The Meaning of “Necessary” Versus “Contingent” Truth

Billiard balls ready to be brokenThere is a long history in philosophy of distinguishing between truths that are “necessary” and truths that are “contingent.”

A necessary truth is a true statement whose negation must imply a contradiction in reality, such that the negation would be impossible.

So, if “One plus one equals two,” is a necessary truth, then the statement “One plus one does not equal two” will imply a contradiction. Given the meanings of “one” and “two,” we can immediately see that the addition of two “ones” (units) always does yield “two,” yet the statement “One plus one does not equal two,” contradicts this. It’s incomprehensible that one plus one should ever add to anything but two. So “One plus one equals two,” is commonly held to be a necessary truth, with its negation being impossible.

A contingent truth is a true statement whose negation does not imply a contradiction in reality, such that the negation could have been the case.

So, if “John married Jessica last Sunday,” is a contingent truth, then the statement “John did not marry Jessica last Sunday,” could have been true, without implying a contradiction in reality. Since John could have chosen not to marry Jessica, or to have married her on a different day, we can see that this is indeed a contingent truth.

The Objectivist View on the Necessary/Contingent Distinction

Objectivism-The Philosophy of Ayn RandCausality (the Law of Cause and Effect) is the Law of Identity applied to action. This means that an entity’s actions follow from its nature. That is, the nature of the entity (its attributes, properties, etc.) causes the action it will take in any given situation. In any given context, there is only one action open to it: the one in accordance with its nature. Any other action would contradict its nature.

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Ontology and The Problem of Universals: An Objectivist Comments

shiny_red_applesAyn Rand is sometimes accused of misunderstanding the “Problem of Universals,” that philosophers such as Plato, Aristotle, Boethius and William of Ockham have dealt with for millennia.

The Problem of Universals consists of the question: To what do people refer when we use terms that can be applied to different particular things? For example the term “man” is applied not just to one entity, but to many entities that are each called a “man.” Another example is “spherical.” Many different things can be said to be “spherical.” An answer to the Problem of Universals will explain how this use of single terms for multiple different objects works.

In Introduction to Objectivist Epistemology, (ITOE) Rand claims to have solved the ancient Problem of Universals. She describes in detail the process by which man forms generally applicable concepts from his perceptions of particulars in reality. Critics sometimes charge that Rand is giving us an epistemological theory when a solution to the Problem of Universals calls for an ontological theory. (Ontology, properly conceived, is the branch of metaphysics that deals with the most fundamental classification of existents; it is the study of “what there is,” metaphysically.)

But considering the Problem of Universals purely ontological, and thus considering Rand’s theory of concept formation irrelevant to it, improperly privileges variants of “Realism” (about universals) by treating the rejection of such abstract objects as sufficient to define a single theory (variously referred to as “Nominalism” or “Anti-Realism.”) The rejection of universals in external reality does not specify a positive theory of what universals are and how they are related to external reality. Much more explanation is required to do this, as evidenced by the various subcategories of Nominalism/Anti-Realism. In ITOE, Ayn Rand presents an alternative theory on the level of the variants of Anti-Realism in the Internet Encyclopedia of Philosophy. (i.e. Predicate Nominalism, Resemblance Nominalism, Trope Nominalism and Conceptualism.)

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Proceeding from Axioms in Objectivism – YouTube Edition

Well, it’s finally happened: The impoverished reasoning methods employed by academic philosophy have infected YouTube comments….Shocking, I know….

But, all kidding aside, when most academic philosophers (who aren’t deeply acquainted with Objectivist literature and lecture courses) read about Ayn Rand’s axioms, they tend to deride them as tautologies. They can’t possibly imagine how you could deduce a whole philosophical system from such tautologies. Well, they have something in common with my interlocutor (mirabileamavi) in the comments of a YouTube video. Hopefully, my concise answers to him (her?) should be clarifying:

Interlocutor: …How do you derive causation from tautologies?

Me: The “tautologies” you speak of are axioms. If something is truly an axiom, it is too fundamental to be conceptually analyzed, but is perceptually self-evident. You need only observe reality to see that it is true.

An entity is itself, therefore it acts as itself. This mode of action consistent with its nature is causality. See:­ms-of-objectivism.html

Int: i still dont understand how you can derive causation from tautologies.

