OTI post #4 - The Law of Identity

In previous OTI work I had covered the basic context, existence, and consciousness. Now it is time to pay attention to the Law of Identity.


Basic meaning
There are a few different ways of expressing this fact. One is as stated, that a thing is itself. Another is “what is, is what it is”, and another again is “A is A”. In any event, they are all forms of what is known as the Law of Identity. Its basic meaning is that everything that exists is of a certain nature, that each existent is the integration of all its attributes.

Reducing identity and nature
The fundamental concept is that of “identity”. I think there are two paths of reduction, here.

The first path of reduction comes from noting that, in the context of a variant of the Law of Identity, the other related concepts are basically synonyms of identity, and differ merely in degrees of focus or linguistic register or both. These other concepts include: thing, something, itself, and nature.

The identity of any given thing - that is, the nature of anything - is whatever makes that thing that particular thing. The referents for these two concepts, then, are the concepts of attribute classes. As a prelude to the express knowledge of the concept of identity, a child therefore needs to know a notable range of concepts of attributes sufficient to describe an entity in some detail. This amount should also be sufficient for a child to comprehend the concept of “attribute” - though the concept of “attribute” itself isn’t necessary, where what is important is the understanding of the notion of it, which understanding is evidenced by the child comprehending what is meant by “about” in the question “tell me something about X”.

These attributes are in turn either are reducible to or already are perceptual-level observables by the five senses: weight, texture, flexibility/inflexibility, brittleness, smell, taste, sound, colouration, and so on. These are the only root means by which we may come to know of the nature of anything, with all other means being indirect connections to these observables. This is particularly obvious in the case of a child, who has no other means of knowing a thing but by those directly perceivable facets of that thing.

The other part of reduction is noting that the notion of attributes cannot be applicable to anything other than entities. Have you ever seen an attribute floating about looking for an entity to descend upon? Obviously not. Quite the opposite - one cannot comprehend any particular attribute, nor the notion (never mind the concept) of attribute except by abstracting from the possession of attributes by entities. It is only by observing attributes as attributes of entities that one can gain the abstract awareness of this or that attribute. Thus before one can comprehend identity explicitly one must first comprehend entity in at least some implicit form or better. This also ties in with the above reduction because those lesser synonyms are also considerably synonymous with entity too, differing only in terms of focus.

Before I leave, I can note that there is also a use of the word “identity” to refer to the fact that two things are equal to and interchangeable with each other. From what I can gather, this is the word in the form of an abstract noun referring to a relationship between two items of consideration rather than the character of one item of consideration, and that this is mostly to do with definitions and how the same one thing has different labels for different contexts, and also in mathematics. For instance, the square root of -1 is represented by i, so the formula “SQRT(-1)=i” is said to be “an identity.” As far as I can see, this is a derivative of the Law of Identity, though not interchangeable with it (note Dr Peikoff being vociferously unimpressed by those who state the Law as “A=A,” which I was once guilty of on an online avatar.) Similarly, and also in mathematics, the square matrix with ones running top-left to bottom right with zeroes everywhere else is said to be the identity matrix, because it is the matrix equivalent of unity and so when another matrix is multiplied by it the result is that same other matrix. Again, these are advanced derivatives, are well beyond the ken of pre-teens, and so should not be allowed to get in the way of a basic understanding of what “identity” means at the most fundamental level.

Perceptual roots
As foundation to all of the above, and also the further reductions below, we are back to the capacity to identify entities as such as a mechanical-perceptual skill. Again, after this skill is acquired the existence of actual entities is subsequently taken for granted by consciousness until later explicitly identified. Making that identification requires cognitive effort, part of which involves successfully learning the above concepts and all that goes into them.

An additional part of that skill, acquired a little later in life, is the ability to make selective focus on the attributes themselves rather than their integrated sum. In the early stages of learning concepts, this is another thing that is implicit and which it is an achievement to do explicitly again by conscious effort and focus.

Reducing “A thing is itself”
Most often, one would never reduce every single word in a proposition describing a whole concept or principle one is trying to reduce. Here I will make an exception, partly because I went ahead and did it anyway before even considering the propriety of it until after the fact, but also because I thought that it might be instructive and I had already resolved to leave no stone unturned at this foundational level.

A
The word “a” is a grammatical tool for use in conjunction with concepts of entities. It is the indefinite article, indicating that there is a single instance of the concept to which it refers (ie the article) and where any of those members are interchangeable with the instance being referred to (ie the indefinitude). In short, until further notice the instance so referred to is not of special interest, other than that it is one being singled out for momentary attention. For example in “Joe ate an apple” he ate one apple out of a broad selection from which he could choose, and that we, the audience for that statement, are for now at least not given reason to pay that apple further mind.

