The Thingness of Things
$\newcommand{\Z}{\mathbb{Z}}$
What's a thing, in general? Minds deal with things, so this question comes up in trying to understand minds. Minds think about things, speak of things, manipulate things, care about things, create things, and maybe are made of things.
1. Things
Examples of things: table, elephant, carbon atom. France, Martin Luther King. Insertion sort. Chess. Unicorn. Learning. Seven. Towel, strand, wing, crystal, finger, space, diffraction. The laws of electromagnetism. The first World War.
2. Non-things
What about non-things? It might be hard to list non-things because what we have words for, tend to be things. Redness seems like sort of a thing, but less so. Laws of physics also. Also ghosts. One might say "the ideal gas law is totally a thing" or "ghosts aren't a thing", though I think ghosts are a thing. Events can be things; WWI seems like a thing to me. But a minute ago I picked up my bottle of water and drank from it; that's clearly an event, a real one, but it doesn't feel that much like a thing. The abstract [drinking from a water bottle] feels like a thing though.
(There are some usual critiques of thingness. Yes, there's no sharp dividing line between a wave and a trough, but clearly waves are a thing. Yes, seven is not a physical object you'll ever bump into, but it's clearly a thing. The ideal gas law isn't localized in space or time, but it's a thing. Unicorns aren't real, in that you'll bump into people speaking about them but you won't bump into unicorns themselves and won't be constrained by unicorns in the way you're constrained by seven, but they're things. The world of Ender's Game isn't real, though it's a remote possibility, and it's a thing.)
3. Features of things
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Coherence. A thing usually has properties, parts, aspects that are coherent with each other. Some things are big, some things are small; but usually there's nothing like a table that's both big and small.
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Prediction, homogeneity, constancy, constraint. A thing usually has some predictive meaning; its presence implies constraints on other things or the future, and it implies some constancy in some features.
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Expression. Related to prediction, a name that names a thing or an idea that's about a thing contributes to expressing thoughts about situations involving the thing. Expressing thoughts about the thing contributes to further behavior such as successfully predicting or manipulating the thing.
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Cluster. A thing that's an instance of a type of thing, has multiple features mostly shared by most things of that type and not mostly shared by most things not of that type.
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Exterior, relations. A thing usually can "impinge on other things from the outside". "Reality is that which, when you stop believing in it, doesn't go away."
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Indicatability. A thing can be indicated. A physical object can literally be pointed at, seven can be pointed at by showing how to count and showing sets of seven like things, and many things can be pointed at by saying the word for that thing.
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Truth, solidity, fixed import. "True" comes from PIE *deru- ("be firm, solid"), cognate with "trust" and "tree" and possibly "durable". Things have truth to them; a thing makes a promise of agreement between minds on questions about the thing upon further independent investigation. Beyond indicatability, the truth of a thing implies that the thing can be advantageously treated and used in a fixed way.
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Hollowness, cavernousness. The more comprehensively the history, features, changes, components, causes, internal relations, overarching structures, and explanations of a thing are kept in mind, the less there's a need to think of "the thing itself". One can stand under the cavern more thoroughly, but one never arrives at the thing itself.
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Interior, promise. A thing usually has something going on with itself, separate from other things; it has internal elements or dynamics. And it promises that it's hiding more depth, there's something further to be understood by looking into the thing more.
4. Indication
How is it that things can be indicated? I can point at a table and ask "where did that tree grow?", and after a moment of confusion and an hour of investigation, you might be able to find an answer; and most people given the same task will probably find the same answer, if they find one. The indicatability of things is strong enough that a straightened finger indicates the table, the table indicates its wooden material and manufacturer, which indicates the lumber company, which indicates a forest, which indicates a location.
Clusters of features are a kind of indication. If the features {wooden, 3 feet tall, has small objects on top, nothing under the top except legs} are perceived together, that indicates the features {flat top, is called "table" by people}. "Indicate" comes from a root meaning "to point out", which involves an agent; that assumes too much, the table doesn't need someone to point. Instead I'll say "reference", in the etymological sense "re-fer", "carry back". If there are clusters in the product space of all features, then specifying the values of some features consistently with a cluster refers you, carries you back, to the rest of the cluster.
5. Inadequacy of "clustered"
Clusteredness, though, doesn't cover all the thingness of all things.
Sevens
I think seven is a thing, but it's not a cluster; there's only one seven. Maybe not, though, maybe there are many sevens, which form a cluster?
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$7 \in \mathbb{N}$, $7 \in \mathbb{Z}$, $7 \in \mathbb{Q}$, $7 \in \mathbb{R}$, $7 \in \mathbb{C}$, $7 \in \mathbb{H}$, $7 \in \mathbb{O}$, $7 \in \mathbb{Q}_p$, ...
