# "A is A", not "A = A"

## 25 posts in this topic

I've been wanting to bring this up for awhile. It seems like there are some people, even a few Objectivists, that, when wanting to state the Law of Identity, say "A equals A". I find this rather surprising in the case of people who say they are Objectivists. It's practically fundamental to me that in order to understand the all-important role the Law of Identity takes in the understanding of Objectivism--and, of course, in the integration of all knowledge--one must understand that the axiom is qualitative, not quantitative. As I recall, in Algebra there is something called the "identity property", which does state that A equals A (mathematicians, please correct me if I'm wrong). That only sounds right, sense mathematics is the science of measurement. But when you apply the Law of Identity to anything, you're not measuring it. The issue is not the amount, size or degree of something. The issue is the identity of something (and can include its nature). The issue is what something is. "A is A".

##### Share on other sites

If you don't understand meaning and necessity of the law of identity then it doesn't make any difference whether you use "is" or "equals", and neither does it matter as long you do understand it even though the usual formulation is "A is A". Either way "A is A" or "A = A" is only a shorthand formal formulation of much more. From IOE:

This underscoring of primary facts is one of the crucial epistemological functions of axiomatic concepts. It is also the reason why they can be translated into a statement only in the form of a repetition (as a base and a reminder): Existence existsâ€”Consciousness is consciousâ€”A is A. (This converts axiomatic concepts into formal axioms.)

You should go back and reread the chapter on Axiomatic Concepts in IOE and not worry so much about the 'meaning of is'.

##### Share on other sites

I disagree. Once again, the word "is"--instead of "equals" or some other word--is used for a reason. It means something very distinct and specific. It pertains to the identity of something, and nothing else. The level, volume, amount, degree, dollar value or size of something is a distinctly separate issue.

##### Share on other sites

You are missing the point of the principle. It is not to state that something "is" something as opposed to "how much" it is. "A is A" is the formal, axiomatic statement of an axiomatic concept. If someone uses "equals" as meaning "the same as" instead of "is" and understands what he is talking about then he is making the same statement: No one runs around making gratuitous statements about a quantity called "A" being the same quantity as itself. If someone doesn't understand the axiomatic concept and its purpose, then using "is" instead of "equals" as "the same as" doesn't help him and it makes no difference. In neither case do those listening to him have any idea of why is walking around pompously repeating "tautologies" with either an "A is A" or "A equals A" mantra, and usually neither does he. Obsessing over "is" versus "equals" as "the same as" is irrelevant context dropping linguistic philosophy.

##### Share on other sites

The Law of Identity concerns identification, not measurement.

##### Share on other sites

The law of identity concerns the fundamental nature of everything that is and is implicit in all knowledge, it not about either specific "identification" or "measurement" as a form of identification.

It is not the abstraction of an attribute from a group of existents, but of a basic fact from all facts. Existence and identity are not attributes of existents, they are the existents. [emphasis in original]
The units of the concepts "existence" and "identity" are every entity, attribute, action, event or phenomenon (including consciousness) that exists, has ever existed or will ever exist.
The concept "identity" does not indicate the particular natures of the existents it subsumes: it merely underscores the primary fact that they are what they are.

##### Share on other sites

So far, this discussion has been very abstract. Could either of you give a CONCRETE example where "A is A" vs. "A = A" makes a difference?

##### Share on other sites

'Equals' is usually associated with comparisons of two separate entities, so it is clearer to use 'is' in this case, since we are saying that an entity IS what it IS.

##### Share on other sites

The amount of apples in this basket is equal to the amount of oranges in that basket, because A = A. But an apple is an apple, and an orange is an orange; that's because A is A.

##### Share on other sites

So far, this discussion has been very abstract. Could either of you give a CONCRETE example where "A is A" vs. "A = A" makes a difference?

The axioms are very abstract, the widest abstractions possible. We assume that the chapter in IOE on axiomatic concepts, referred to above, is understood. The error is in trying to trying to reduce it to statements about identifying particulars, then making assumptions about someone else means by "equals".

##### Share on other sites

'Equals' is usually associated with comparisons of two separate entities, so it is clearer to use 'is' in this case, since we are saying that an entity IS what it IS.

That is true, although "equality" can be used the same way, but that does not address the fundamental nature of the axioms as opposed to arguing over "equals" versus "is" and particular identification versus identifying particular quantities with no idea of what the unspecified people he refers to mean by either and without knowing if they understand the law of identity and its significance (chapter 5 in IOE).

##### Share on other sites

So far, this discussion has been very abstract. Could either of you give a CONCRETE example where "A is A" vs. "A = A" makes a difference?

The axioms are very abstract, the widest abstractions possible. We assume that the chapter in IOE on axiomatic concepts, referred to above, is understood. The error is in trying to trying to reduce it to statements about identifying particulars, then making assumptions about someone else means by "equals".

What I am looking for is a concrete application where "A is A" vs. "A = A" would produce a different or incorrect result. For instance, is saying "Roark is an architect" the same as saying "Roark = an architect?"

##### Share on other sites

Let's say Roark is a composer. One could say, "Roark, as a composer, is equal in ability to the architect, Frank Lloyd Wright." Or let's say Roark's profession is not specified: "Roark is equal in ability to the architect, Frank Lloyd Wright." In either case, it is not critical to state Roark's profession; whether he's a composer or something else, he is equal in ability to Frank Lloyd Wright. We're trying to show the level of his ability here. But if we want to state the nature--the identity--of his profession, than "equals" will not work or apply. One must use "is": "Roark is a composer."