The chief contrast is the definite article “the,” which indicates that closer attention should be paid or that the entity so referred to is in some notable way differentiable from other instances of that same concept. For instance in “The apple that Joe ate was tasty,” it refers to the particular apple he ate as an item of interest separate from other apples, many of which may not be as tasty as the particular one eaten by Joe, such as say the apple eaten by Sally in “but the apple that Sally ate was bland.” Note again that the “the” in this second half of a compound sentence indicates a closer attention to a particular instance is to be paid, in this case that her particular apple was of poorer quality than most other apples.

The other contrast is, again, the use of the word “some” in an article-like fashion. In this case, as partly already indicated, the word “some” in this context is not separate from “thing” but concatenated with it to create a single word. Again, I won’t go into this here - all that matters is the fact of contrast so as to understand what the concept “a” means.

Thing
The concepts “thing” and “something” are less high-minded terms for “entity.” In part, the difference between the two is chiefly of a grammatical nature, but there is also a difference in emphasis. Thing refers to the general fact of being an entity, whereas something has added reference to the fact that the thing does have some identity that is unknown or unspecified.

There is also a grammatical difference between the two, in that “something” does not need an article if it is the subject of a sentence, whereas “thing” does. To that extent, the single word “something” is a concatenation of the article-like “some” and regular “thing”. I don’t think I need to explore this further at this stage.

The concept of “thing” is not a first-level abstraction. It is a reference to entities in their capacity as entities of some kind where the specific word attachable to any given entity or class of entities is either unknown or at least just unspecified. Thus prior to knowing of the concepts “thing” and “something” it is necessary to identify at least some names of particular entities (such as family members, family pets, friends, and other people, and later also places with names such as streets and cities etc), and the words for concepts (ie of whole classes of entities) - and then it is necessary to have occasion to speak or write a word of some kind to refer to a given entity despite the lack of desire to name it or perhaps in the lack of knowledge of that name. Indeed, the invocation of the word “thing” is frequently in a context of some kind of exasperation, such as “what the blazes is THAT thing!?” and “this thing’s STUCK!”, though this is hardly the whole of the context for using “thing.”

Is
The reduction of “is” was done as part of comprehending the meaning of “existence exists.”

Itself
The word “itself” is, according to the dictionary, the reflexive form of the word “it,” where “it” is a pronoun that refers to an entity that has just been specified or is just about to be specified (except in the “prop ‘it’ ” usage, such as in “It is raining,” which usage is only a grammatical construction and so isn’t further examined here). What is additional about the word “itself” is that it is also used to refer specifically to the nature of the thing that is the “it” so reflected upon. It is of course, then, in this context that the word is used, the context being a statement of the Law of Identity. The key concept is thus “nature,” where the statement “A thing is itself” is a simpler way of saying “A thing is of a certain nature.”

Much of this, then, has already been discussed. The nature of anything is what makes that thing that particular thing. This cannot be anything other than the complete set of the attributes of that thing. The referents for the concept of nature, then, are the concepts of attribute classes. These attributes are in turn either are reducible to or already are perceptual-level observables by the five senses: weight, texture, flexibility/inflexibility, brittleness, smell, taste, sound, colouration, and so on.

Reconstructing the concepts
The reconstruction is mostly just the reverse order exposition of the reduction. The mechanical-perceptual skills of being able to perceive entities and selectivity-skills of being able to focus on individual characteristics of entities are taken as the base and are not explained here.

A and itself
The learning of what “a” and “itself” mean mostly comes from grasping grammatical nuances. I’ll just note here that the meanings of the two have already been covered - indefinite article and reflexive pronoun, respectively - and since there is not much point in restating what has already been stated I’ll leave the rest to grammatical treatises to deal with.

Thing
The concepts of “thing” and “something” are predicated on a child knowing (implicitly at least) that there are indeed entities, and also only once development of the ability to speak is already well underway. This requires the implicit knowledge and expectation that there are such things as names of individual entities and words for concepts. The words “thing” and “something” are learned ostensively in most cases after a host of such names and words is under the belt, by learning the words and then learning that they mean recognising an entity as an entity but either not being able to identify that entity either by proper name or by reference to known concepts of entities or by not bothering to make that identification. The former is achieved when a child is able to ask questions such as “What’s that thing?”, make pronouncements such as “I want something to eat” and make assertions such as “There’s something in my wardrobe!” and the latter is achieved when a child is able to say “I don’t like that thing” when he knows very well what the “thing” is.

