All that Exists

Stephen Boydstun's picture
Submitted by Stephen Boydstun on Fri, 2007-07-20 12:55

Does existence exist as a whole? Is there an existent that is a totality of which all organisms, planets, galaxies, and intergalactic space are parts? Is there an existent that is a whole and not part of some yet larger entity? We all answer: "Yes, there exists such a whole, only one such whole, and it is called the universe."

We know that answer at least in part by common experience and by science. Do we know any part of that answer by metaphysics, beyond common experience and whatever the stage of scientific knowledge? What metaphysical proofs demonstrate that there is an existent, exactly one, that is the totality of all existents?

( categories: )

Difference as measurement

Ptgymatic's picture

I had said that on Rand's theory of concepts, differences were measurements. You reply that "measurement-omission analysis of concepts" does not maintain that difference (or sameness) "amount to measurement." I'm going to take that as directly contrary to what I had said.

Attributes possessed in different measure are differences. The point of Rand's theory of abstraction through measurement-omission is to see all differences as merely differences of measurement, implying sameness of the measured dimension. Interpreting differences as measurements is the whole point of the theory of measurement-omission.

This is highlighted in the application of the theory of measurement-omission to the Analytic-Synthetic Dichotomy, as in Peikoff's article, which was included in later editions of ITOE.

You say, "...measurement omission means release of the particular identities of the class members..." (next to last paragraph.) For that to be true, everything that goes into the particular identities of every class member must "be" a measurement.

Of course, I am speaking here of Rand's theory, and you are speaking of that and other positions.

I was hoping you would respond to my challenge to your alternative, that every existent is either an entity, an action, or an attribute.


Determinates and Determinables

Stephen Boydstun's picture

Determinates vs. Determinables

From “Universals and Measurement”

“Concepts can be analyzed, according to Rand's theory, as a suspension of particular measure values of possible concretes falling under the concept. Items falling under a concept share some same characteristic(s ) in variable particular measure or degree. The items in that concept class possess that classing characteristic in some measurable degree, but may possess that characteristic in any degree within a range of measure delimiting the class (Rand 1966, 11–12, 25, 31–32)[5]. This is Rand's ‘measurements-omitted’ theory of concepts and concept classes.

5. Pale anticipations of this idea of Rand’s may be found in . . . Johnson (1921, 173–92) . . . .

“Johnson, W.E. [1921] 1964. Logic (Part 1). New York: Dover.”


Mindy, neither the measurement-omission analysis of concepts nor the modern theory of measurement maintains that difference and sameness amount to measurement. Difference and sameness are more primitive than measurement, more primitive than even “absolute measurement” (e.g. counting). A scheme that succeeds in analyzing the concepts difference and sameness in terms of omission of measurements will have to loosen the measurement-omission definition of concepts as I did in the section “Amended Measure-Definitions of Similarity and Concepts”; or it will have to weaken its claims about omissions of measurement values in all conceptualization by weakening the type of minimal required measurement structure from ordinal to absolute. The latter would make Rand’s theory (analysis, not theory of genesis) less radical, as indicated in the excerpt below from my essay. Still, even if the concepts that are called logical constants, and their presupposed concepts such as different and same, were excluded from the purview of measurement-omission analysis altogether, it would be very substantive to maintain that all concretes can be placed under one or more concepts amenable to measurement-omission analysis at the level of ordinal measurement.

All that said, to analyze a concept in terms of measurement omission follows on defining the concept and is not the same as defining the concept. See previous. To analyze the concept difference itself in terms of measurement omission, supposing that were possible, would not entail that difference was measurement. To say that differences are measurable is not to say that difference is measurement or that difference is a kind of measurement.

Also from “Universals and Measurement”

“Rand gave three definitions of concept. I shall tie them all together in the next section, but for the present section, we need this one alone: Concepts are mental integrations of ‘two or more units possessing the same distinguishing characteristic(s ), with their particular measurements omitted’ (Rand 1966, 13).

“The units spoken of in this definition are items appropriately construed as units by the conceiving mind. They are items construed as units in two senses, as substitution units and as measure values (Rand 1969, 184, 186–88). As substitution units, the items in the concept class are regarded as indifferently interchangeable, all of them standing as members of the class and as instances of the concept. Applied to concept units in their substitution sense, measurement omission means release of the particular identities of the class members so they may be treated indifferently for further conceptual cognitive purposes. This is the same indifference at work in the order-indifference principle of counting. The number of items in a collection may be ascertained by counting them in any order. Comprehension of counting and count number requires comprehension of that indifference.

“The release of particular identity for making items into concept-class substitution units is a constant and necessary part of Rand's measurement-omission recipe. But this part is not peculiar to Rand's scheme. What is novel in Rand's theory is the idea that in the release of particular identity, the release of which-particular-one, there is also a suspension of particular measure values along a common dimension.”

Blue and blueness

Leonid's picture

"One thing exists, and it is blue."- it exists as result of interaction of existant, mediator of perception-in this case light and human sensory organs. That literally how the surface of object looks to us. This is metaphysical term. Blueness however is a concept, abstraction which is epistimic term.

Level of abstraction of "characteristics."

Ptgymatic's picture

As you say, Stephen, an entity's attributes of relative location and momentum can take on endless values (and, in fact, it seems, that is the case with all objects, viewed from a cosmic point of view.) In order to deny that that makes such an item the owner of endless different characteristics, you summarize all such values as the two characteristics, location and momentum.

It would be possible to move higher in the hierarchy of concepts, and say those two were only one characteristic, identity. The question that comes to mind is: where is it legitimate to draw the line and say that more specific characterizations are not truly different or individual?

It might seem that you have drawn it where the differences are numerical. Since, however, the measurement-ommission theory of concept-formation holds that all differences are measurements, that distinction would seem to reduce to mere obviousness, so that the obviously mathematical differences of velocity, for example, are glossed over, while the subtle measurements that are ommitted when we combine velocity and location into the concept, "attribute" are acknowledged as distinguishing "velocity" from "location," etc.

Are running, walking, and hopping, etc., not three different actions because they are variants of one, more abstractly conceived action, locomotion? A tennis ball struck with slightly less force than necessary will not make it over the net, and will create a fault, costing a point. A ball struck with slightly more force will make it into play, and may result in a point won. As causes, the small difference in quantity of force makes a significant difference of kind in the enterprise of playing the game.

I'm confused by what seem to be two different kinds of argument about metaphysical infinity. One is that a thing's identity excludes one or more attributes, and the other is that there are "infinite possibilities of kind." The latter is easier to satisfy, as infinities may exclude one another. Are both these sorts of argument relevant?

Regarding the question of existence without identity, I do not endorse that view. I don't believe I have said anything that suggests otherwise.
Specifically regarding an entity that has almost no identity: I won't comment on incoherent ideas such as gods, but if the idea of little versus great identity makes sense, then: it doesn't matter how much identity a thing has. To exist is to have identity. Nothing lacks character.



Ptgymatic's picture

I am not confusing "entity" with "object," or "item." I do mean to say that whatever exists is all, or an aspectual part of, an entity.
I recall a transcript of a discussion Rand had with some "students," in which she says that blue doesn't exist, per se. The blue thing exists, but not beside its blueness. One thing exists, and it is blue. My point is that the blueness is fully as real as the colored thing, even though it can't exist without it. The thing and its color are not metaphysically different, just epistemologically different, one being more abstract than the other.

It might be necessary to say something stronger than that, because I want to maintain the point that not only do the actions and attributes depend on the entity, but the entity is nought without its actions and attributes. It is their reality that makes up its reality, as much as it is the entity's reality that devolves on them. Here is where I get closest to endorsing the "existence is identity" statement.

Further post coming to answer your question.


