Criticizing Objectivist Metaphysics


Renee Katz

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Yes, Rand’s target notion of identity is narrower than Dan’s, though as I indicated above, hers is more inclusive than the self-same it-ness of identity. Her notion of identity also includes the what-ness of a thing. Given things in Rand’s metaphysics include not only entities, but actions and attributes and relationships. Given things in her metaphysics include alterations of entities, of attributes, and of relationships. Given things include temporal and spatial relationships. In “A is A” or “A thing is itself and what it is,” which latter better captures Rand’s target notion of identity, the thing could be an action, attribute, or relation. It need not be only an entity, her primary form of existent.

That, Bob, is part of the way Rand’s “A is A” deals with the reality of change. But, as you will recognize, she went on to speak of causality as her law of identity applied to action. She emphasized that the actions of entities are part of their identity, especially their what-identity, their specific nature. Application of Rand’s identity to action clearly also includes the mere sameness of a thing over time. Such would be the earth spinning. Her application of identity to action would include also the change in angular velocity of a top spinning on the floor. It would include as well the entities and properties in their roles of making the top slow down.

Rand emphasized the causal connectedness of things in Atlas. She wrote in ITOE that a thing having no power to affect or be affected would be nothing. Such powers are part of the identity necessary to concrete existence. Dan, yes, Rand could not concur in your conception of identity as being (as I understand you) any relatedness. For example, she can take the relatedness that is similarity, like most of us take it, as not identical to identity, though she can take mere self-sameness identity as related to similarity by being an extreme of similarity and as otherwise being an element of similarity conceived as a join of identity and difference. Moreover, for Rand, all concrete relations involve identity in her broad sense, including involvement of the simple it-ness identities. By the way, Merlin Jetton has written of a certain sort(s) of priority of similarity over identity (it-ness identity). Perhaps he will illuminate this thread with a summary of his conception and its differences with Rand and with David Kelley.

Dan, yes, in Rand’s system, identities are specifics and particulars of existents. Identity is indeed a handle for grasping what things are in perception and conception, including in the latter, identities stated in definitions and in scientific findings. Identity can be that handle and be all-covering, applying to anything that is. The specific and particular identity of a particular existent are occasions of identity in general, as in the axiom “Existence is identity,” which is a commonality, a unity, of all existents.

The charge of one electron is identically the same thing and same strength as the charge of another electron, even as they are two electrons, whose charges combined are twice that of either alone. That is part of what we mean in saying electrons are identical with each other in certain ways (very extensive ways in the case of electrons). Dan, two cups have sameness of shape to a certain degree of closeness. Rand concurred in that. But when I say that surfaces of three dimensional shapes can be specified by sets of pairs of numbers, each pair attached to a point of the surface and informatively related to number assignments at other points, words like surface, shape, three-dimensional, and pairs say things the very same no matter which cup they are rightly said of. That is part of our power of conceiving in terms of identity.

Power, too, of identity and analysis in terms of it: Think of the shape of a basketball, think of it as in geometry, as perfectly smooth. We let the air out of our ball and push it down to become a concavity. The set of those pairs of numbers (each pair specifies values of the two principal curvatures at that point) specifying the shape of the basketball when inflated has changed in the values of the pairs as we pushed down the ball. The set of number pairs suited to the deflated shape is closer to being identical to the set of number pairs specifying the shape of a Japanese teacup (no handle) than it is to the set specifying the shape of a sphere. How identity and nearness to it in mathematical analysis speaks our perceptions of comparative similarities! We perceive, without the mathematical analysis, that the shape of a deflated basketball and the shape of a Japanese teacup are more like each other than either is like the shape of a spherical ball.

The shared dimension of the shapes (shapes, not sizes) of these surfaces, as well as surface of torus and of cup with handle finger-through, are the two principal curvatures attaching to points of those surfaces. Curvature is the crucial dimension, a two-dimensional dimension (for 3D objects), for our best-informed concept of shape.