##### Share on other sites

Dave, a supporter of a free market for medicine: "What is Obamacare?"

Robert, an Obama supporter: "It's really big."

Dave: "Okay. But what is it?"

Robert: "It's really good."

Dave: "Once again, what is it?"

Robert: "It's very benevolent."

Dave: "One last time--what is it?"

Robert: "It's government-controlled healthcare."

Dave: "That's the kind of answer I'm looking for--an identification of Obamacare, not a measurement of it's size, it's value or it's benevolence."

Robert is using a "law of equality"--"A equals A"--but is not responding, until later, to a Law of Identity question. Dave is not asking for a measurement of Obamacare, he wants to know its nature, its identity.

##### Share on other sites

So far, this discussion has been very abstract. Could either of you give a CONCRETE example where "A is A" vs. "A = A" makes a difference?

The axioms are very abstract, the widest abstractions possible. We assume that the chapter in IOE on axiomatic concepts, referred to above, is understood. The error is in trying to trying to reduce it to statements about identifying particulars, then making assumptions about someone else means by "equals".

What I am looking for is a concrete application where "A is A" vs. "A = A" would produce a different or incorrect result. For instance, is saying "Roark is an architect" the same as saying "Roark = an architect?"

Why is that an "application" of the law of identity?

If someone says "Roark equals an architect" he means, though awkwardly, that he is an architect. Other examples might be more ambiguous regarding characteristics versus quantity as a kind of characteristic. But specific identifications are not the purpose of the law of identity as a philosophic axiom formally stating the axiomatic concept.

##### Share on other sites

Dave, a supporter of a free market for medicine: "What is Obamacare?"

Robert, an Obama supporter: "It's really big."

...

Robert is using a "law of equality"--"A equals A"--but is not responding, until later, to a Law of Identity question. Dave is not asking for a measurement of Obamacare, he wants to know its nature, its identity.

That is not a "law of identity question".

The response "it's really big" did not answer the original question.

##### Share on other sites

You say, "The response 'it's really big' did not answer the original question." That was exactly my point. Dave asked Robert to identify what Obamacare is, and Robert gave him only an estimate of its magnitude in response.

Also, if someone says "Roark equals an architect", he might mean that Roark is an architect, but you as the listener don't know that simply from his statement. He could very well be talking about a different Roark--say, a composer--who is equal in ability to an architect. He also does not tell you in what way Roark equals an architect. Does he equal him in mathematical ability (which would be helpful in composing music)? Does he equal him in artistic ability? Does he equal a particular architect in how he conducts his personal life? Does he equal him in ethics, morally? The statement "Roark equals an architect" says very little.

But if you say, "Roark is an architect", that actually says a lot, because so much in involved in the art/science of architecture. Again, you've identified what Roark is, professionally.

If anyone wonders why I consider this issue of "is" versus "equals" so important, it is because I believe the clarity of one's thinking--especially in the realm of axioms, which are basic to all of one's thinking--is critical. Ultimately, it's a life-or-death issue.

##### Share on other sites

I wrote that it "is not a 'law of identity question'". Why that is the case has been explained several times, which you have ignored while you repeat linguistic analysis, which is not "life or death".

##### Share on other sites

I think you would agree, though, that clarity of thinking in regard to axiomatic ideas is, ultimately, a matter of life-and-death. I don't think you'd want to be worked on by a surgeon who thought, "The cessation of this person's heartbeat is equal to the turning-off of a light switch, so it's not that big of a deal." I think we both would much prefer a doctor who thought, "The cessation of this person's heartbeat is what it is--the cessation of his heartbeat. It is not the mere turning-off of a light switch; that is not a problem, because the light can easily be turned back on again. But the stopping of a heartbeat is a direct threat to this person's life, and it's not usually an easy task to get it beating again, not by a long shot. I (and any assistants who can help) must act now!"

And don't you want to apply the same consistently "A is A" thinking to the direction of your own life? To the choice of your career (which millions of others, and a few philosophers over the past two thousand years or more, would love for you to be imprecise about)? To the identification of essential, basic values you want to seek in a soulmate, a future "final choice" in romantic love? To the values you find and wish to find more of in art?

It is true that A equals itself. But it is more important for the sake of cognition that A is itself.

##### Share on other sites

I'd like to add that before A can equal itself, it has to be itself. A law of equality--which is a necessary principle for measuring anything--would depend primarily upon the Law of Identity.

##### Share on other sites

We already know what the law of identity is and why it and rationality are important. That does not make your linguistic analysis of "the meaning of is" as a substitute for the meaning of the axiomatic concept, together with all the speculations about what unspecified others mean (why don't you ask them?), a matter of life and death.

##### Share on other sites

Would you consider the word "is" to be an unnecessary word? Would it be okay if it were eliminated from the language?

##### Share on other sites

Isn't the dispute over whether "equals" can be substituted for "is" in ALL cases. If the answer is yes, then "A = A" is a valid restatement of the law of identity. If it cannot be always substituted, then it is invalid.

##### Share on other sites

As you could have probably predicted, I agree with the latter statement. Either "equals" is a substitute word or it is not. And since words means things--with "is" being a form of the verb "be", and "equals" meaning "to be equal to"--"equals" could not be a substitute.