None Such

Stephen Boydstun's picture

Taking metaphysical infinity to be infinite possibilities for the kinds of features or qualities had by an item, I have maintained, in step with Rand, that there can be no such item. That a certain kind of feature, such as shape, comes in an infinity of variations does not make the feature more than one kind of feature. Similarly, that the attributes of relative location and momentum can each take on an infinity of values does not make those characteristics more than two kinds of characteristics.

Shape, location, and momentum are physical traits having mathematical characterizations. To the thesis that there can exist no physical existent having infinite possibilities for kinds of features or qualities it possesses, I would also maintain that when we turn to pure mathematics, there are also no items having infinite possibilities for the kinds that an item is. In mathematics, proof is sufficient to establish existence, but it is also necessary. If an item has no limitations as to kind beyond saying it is a mathematical kind, then it has no mathematical definition. Then no proof can be given to establish its existence.

It will not help to add that the posited mathematical item is limited in its nature by being self-consistent, rather than possibly self-contradictory. An identity consisting only of being self-consistent and mathematical and not physical is an identity inadequate for mathematical existence. Similarly, to posit an existent whose only limitation is being subject to non-contradiction, being subject to principles of mathematics, and being not part of the natural world is identity inadequate for existence.

Concerning your note on Rand’s categories, Mindy, I wonder if some of your occasions of using the term entity, are in its more general meaning of simply an item. Rand used entity in a mixed way in the 1957 exposition of her metaphysics, but contracted usage uniformly to a more narrow meaning later; see third and fourth paragraphs of Section A here.

Mindy, you neglected my question to you: Do you think that an existent so free of identity as the God of Aquinas is free of identity is a real possibility? I hope that you are not refraining from answering that question because your answer is affirmative and you are afraid that participants will make small of your mind or character. I do not attack my acquaintances who answer that question with Yes. I’ll just stick to the ideas unfolding in the exchange, and hope other participants will too.

An exclusionary alternative challenged

Ptgymatic's picture

“All that exists includes all entities and all actions and attributes. All that exists is not metaphysically infinite. Therefore, it is delimited by being one way rather than another. One of those ways is that every existent is either an entity, else is an action or attribute; rather than not being either an entity, else an action or attribute. Another of those ways is that every entity in existence has actions and attributes rather than being of actions and attributes.
These ways are part of an account of how it can be meaningfully said that all that exists is not metaphysically infinite.” Stephen Boystun, post 7-01-09, Thread, “All That Exists.”

To be an action of an entity is to be that entity, at the particular time and in the particular respect that that action names. Being an action of an entity is not, therefore, an alternative to being an entity, though it is still not the same as being the entity, without temporal condition. It is the entity, in the relevant respect, during an episode of that entity's natural history.

The abstraction that names that type of episode, the action in question, means every entity which performs that action, only in the limited period during which it takes place and in that particular respect, however many times it takes place. As a result, the referents of "entity" include the referents of "actions of an entity."

The same is true for "attributes of an entity." Attributes are entities, in one aspect. Some aspects are permanent of the entity, others are episodic. To refer to an attribute is to refer to every entity that has or has had that attribute, in the specific respect described. In this limited way, to refer to an attribute is to refer to one or more entities.

Take an entity, and strip it of its actions and attributes, and you have dissolved it into nothing. In that sense, there is no entity except in the form of actions and attributes.

Where, then is the alternative? To be an entity is to be attributes and actions, and nothing else. To be an action is to be an entity, for a period, and to be an attribute is to be an entity, in one part or aspect. A thing is not its attributes, its actions, plus something else. If you say a thing is what has attributes and acts, that “what” is nothing besides, perhaps, other attributes and/or actions. There is no deeper reality than that of actions and attributes. These terms separate in mind what cannot be separated in reality. If entities, and their aspects (actions and/or attributes) cannot be separated, what is the ontological force of the alternative, (Stephen’s formulation:) to exist is to be an entity, an action, or an attribute?

“To speak of existents is to speak either of an entity, an action, or an attribute,” does not involve the same problem. All concepts, as, indeed, all percepts, are abstract. “Entity” is less abstract than either “action,” or “attribute,” but none, alone, determines their referent. That means there is more to be said on the subject given by “entity,” “action,” or “attribute.” And that means they do not, in principle, exclude one another. Yet it is exclusion that is needed in Stephen’s alternative.

Stephen speaks of the difference between “having actions/attributes” versus “being of” an entity. Entities “have” actions and attributes, while actions and attributes are “of” entities. Does this make a difference to my argument against the exclusionary force of Stephen’s alternative?

Is there a greater degree of actuality in “having” versus in “being of?” It is not a symmetrical relation, giving the “having’ a superior status, but, I will argue, this is only due to the hierarchical organization of our concepts, not to a difference of metaphysical status. We use the term, “entity” when we want to speak of an independent existent on the whole, which means, of course, all its attributes, etc. If we wish to narrow our focus, we can speak of only one aspect of the entity, using a term we classify as “action” or “attribute.” The “being of” of an attribute or action is merely the subordinate conceptual status, which means an explication of those two terms requires mention of the superior term.

To exist is always to be an entity. Actions are entities doing their thing, and attributes are entities being themselves. We can refer to existence with differing degrees of abstraction, but it doesn’t come in degrees.



seddon's picture

Thanks for the info.


Generalization and Composition

Stephen Boydstun's picture


Not every generalization from components to their collection is a fallacy of composition. If someone says every pound of rock belonging to the earth is easy to lift, therefore the aggregation of all rock of the earth is easy to lift, we know there is a conceptual fallacy. But to say that every portion of the material earth has a definite mass (the particular value for any portion knowable in principle by weighing the portion or by inference from the portion’s particular orbit about the sun), therefore the material earth has a definite mass (the value knowable by inference from its particular orbit about the sun) is conceptually sound. To say that every bit of matter composing the earth has a net negative charge or net positive charge or is electrically neutral, therefore the earth has a net . . . is conceptually sound. It depends on which concepts one is using.

The conceptually sound generalization can be proven false by producing a counterexample. Then the generalization can be reined in and given a specified restricted domain of true application.

Every existent identified in our intelligent life on the earth is a concrete particular or an abstractive relation over concrete particulars. Moreover, every concrete existent in our experience and science is part of a larger concrete existent. My two examples in the next to last paragraph of Metaphysically Finite did not really reach being statements said of the totality of concrete existents. Let me try this example: The largest class of concrete existents that is all concrete existents is, like any portions of that class sufficient together to compose that class, nothing but a composite of entities, actions of entities, and attributes of entities.

But what do you think of the thesis, Mindy, that the universe has identity? How much? You do think that to exist requires identity. Do you think that an existent so free of identity as the God of Aquinas is free of identity (free of way down close to, but just shy of, zero) is a real possibility?



Yes, and others.


seddon's picture

I take it that Professor B is Gotthelf. Do you know the identities of the other professors?



Ptgymatic's picture

I was referring to your final quote of Rand in your next preceding post, the quote from ITOE, pg. 273.

It seems that a mere nomination is made to count as a unifying condition. Surely you would not say that by referring to all that exists with a single term, all that exists is thereby unified.

There's something radically wrong with the argument that says each thing that exists is either a, b, or c, therefore the universe at large is either a, b, or c. The premise is an inductive classification of particular things, excluding the universe itself, right? How does the extension of such a generalization to everything that exists, when taken as a whole, work?

Constants of Identity

Stephen Boydstun's picture

Mindy, I imagine you are referring to two of Rand’s statements taken together.

1. Rand’s 1973 text “All the countless forms, motions, combinations and dissolutions of elements in the universe—from a floating speck of dust to the formation of a galaxy to the emergence of life—are caused and determined by the identities of the elements involved” (MvMM 25). That statement resonates with these statements in 1957: “An atom is itself [is what it is], and so is the universe; neither can contradict its own identity; nor can a part contradict the whole” (AS 1016). “The nature of an action is caused and determined by the nature of the entities that act; a thing cannot act in contradiction to its nature” (AS 1037).