We have, to be sure, other kinds of knowing shapes, also splendid, than our conceptual knowing of them.

~~~~~~~~~~~~~~~~

Dan will be away from home base for a week now, visiting family, and may be infrequent here until after that vacation.

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Ah, I'm back from vacation! Thanks so much Stephen for that amazing answer (you're right Ba'al)! Your description helps me understand more clearly the extent to which Rand likely defined identitiy-- her "A=A" "what-ness" versus merely "it-ness" is a great summation of Objectivist philosophy as I understand it in ITOE. I even agree with this idea in trying to set denotative definitons for things-- I think it is important, and probably essential for any effective language, communucation, or understanding to set formal (no matter how broad-based) limits on our commonly held conceptions of things. Science and mathematics often seem to help us better fine-tune these denotative defintions to essential attributes. There is no doubt in my mind that the mind and outside world connect somehow, that any rational basis for knowledge needs identity underpinning it, and even that there are likely common attritbutes existing from object to conceptualization that can be isolated and integrated from world to mind, to other minds, and back into the larger world. I guess my problem, Stephen, is that by proposing identity, or the idea of "A=A" as an axiomatic concept, as an inescapable, all-encompassing truth, in effect removes from its own defintion the luxury of attributing any specific connection of mind to outside world. The second we specify those connections, the idea seems to become too limited to be all-emcompassing. I imagine why many Objectivists do not want to lose that specificity in their conception of identity, is the fear that it will destabilize the validity of concepts-- if identities can involve any relation of mind to outside world, then a lot of nonsensical concepts could arise without critical analysis of their truth or actuality. I get it. But can't these more specific limitations to identities be handled as knowledge/things naturally become more specific, perhaps with concepts like "form" and "content," that would start to deal with how a basketball, cup, top (or any of the actions or attritbutes that make those things move or function) more specifically connect with, or more denotatively exist in, the outside world?

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I am the ignorant person here.

However, my understanding of the Aristotelian statements on which Ayn dedicaed the three (3) parts of Atlas to Aristotelian concepts.

Non-contradiction;

Either-Or; and

A is A.

It seems that many Objectists recite the last principle only.

A piece of toast cannot be moldy and not moldy at the same time.

A...

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I am the ignorant person here.

However, my understanding of the Aristotelian statements on which Ayn dedicaed the three (3) parts of Atlas to Aristotelian concepts.

Non-contradiction;

Either-Or; and

A is A.

It seems that many Objectists recite the last principle only.

A piece of toast cannot be moldy and not moldy at the same time.

A..

Well it could be moldy with green mold and not moldy with red mold at the same time.

It could be moldy with either, both or neither. of course not at the same time.

Ba'al Chatzaf

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. . . I guess my problem, Stephen, is that by proposing identity, or the idea of "A=A" as an axiomatic concept, as an inescapable, all-encompassing truth, in effect removes from its own defintion the luxury of attributing any specific connection of mind to outside world. The second we specify those connections, the idea seems to become too limited to be all-emcompassing. . . .

As she spells out immediately upon introducing the formula “A is A” in Galt’s speech, Rand uses the expression as a shorthand for “A thing is something, what it is,” indeed as a shorthand for “Any existent consists of identities, of specific characters, of some ways of existing and not others.” Rand’s connection of mind to world is by the relation of identification to identity, which is to say, by relation of identification to any existent, including to the mind itself. Connection of mind to world as identification, where all the world is specific and particular identity, allows connection of mind to all the world, always in specific ways. Indeed, Rand rejects as invalid any most basic concept of conscious mind as not an identifier of outside world. The fact that the mind has various specific ways of identifying existents does not change the general situation that conscious mind most basically is mind identifying existents.

(On Rand’s development of these basics and relation to Schelling, see here.)

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In second order calculus: (x)Ep[p(x)]. For every x there exists a property p such that x has the property p. In short everything is something.

edit: on second thought that says everything is something. Is that really true?

It also says there does not exist x which does not have some property or other. Is that true?

Ba'al Chatzaf

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Cute, Bob. Where it is understood that your capital E is pinch-hitting for the symbol that is its left-right inversion.

~~~~~~~~~~~~~~~~

Adam, re: #53

The sequence in which those titles are assigned to the three Parts of Atlas have to do with the way the story proceeds. You might like to look into that in Onkar Ghate’s paper “The Part and Chapter Headings in Atlas Shrugged” in Essays on Ayn Rand’s Atlas Shrugged (2009). One thing I noticed when first reading Atlas was that the “A is A” heading was in the mood of “Here is the answer.” You turn the page, and there is Galt, and there is Dagny (she survived!) beholding the answer to all the unanswered of her life.

Rand in Galt’s speech took identity as the positive existential basis for rules of right thinking: non-contradiction and excluded middle. This conception went into Branden’s Basic Principles lectures in the ’60’s, into Peikoff’s history of philosophy lectures in the ’60’s, and into Peikoff’s Philosophy of Objectivism lectures from 1976.

In Atlas Rand rightly understood that she was supplementing Aristotle by her principles “Existence is Identity, Consciousness is Identification.” But she gave Aristotle a little too much credit for the logical principle “A is A.” Aristotle failed to see the logical results that could be gotten by using that formula as a premise in syllogisms.* Of course that is no great demerit next to his achievement of having discovered the syllogistic logic. Both Leibniz and Kant, by the way, saw the law of identity as the fundamental principle of logic. But Rand was right to credit Aristotle with the metaphysical use she made of identity in Atlas, for the place she quotes his statement of the non-contradiction principle is not expressly as a rule for right thought, but as a metaphysical statement of a way in which no thing can be. And that is tantamount to her conception of identity as the general way things are if they really exist.

Before Rand’s magnification of identity in philosophy, different magnifications of identity had been made by Schelling* and by Meyerson.*

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Okay, Rand stated "Existence is Identity." Does she mean by this that existence is exactly the same concept as identity? I wouldn't think she'd say that. There would be no reason for the two ideas if they were exactly the same thing. She must be using the statement to mean existence is very very close to the idea of identity. And I don't think she'd say identity is dependent on consciousness either, right? I mean consciousness as far as we know it is only an animal ability, but all things are what they are within certain spatial-temporal contexts, and some spatial-temporal contexts seem to lie outside of our conscious abilities. So I understand how the idea of existence underscores how anything, to be real, must exist. "Nothing" if it is real, must still exist, for example. So to me if existence is anything and everything, it is the widest possible concept that can be posited-- and that is why it grounds all other knowledge and is axiomatic.