‘john’, from that i can infer ‘john’ is ‘john’ but i can’t infer that ‘john is a fireman’ can i? the predicate ‘is a fireman’ is not contained in ‘john’. while ‘john’ is ‘john’ is necessarily true and tautological, ‘john is a fireman’ certainly is not. from a=a we cannot infer that a=b.

heres an example: ‘frank ramsey’, who is his father, what is his occupation? obvious all you can infer is that F.R. is F.R., nothing else.

Me: At the level of bare axioms, all we can say is that, because John is John, John must act as John. That’s it: causality is a corollary of identity. But to identify John as a fireman, we cannot simply deduce from the axiom. We must specifically observe firemen in order to form the concept “fireman.” We must then observe John and see that he fits the concept. (Intro. to Objectivist Epistemology) Once we have observed he is a fireman, causality tells us he can’t swim and lay eggs as a female squid.

Int: ‘is’ is not equivalent to ‘act’.

okie, look at this from another angle. since identity is universally necessary, 2 is 2 is also an identity statement. but what does it mean to say that 2 act as 2? or for that matter, john act as john? if not just ‘john is john’.

from john is john nothing else follows. not causality, not anything. let me ask you again, what casual anything can you deduce from ‘frank ramsey’. thats right, nothing.

Me: An entity’s identity includes its qualities and capacities for action/reaction. We can isolate and focus on them in our thinking, by abstraction, but they cannot be separated in concrete reality. Causality is a corollary of identity, not a separately deduced fact. As a corollary, it is simply another way of looking at the same fundamental fact: an entity is itself. It’s self-evident: look at reality.

2 is a quantitative abstraction. Whatever 2 entities you are focusing on will act as themselves.

Int: take our friend ‘fr’ as an example, obviously we can infer ‘fr’ is ‘fr’ via any standard of formal logic. but we can’t infer ‘fr’ is also p. why? because additional information is needed to establish the new inference.

to say something is corollary is to say that something follows from another. but how do you infer from ‘fr’ without the additional info. that ‘fr’ is also p? can i seriously validly infer that A, therefore B, C, D, X…?

i.e. how am i justified in seeing arsenic for the first time to infer that it can or cannot kill? surely none of its properties follows from my visual perception of it or the mere knowing of its name. yes we can know its effects/properties through observation, but thats an additional step, not something that merely follows from our acquaintance with it.

Me: For the last time, Objectivism doesn’t say you can infer any specific properties/actions of entities from “A=A.” To see that arsenic is deadly, you make specific observations of its effects. Once you have induced that arsenic is deadly, you know that once you have identified a specific sample as arsenic, it will be deadly when taken. Without causality, arsenic wouldn’t have to behave as arsenic, and there’s no way to know what will happen if you ingest it; it could make you live 1000 years.

So the basic point here is that, in Objectivism, proceeding from the axioms does not mean deduction, but induction. The truth of the axioms (including the validity of the senses) makes induction from observation possible (that is, generalization; including concept formation as a certain type of induction.)

The major model of system building in modern Western philosophy has been that of the rationalists, who deduce consequences from “a priori postulates,” “intuitive” starting points, or mathematical axioms. Thus, when confronted with a philosophic system like Objectivism that claims axioms, most contemporary philosophers simply assume that the axioms are intended as a deductive starting point. They then rightly observe that nothing can be deduced from the axioms alone, and claim that Objectivism is a failure, or is not “serious” philosophy.

This is what I was referring to by “the impoverished reasoning methods employed by academic philosophy”: Real induction, which is a method of generating principles, has been largely supplanted by probabilistic reasoning, which most contemporary philosophers call “induction.”

The details of how induction works in various fields of knowledge is an active area of research among Objectivist philosophers. But we have cases of induction and general guidelines for how to form valid inductions left by Ayn Rand, and explicated by Leonard Peikoff. I recommend Understanding Objectivism: A Guide to Learning Ayn Rand’s Philosophy and Objectivism Through Induction by Leonard Peikoff.

The video below is not directly relevant to the above, but is an excerpt from one of Rand’s essays that makes general points about philosophy, reason and emotions.