2. Rand’s oral remark circa 1971 “Actually, do you know what we can ascribe to the universe as such, apart from scientific discovery? Only those fundamentals that we can grasp about existence. Not in the sense of switching contexts and ascribing particular characteristics to the universe [which is the informal Fallacy of Composition], but we can say: since everything possesses identity, the universe possesses identity” (ITOE 273).

Should Rand say that since every concrete stands in temporal relations, the universe stands in temporal relations? In one sense, No. In another, Yes. Since there is nowhere for the passage of time outside the universe to be, the universe stands in no temporal relations that go outside itself. Yet just as Earth, Sun, and Milky Way have histories, so does the universe. The universe has a temporal relation to its own past and future. So it is not a conceptual fallacy to ascribe time to the universe as a whole in a purely internal way, as when Rand writes that “existence exists” entails that “the universe as a whole cannot be created or annihilated, that it cannot come into or go out of existence” (MvMM 25).

Rand held also that if any concrete stood in no measurable relationships (magnitude relations ordinal or higher) “it would not exist” ( 39). The universe is a concrete existent. Looking not outside the universe, but only inside, it is not a conceptual fallacy to maintain that not only do galaxies and intergalactic matter and radiation possess definite amounts of mass-energy, but the universe itself possesses a definite amount of mass-energy.

The amount of mass-energy changes in local situations, but looking to a larger, containing situation, it is constant. We have lines of good reason for the current hypothesis that the mass-energy of the largest, containing situation—the universe—is constant too. Moreover, that the characteristics of the universe are caused and determined by the identities of its constituents does not imply that the universe must be unchanging in every way.

Apart from the discoveries of science, however, the kinds of things Rand was taking to be justifiably ascribed to the universe as a whole are things that are unchangingly true about every concrete constituent of the universe. It is unchanging that every concrete, small or large, possesses identity. One thing we can say of any concrete existent, including the concrete existent that is the universe, is that it is either entity, else action of entity or attribute (subsuming relations under attribute) of entity or both action and attribute. That disjunction of identity is also unchanging for every concrete, small or large.

The identity of the universe...

Ptgymatic's picture

...would be constantly changing if it is derived from the identities of its constituents, which are constantly changing. The identity of the universe as being the conglomerate of all that exists is constant, however. What is meant in Rand's statement?


An oldie, but a goody

Ross Elliot's picture

God's infinite power. That must be a contradiction.

If God's power is infinite, then he can create an object that is infinitely massive; too massive for even him to move. Which, of course, is impossible, since his power is infinite. Yet he's limited to creating things that don't exceed his power, which makes his power finite.

Metaphysical Infinity

Stephen Boydstun's picture

Against the proposition that God is infinite, the authority of Aristotle might be invoked, for Aristotle had held “finite and infinite belong to quantity. But there is no quantity in God, for he is not a body.” Another consideration against the infinity of God: “What is here in such a way as not to be elsewhere is finite according to place. . . . That which is this thing in such a way as not to be another thing is finite according to substance. But God is this, and not another; for he is not stone or wood. Therefore God is not infinite in substance” (ST Q7 A1).

To the contrary, Aquinas argues: “a thing is called infinite because it is not finite. Now matter is in a way made finite by form, and the form by matter. Matter is made finite by form inasmuch as matter, before it receives its form, is in total potentiality to many forms; but on receiving a form, it is terminated by that one. Again, form is made finite by matter inasmuch as form, considered in itself, is common to many; but when received in matter, the form is determined to this one particular thing” (Q7 A1).

“Now being is the most formal of all things” (Q7 A1). Why? God is the first principle in the order of efficient causes. “An agent, as such, is in a state of actuality. Hence, the first active principle must needs be most actual,” not material, not potential. “Being is the actuality of all things, even of forms themselves.” Previous to matter, “previous to that which is potential, must be that which is actual, since a potential being can be reduced to act only by some being most actual” (Q4 A1).

Now “a figure which consists in the termination of quantity is a kind of quantitative form. Hence the infinite of quantity is in the order of matter, and such a kind of infinite cannot be attributed to God” (Q7 A1; cf.).

Against the proposition that only God can be essentially infinite, consider that “primary matter is something other than God. . . . But primary matter is infinite.” To the contrary, Aquinas argues that “things other than God can be relatively infinite, but not absolutely infinite. For with regard to the infinite as applied to matter, it is manifest that everything actually existing possesses a form; and thus its matter is determined [delimited] by form. But because matter, considered as existing under some substantial form, remains in potential to many accidental forms, what is absolutely finite can be relatively infinite” (Q7 A2).

As an example of such matter, Aquinas uses wood and the infinite variety of shapes into which it might be crafted. As for primary matter, it “does not exist by itself in nature, since it is not actual being, but only potential. . . . Nevertheless, primary matter even as a potentiality is not absolutely infinite, but relatively, because its potentiality extends only to natural forms” (Q7 A2). The existence of created being is not identical with its essence. Only uncreated, subsisting being—namely, God—has essence identical to its existence, a requirement for the absolute infinity to be essential.

Furthermore, even as God, “although he has infinite power, cannot make a thing to be not made, . . . so likewise he cannot make anything to be absolutely infinite” (Q7 A2).

This absolute infinity that Aquinas writes of, which goes beyond the possibilities of nature and even includes a power to create the natural world, could be reasonably called a metaphysical infinity. What might be said of this metaphysical infinity from Rand’s perspective (and mine)?

Rand would of course reject the view that the natural world was created and the view that there is anything real not within the natural world. Concerning the subsistent, wholly natural world, Rand (ITOE 286) rejects Aristotle’s view of material existence as a composite of primary matter (an undifferentiated potential for qualitative and quantitative distinction and identity) and substantial form (the contributor of qualitative identity).

The infinite possibilities of shapes that might be imparted to wood are only quantitative distinctions of curvature over the two-dimensional surface of the three-dimensional object. Curvatures at each point and its neighborhood on the surface are a certain type of spatial feature. That wood has infinite possibilities for the sets of surface curvatures does not give it infinite possibilities for kinds of features or qualities to have. Surface curvatures is one quality wood has, along with definite others (note). This is a highly constrained sort of infinity, a physical and mathematical one, not a metaphysical one.

What about existence as a whole? Discarding being that is beyond nature and discarding the form-matter composition, how like Aquinas’ absolute infinity are the infinities of all that exists, taken all together? The natural infinities applicable to wood, to stone, . . . will never amount to the absolute infinity of Aquinas. It is this sort of absolute infinity Rand was declining when she remarked: “Since everything possesses identity, the universe possesses identity. Since everything is finite, the universe is finite” (ITOE 273).

The absolute infinity conceived by Aquinas does not exist. Spinoza and Hegel have their metaphysical infinities too. I bet they are unreal.

A rough explanation.

Ptgymatic's picture

Don't know if Stephen will be posting soon, so I'll offer a rough explanation of the metaphysical sense of infinite, which he expresses with respect to "kind."

Metaphysical infinitude is more about identity than any sort of extension, numerosity, or duration. It is about having attributes such that the thing can be said to be of a certain kind or type of thing. Something that was metaphysically infinite could claim to be of every kind there is.

If you read Stephen's earlier "Axioms" posts, which were linked here, you'll see how he uses the notion. It is a relatively modern distinction.



jeffrey smith's picture

..but infinity doesn't imply inclusivity. Think of two parallel lines. Each has infinite points, but neither contains the points of the other. So even a numerical infinity of attributes doesn't imply a contradiction.

That wasn't my point, which was that (to keep in mathematical terminology) a set can be stricly defined even if it has an infinite number of members: thus a line can be defined even though it is a set containing an infinite number of points, and similarly with a plane. Therefore, if the universe is defined as the set of all entities that exist, there could still be an infinite number of entities that exist, yet the universe would still be strictly defined.