I just think Rand failed to broaden the idea of identity to this same level as existence, just enough to separate it from that concept, and still make it wide enough to be an inescapabe idea-- an axiomatic concept. Identity, beyond things merely being themselves (which may be better encapulated with an axiomatic concept like "self"), as any/all relations of, within or between things, seems to more accurately unfold its wider definition, making this definiton more worthy of axiomatic distinction, whereas if we entwine the idea of identiy with truth, then I think it gets unecessarily caught up in the idea of consciousness, of how well the mind and outside world relate ( which is how I think of truth--as more contextual).

I think the law of the excluded middle, which you may be saying she has embeded within her idea of identity, may be causing this error. From what I understand of this idea, it means a thing is either true in one respect, or true in some negation of that respect. However the excluded middle seems to restrict truth, not to mention identity, in a way that is not entirely useful or even, to me, fully accurate. For example, the way we view light bouncing off an object can make that object appear red to us even if the natural color, with different lighting, or standing in a different position, is green. Rand seems to want to make the context specific when it suits her argument (i.e. red cannot be green in the exact same context as discussed above), and then change that argument with identity, in trying to define it loosely as "A=A," so that mind and outside world automatically connect to ideas of truth, consciousness and concept formation, yet still give the idea a broader idea as "what-ness" as opposed to "it-ness." Why not make the concept of identity wider to include all relations, if we can still understand it as including the idea that things are what they are, whatever that is? Doesn't such a definition instead expand our ideas of truth, and help us understand contextual relationships within an Obejectivist philosophy rather than undermine Rand's notion of identity?

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Well, I guess it may undermine Rand's notion of identity to some degree, but I don't think it destabilizes identity axiomatically-- I think understanding identity as any/all relations of, within or between things actually helps strengthen the concept to include all ideas, all contexts, all knowledge, not just denotative, or essential definitions of things.

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Dan,

Welcome to OL. It sounds like you're asking the right kinds of questions. But, it also sounds like you want to stretch the concept of identity to mean something that it doesn't. The concept of identity is the concept that an entity, attribute, relationship, or action has a specific nature.

The nature of an entity doesn't depend upon what anyone thinks about it or whether anyone thinks about it at all. So, the identity of an object doesn't depend upon a definition, denotation, or essential characteristic. Neither does the identity of an attribute, relationship, or action.

"Definition", "denotation", and "essential characteristic" are notions of epistemology. They relate to what we think about objects, not the objects themselves. Of course, "axiom" is a notion of epistemology too, but the axiom of identity is simply a recognition of the fact that each and every entity, attribute, relationship, or action has an identity. Each and every entity, attribute, relationship, or action has a specific nature.

When Rand stated that "existence is identity", what she meant was that every thing that exists has an identity. To exist is to have an identity. To exist is to have a specific nature.

The fact that things have a specific nature makes it possible to describe them, to define them, to identify their essential characteristics, to denote them symbolically, or to otherwise refer to them. If an object had no specific nature, then any reference to it would be meaningless. If all of existence were an undifferentiated blob then no reference to any specific thing would be possible. So, we know that entities have a specific nature due to the fact that we are able to refer to them. But, their nature does not in any way depend upon the fact that we have knowledge of them.

Darrell

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I concur with Darrell in #61.

Dan, concerning #59, in Rand’s system, identity is concurrent with any and all existents. As you say, consciousness is not. Identification is not. Actions are a part of the identity of any concrete existent. So are the attributes of that existent. So are that existent’s susceptibility to standing in certain relations to other existents. That last includes an existent’s susceptibility to being identified, to being an object of consciousness. But that does not slide such an existent itself from simply being the identities it is to being identification, to being truth. There is a metaphysical way in which philosophers and poets have spoken of truth, but in Rand’s explications of her mature metaphysics, truth is recognition and identification, which means truth requires activity of consciousness, which as you say, is not concurrent with any and all existents. Only the affordance of truth, only identity, is concurrent with any and all existents.

Consciousness in Rand’s system is an existent of a certain sort, but it is an existent. And consciousness at our level, consciousness able to grasp the statement “Existence exists” is able in that grasp to recognize also that it is itself in existence (AS). That too is a unity of mind with existence in general, a unity alongside the unity of correct identification of what exists, correct identification of identities.

The axiomatic character of each concept—existence, identity, and consciousness—has its distinctiveness, which I would say is brought into show only by constructing the detailed proofs of their axiomatic status. And any full showing of the axiomatic character of these concepts must include proofs of the axiomatic propositions “Existence exists,” “Existence is Identity,” and “Consciousness is Identification.” Rand composed a few of the required proofs in Galt’s speech. I hold that “Existence is Identity” has a handful of fundamental forms, and it is by proving (after discovering which propositions they are) the axiomatic standing of each that one fully characterizes the headline “Existence is Identity.”