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$\mathbb{Z}_7$, a spiral with seven arms
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the term 7 in Peano Arithmetic, or Robinson Arithmetic, or $\textsf{ZFC}$, or $\textsf{WKL}_0$, or some non-classical logic, or some type theory
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the finite category $\textbf{7}$
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whatever humans mean when they say "fetch seven apples"
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the number after six
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the class of all sets bijectable with { . . . . . . . }
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0b111
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the fourth prime
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$\lambda f. \lambda x.f(f(f(f(f(f(f(x)))))))$
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VII
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the number of Snow White's dwarf friends
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$\lambda x.[x,x,x,x,x,x,x]$
Yes, it's not wrong to say that these are many sevens, but (1) the way in which the sevens form a cluster involves features that are heavily dependent on interpretation (e.g. partial translations between logical systems), and (2) the sevens are connected by a lot more than just forming a cluster in featurespace: they play analogous roles in their respective contexts, so that passing between contexts preserves Seven-ness.
Unique things
I think WWI is a thing; it's clearly a member of various clusters like "war" and "20th century human event", but it's unique, and what makes WWI be WWI isn't that it's a member of certain clusters (even if its cluster memberships locate it uniquely). (We can interpret even unique things as clusters: A fabrege egg is a cluster in the space of possible sense-perception-moments, and seven is a cluster in the space of possible thoughts. To me this seems to do some violence to the thing; the thing gives rise to the cluster, but there's more to the thingness than the clusteredness.)
Even if seven and WWI are single, unique things, they have a structure. Seven involves:
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algorithms (making seven of something, performing addition)
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features ("is in bijection with [.......]")
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context (a language, a mind, a logical system, a computer operating system)
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mental events (picturing seven things, counting to seven, saying or hearing "seven", remembering that there are seven apples)
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symbols ("7", "seven"), expressions (5+2, 21/3)
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physical objects (seven of something, neurons thinking about seven, electrons arranged in capacitors in computer memory, sound waves emitted by someone pronouncing "seven", the letters s e v e n written on a page, whatever genes control Graptopsaltria nigrofuscata's allegedly seven-year lifecycle (Lloyd, Dybas))
6. Inductive nexus of reference
What relates all the stuff in that list? How do these things constitute seven as a thing? It seems like there might be a lot more here, but this essay just wants to describe the situation like this:
The thingness of a thing lies in its being an inductive nexus of reference.
Reference
By reference, I mean any re-fer-ence, any bringing-back. X references Y if, when minds think about X, they soon after think about Y. This notion of reference doesn't assume (or exclude) any asymmetry between X and Y: often X references Y and Y references X, as in, the table references supportiveness and supportiveness references tables. There's no separation between stuff that can reference stuff and stuff that can't reference stuff; types and tokens, symbols and meaning, idea and reality, sign and signified, can all reference each other. (This formulation is agnostic about why thinking about Y follows thinking about X. Thinking of X may cause thinking about Y, or they may have a shared cause, or it may be useful to think about Y along with X regardless of the psychic causality.)
Nexus
By nexus (cognate with "connection", "annex", more distantly "node", "knot"), I mean a bundle, a knot, a region in the graph of reference that's particularly clique-y, particularly highly connected. The shape of the table, the joins between the wood of the leg and the wood of the top, the motions of the carpenter's tools in making the table, all reference each other.
Inductive
By inductive, I mean that the nexusness is inductive: the highly-connected-ness in the reference graph can correctly be taken to indicate that further investigation would reveal even more highly-connected-ness.
We can notice that dogs share many features with mice and lions that aren't shared by spiders, octopi, and trees: warm, furry, four-limbed, social. Then we can correctly predict that on further investigation, {dogs, mice, lions} will share many further features also not shared by the other living things: red blood cells, a spine, a womb, a spleen.
A non-cluster example: If I hear someone say "seven", I might send blood to the neurons that orchestrate a visualization of seven objects. If I see seven objects and wonder why I'm seeing what I'm seeing, it might be helpful to imagine some process creating seven objects. If I count seven things, and count another set of things, and then announce the total count, I make use of [seven, the thing that can be added]. When I reflect on all this activity, I find that my thoughts can be related to each other, and can be followed "inward, to seven-ness", to think about seven as a real number, as $\mathbb{Z}_7$, as iterating processes seven times, and so on. I find connections between all these things. $\text{Aut}(\Z_7)$ acts transitively on $\Z_7\setminus{0}$, "because" $\langle 7 \rangle$ is a maximal ideal of $\Z$, "because" you can't fairly give out 7 apples to multiple friends. All this about seven is tightly interconnected, predictably from first noticing some of the connections.
7. Discussion
Amusingly (to me), this essay is trying to demonstrate that thingness is a thing. Note that since things have thingness, so that their nexusness is inductive, family resemblances aren't mere.
A Thing is a cavern
So a thing, a nexus of inductive reference, is like a cavern encountered while wandering in a world of caves connected by tunnels. A cave is a small pocket of empty space with a few narrow "in/out-going" passages, on a background of rock. Entering the cavern, at first it seems like just a cave, but stepping in a little further, you find a densely connected maze, many paths connecting the empty spaces; not an empty space on a rock background, but more like a background of empty space contained by walls and broken up by some pillars and stalagmites and stalactites and boulders and rubble.