But I'm still flummoxed by the term "metaphysical infinity", and what exactly is meant by that.

Your re-formulation of the same fact as different attributes won't fly, either. Not having an attribute isn't having an attribute. That goes for having the "attribute" that one does not possess a certain attribute, which is your way of putting it

It was a flying thought, and I wasn't intending to press it.

Not meaning to limit your fun, Jeffrey,

Ptgymatic's picture

...but infinity doesn't imply inclusivity. Think of two parallel lines. Each has infinite points, but neither contains the points of the other. So even a numerical infinity of attributes doesn't imply a contradiction.

Your re-formulation of the same fact as different attributes won't fly, either. Not having an attribute isn't having an attribute. That goes for having the "attribute" that one does not possess a certain attribute, which is your way of putting it.


Sorry, you're losing me...

jeffrey smith's picture

Metaphysical infinity pertains to lack of limitation of kind, whereas physical infinity pertains to lack of limitation of magnitude.

I don't understand what "lack of limitation of kind" means. Could you translate that into English? Smiling

I have yet to craft that sort of demonstration for the case in which the existent is an attribute-bearing entity and the identity is a limitation on kinds of attributes.

First thought: if attributes could be infinite, then you would end up with an entity that was both A and not A: it would have both attribute A and another attribute B that contradicts A (for instance, large and small). In fact it would have every attribute A as well as every attribute not A. Therefore attributes can not be infinite.

Second thought: if an entity has an attribute A, then it also has a set of attributes whose commonality is that they are not A. For instance, the attribute of being 5 feet tall implies as well the attribute of not being 5 feet one inch tall, the attribute of not being 4 feet 11 inches tall, etc. And that set of attributes can be infinite (since it includes an attribute corresponding to every possible height). Therefore attributes can be infinite.

There, aren't I a helpful son of a gun? Evil

Metaphysical, Not Physical

Stephen Boydstun's picture

Mindy and Jeffrey,

That there is nothing metaphysically infinite does not imply that there is nothing physically infinite (in the small or in the large). Metaphysical infinity pertains to lack of limitation of kind, whereas physical infinity pertains to lack of limitation of magnitude. (See also.)

My demonstration that there can exist no entity that is without limitation in its kind, no entity whose kinds are not to the exclusion of other kinds, is given in Part A of the “Existence-Is-Identity Axioms” presentation at SOLO. My demonstration that no action-bearing entity is without limitation in the kinds of action it bears, no action-bearing entity whose kinds of actions borne are not to the exclusion of other kinds of actions borne, is given in Part B of that presentation. I have yet to craft that sort of demonstration for the case in which the existent is an attribute-bearing entity and the identity is a limitation on kinds of attributes. This third (and last) has been much discussed in the history of philosophy, including right across the twentieth century to Rand’s 1957 and beyond. I have looked forward to formulating and demonstrating axiom(s ) in this third category for a long time now. It will come around.

If you have objections to specific steps in the two demonstrations I have composed so far in the “Existence-Is-Identity Axioms” presentation, please do let us know over in that thread. I would be delighted.

I may be diving in over my head here....

jeffrey smith's picture

These ways are part of an account of how it can be meaningfully said that all that exists is not metaphysically infinite.

First of all, I'm not sure what you mean by metaphysically infinite. As best as I can understand it, your argument is that an entity must be definable and therefore finite. But does metaphysically infinite equal physically infinite? If it is, then if the number of entities existing in toto is infinite, then the universe is not a single entity (since otherwise the universe would be infinite and therefore not definable). If the number of entities existing in toto is not infinite, but merely not measurable by (current) human capacities, then your conundrum remains unanswered.

On the other hand, the universe might be defined on the pattern of mathematics. A line is a certain set of points which meet certain conditions but are infinite in number; a plane is a certain set of lines which meet certain conditions but are infinite in number; the set of integers is a set of numbers which meet certain conditions but are infinite in number; etc. The universe is the set of all entities which meet your conditions allowing them to be called entities (so we can always say whether or not the individual entity is actually an entity), but the number of such entities is infinite. In such a case, what exactly do you mean by metaphysically infinite?

[Mindy: I think I understand the point you're questioning: to define something means to place a limit or a bound on it, to say that this is this and not that; and since infinity is by definition* the state of being without limit or bound, something that is infinite can not be defined.]

*By defining infinity, I've just placed a limit on the state of being without limit. Have I just committed a paradox?


Ptgymatic's picture

...right at the beginning. How do you argue that exclusionary identity entails finitude?


Metaphysically Finite

Stephen Boydstun's picture

Rand denied the reality of infinity in the metaphysical sense. “Infinity in the metaphysical sense, as something existing in reality . . . . means something without identity, something not limited by anything, not definable” (ITOE 148; see further A, B).

One way in which it is rightly said that every existent is finite is by way of saying that every entity, action, or attribute has an exclusionary identity. An existent is this way rather than that way. One of the things I have demonstrated so far in the study Existence-Is-Identity Axioms is: “All entities are of some exclusive kinds . . . and this postulate must be accepted on pain of self-contradiction.”

For existence as a whole, for all that exists, it would seem that only the nonexistent is excluded. The nonexistent has no ways it is as opposed to other ways (cf.). To exclude only the nonexistent is to exclude nothing at all.

Are there real ways in which all that exists has exclusionary identity? All that exists is every thing that exists. Every thing that exists is an entity; an action of entities, where action subsumes events, motion, statics, kinetics, kinematics, dynamics (including thermodynamics), locomotion and any other activities of living things or of their artifacts; or an attribute of entities, where attribute subsumes properties and relations. Actions and attributes are not exclusive categories; an occasion of locomotion is not only an occasion of action, but an occasion of properties such as strength and relationships such as weight. But the category entity is exclusive the category action and the category attribute. That is not to say there can be entities that have no actions or attributes (note C, D). Rather it is to say that actions and attributes are always of entities; whereas entities have actions and attributes, entities are not of actions or of attributes. Every thing that exists is either an entity or not. If not an entity, then it is an action or attribute.

All that exists includes all entities and all actions and attributes. All that exists is not metaphysically infinite. Therefore, it is delimited by being one way rather than another. One of those ways is that every existent is either an entity, else is an action or attribute; rather than not being either an entity, else an action or attribute. Another of those ways is that every entity in existence has actions and attributes rather than being of actions and attributes.

These ways are part of an account of how it can be meaningfully said that all that exists is not metaphysically infinite. It remains, however, that I have no maneuver from the thesis that all that exits is not metaphysically infinite to the thesis that all that exists is an entity. (Furthermore, E, F)


Landon Erp's picture

As a person who has interests that tend to occupy a fairly small niche myself I have to agree with your sentiment.


Never mistake contempt for compassion, or power lust for ambition.

Super Hero Babylon


gregster's picture

My apologies if that was offensive Stephen.

There is not much sense in this thread or perhaps it goes over my head.


Stephen Boydstun's picture


I’ve been around the sun 60 times now. There are many different kinds of worthwhile interests and types of good lives.

I’ve never said anything unkind to you or to anyone else here at SOLO. People here have various interests and levels of education. That can be a harmonious thing, even a thriving thing, if we work it right.


Mindy and Stephen

gregster's picture

A marriage made in heaven. I haven't read as much absolute bullshit as you two in your perverse flirtations.

Get a life?

Measureable Attributes

Stephen Boydstun's picture


Thank you for the comments.