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Thank you both, Darrel and Stephen, for such excellent explanations-- these clarify some things for me about Rand's view of identity, and how likely most Objectivists define identity. It is good to know she didn't slide identity and truth together into the same concept. I actually agree with most all both of you are saying as well. Darrell-- you are absolutely right-- definitions are epistemological-- I didn't mean to confuse epistemology with metaphysics. I know what you mean when you say things have a specific identity, and this is what allows them to be identified, yet the identity itself and the process of identification are different things. But let me see if can explain my problem with her, and most Objectivists definiton of identitiy more succinctly.

As you explain Darrell, the Objectivist notion of identity rests on the fact that all things have a specific identity that makes it possible for us to identify their natures. I don't dispute this idea in general, but I'm wondering how you, Stephen, Rand, other Objectivists, would define the term "specific" in this context. Most would probably say that quantum physics today reveals that that the exact, often minute qualities and quantities within entities change every instant, so that their identities (especially any of their dual properties [as explained by the Heisenberg Uncertainty Principle]), as we apprehend or grasp them, are not this exact. Rand's open-endedness of concept formation helps us understand that we don't need this level exactitude to get at or scope out something's identity (e.g. her identity as "what-ness" vs. "it-ness" as explained previously). And concepts like Rand's existnece are so wide they can include everything, so this concept is not specific at all. The concept existence is also axiomatic, or self-proven, which to me makes me think its definition automatically links with anything or everything that lies inside or outside our mind, or all things metaphysical. So if "Existence is identity" (thank you Stephen for expalining how Rand arrived at that statement) then why can't it be as wide-reaching as her notion of existence. Any/all relationships (whether within or outside any mind) would broaden the idea so that we could include any interactions of matter, thoughts, imaginings, whatever, and still be able to do away with ideas like "mind-body" irreconsilable dichotomies because it underscores that any/all things interconnect. Can't the idea of truth instead, depending on how it is defined, do away with the need for having to link the identity of any/all things to some "specific" character. Also, if identity is not dependent on our minds anyway, how can we say with axiomatic certainty that "what things are" has some "what-ness" level of specificity, just by positing the concept identity?

I know this is a redefining of identity, especially as Objectivists define it. I guess I would ask what term you would give to what I am saying, if you don't think identity is capable of this wider abstraction? Do you think this wider abstraction is acutally axiomatic like I do? If not, why not?

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Dan, it is one thing to propose that something is always true and very widely in play, perhaps even in play in anything existent. The truth of the claim could be supported by appeal to experience, by showing it holding in various sorts of experience and coming up empty handed in a search for counterexamples to the claim. It is another thing, a further claim, to claim that something is axiomatic. To show that a proposition or a concept is axiomatic, in Rand’s sense of the philosophically axiomatic, requires showing that if one denied the proposition or concept, one would be relying on the truth of that very proposition or concept in making the denial.

This conception of a philosophical axiom relies on the method of indirect proof, and that depends on the law of excluded middle, which is part of Rand’s conception of identity. One might try to justify a different concept of the axiomatic, one not requiring a showing of the general truth’s immunity from denial on pain of self-contradiction, yet one that is something in addition to being a generalization from experience. That is, one might formulate a conception of the axiomatic that requires a showing of some sort of new special defensibility, which sort needs to be spelled out.

The notion of identity you seem to be crafting (and you have given some hints as to what you think it accomplishes), a notion including but adding to Rand’s notion, strikes me so far as one that has to drop part of Rand’s (and Aristotle’s) notion. Namely, yours suggests that not all of existence is subject to the law of excluded middle, that some existents are at least partly indeterminate, not just unknown, but fundamentally indeterminate.

I don’t mean quantum mechanics. That pairs of canonically conjugate dynamical variables have determinacy only down to a minimal nonzero value of their join (which join is always the quantity in physics called action, which in every guise has the units of angular momentum) might mean only that a reordering of physical concepts as to which are more fundamental and in what ways is in order. That is, the physical indeterminacies of quantum mechanics (which I have always accepted and do not wash away as mere occasions of our inability to get to determinate values of the quantities at issue in the physical setups at issue) might well be not fundamental indeterminacies in existence. I would point out that today’s versions of what is known as quantum logic no longer include a denial of the law of excluded middle.

The picture I’m getting from you so far is reminiscent of Aristotle’s composition of matter and form, where yours is a composition of existence and identity. I would be wary of reification in a full assimilation of identity to Aristotle’s form, but perhaps Aristotle’s arguments concerning form's ever-presence could be useful to your reach for axiomatic status for your notion of identity. Do you find his metaphysics (or that of other Greeks) and his place of mind in the world has more unity than Rand’s and in a desirable way? Are you familiar with the identity theory of truth? Would difference between that theory of truth and Rand’s be a fair indication of the difference between your conception of identity and hers?

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Thank you Stephen,

I'll do my best to address your concerns/questions, although you have much more knowledge of the history of philosophy than I do.