[Edited: 9-1-12]


Related Articles:

The Structure of Objectivism

The Axioms of Objectivism

The Axioms of Objectivism

Barred spiral galaxy in space. Represents science and philosophy.An axiom is a statement that provides the basic foundation for other knowledge. It is a statement that cannot be proved by reference to any more basic statements, because it provides the most basic conceptual foundation of all proofs. A genuine axiom must be self-evident, because a statement that cannot be proved in any manner, yet is not self-evident, is simply an arbitrary assertion. And arbitrary assertions don’t constitute knowledge, but are just groundless fantasies or imaginings.

The philosophy of Objectivism has three axioms that it holds are implicit in any claim to knowledge of any sort. They are as follows:

“Existence exists.”

“Consciousness perceives existence.”

“An existent is itself.” (Often referred to as “A is A,” or the Law of Identity.)

These three metaphysical axioms form the fundamental base of Objectivism. A corollary of the Law of Identity is the Law of Causality, which states that an entity acts as itself.

“Existence exists.”

This first axiom states, in effect, “There is something, as opposed to nothing.” That something exists is perceptually self-evident, and is presupposed by every statement, action or thought. What does it mean to “exist?” The concept of existence is not reducible to any more fundamental terms. The term does not have a conceptual definition. (Any attempted definition must employ the concept of existence, and is thus circular.) The only way one can “define” existence is ostensively–that is by pointing out instances of “existence,” which are particular existents.

Note that this axiom does not say anything in particular about what exists, or how to find out what, in particular, exists. It does not even specify that a world of physical objects exists. All it says is that something exists.

“Consciousness perceives existence.”

In order to be aware that existence exists (and of any particular existents or facts), one must have consciousness, the faculty of perceiving existence. As with the first axiom, this is perceptually self-evident. In the act of perceiving that which exists, one implicitly confirms that there is something to perceive, and that one is perceiving it. (1) When one reaches the conceptual identification of consciousness, such that one can say explicitly, “Consciousness perceives existence,” this axiom can be stated equivalently in the form of a definition: “Consciousness is that faculty of an entity which perceives existence.” One’s own experience of one’s own consciousness (perception) is the self-evident basis (validation) of that axiomatic definition of consciousness. (2)

Note that this axiom directly implies that existence is, in some sense, independent of consciousness, since existence is the object of consciousness.

“An existent is itself.”

Every thing that exists, exists as something specific, not some indeterminate “nothing in particular.” Whatever an existent is, it is. It is itself and not something else. Something that has certain intrinsic characteristics cannot, at the same time, have the opposite characteristics. Contradictions cannot exist in reality. This, too, is perceptually self-evident. A rock that is very dense and that falls in the earth’s atmosphere, cannot simultaneously be a helium balloon that floats in the earth’s atmosphere. A conscious human being cannot simultaneously be an unconscious plant. (3) (4)

The Law of Causality

The Law of Causality is, in Ayn Rand’s words, “the Law of Identity applied to action.” It is a corollary of the fact that an entity is what it is, that that entity will act (or react) as what it is. (5) Whatever the nature of a particular entity, it is this nature that will determine what action(s) or reaction(s) is/are open to it in a given situation. An entity cannot act in contradiction to its nature.

It should be noted that this formulation of the Law of Causality does not require that an entity respond mechanically to an antecedent action of another entity. It does not require that an entity only be capable of one response in a given situation. Whether a single mechanical response is all that is open to the entity, or a vast range of possible responses/actions, is determined by the specific nature of the entity in question. In fundamental terms, the Law of Causality only links an action to the entity that performs it, not to the actions of other entities. (Put somewhat more technically: By the Law of Causality, not every action taken by an entity must have a set of prior actions that comprise a sufficient condition for it to occur. The only cause of the action that need be present in all cases is the entity that acts.)

If I stand on a rooftop and release a stone over the edge, it falls. This is the only response to the earth’s pull that is open to the stone in that situation: a simple response consistent with its nature as a stone. If I release a helium balloon over the edge, it rises. This is a very different response to the same situation that results from the different nature of the balloon. (The difference, of course, is a difference in the property of density possessed by the object.) If I am on that rooftop, and I attempt to push a man off the edge, he may push back, fight me, pull out a knife, attempt to run away, yell, or resign himself to being pushed off. His nature as a man opens up a vast array of possible responses not open to an inanimate object like a stone, or balloon. (6) (7)

Axioms are Validated Ostensively

Because the axioms are the most fundamental premises possible, they are implicitly presumed, not only in every claim to knowledge of any sort, but also in every attempt at proof. Any attempt to prove them conceptually must, itself, presume them. Thus, the axioms are too fundamental to prove using any other ideas as the basis of proof. The only way to validate them is by directly observing reality and recognizing the self-evidence of the axioms in that perception. This is the process of ostensive validation.

