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Base on the quote below:

Axioms are usually considered to be propositions identifying a fundamental, self-evident truth. But explicit propositions as such are not primaries: they are made of concepts. The base of man’s knowledge—of all other concepts, all axioms, propositions and thought—consists of axiomatic concepts.

An axiomatic concept is the identification of a primary fact of reality, which cannot be analyzed, i.e., reduced to other facts or broken into component parts. It is implicit in all facts and in all knowledge. It is the fundamentally given and directly perceived or experienced, which requires no proof or explanation, but on which all proofs and explanations rest.

The first and primary axiomatic concepts are “existence,” “identity” (which is a corollary of “existence”) and “consciousness.” One can study what exists and how consciousness functions; but one cannot analyze (or “prove”) existence as such, or consciousness as such. These are irreducible primaries. (An attempt to “prove” them is self-contradictory: it is an attempt to “prove” existence by means of non-existence, and consciousness by means of unconsciousness.)


I'm going to assume the answer is no.

asked Jun 21 '12 at 02:08

Humbug's gravatar image


edited Nov 04 '13 at 18:41

Greg%20Perkins's gravatar image

Greg Perkins ♦♦

Why would you assume the answer is No? There is endless evidence that the opposite is the case.

(Jun 21 '12 at 02:39) Greg Perkins ♦♦ Greg%20Perkins's gravatar image

If all axioms consists of axiomatic concepts, which is the identification of a primary fact of reality, then why is there a need to believe in an axiom at all? Isn't that the tool of rationalism?

(Jun 21 '12 at 03:05) Humbug Humbug's gravatar image

I suspect your meaning for "belief" is the issue here. "Belief" doesn't equal "divorced from reality" or whatever -- that's far too narrow. Belief is simply assent-to or agreement-with a proposition... and one can of course do that for good reasons (i.e., reasons based in reality) or for bad reasons (like, say, a Rationalist who is indifferent to reality).

(Jun 21 '12 at 03:52) Greg Perkins ♦♦ Greg%20Perkins's gravatar image

So why is there a need to believe in axioms at all? Because there's a need to believe EVERYTHING one knows. Conceptual knowledge is held in propositional form, and if you don't assent-to/agree-with/uphold said propositions then I wonder in what sense you actually know those facts, much less how you could possibly act on them.

(Jun 21 '12 at 03:54) Greg Perkins ♦♦ Greg%20Perkins's gravatar image

By belief I assume you mean recognize and accept. The fun thing about axioms is that they exist whether you believe in them or not. It is that choice, to recognize them, that makes the difference. A belief in any particular axiom comes with certain benefits. Without the axiom of existence, we couldn't identify anything as real. Sure its metaphysically given, and so we can neglect the fact if we want. But accepting that existence exists and that only what exists, exists, gives you the ability to approach reality efficaciously. It is a rationalization to say that we do not need to recognize it.

(Jun 22 '12 at 05:06) CDObjectivist ♦ CDObjectivist's gravatar image

"The fun thing about axioms is that they exist whether you believe in them or not. It is that choice, to recognize them, that makes the difference."

Careful. Axioms are human creations, just as concepts are. Correction:

"The fun thing about axioms is that they are true whether you believe in them or not. It is that choice, to recognize them, that makes the difference."

(Jun 22 '12 at 09:00) John Paquette ♦ John%20Paquette's gravatar image

Then what is meant by "the base of axioms are axiomatic concepts"?

(Jun 22 '12 at 11:59) Humbug Humbug's gravatar image

You're right John, thanks for the correction.

Humbug: I would say that the answer to your question is that any axiom has to rest on a foundation of primary axioms (Existence, Consciousness, and Identity).

(Jun 22 '12 at 13:05) CDObjectivist ♦ CDObjectivist's gravatar image

In the quote given above: Rand says that Existence, Consciousness, and Identity are axiomatic concepts, not axioms....

(Jun 22 '12 at 13:41) Humbug Humbug's gravatar image
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You're right Humbug, I am getting the two confused. Here are a few quotes from the lexicon I found useful in this issue and I think help clear up the question. They are said better than I can say it, so here are the direct quotes:

"[The] 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 exists—Consciousness is conscious—A is A. (This converts axiomatic concepts into formal axioms.)"


"Since axiomatic concepts refer to facts of reality and are not a matter of “faith” or of man’s arbitrary choice, there is a way to ascertain whether a given concept is axiomatic or not: one ascertains it by observing the fact that an axiomatic concept cannot be escaped, that it is implicit in all knowledge, that it has to be accepted and used even in the process of any attempt to deny it.

For instance, when modern philosophers declare that axioms are a matter of arbitrary choice, and proceed to choose complex, derivative concepts as the alleged axioms of their alleged reasoning, one can observe that their statements imply and depend on “existence,” “consciousness,” “identity,” which they profess to negate, but which are smuggled into their arguments in the form of unacknowledged, “stolen” concepts.

It is worth noting, at this point, that what the enemies of reason seem to know, but its alleged defenders have not discovered, is the fact that axiomatic concepts are the guardians of man’s mind and the foundation of reason—the keystone, touchstone and hallmark of reason—and if reason is to be destroyed, it is axiomatic concepts that have to be destroyed."

Here also is the hyperlink for where you can find and read these and others in depth: http://aynrandlexicon.com/lexicon/axiomatic_concepts.html

What I think is meant by "the base of axioms are axiomatic concepts" is that prior to the statement/axiom "Existence exists" one must have a concept of existence. That is, they must be aware that things exist, formulate the concepts via conscious thought and understand that they are axiomatic concepts, that all other knowledge rests upon those concepts. Once this is understood, once you have formualted the axiomatic concept of existence, you can make the statement; "Existence exists" with confidence and know that that statement is an axiom based on axiomatic concepts. Where as, should you choose not to believe what is in front of you, or to dispense with the concept as useless because it is given, you could never be confident in what you know, how you know it and how to apply it to a wider spectrum of ideas.

Thanks for challenging my earlier statement, it would seem my epistemology and metaphysics are a little rusty.

answered Jun 22 '12 at 20:41

CDObjectivist's gravatar image

CDObjectivist ♦

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Asked: Jun 21 '12 at 02:08

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Last updated: Nov 04 '13 at 18:41