First off, I think both the law of non-contradiction and the law of the excluded middle are important components of the law of identity when dealing with probably any specific, and definitely any one-of-a-kind, space-time, physical context. Looking back on my comment on the law of the excluded middle, I may not have been seeing it in a broad enough light. However, I think both of these ideas fail to be complete enough on the widest of metaphysical levels, because as with the concept of existence (as anything and everything), it does not specify anything about what a thing is, e.g. that it can't both be itself and not itself at the same time, just that something, whatever it is, is. And I think if identity is to have the same kind of status, it can't go to the kind of specificity these laws go to, either.

You're probably right that I'm stretching and/or limiting the idea of axiomatic concepts as commonly conceived. I guess when I try to understand what Rand was implying with an idea like existence, is that both mentally and in the outside world, whatever is there is there, be it real or a fantasy, substance or illusion, something or nothing. We can't posit anything about anything without first positing that it exists. To me, that idea is truly inescapable, not because we can't say she is wrong, but because any act or thing we do has to exist, metaphysically speaking. I think her other main axiomatic concepts--identity and consciousness, don't possess this same level of inescapability, at least as she has defined them. They may have some complete level of mental or logical self-proof in them, but their full metaphysical all-pervasiveness does not seem to be there. So to me, they don't seem as useful as they could be as an armature for all other knowledge, if they can't be expalined in purely metaphysical terms.

In response to your insightful comment,

"The notion of identity you seem to be crafting (and you have given some hints as to what you think it accomplishes), a notion including but adding to Rand’s notion, strikes me so far as one that has to drop part of Rand’s (and Aristotle’s) notion. Namely, yours suggests that not all of existence is subject to the law of excluded middle, that some existents are at least partly indeterminate, not just unknown, but fundamentally indeterminate."

I would say this is not exactly what I am saying--I wouldn't use the phrase "fundamentally indeterminate," but that you're right in concluding that I believe no finite being can know just anything and/or everything. I think all things can be scoped out, studied, known to whatever degree our unique place, time and abilities allow us to understand. But yes, some things have happened so far in the past or are yet to known in the future (i.e. past and future cosmologic horizons), or in the present are physcially incapable for us to get to in our spatial-temporal range of knowing. However, I think if axiomatic concepts are redefined to understand them as metaphysical, all-pervading absolutes, then we can use them in both purely material and mental ways, to underpin and structure all other things.

I think there are some crossovers into Aristotle's "matter (or sustance) and form" with my "existence and identity, " but I think Aristotle is thinking about these ideas more physically and in a more limited way than I am. Perhaps his "ever-presence" idea is the kicker here. I think metaphysical means physical but in some way infinite, never-ending or ever-present in some way. Because Rand never extrapolated on her metaphysics in as detailed a sense as she did her epistemology, it is hard to say exactly how she conceived of the physical universe more basically, but I do know that her conception of existence is in all practical ways, the same metaphysical idea as mine. I wouldn't limit the idea of existence to some basic substance-- because it also could be any complex form of that substance, or really any other idea or thought we may want to throw in there, becasue on its own, in full defintion, it entails no specific character. What I do find more intriguing about Aristotle's view as opposed to Rand's is that he tries to physicalize all things. Rand used more pure logic and in this way, I believe, she was satisfied with identity being self-proven to the level of the laws of non-contradiction and the excluded middle, and consciousness to the level of being self-proven within our own thinking processes. But this in turn, limits how much we can apply the concepts to all things.

Unfortunately, I'm not aware of the identity theory of truth, but I hope my explanation here better pinpoints where I'm going with my idea, and why I think it can expand and not diminish, the power of axiomatic concepts. What are the main points of the identity theory of truth--who formulated it?

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No, the underline in my last post indicates a hyperlink. We should all start with reading that, at Stanford, for synopsis of the identity theory of truth.

Here are some excerpts from the text of Plotinus cited by the author, but not displayed, for early example of an identity conception of truth:

The contemplation must be the same as the contemplated, and Intellect the same as the intelligible; for if not the same, there will not be truth; for the one who is trying to possess realities will possess an impression different from the realities, and this is not truth. For truth ought not to be the truth of something else, but to be what it says. (5.3.5)

The real truth . . . does not agree with something else, but with itself, and says nothing other than itself, but it is what it says and it says what it is. (5.5.2)

Plotinus’ depictions here concern Intellect, which is second in divinity only to the One, and Intellect is not us, but what is truth, a kind of cosmic knower whose knowledge is numerically identical that which it knows. The question for our own knowing would be if any of it is like that. Is any of our knowing such that what is known is numerically identical with what is known? I’d go with Rand (and others before her) who would have the most fundamental type of knowing, the most basic form of truth, be of externalities to the knowing subject. And the identity model of truth, at least in the form Plotinus conceived for Intellect be some model, perhaps, of consciousness knowing some things of its acts, which would be derivative, not prior a correspondence kind of truth in which one says of what is that it is and in the way it is and says of what is not that it is not. But we should look at identity theory of truth beyond Plotinus.