Rand and I do not contend that attributes are “nothing more than measurements.” We do propose that all attributes stand in magnitude relations, which is to say, in potential measurement relations. That does not reduce attributes to nothing but measurements nor to nothing but susceptibility to measurement. Heat, for example, is a measureable attribute, but it is not the measurability of heat that gives it its causal powers. Given its causal powers, we expect it is measurable.*

Rand and I diverge (note 3) concerning the epistemological character of the idea that “all concretes, whether physical or mental, have measureable relations to other concretes (ITOE 7–8, 29–33, 39; App. 139–40, 189, 199–200, 277–79). Every concrete thing—whether an entity, attribute, relation, event, motion, locomotion, action, or activity of consciousness—is measurable (ITOE 7, 11–17, 25, 29–33; App. 184–87, 223–25)” (fourth paragraph). Still, like Rand, I take the idea for true.

My work on a measurement analysis of concepts is not a theory of concept formation. Rand’s theory about how concepts can be formed by a process of measurement omission implies that the resulting concepts are analyzable in terms of measurements with specific values replaced by variables. However far that analyzability holds, that far or less the measurement-omission formation process might hold. The fact that a concept can be analyzed in terms of measurable characteristics of the items falling under the concept does not show that the concept was first formed by a process of measurement omissions. Broad philosophic accounts of the formation process need to be informed by developmental psychology.**

In her measurement-omission account of the genesis of concepts, Rand writes that the child is “aware of attributes while forming his first concepts, but he is aware of them perceptually, not conceptually. It is only after he has grasped a number of concepts of entities that he can advance to the stage of abstracting attributes from entities and forming separate concepts of attributes” (ITOE 15). This much seems to square with findings of current developmental psychology.

It is an additional step to propose that attributes or dimensions are measurable ones. If there are particular attributes or dimensions that are not measureable, concepts of those particular dimensions cannot have been formed by a process of measurement omission (unless one holds to a nominalist theory of measurement and a nominalist theory of concepts, which Rand and I do not). (See also the subsection “Analytic Constraint” in G.)

Concerning your paragraph on the analytic-synthetic distinction and the import of a measurement analysis of concepts for it, I should say that that work is not work anyone has yet carried out. In my own approach to the work, I don’t presuppose that the distinction is valid or invalid. For all I know, some valid cousin (a, b) of the distinction may emerge as I execute the “with-measurement” program.

Concerning the idea that consciousness is sui generis in the sense of standing in a total dualism with matter and energy, or more specifically, in a total dualism with brain processes and the material world perceived by consciousness: I say No, and No for Rand on balance.


*The attribute that is heat will always come with particular magnitudes on its particular occasions. Magnitudes of attributes on particular occasions are not separable from those attributes and are factors of the causal power. Magnitudes are susceptible to measurement, but it is not that susceptibility that gives an amount of heat supplied the ability to boil water.

**As in Early Development and "Capturing Concepts" and "Pursuing Similarity" and

David Kelley (1984). “A Theory of Abstraction” Cognition and Brain Theory 7:329–57.

David Kelley and Janet Krueger (1984). “The Psychology of Abstraction” Journal for the Theory of Social Behavior 14(1): 43–67.

On concepts of action and the acquisition of verbs:

Action Meets Verb (OUP 2006), Kathy Hirsh-Pasek and Roberta Michnick Golinkoff, editors.

"Dimension" is a fait accompli

Ptgymatic's picture

If you set out to "analyze" things in terms of their "dimensions," you will always abstract measurable attributes.

The issue, for concept-formation, is not whether all attributes are measurable, but whether they are nothing more than measurements. Your definition says measurement is an association of numbers/vectors, etc. to a class's attributes. This implies the existence of a class. The formation of that class cannot involve measurement, explicit or implicit.

Perhaps you would say that we form such a class, a "pre-measurement class," through a recognition of similar things? But doesn't that capacity then negate the need for, and usurp the role of measurement-omission in concept-formation?

This is much further down the line, but I think it is tale-tell: Whatever is omitted in forming a concept, measurements or qualia, can then be predicated of some instance of that concept. That means we can predicate precisely what is omitted from a concept. Doesn't that fail to accomplish the A/S task, that is, doesn't that prove the omitted-measurement formulation fails to accomplish a dissolution of the A/S Dichotomy? 

Also, isn't "consciousness" supposed to be sui generis?

I whole-heartedly agree that genus-species organization of knowledge is key. Measurement may be exemplary of that organization, and seductive as a result, but measurement is but one sort of genus-species organization. Measurement is secondary/derivative, and limited in its capacity to yield "faithful representations" of all that exists.

= Mindy

Measurable Dimensions

Stephen Boydstun's picture


In showing that a concept such as shape or hardness can be analyzed in terms of the suspension of particular measurement values within a range along certain dimensions, one necessarily is also exhibiting those dimensions and their measurability. To maintain that there are measurable dimensions in terms of which the concept be cast is to maintain (on Rand's view and mine) that those dimensions are with magnitude relations that we can ascertain through measurement.

You mentioned the definition of measurement I endorsed in another note. Following Foundations of Measurement, I take measurement to be the association of numbers (or other mathematical entities, such as vectors) to the attributes of some class of object or events “in such a way that the properties of the attribute are faithfully represented as numerical properties.”

That definition is fairly broad. One class of measurements it would include is the one known as absolute. This is the measurement type that includes counting, compiling histograms, and discerning probabilities. It is no great consequence whether one calls counting a form of measurement or disqualifies it by adopting a more narrow definition of measurement. It will remain that in counting one is attaching numbers, in a particular way, to the numerosities of collections. Counting is an abstract characterization appropriate to a certain sort of magnitude relation in the world, a characterization distinct from (lower structure) the assignment of numbers to football jerseys and from (higher structure) the type of measurement known as ordinal (e.g. scratch hardness).

Questions of whether perceptual processes are rightly characterized as (mostly nonconscious) measurement processes and whether concepts (say, all the ones extra to the concepts in formal logic and set theory themselves) can be analyzed in terms of the suspension of particular measurement values, at ordinal level or higher, along measurable dimensions are questions of interest in their own right; of interest for their join with scientific conceptualizations; and of interest for any light they shed on traditional philosophical problems. Naturally, people can perceive and conceive without knowing that a measurement characterization of these cognitions is possible.

It is a marvelous thing that when we seek a genus-species definition for some concept, we can find one. Marvelous, too, beyond that, if the concept and its definition can be given a measurement analysis.

Further: "Universals and Measurement"

In Objectivity SUBJECT INDEX are these related entries:

Brain, Computational / Concepts and Sets / Learning of Dimensions / Measurement; Implicit; Omission of; in Perception; and Similarity / Neurons and Artificial Neural Networks / Numbers; and Counting; Learning of / Perception; Categorical; of Numerosity; of Sets; of Shape; of Similarity / Quality and Quantity / Quantity and Dimensions / Relations; Membership; Part-Whole / Similarity; and Part-Whole Relation; and Proximity / Unity of a Concept

"Measurable" versus "measurement"

Ptgymatic's picture

I have long been troubled by the apparent equivocation in some Objectivist material/lectures, etc. between these two concepts. Claims that what is omitted in a concept were "mere measurements" seem to turn into proofs that what was omitted was measurable.

Your analyses go beyond my mathematical comfort zone. If the answer to this confusion lies in them, though, I'd like to know.

Second: The definition of measurement that you endorse says that numbers are assigned to classes of objects or events. Doesn't requiring the assignees to already be classes defeat the epistemological relevance of measurement-omission?

= Mindy

Below Entity

Stephen Boydstun's picture

Every concrete stands in measurement relations—at least up to ordinal scale—with other concretes (M, MP). If a stands in certain ordinal relations R with b, and b stands in certain ordinal relations R′ with c, then a stands in the composition of ordinal relations R′◦R with c (mathematical composition of morphisms). That does not mean there is necessarily some ordinal relation along a single dimension between a and c. But it means that a stands in at least piece-wise ordinal relations with c, and that yields a relation (R′◦R) in addition to the relation of conjunction.