(Like the cavern, things are strongly (i.e. bidirectionally) connected subgraphs of the graph of references, not just weakly connected. Something that refers to a thing but isn't referred to by the thing, is a mere appearance. That time a few months ago when I took a sip of water from my bottle refers to drinking in general, water in general, hands in general, my hands, and so on, but none of those refer to that particular time I took a drink.)
Talk of "things"
The thingness of things is what we mean when we talk about some stuff being a "thing".
If we say "that's not a thing, that's just some random stuff", we're saying there's nothing to find by investigating that stuff, there's no use in that conjunction of stuff, there's nothing useful or interesting about other stuff that's positioned like that stuff is position, there's no internal structure to that stuff that's relevant to anything other than the separate internal structures of each thing in the assembly called "stuff".
If you ask me "pass me that thing" while pointing, we're relying on the indicatability of the thing, on the reference structure leading from a finger to some stuff, some particular stuff, all of it, and not too much other stuff, all of which I'm led to by the thingness of the thing fairly reliably. You can even ask me "pass me that thing" without pointing, relying on the thingness of the thing to make it jut out ("exist" = "stand out") at me as the thing at the bottom of the basin of attraction of attention set up by our current context. More thingy (at least in a shallow way, and relative to our current context) than the other things, which you would have named or pointed at.
The thingness of [thingness itself] is part of why we talk and think about "things". The activities [dealing with one thing] and [dealing with a totally different thing] have something in common, that is, some Thing in common, namely, the thingness of what is dealt with. So there's transfer of skills between those two activities. And that transfer is usefully inductive: one can learn to [learn, from dealing with one thing, to deal better with any other thing] more effectively than default by investigating the thingness of things, as a thing itself, expecting it to have more referential structure than is currently visible / useable to you, i.e. expecting to be led into more insights about what's in common between things.
(IDK what, if anything, "stuff" is.)
Noumena
"Thing = inductive nexus of references" tries to characterize approximations to (or rings around, or emanations from, or pathways toward) Kantian noumena, things in themselves. Wikipedia's Kant says: Noumena can't be directly perceived and can't be known, they are completely eternally external to and separated from minds. We can understand the structure of phenomena, which are the appearances of noumena, but we can't access noumena. Noumena must exist because there has to be something that appears to us, an object of investigation, something that we think about.
A noumenon as a nexus of reference is an abstraction over the inductivity of its nexusness: to say "there's a noumenon behind these related phenomena" is to say "so far we've seen some phenomena (appearances) which point to a nexus of reference, but there will always be further (deeper, more, bigger, tighter) nexusness of reference to be found, no matter how many additional related phenomena might appear later on". Noumena say, "what you have is permanently incomplete".
It's maybe like infinity: to say "there are infinitely many natural numbers" is to say "there will always be more natural numbers that we haven't already seen, even if we see more natural numbers later on". Infinity abstracts over the inductivity of the succession of natural numbers. The fact that things-in-themselves / noumena live in a sort of "remote exterior" from our experience or mental grasp, comes from the use of the concept of "thing-in-itself". The concept of "thing-in-itself" is specifically about that which we haven't already grasped, maybe kind of like how infinity is greater than all natural numbers because "infinity" is used specifically to discuss what's beyond any natural numbers already considered.
Non-thingness
What would a non-thing be? It would be someth--... some stuff, some event or some happenings, that doesn't have anything more to say, and doesn't separate itself from its surroundings by being itself, is uninteresting, doesn't lead anywhere.
A region on a large wall that's meaninglessly shaped, doesn't encode anything by its position or shape, doesn't surround anything at all special in the wall different from any other part of the wall, would be sort of a non-thing, though it would be hard to produce without making it a thing.
Maybe an example would be a particular instance of perceiving red. Redness in general, and perceiving redness in general, and whatever caused the particular perception of red, would all be things. But the perception of redness itself doesn't seem to offer much; it's at most an appearance of its cause, pointing to the traffic light or the sunset or the anger or the cardinal or the raspberry, and an appearance of perception of red in general, but it's got nothing to it itself, and isn't referred to by those things it refers to.
Maybe combining unrelated sense perceptions also gives non-things; {redness, a slightly flat C# tone, the sense of roughness on your chin} could co-occur but never co-occur again, co-occur for no referential reason, and cause no thoughts beyond what's caused by the individual sensations. Blue is a thing, green is a thing, but grue and bleen not so much; if you investigate bleen, you will be led to blue and green and color in general, and not vice versa, unless you're a philosopher.
Subjectivity
I don't like that this notion of thingness relies on reference, which relies on minds, making it seem subjective. At least it can be made maximally intersubjective by saying "minds in general are led from X to Y", which is kind of like being objective.