I should ask you, Dan, if you think something like Plotinus’ Intellect is a layer over all existence. I mean is how you conceive identity and consciousness, beyond the confines you would find in Rand (or in other writers here), something like that?

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Stephen, I'm sorry I didn't notice the link before-- thank you. I didn't read the article all that thoroughly, but I think I get the gist of the identity theory of truth. It may hard for me to answer your question. I do not believe there is any one-to-one, perfectly direct, assimilation of any specific, physical thing's identitiy from external world to mind. I believe there is a gap of translation from any physcial referents to the sensory-perception of them, and again to the conceptualization of them, where it is possible as human we can make errors in judgement or propose false concepts or claims, as Rand, I think would concur. However, I do think there are overridding, all-encompassing, and thus non-specific, metaphysical referents embodied in "axiomatic" concepts, and these infinite qualities or things are not subject to the same gaps of sensory-perception to conception that spatial-temporally finite forms possess, because they are intrinsic all things, and thus the act of thought or knowledge itself cannot escape them. Thus they not only have to underride all knowledge but all physical processes, and so an "axiomatic structure" formed from these kinds of concepts can inform us on some univeral, interlinking pattern within the nature of all things, and thus all knowledge.

I wouldn't describe this "axiomatic structure" as a layer over all existence (that's maybe where the identity theory of truth becomes mystical--outside the physical), but an underpinning and embodiment channelling all things. Does that help?

I guess my main question is do we really need the specificity aspect of identity to assert it as an inescapable "axiomatic" concept? Isn't it enough, in its purest, widest form, just to assert that any/all things connect to and compase each other in some way, so that "A" has to connect to something else regardless if it is another "A" type thing or if is is "B" or even "$" or some nonsense like "Tiuyiofaos"? If truth is a different notion than identity (because obviously we can make false claims evne though things are what they are), why can't that concept (and/or perhaps others) set the detailed parameters for more specific "A=A" assertions? Can't interconnection, or interrelationship, still be logically self-proven by the "A=A" assertion, being that this can be primarily a "what-ness," open-ended relationship, and also better refute any "A is not A" argument by referring to any/all relations (e.g. A=B, etc. as explained above)?

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Rand had stated in Galt’s speech what it takes to show that a concept or proposition is a philosophic axiom, and she gave some indication there of what are the distinctive functions of such axiomatic knowledge. In ITOE, as you also know, Rand wrote that axiomatic concepts are concepts of circumstances in any and all experience; they are implicit in each experience, but as concepts, they are identified abstractly (55). And part of that abstract identification of such concepts is showing their axiomatic status by showing the need to use them in any denial of them.

As to the function of axiomatic concepts, Rand stated they “are the constants of man’s consciousness, the cognitive integrators that identify and thus protect its continuity” (56). Moreover, “axiomatic concepts are the foundations of objectivity” (57). In Rand’s epistemology seminar following on her treatise ITOE, Peikoff summarized three interrelated functions of axiomatic concepts, and asked if these were right by her conception of such concepts. Those functions were the continuity function (“enabling human consciousness to preserve continuity, the idea of the continuity of existence and consciousness”), the objectivity function (“generating the ability to be objective by emphasizing existence, with identity, as independent of consciousness”), and the underscoring of primary facts, this third role having been mentioned on page 59 of the treatise (260–61). Rand thought that was a correct representation of her conception of the functions of axiomatic concepts.

In Rand’ view, concepts compose propositions and affirm some propositions in their affirmation. In the case of her axiomatic concepts, that would include the axiomatic propositions “Existence exists, existence is identity, and consciousness is identification.” I have worked mainly on the axiomatic character of “Existence is identity.” I have shown that certain subsidiaries of that heading are axiomatic, satisfying the requirement that their denial entails self-contradiction. These include the propositions:

(i) Every entity is of a kind excluding it being some other kind of entity.

(ii) Every action-bearing entity bears certain kinds of actions and not others.

But there were propositions close kin of those for which I concluded no proof of axiomatic standing can be composed. These I have called postulates, rather than axioms. They include the propositions:

(i) Every concrete entity bears changes in its attributes and relationships, including its changes that are actions, and every concrete entity is capable of acting and being acted upon.

(ii) All actions are actions of entities and require efficient causes.

(Cf. RK and SB 2007.)

It is no lowly standing to be such a proposition that is not an axiom. Such propositions are close kin of the axioms and function with them to the same ends. Rand likely thought of what I have sorted into only postulates as somehow part of her axioms. They are part of the cohort "Existence is identity," though they are not axioms. Rand also took as axiomatic her thesis that every existent is measurable in some way or another (39). She supposed that any concrete bearing some relationship to the rest of the universe bears some measurable relationship to the rest of the universe. So far I have no proof that this proposition is an axiom, and I take it as a postulate, one I think true.