Further, the two words also generally refer to non-human entities when that fact of non-humanness is known. Note on that score that it is an insult to deliberately refer to a person as a thing or a something, though quite alright to say “something hit the wall” if one could not identify what it was where the something was in fact a someone (or part of their body such as a fist or foot). Similarly, referring to something as a thing when one knows very well what particular type of thing is often also an expression of annoyance or disapproval, such as “this thing is stuck!” and “that thing stinks!” Of course, taking the easy option of a simple word rather than a more complex name or concept also plays a part, usually when the identity of the thing in question is also known to the audience of the statement: contrast “this thing’s stuck!” with “this ute latch is stuck!”

Aside from the contrast of entities of known versus unknown identities (be that in terms of individual names or classifications), technically speaking another contrast to “thing” and “something” is “stuff.” “Stuff” often refers to material that comes in a continuous form, or is at least referrable to as such, rather than as discrete entities as the primary consideration. For a child this is mostly in the form of gasses (eg mist, spray, steam, smoke), liquids (water, juices, milk), thick oils (butter, peanut butter), slurries (porridge, pureed fruit, mud), gels & emulsions (jam, cream), and powders (salt, pepper, sand).

Yet even so, definite amounts of stuff (eg containers-full or internally cohesive globs) are also entities, and likewise may be constructed of readily observable entities (eg grains of salt, individual beans from a beans-and-sauce mix or individual oats from porridge). Not surprisingly, the concepts of thing and something can be regularly applied to stuff because the key characteristics we are interested in and which are the context for the concepts - the fact that they are all existents of unknown or unspecified nature - is there in equal measure in both “thing” and “stuff.” Accordingly, the philosophical implications are the same, with the distinction being non-sharp and mostly of a non-philosophical nature that I needn’t look at further.

Similarly, “stuff” does sometimes get used to refer to a collection of things, be that collection closed or open-ended. An example of a closed-ended use is to refer to “Go put your stuff back in your bag” and an open-ended example is “All the best stuff comes from there,” where in both examples “things” is interchangeable with “stuff.” I don’t think there is anything important to be gained in pursuing these nuances as this kind of usage strikes me as just grammar and linguistics, along with how it frequently reflects sloppy thinking.

Nature
One meaning of “nature” is the reference to the natural world. This is obviously not what is meant here, though there is an evolutionary origin for the two meanings. I won’t go into that right now, if ever.

If not expressly taught it first, a child could be introduced to the word by over hearing a fragment of a conversation such as “or something of that nature”. Another source is movies and television, such as the last line from the introduction to the Japanese TV series ‘Monkey’: “The nature of Monkey was irrepressible!”

The word itself can be taught by showing that different entities have different attributes, and that the nature of something is the complete set of those attributes. In regards to Monkey, for example, that line was a reference to the fact that, in the Chinese story “Journey to the West”, Buddha tried to tame Monkey’s wild character by trapping him under a mountain but this experience failed to change him. The contrast required for “nature” is therefore the different actual natures of individual things and classes of things. A contrast for Monkey is the natures of Pigsy, Sandy, and Tripitaka, for example. In the TV series at least, Pigsy’s nature did change to become more human, with express attention drawn to that fact.

An important point is not to confuse “nature” with any particular class of attribute that one is showing as a contrast. Different classes need to be pointed out, such as that different things have different hardness, different weights, different colours, different smells, and so on. Then one can say that the nature of something is the whole integrated sum of all the features about any given entity or material. The nature of an apple is the fact that it is sweet, the fact that the skin is red or green or yellow, the fact that it has a core, and so on, as contrasted to both how an orange is orange, has a different kind of sweetness, that it doesn’t have a core, etc, and also to how a given brick may be pale yellow, is rectilinear and oblong, is heavy, is hard and brittle, is man-made, and so on.

There are additional nuances of nature, but these relate to essences and as such are epistemological in nature rather than metaphysical, so I won’t deal with them here. As far as each entity is concerned, it is the whole of what it is. All attributes of an existent are equally important in making that entity what it is. Change any one of those features and the identity of that existent changes. It is only we, from the epistemological perspective, who assign different weights and imports to different attributes and changes therein. For example, scratch a rock slightly and the kind of thing it is changes, but as far as we are concerned the rock is still the same plain old rock - unless there were a particular reason for our own needs that the presence or absence of man-made scratches is a game-changer in terms of how we deal with that rock, such as the scratch being contamination of archaeological or palaeontological evidence for some theory or rendering the rock unfit for decorative use.

Identity
The concept of identity is predicated on knowledge of the concept of nature. The concept of “identity” in this context is another way of viewing the concept of the nature of a thing but in a more on-a-pedestal kind of contemplation of the integrated sum. In some circumstances the words are interchangeable: “The nature of the cause was X” and “The identity of the cause was X” mean the same thing. But in other circumstances they are not, such as how in “I want something of that nature” is common whereas “I want something of that identity” strikes the ear as off. The difference is, again, subtleties in grammatical use, though with foundation in slight differences in attitude and formal treatment.