Now, invoking mathematical induction (ordinal), and perhaps some petite propositions supplementing Rand’s thesis that all concretes stand in (at least ordinal) measurement relations to some other concretes, I might be able to demonstrate that every concrete stands in some piece-wise ordinal relations to every other concrete. That would show a unity to all that exists beyond conjunction.

I do not think that such a result would establish that the concrete existent that is all that exists is an entity, because I conjecture that entities are best conceived as entities only if standing in some measurement relations above ordinal (viz., interval and ratio and multidimensional spaces of these). So I reject the slide from existent to entity and the rationale I offered for it in the third paragraph of Good Points.



Frame for this Research

Six years ago, I composed the study “Universals and Measurement” which appeared in The Journal of Ayn Rand Studies 5(2):271–305. In that work, one of the ways in which I characterized the distinctive magnitude structure for metaphysics implied by Rand’s measurement-omission analysis of concepts was according to mathematical category. I reached this result:

“The magnitude structure entailed by Rand’s theory has the algebraic character of a lattice, which has more structure than a partially ordered set (or a directed set) and less than a group (or a semi-group). In terms of the mathematical categories, Rand’s magnitude structure for metaphysics is a hybrid of two: the algebraic category of a lattice and the topological category of a uniformity. Rand’s structure belongs to the hybrid we should designate a uniform topological lattice” (280, AOM).

What qualifies as the mathematical structure that is called a category? A category consists of three things: (i) a class of elements, which are called objects (ii) a set of morphisms from any one of those objects to another of them, (iii) a rule for composing a new morphism from any two morphisms, where this composition is associative. Included in the set of morphisms under (ii), there must be an identity morphism. There are certain further notions that are available in every category, such as the notions of monomorphism, epimorphism, isomorphism, and subobjects.

To specify a category, we must specify the objects, their morphisms, and the compositions of morphisms; and we must show that all the requirements of a category are met. Here are some categories. In the category of sets, the objects are sets, the morphisms are mappings from one set to another, the monomorphisms are one-to-one mappings, the epimorphisms are onto mappings, and so forth. In the category of vector spaces, the objects are vector spaces, the morphisms are linear mappings from one vector space to another, and so forth.

Examples of algebraic categories: sets, partially ordered sets, lattices, Boolean algebras, semigroups, groups, abelian groups, rings, fields, vector spaces, associative algebras, Lie algebras. Examples of topological categories: topological spaces, Hausdorff topological spaces, and uniform spaces. (Topological spaces have a notion of “points sufficiently close; neighborhood of point.” Uniform spaces have in addition a notion of “comparatively close; comparative size of neighborhoods.”)  Examples of hybrid categories: topological groups and topological vector spaces.

The category I have targeted as reflecting the metaphysical magnitude structure implied by Rand’s measurement-omission form of concepts is the hybrid category resulting from combination of the algebraic category of lattices and the topological category of uniform spaces. In this category, the objects are lattices, and the morphisms are uniformly continuous lattice homomorphisms. The category of lattices (and uniform lattices) includes the binary operations of meet and join as well as morphisms, called lattice homomorphisms. These map one lattice to another, are order-preserving, and satisfy category requirements.

I noted in Ocean of Concretes that “there remains the question of what various levels of unified wholeness can be identified for all that exists beyond its unity as a concrete existent and its thoroughgoing contrast with a singular nothing.” Demonstrating that every concrete stands in some piece-wise ordinal relations to every other concrete would be a characterization, in terms of minimal measurement-affordance, of the right level of unified wholeness that can be rounded (without physics) from the magnitude structure implied by Rand’s measurement-omission analysis of concepts. A companion characterization of that unified wholeness in terms of the mathematical category of the magnitude structure implied by Rand’s theory also awaits discovery.

Conjunctive Correspondence

Stephen Boydstun's picture

In addition to the references I listed in the note Easy and Not, I should have mentioned the following one:

Newman, Andrew. 2002. The Correspondence Theory of Truth. Cambridge.

See especially Chapter 8 "The Correspondence Theory and Complex Propositions" with cross hair on 8.3 "Conjunction as a Function."


Complementary to the work of Newman, is that of Eric Wefald in Truth and Knowledge (TK), which appeared in 1996. In my review of this book, a review titled “Mapping Reality,” I mentioned Wefald’s view of knowledge by direct acquaintance:

“In acquaintance we know not only objects, but relations and structures. That is to say, in acquaintance we can know facts. Wefald interprets Wittgenstein’s dictum ‘The world is everything that is the case’ (T 1) to be asserting not ‘that the world is the set of all facts, but rather is the one total fact of which all other facts are substructures’ (TK 9). A structure consists of objects and relations. . . . Wefald would not identify a relation fundamentally with its occasions or its extension, but with its intension. . . . Intensions are not intentions. Possibilities, relations, and intensions are in the world without mind (contrary to Leibniz).” (pp. 229-30)

The entire review is available at Objectivity Archive. Click on V2N4. The review is on pages 227-33.

Finite Number of Dimensions

Stephen Boydstun's picture

At her epistemology seminar (c. 1970), responding to a question from Harry Binswanger (A), Rand remarked that the concept infinity, taken as existing in reality, “means something without identity, something not limited by anything, not definable” (ITOE App., 149)

Within the text of her Introduction to Objectivist Epistemology (1966), Rand writes: “It is only after the child has grasped a number of entities that he can advance to the stage of abstracting attributes from entities and forming separate concepts of attributes” (15). I assembled developmental psychology research supporting this thesis in my 1990 essay “Capturing Concepts” which can be read in V1N1 at Objectivity Archive.

“The fundamental question of how particular men learn concepts and the question of what concepts are, are two different issues. . . .” But as an example of a plausible route, Rand shows how concepts of various objects—such as table, chair, bed, or cabinet—could be integrated, in accord with her measurement analysis of concepts, into the wider concept of furniture. The particular kinds of furniture stand as units within the wider scope of the concept furniture. “The distinguishing characteristics of these units are specified categories of measurement of shape, such as ‘a flat, level surface and support(s)’ in the case of tables” (21, italics added). (See further an exchange between Binswanger and Rand on pp. 146–47.)

The “categories of measurement” refers here not to the various kinds of measurement we have—such as ordinal, hyperordinal, interval, and ratio—rather it refers here to dimensions, such as the dimensions of shape, along which measurements can be made. (See also the exchange between Leonard Peikoff [E] and Rand on pp. 198–200.)

Would it be possible for some existent(Drunk to have an infinite number of dimensions? The question I here pose is not whether it is possible for a mathematical entity, such as a function, to have an infinite number of dimensions. The question here posed is whether from metaphysics and epistemology one should rule out the possibility of a concrete existent having an infinite number of dimensions.

In our ordinary and scientific experience, we have no indication of there being such a thing. Our hard-won identification of the dimensions of things indicates that for concrete existents there are only a finite number of dimensions had by them. The clock beside me has only a finite number of dimensions even if I don’t know all of them. The number of dimensions whose measure is being marked by the clock is also finite, for it is exactly a single dimension (which also happens to have invariant magnitude, presumably infinitely divisible, in all inertial frames).

Is our knowledge that the number of dimensions of any concrete existent, including the totality that is all that exists, a finite number (indeed, some very large, but particular, positive integer) something we can demonstrate in a proof? If we suppose that either a leaf or a stone has an infinite number of dimensions beyond the ones we know, can it be proven that the identities of leaf and stone would, contrary to fact, not be distinct? So far, I doubt that such a proof can be constructed.

(In the Part 1 of Spinoza’s Ethics [P1–P23], he constructs arguments to the contrary result that the number of dimensions of widest existence must be infinite. I leave the assessment [presumably negative] of Spinoza’s labor to thine own sagacity, gentle reader. Do not neglect his definitions.)


Casey's picture

Are you aware of the Objectivist position on the primacy of existence?