I think sorting axioms from their close kin, sorting by finding or failing to find proofs of axiomatic standing, is profitable. At least, it is interesting that such self-contradiction proofs can be found for denials of some of these fundamental formulas, but not for others. (My current writing project* has brought me to consideration of entry of axioms [and kin] into all objective judgments, but I don’t yet have verdicts on these possible roles.) I incline so far to think of what you would add to metaphysics as something likely to be added to the team of postulates. Rand and others before her agree with your idea that all things are connected (excepting nothing, no thing really), anyway, connected to something other than itself and such other connected to yet others till we get up to the totality of existence. You might want to try to articulate any ways in which the connectedness you are after is different from the kinds you find in Rand’s picture. And perhaps a different underscoring (maybe a lot different) of some connections only slightly noted in Rand’s writings.

I realize the more important thing is your own resulting positive picture, not its relation to other thinkers and their pictures. But these comparisons are helps to one’s own fundamental formulas of the world.

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PS

For everyone I’d like to reiterate from Michael’s remark on the first page of this thread notice of Ronald Merrill’s reflections on Rand’s axioms in his Objectivity essay “Axioms: The Eightfold Way.” That is on pages 1–15 of V2N2 (1995). In that same issue, on pages 131–35, is another very stimulating and original reflection on Rand’s axioms. That is the little essay “Existence is Independent Individuality” by Peter Chriss.

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Stephen, thanks again. You're defintiely right that I should be more aware of other theories out there. I've studied a lot of Rand and Objecticvism, but much less of Socrates/Plato, Kant, Aristotle, Newton, and Einstein, and the history of science and philiosophy in general, so I only have general notions about what other main groups of thinkers have explored. I also have a background in visual art, so I think I have some understanding of how that history and the ideas explored throughout it, relates to philosophy more generally. I apaologize if I coming off as arrogantly ignorant, and I hope I'm not boring you with my idea, if you think that it has already been explored and concluded by yourself and/or others to the widest reaches it can be. But I'm finding the conversation really delightful, and insightful--I've never really been able to understand Objectivism with as much clarity as you are bringing it to me.

I read Part 1 of your article that you linked me to titled, Identity as to Kind. I'm just going to qoute it all here as a reference. Rand (like you) and I have different conceptions of what an entity is as opposed to actions, attibiutes and relationships (I see there is another thread on entities here which I'll have to read) . First, Rand's/your Objectivist idea:

"Rand states her finer structure for the law of identity as follows. “Whatever you choose to consider, be it an object, an attribute, or an action, the law of identity remains the same. A leaf cannot be a stone at the same time, it cannot be all red and all green at the same time, it cannot freeze and burn at the same time. A is A. . . . A contradiction cannot exist. An atom is itself, and so is the universe; neither can contradict its own identity; nor can a part contradict the whole” (AS 1016).

Rand’s law of identity entails that objects come in some exclusive kinds. Leaf and stone are kinds that are exclusive with respect to each other. Any object is also of kinds that are not exclusive of each other: a leaf is a kind of plant part, it is a kind of light catcher, and it is a kind of drain clogger. To say that an object is a leaf and a stone violates identity in Rand’s sense; it is a contradiction. But to say that an object is a leaf and a drain clogger is no contradiction. Objects come in some exclusive kinds, and it is sensitivity to these sets of kinds that is written into Rand’s conception of non-contradiction concerning the kind-identity of an object. (Cf. Plato’s Sophist 252e–54b.)

Rand clearly intends that what is here proposed for objects is to be generalized to entities. Every entity is of some kinds that are exclusive relative to other kinds of entity. Rand uses the term entity in the paragraph preceding the object examples of leaf and stone. That is, she uses entity in the initial statement of her law of identity: “To exist is to be something, . . . it is to be an entity of a specific nature made of specific attributes” (AS 1016). On that page, it is clear that she takes for entities not only what are ordinarily called objects such as leaf, stone, or table, but micro-objects such as living cells and atoms, super-objects such as solar system and universe, and substances such as wood.

Now we have a modest problem. If we say “to exist is to be an entity of a specific nature made of specific attributes,” we seem to say that attributes are either entities or are not existents. Consider for attributes “the shape of a pebble or the structure of the solar system” (AS 1016). To avoid the patent falsehood that the shape of a pebble does not exist, shall we say that not only the pebble is an entity, but its shape is an entity? Rand reaches a resolution by a refinement in her metaphysics nine years after her first presentation. In 1966 she writes “Entities are the only primary existents. (Attributes cannot exist by themselves, they are merely the characteristics of entities; motions are motions of entities; relationships are relationships among entities)” (ITOE 15). Let us say then that to exist is either (i) to be an entity of a specific nature made of specific attributes or (ii) to be some specific character in the nature of entities.

In ITOE Rand also makes the refinement of taking materials, physical substances, to be not fully specific entities. “Materials exist only in the form of specific entities, such as a nugget of gold, a plank of wood, a drop or an ocean of water” (ITOE 16). Materials, for Rand, would seem to fall under both (i) and (ii), and I do not see any defect in that.