That being the case, I take the reconstruction of “nature” as already doing the legwork for the reconstruction of “identity,” and note that the latter is a more high-brow concept whose word for it gives a closer indication of relationships to entities: entities are identities.

The first introduction that a child is liable to have to the word “identity” is in being asked to discover the identity of something or someone, such as “the identity of the thief.” In this case, the child is starting with knowledge of a few of the characteristics of some entity and is being required to identify other characteristics and in time able to isolate a specific entity or class of entities by name. While this is a derivative of and dependent on the full philosophic meaning of identity, this usage is not quite what is meant in philosophy - but for a child to get to that this just requires knowledge of and integration with the concept of nature and the formal philosophic treatment of each. I don’t think I need to go deeper into that, here.

Reconstructing “A thing is itself” and “A is A”
Again, the statements do not come about merely by slapping words together in a convenient fashion. Rather, they come from a simple realisation of a fundamental fact from the entire history of what has been observed about all entities and materials, and then formulating means of expressing that fact by use of concepts.

The fact identifiable from observations is that every single entity or material ever observed to exist or imputed to exist is always of a certain nature. There is no entity or material that is ever identified except by means of particular attributes that let its existence be known by some definite means. Every single individual entity or actual quantity of material is of a definite nature, that each exists and has an entire set of attributes that go into making what each entity or amount of material is.

Even the non-descript and the nebulous are of definite natures. Something being “non-descript” just means it is commonplace and not worth remarking on, not that it has no features capable of being described. A description could be made if there were call for it - but there was no call, hence no description made. Similarly, to be nebulous is necessarily to be of a certain nature, to wit, thin and wispy, consisting of microparticles of varying inter-particle distances yet all moving in some fashion as part of a loose structure acting to some degree as though part of a larger body, such as a cloud moving in the sky or a fog rolling in from the sea or some smoke rising from a fire. To be constantly changing in the precise details of identity (mostly of shape, density and opacity) is just that and only that, and does not mean the absence of an identity at any given time.

The statement “a thing is itself” is a summation of the above facts in the form of a universal principle. It consists of the connection of the fact that each thing (including set amounts of material) is an existent and that it is a definite “itself,” ie that each thing is itself. A thing is the whole of its attributes, where reference to “itself” indicates that the sum is the item of contemplation and to be connected to the entity as an item of contemplation.

The second statement, “A is A,” is a more formal way of expressing the Law of Identity. The first “A” stands for the name of some entity or class of entities and the second “A” stands for the integrated sum of the attributes of that entity. The two are linked by “is” because a thing is the integrated sum of its attributes. It can also be the other way around! Either way, it is a blunt underscoring of the fact that things are what they are and that is that, irrespective of any wish or desire that they be something else.

Existence and identity
In the reduction, note that the statement form of the Law, “a thing is itself,” was as simpler way of saying “a thing is of a certain nature.” Note that the linking verb there is “is,” not “has.” This is important, because this mode of expression is used to indicate that a thing is nothing other than itself, that it is invalid to talk of a thing with no nature at all. An existent is the integration of all its attributes, all of which are elements of existence. It is nonsensical to separate an entity from its nature, as though there were some vaporous capacity for something to be and where attributes descend upon it to give it corporeal form - a thing without attributes is no thing at all.

Recall from before that there was a distinction in focus between “thing” and “something,” that the former was entity-oriented while the latter was identity-oriented. Again, we can see that the two are variants of the same fact: to be a thing is to be a something - to be a thing is to be a thing of some kind. Taking it back to the law of identity, the connection between existence and identity can therefore be expressed by noting that to be something is to be something.

Moreover, observe that attributes do not exist except as attributes of entities. There is no greenness floating about independently of things that are green. This is flipside of the fact that a thing is the integration of all its attributes. The whole of an entity’s attributes constitute its existence - existence is not a single attribute on equal footing with the other attributes. Rather, each and every attribute exists and can only exist by means of being attributes of something that exists. Just as it is absurd to posit a thing without any attributes at all, it is equally absurd to posit some grand integration of attributes that lacks only the “attribute” of existence.

It is for these reasons, notes Dr Peikoff, that Rand created the formulation “existence is identity.” The former - existence - is the fact of integration of attributes, while the latter - identity - is the fact of integration of attributes. The two are therefore not inseparable but two are different ways of looking at the same one phenomenon, differing only on what element is the datum of consideration.

You could look at the above and say “that is going around in circles!” My response to that is: “precisely.”

JJM