If you haven't taken the extended courses on these issues by Peikoff I can understand that there could be misunderstandings about these issues.

The courses on these issues are a revelation one can not, on the other hand, ever turn back the clock on in terms of understanding sense perception and logic's lock-step relationship with truth, and the difference between the metaphysical and the man-made, the perceptual and the conceptual. I really don't regard anyone as being an objectivist even lower case if they haven't taken these courses. They are essential. The rest is just "I read her novel and loved it." Which is great and everything, but it's not the fullness of her philosophy which is set down and forth by Peikoff in his courses. Anyone interested in this must take these courses. You'll be blown further away than you ever thought you were by the books. Critics, especially, must take these courses, or have no credibility with me.


Ocean of Concretes

Stephen Boydstun's picture

So all the concrete existents in the room, together, constitute a concrete existent. All of them together in the room during the first second of the last hour constituted a single concrete existent. They constitute a concrete existent among all the concrete existents of the past (right up to and including the initial singularity [an existent], if you want to incorporate the possibility posed by classical general relativity). Then they with all the concretes in all the compartments of space and past time constitute an existent that is all the concrete existents of the past.

All the concrete existents of the past could be an infinite number, yet constitute a single existent. Forget not the divisibility-candidates of one second of duration, an existent. And forget not that all the concrete existents of the present together constitute a concrete existent.

Not an entity, by the reckoning this far, but a concrete existent. Constituent entities of a concrete existent have not been shown to necessarily combine into a single entity. Whether the concrete existent that is all of present and past existence is necessarily an entity remains to be argued from “existence exists” and “existence is identity.”

If we restrict sufficiently the class of existents we want to designate by the term entity, we can say up front that the totality "all that exists" is not an entity. From page 1016 of Atlas, one gets the impression that Rand would call by entity the following things: leaf, stone, man, table, cell, molecule, atom, and the universe. That would be a natural way. But whether one would call all these things entities or restrict that designation so as to exclude the universe, there remains the question of what various levels of unified wholeness can be identified for all that exists beyond its unity as a concrete existent and its thoroughgoing contrast with a singular nothing.

Concrete Existents

Stephen Boydstun's picture

Rand held that fundamentally, “that which exists is concrete” (P-E of Art 23). I imagine Ross, Casey, and Jon hold this view as well. I hold it, you bet.                   

One can hold that fundamentally existents are concrete without also holding any and all of them to be perceivable directly. Some concretes are perceivable directly, some are not. Some concretes directly perceivable are the foundations through which we know what we know. But there are other concretes, not directly perceivable, that we come to know by way of perceivable concretes.

Concrete existence is more than the concretes we directly perceive or could directly perceive. Fundamentally, all the existents here in my library are concrete particulars. Whether they are concrete entities, attributes, actions, or relationships, they are concrete particulars. These are the fundamental existents in the room (fundamental to any abstractions concerning them). All of those concretes are in the room concretely, even if many are not directly perceivable and even if many are not yet known specifically by us at all. And we know that. A proof demonstrating the truth of that knowledge claim might be helpful in discovering proof(Drunk that there is an existent, fundamentally concrete, that is the totality of all concrete existents.

Meanwhile, I should make explicit the following thesis. I hold that this concrete particular existent and that concrete particular existent are a concrete particular: just this one and that one, conjoined in reference as an existent because coexistent. Coexistence of concretes is a concrete relation, whatever further concrete relations may exist between them and whatever be the abstract relations (sets or concepts) in which we might place them. The coexistence of concrete particulars is a concrete circumstance obtaining without us. Rand and I are evidently together on this pertinent point (ITOE 37, 197).


Ross Elliot's picture

"The collection of all that exists is a determinate existent whether or not it is finite."

But it's only conceptual, in that it relates to, or embodies, lesser, directly perceivable things. The universe as a whole--your universal existent--is not perceivable on its own. It's only an idea, and as such we use it for convenience, for the purposes of discussion and other things. As such it can't be finite; it's an abstraction and therefore can include infinite concretes. Surely.

Determinate v. Finite

Stephen Boydstun's picture

The first statement in my previous post was: “Anything more than existence is nonexistent.” In view of Jon’s concerns, I should stress that by my use of more in that statement, I am not prejudging whether the total number of existents is finite or infinite.

There are things that do not exist (all of them the same nothing, really), whether or not the number of existents is finite. The collection of all that exists is a determinate existent whether or not it is finite.

Sometimes the term finite is used simply to mean determinate. That is fine, but as Jon has pointed out, it is incorrect to suppose that finite in that sense entails finite in the sense that the number of one’s fingers is finite.

Beside me is a clock. Its hands tick off the seconds. The ticks are existents, specifically, events. The duration they mark is an existent. To say that this existent is determinate does not prejudice whether the duration of one second consists of: (i) a large finite number (say 10exp25) of indivisible durations, (ii) infinitely many divisible durations, where the infinity coincides with the rational numbers, or (iii) (as we suppose in our physics today) infinitely many divisible durations, where the infinity coincides with the real numbers (rationals and irrationals).

Now, a finer point. I stated in the previous post that everything that exists is bounded by a single nothing. Duration is no exception. Duration is only what it is and not anything else. Duration that is what it is not does not exist. Duration is bounded by that same metaphysical zero. Here is the finer point: Other boundaries of duration not nothing are existents. The boundaries of a particular duration of one second are existents. True, they cannot exist without durations, nevertheless, they exist.

Non-Existence is Singular

Stephen Boydstun's picture

Anything more than existence is nonexistent. Every nonexistent is the same single nothing. The fact that my pencil is a hexagonal prism, a solid material, and contains graphite means that the instrument with which I write is not round, not liquid, and not free of graphite. The nonexistent that is the nonexistent round pencil in my hand is, in reality, not different than the nonexistent liquid pencil in my hand or the nonexistent graphite-less pencil in my hand. Moreover, the never-existing pencils like mine (hexagonal, solid phase, and containing graphite) are the same single nothing. The nonexistent does not progress from the singular to a some more than one nor to an all more than one.

Existence—all that exists—is bounded by a single nothing. In this way, whatever other ways there may be, all that exists constitutes a single whole.

If this much is a sound philosophical argument, what other ways in which all that exists is a single unified whole can be proven by such philosophical demonstrations? I drafted the argument above just this morning, after reading Jon’s latest post, so perhaps my present argument will not stand up even for such a minimal degree of unified wholeness. Criticisms welcome.

Can't know it philosophically

Jon Letendre's picture


You say you are interested in a philosophical (metaphysical,) as opposed to scientific proof of the existence of a single existent that collects and includes all existents. As you know, I hold that no such proof is possible.

The best attempt I have seen goes like this: We know that some things exist, since we perceive entities, their relationships, etc. Further, we know that every entity, relationship among entities, etc. we have ever perceived is finite. So we form the abstraction “the universe” as the collection of all that exists. It’s like a very big basket into which we mentally place every existent. Once everything is inside the basket, and nothing left out, we have a single, very big collection. Its constituents are finite, so the collection is, too. It’s the biggest of big entities. It cannot have any relationship to anything else, because there is nothing else—so nothing, not even relationships, is left out. Like every other entity, it is finite. Therefore, the universe is finite, and, qua collection, it is a single existent that includes all existents.

The problem with the above is its commission of Primacy of Consciousness that Casey refers to (imputing it to the wrong side of the argument.) The problem is in thinking that if the “very big basket” can be imagined as leaving out nothing, then it is true that there is such a collection which leaves out nothing. In other words, the above “proof” ASSUMES that the universe is finite. But what if there is no limit to the entities in existence? Then you could never finish putting things into the basket, because there would always be something else to put in. And if you can’t finish filling the basket, then you can’t say there is an existent (the basket) that includes all existents.

I think we can still speak of “the universe” and be understood. It’s just that we can’t say it is necessarily finite.