Let us now expose self-contradictions that obtain in denial of the ramification of "existence is identity" that entities are always of some exclusive kinds. Suppose an entity exists and is not of any kind that excludes it being any other kinds. If the supposed entity is nothing but existence itself, then there is no contradiction; one is simply talking about existence as a whole. So suppose an entity exists and is not of any kind that excludes it being other kinds and is not existence as a whole.

Then the supposed entity could be one with any other entities that are of exclusive kinds (just as a leaf that is a drain clogger could be one with a leaf that is dead, maple, and wet). For it is not an entity of any kind excluding it being other kinds. But to say that an entity is not of any exclusive kind and that it is one and the same with another entity that is of some exclusive kind(s) is a contradiction. (Non-A is A.) Indeed if some entity were not of any exclusive kind, then it could be one with the person who supposes such an entity. Then to suppose an entity that is not of any exclusive kind is to suppose that one’s person could be an entity not of some exclusive kinds. But that supposition contradicts the presupposition that one is of the exclusive kind person, a person who makes the (errant) supposition. (Cf. Aristotle’s Metaphysics 1007b19–1008a28.)

So I have argued the axiomatic standing of “existence is identity,” where the existents are entities and the identity is kind-identity. All entities are of some exclusive kinds—a leaf cannot be a stone at the same time—and this postulate must be accepted on pain of self-contradiction.

~~~~~~~~~~~~~~~~

Beyond the Axiomatic

Philosophers often use the term entity to mean any item whatever. That is one customary usage and perfectly all right. Rand wanted to take entity into her technical vocabulary as something more narrow. In her sense, entity is much like Aristotle’s substance, but wearing identity on its sleeve.

In her 1966-67 treatise ITOE, she writes that "entities are the only primary existents" (15). She goes on to name some things that cannot exist without connection to entities: attributes, motions, and relations. She takes all of these as genuine existents. Into the pool with attribute, motion, and relation, Rand also places event, locomotion, action, and activity of consciousness (7-8, 29-33, 39).

All of those characters are, for Rand, concrete existents; but they are not entities in the way she intends her concept entity. To qualify as an entity, an entity has to do more than be able to stand as the subject of predication (or as the argument of a propositional function). Running can be the subject of predicates, but it is an action, not an entity.

I conjecture that concrete existents are best conceived as entities only if standing in some measurement relations above ordinal (viz., interval and ratio and multidimensional spaces of these)."

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My metaphysical view is different than this in that I don't see entities as the only fundamental existents, and I don't think the idea "Existence exists" innately has to imply that they are. "Existence is identitiy" may have to, but I'm not really convinced this axiom is true in the way it is laid out above. I think entities are dependent on actions, attributes and relationships, as much actions, attributes and relationships are dependent on entities-- I don't think something can exist without being actively present in time, without being compsed of something, or relating to something else. All things (at least physical ones) have actions, some specific form as entities, and some relation to other things, simultaneously. I don't think they are mutually exclusive properties, and I think it is epistemologuically clearer to focus on "what" things are before defining their actions, attributes or relationships, I don't think metaphysically we can single out entities as being the source for all the others. However, metaphysically, in some infinite physical way, what I think of to be true "axiomatic" inescapable concepts, there seems to be an order to the logic, which may be reflected epistemologically in in the enitity-action-attribute-relationship construct through the ideas Existence-Knowledge-Self and Identity. Although as you know I've wirtten a book on this, and it really is probably too complex for me to summate here, but going to throw the ideas and their axioms out there to see if they make any sense.

"Existence exists" Any/all possible things, whatever or whenever they are, just are, whether we know anything about them or not.

"Knowledge is known" Any/all possible things we know, whatever or however we may know of them, whether conscious or not, whether inside or outside any mind, are actively there.

"Self is anything" (but not all things, or existence in total) Thus self becomes a metaphysical assertion of difference, or any/all different things.

"Idenity is any knowledge" (but not all knowledge, or knowledge in total) Thus identity becomes a metaphysical assertion of relation, or any/all relations of, within and/or between different things.

Of course this sets up a very different metaphysical picture of axiomatic concepts and knowledge (and thus identity) than is commonly conceived by Objectivists (and really most people in general). Rand really didn't go into the axiomatic nature of self much, but according to her post interview in ITOE, she said she did think it was an axiomatic concept. The beauty of this set-up, versus what is conmmonly conceived by Objectivists, is that it frees us from needing to tie up knowledge or identity with notions of truth, kind, specific entities, actions, attributes or relationships on this wide-abstract level. I don't think it has to take away from the importance or necessity of knowing things truthfully, simply because identity isn't directly tied to any "specific" knowledge yet-- other concepts, and "propositions of close kin" as you say Stephen, can help us accurately defne things in relation to their material understructures, as these metaphysical things naturally become more specific.

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When I said "and I think it is epistemologuically clearer to focus on "what" things are before defining their actions, attributes or relationships, I don't think metaphysically we can single out entities as being the source for all the others." I meant "and although I think it is epistemologuically clearer to focus on "what" things are before defining their actions, attributes or relationships, I don't think metaphysically we can single out entities as being the source for all the others." Sorry I shoud proofread these better before submitting. I'm just too excited to reply!:)

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