumed or asserted, because since a “species” is based on inter-breeding, it does not follow that there is as strictly uniform a template called “human” with extremely uniform, qua universal characteristics, but we may find objectively that the coherence between different organisms descended from human’s LCA (last common ancestor) have some coherence, but it might be to a degree with more variation than we realize, like 70% or something (see post-humanism).

My question is, what mathematical function actually calculates the idea of coherence? I wish to know in physics, for example, coming from statistical physics, thermodynamic entropy, and Shannon entropy, some analogous idea that a thing is intrinsically ordered or non-arbitrary, presumably by some way of comparing its state to an idea of randomness or of all possible states it could have, given what it is made of (ie particles) - some way of seeing maybe that something is not “accidental”, I’m not sure. But these links are in the ballpark:







  • 4
    That must be the longest question I've ever seen on the network :)
    – Joachim
    Commented Jun 3, 2023 at 22:01
  • If you are looking for the mathematical concept corresponding to coherence, or at least "consisting of only one piece," do you mean connectedness? en.wikipedia.org/wiki/Connected_space Also Searle wrote a book called The Construction of Social Reality, in which he contrasts "brute facts" that are true about the world, versus social facts like legal contracts and such. amazon.com/Construction-Social-Reality-John-Searle/dp/… I only read your first and last para, could you cut down the question a little?
    – user4894
    Commented Jun 4, 2023 at 7:14
  • post is too short to answer, please add more. Commented Jun 4, 2023 at 21:45


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