Casey's picture

You wrote, "I think we can have that much knowledge of the universe before we get the specific dimensions, quantities, structures, and activities of the universe from our exquisite modern science."

The concept of universe is not "knowledge." It's a bucket for putting knowledge into. The concept of "universe" philosophically speaking does not tell us anything about the universe -- it merely provides a folder in which everything can be filed. It's the equivalent of a library that excludes nothing and includes everything. It's not physics, it's philosophy.

Easy and Not

Stephen Boydstun's picture

Proof of the “exactly one” clause appears easy. I composed this one in a few minutes:

If there is at least one totality existent that includes all existents, there may be one such totality or more than one such totality. If there is more than one, then some existent in one is not in some other. Otherwise, those two totality existents would be one, not two. But all existents must be included in any one totality that includes all existents. Therefore, if there is at least one totality existent that includes all existents, there is only one such totality.

Proof of the antecedent in the preceding proof seems to be more difficult. That would be proof that there is one totality existent that includes all existents, rather than no such totality.

The following books contain work pertaining to the present challenge. The considerable dividends of having the thesis “there is an existent that is the totality of all existents” are set out by David Armstrong (1997, 2004).


Armstrong, David. 1997. A World of States of Affairs (Chap. 13). Cambridge.

--------. 2004. Truth and Truthmakers (§§5.2, 6.3). Cambridge.

van Fraassen, Bas. 2002. The Empirical Stance (Chap. 1 & App. A). Yale.

Lewis, David. 1986. On the Plurality of Worlds. Blackwell.

--------. 1991. Parts of Classes. Blackwell.

Totality Referent

Stephen Boydstun's picture

Ross and Casey:

From standard modern physics, we know that the universe has a definite total mass-energy and a definite total angular momentum (which we think is zero by observations thus far) and that these two quantities remain constant though time. The parts of the universe are tied together throughout the whole by gravitational attraction and by conservation of angular momentum.

Some might say that from philosophy, without science, we can only speak of “all existents” and leave open whether all existents taken together compose a whole, an existing totality. Then let science investigate and find, as it has: “It turns out that all existents are a definite total, and they have such-and-such specific characteristics totaling to certain definite values which we are tracking down.”

I think philosophy can go a little further even before the light from modern science. Our concept of “all existents, however many they may be and whichever characteristics they may share” is a concept targeting all of existence. It is not only a concept, but has as referent: all that exists. I think we can have that much knowledge of the universe before we get the specific dimensions, quantities, structures, and activities of the universe from our exquisite modern science.

Whatever the stage of scientific knowledge, I think we can know that “there is an existent, exactly one, that is the totality of all existents.” In search of proofs.

It's a concept with measurements omitted

Casey's picture

The "universe" is a concept, not an "existent." It is all existents however many that may be. There is nothing in reality that specifically ties them together into an "entity" any more than the words "all planets" or "all apples" apply to some kind of unit in reality. The universe refers to everything which ever did, does or ever will exist. Whatever that might comprise.

Let's not start confusing the metaphysical with the manmade!


Ross Elliot's picture

"Can we deny that “there is an existent, exactly one, that is the totality of all existents” and show a contradiction with “existence exists” or “existence is identity”?"

Well, we can't deny that we have a *concept* for all existents, which we call existence (the universe). But I'm just restating my original reply. It's just a collective noun, isn't it? Just like a herd of cattle is comprised of individual animals. The herd can only be held to exist as long as its constituents (cows) do. If existence is an existent in and of itself, then it wouldn't depend on its constituent existents which, like a herd, it obviously does. Existence without anything actually existing is a contradiction.

When I read your original post--and this may be testament to the power of art--I immediately thought of the final scene in the original Men in Black. As if reversing a film, we pull back from the Earth, past the moon, past the outer planets; our solar system recedes to show the Milky Way, which itself shrinks to reveal millions of such galaxies, and finally our universe is revealed... inside a *marble*, one of many little marbles being played with by an alien, whose hand comes down into frame and scoops the marbles into a cloth bag.

Of course, that stunning sequence doesn't stop us contemplating where the retrogression stops. Smiling

Good Points

Stephen Boydstun's picture

Ross and Jon,

Yes, our concept existence is our concept of all existents taken together. Rand once remarked to Allan Gotthelf: “The concept existence, at least the way I use it, is in a certain way close to the concept universe—all that which exists” (ITOE app. 241). The referent of this concept of existence includes entities and their attributes, actions, and relationships. As you will recall, Rand used entity not as an equivalent for existent, but as the primary existents, the existents in which attributes, actions, and relationships have their existence. All of these are existents, and they can all obtain concretely, not only abstractly.

Philosophers often use the term entity to mean any item whatever. That is one customary usage and perfectly alright. 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.

I spoke of “an existent that is a whole and not part of some yet larger entity.” That shift from existent to entity is sprung by the phrase “whole and not part of some yet larger.” I am hasty in calling a largest existent comprising all existents an entity. Staying with Rand’s more restrictive sense of entity, I should first speak of “an existent that is a whole and not part of some yet larger existent.” Then I should justify the transition from existent to entity as the last word in that formula. After all, attributes, actions, and relationships can also stand in part-whole relations. But since they stand in part-whole relations inhering always in entities, allow my haste here from existent to entity.

Jon, I distinguish between a collection and a set in the logical/mathematical sense of set. The lamp, the inclined editor’s desk, the pen in my hand, and the sheet of paper on which I write are a collection. They exhibit the finite set that is the number four. But they are a collection, the concrete collection they compose, quite apart from our abstract set-theoretic comprehension of them. (Thanks to modern science, we may say further that this collection has the combined rest mass it has now, available to our measurement if we want to know it.) To be sure, we use set in an everyday way too, by which we simply mean a collection. Perhaps that is all you meant by the term.

(It is only with the logical/mathematical rendition of set that we encounter the set-theoretic paradoxes, which were exiled by the modern axioms.)

The abstraction “all of the apples in the bushel basket” is truly an abstraction. But things arrived at by abstraction can sometimes also be concretes existing without the abstraction. We concur in this: The thesis that all existents taken together do in fact exist as a collection does not entail that their combined mass-energy or their collective spatial extent is finite. That is a good reason for Rand stopping short of identifying “all that which exists” tout court with “the universe”. Perhaps it is best to reserve universe for “all that exists” or “all of existence” only when these are more specifically characterized and informed by common experience and science.

I do think, as Ross writes, that “to claim that existence [all of existence, as a whole] itself was an existent . . . you’d be implying that it was only one of many such [subsidiary] existents.” (Please correct me if my interpolations change what you meant to say, Ross.) That’s neat. I am hoping to unearth the nature of that implication. I hope we can further explicate the implication on which our implying rests in this case. Can we exhibit the implication in a proof, a metaphysical proof? Can we deny that “there is an existent, exactly one, that is the totality of all existents” and show a contradiction with “existence exists” or “existence is identity”?

Ross,I agree with you. I

Jon Letendre's picture


I agree with you. I have a problem with calling the universe an entity. Rather, it is a SET of entities. A bushel of apples is not an apple. “All apples” is an abstraction, not an entity, just as “all entities” (the universe) is not an entity.

In my experience through various discussions over the logical possibility of an infinitely extensive universe, the side arguing for logically necessary finitude trots this out so they can employ the Law of Identity: Identity requires that every entity have a specific, delineated, finite nature— the universe is an entity—therefore, the universe is finite.

Of course, every particular entity has a specific, delineated, finite nature. The question is: how many entities exist? Can we know, a priori, that logic requires there be a limit? They avoid the issue by defining the set as itself an entity.


Ross Elliot's picture

Existence is a concept, subsumed within which are the actual existents of the universe.

I'd have thought that to claim that existence itself was an existent, that you'd be implying that it was only one of many such existents.

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