If one looks at the world around him he will see directly that there is something of which he is aware. That phrase in bold holds all three of the axioms in it. There is something (existence and identity) of which he is aware (consciousness.) To stress identity: everything he sees appears as some particular thing. (8)

The Rejection of Axioms is Logically Self-Refuting

Since the axioms are assumed in every claim to knowledge of any kind, any argument, any reasoning, and any thought, they are implicit in any attempt to deny their validity. (9)

If someone says, “I do not accept that existence exists” then one can show that that sentence can have no meaning if it is true (note the self-contradictory phrase in the bold italics): “‘I‘? To what are you referring when you say ‘I’? If nothing exists, there is no ‘I’ since there is nothing. ‘Do not accept’? This implies that it is possible to accept something, but that ‘you do not.’ But if nothing exists, then there is nothing to accept or reject. ‘Existence’? Since you say there is no such thing as existence, and this is the broadest possible concept, encompassing everything, you are left with nothing to refer to, at all, and no one to speak to, at all, including me.”

The denial that “consciousness perceives existence” is also self-refuting. To see why, we should recognize that, for each of us, our fundamental, primary experience with consciousness is our own. Your own consciousness is your fundamental standard of what consciousness is. It provides necessary material for the concept, such that before anyone can grasp the idea of consciousness outside of oneself, he must grasp that he is in possession of consciousness. (Indeed, if you did not possess consciousness, you could not form any concepts at all.) (10) Thus, denying that consciousness perceives existence is denying that your own consciousness perceives existence, and effectively stating that everything you perceive, and to which your concepts refer, does not exist. So any statement made by one who denies this axiom becomes meaningless and void, including the denial. “‘Consciousness?’ There is no such thing, if it is not that which perceives existence. ‘Existence?’ You claim to know absolutely nothing of anything that exists.”

The denial of the Law of Identity is self-refuting, as well. If anything can lack an identity, then contradictions can exist, and no knowledge whatsoever is possible. Anything could also be its opposite at any time, such that for any “true” statement, the opposite could simultaneously be “true.” A statement could be both true and false at the same time. In fact, without the absolutism of identity, the very concept of “identity” would be rendered meaningless: No one could ever know that anything is any particular thing, making identification of any sort impossible, including identification of the concepts of “identity,” “self,” and “disbelief.”

“Existence exists” Necessitates Material Permanence

“Existence exists” pertains to the universe as a whole, and the universe as a whole is simply the sum of everything in it. Thus, one can render the axiom as “Existents exist.” That is, one can apply the axiom to every single existent. (11) Matter, in the broadest, philosophical sense, refers to anything that is a physical entity or set of physical entities, without specifying any particular qualities, actions, relationships, or temporal changes. (Thus, philosophically, matter includes not only atomic particles, but also photons and the like.) When entities change, their qualities, actions and relationships can “come into existence” or “go out of existence.” Metaphysically, such changes are not “creations” or “annihilations,” but simply designate that the entities involved are changing. These changes are only “creations” and “annihilations” epistemologically; that is, they are creations or obliterations of instances/situations in which certain objective, human concepts apply. If, however, matter (broadly, i.e. entities qua independent existents) were to be created or obliterated, this would be a metaphysical creation or annihilation, and would violate the axiom that existence exists.

If an entity exists, then it exists in some form, permanently. It can change into something else, by changing its attributes, it can split into its parts, or converge to become part of something else, but it cannot change into nothing. (12) Saying that something changes into nothing literally does not make sense, since “nothing” does not designate a something that an entity can change into. “Nothing” only designates an absence where one is looking for–or considering the possibility of finding–a particular something; “nothingness” does not exist metaphysically, and is only defined in reference to those entities that do exist.

Are the Axioms “A Priori” Truths?

No. The axioms, like all other forms of knowledge, have their origin in sense-perception. The axioms are implicit in every perception and thus are not dependent on any specific observations, but they cannot be known at all apart from any perception; nor can they be regarded simply as features of human cognition, apart from the rest of existence that is being observed, (as Kant regarded such fundamentals.)

Naturally, the explicit identification of the axioms also rests on sense experience, in that the conceptual structure needed to arrive at the concepts “existence,” “consciousness” and “identity” is built on sense-perception, (in which the axioms are implicit.) (13)


(1)  By “implicitly” I mean taken for granted without being specifically identified consciously/conceptually. When someone accepts a premise implicitly, he generally acts as though that premise is true, without telling himself it is true in his conscious mind. See Introduction to Objectivist Epistemology, Exp. 2nd Ed. (IOE) pgs. 159-162. Also:

(2) Note that this definition is not the equivalent of the claim that consciousness only passively perceives existence and does nothing else. Consciousness involves a great many activities, such as emotion and imagination. But the perception of existence is the fundamental activity that makes all others possible. Since definitions only consist of the fundamental characteristics of existents that enable them to be distinguished from other types of existents, not all the existents’ characteristics, this is a proper definition in its form. (Though it is not a definition in terms of more fundamental concepts, but an axiomatic/self-evident definition, since “perception” is “that which consciousness does with existence,” thus generating axiomatic circularity.) See

(3)  This metaphysical Law of Identity is what underpins the logical Law of Identity and the Law of Non-Contradiction. Since everything in reality is something in particular, and conceptual consciousness (qua consciousness of reality) is the faculty of identifying that which exists, a consciousness cannot accept, as true, two mutually contradictory statements. Contradictions are strictly a phenomenon of conceptual propositions, not of sense-perception, or of reality.

(4) Please see Chapter 1 of Objectivism: The Philosophy of Ayn Rand (OPAR) for more on the axioms. This work is the primary source for this post.

(5) Note here that “entity” is slightly more specific than “existent.” See OPAR and/or this: for more on the distinction. Also, see Action, here, is used in the broadest sense. It includes any self-generated action on other entities, any reaction to other entities, and any internal change.

(6) Please see Chapter 1 of OPAR for more on causality.

(7) Of course Ayn Rand did not invent the Laws of Identity and Causality, nor did she claim to have. Plato was the first philosopher recorded to have stated the Law of Identity. Aristotle was the first philosopher known to have explicitly identified the Law of Non-Contradiction and types of causality. Parmenides had an axiom similar to Rand’s first: “Being is.” (Though what Parmenides took away from it is substantially different from Rand’s understanding, since he regarded all change as an illusion.) Ayn Rand’s primary contributions are to identify what, precisely, it means for something to be an axiom, how axioms can be validated, and her systematic and rigorous presentation/application of the axioms she identified as such. Here is an interesting discussion of the relationship of Ayn Rand’s metaphysics to Ancient Greek philosophy: Existence Exists, or the Modern Parmenides. (It should be noted that, according to Objectivism, Aristotle made a deep metaphysical error in postulating a consciousness that was only conscious of itself. Since this idea was confined to a distant, impersonal Prime Mover, it arguably had little impact on his effective philosophy of this world.)

(8) OPAR pg. 5

(9) Though the axioms are presumed as true in some way in every thought and statement, this does not mean that every set of one or more thoughts or statements reflects consistent adherence to the axioms. A statement may be self-contradictory, thus not conforming to the Law of Identity, but each side of the contradiction depends on the acceptance of the axioms (including identity) for whatever meaning it holds to the speaker. Indeed, insofar as the concepts that the person uses have any meaning whatsoever, they depend implicitly on the axioms (consciousness of reality) for that meaning. Otherwise, they would quite literally refer to nothing.

(10) For the Objectivist theory of concepts, see IOE. I also intend to write a future post on this, but certainly not in the kind of detail the book goes into.

(11) If “existing” were an attribute or action, this would not follow, and would be an example of the Fallacy of Division. But, despite the fact that, linguistically, “to exist” is treated as a verb, “existing” is not an action, but a primary fact. This logical step is the same in character as saying that ten equals ten multiplied by one. That is, if a total of ten things exists, then each one of those ten things exists.

(12) See

(13) I intend to write further on the issue of “a priori vs. a posteriori” and “analytic vs. synthetic” knowledge in a future post. For more detail on these issues, see IOE.

[Edited: 5-6-15: Added first paragraph.]


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