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Axioms: Used In Metaphysics Or Epistemology?

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Plato
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An axiom is a statement that identifies the base of knowledge and of any further statement pertaining to that knowledge, a statement necessarily contained in all others, whether any particular speaker chooses to identify it or not. An axiom is a proposition that defeats its opponents by the fact that they have to accept it and use it in the process of any attempt to deny it.

It seems here Rand is arguing axioms should be used in epistemology. But didn't she use axioms in Metaphysics? Am I missing something? :)

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It seems here Rand is arguing axioms should be used in epistemology. But didn't she use axioms in Metaphysics? Am I missing something? :)

Yes, you are. The axioms are the basis for ALL knowledge and a "shortcut" to finding out whether a given idea is true or false. They are used in Metaphysics as well as in Epistemology, and Ethics, and Politics, and the Arts, and all the other non-philosophic sciences.

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The axioms are the basis for ALL knowledge and a "shortcut" to finding out whether a given idea is true or false.

Silly me. I always thought you have to look at reality to determine "whether a given idea is true or false." Now I can save all that time and use the "shortcut" to determine "whether a given idea is true or false."

They are used in Metaphysics as well as in Epistemology, and Ethics, and Politics, and the Arts, and all the other non-philosophic sciences.

Interesting. Perhaps you can identify one axiom each for "Ethics, and Politics, and the Arts."

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It seems here Rand is arguing axioms should be used in epistemology. But didn't she use axioms in Metaphysics? Am I missing something? :confused:

As a participant in this topic and as a moderator for the Basic Questions Forum, I have two points:

1. When you quote someone -- fictional or not -- please specify the exact source so that your readers can go back to the original (for example, to see the context).

2. You might approach your problem initially by reviewing what you know about the key concepts of your question. For example, what do you mean by axiom, metaphysics, and epistemology? Answers to these questions might help you identify gaps or contradictions in your thinking -- which is what your "confused" smiley face suggests. Of course, here, Ayn Rand has already cleary explained the meaning of "axiom."

Basic Questions Moderator

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Silly me. I always thought you have to look at reality to determine "whether a given idea is true or false." Now I can save all that time and use the "shortcut" to determine "whether a given idea is true or false."

There you go.

Interesting. Perhaps you can identify one axiom each for "Ethics, and Politics, and the Arts."

No, Mr. Speicher. I'm talking about the same axioms. The knowledge of Ethics, Politics and the Arts rests on (is proved by means of) knowledge of Metaphysics (and Epistemology), which in turn rest on (is proved by reference to) the axioms of existence, identity and consciousness.

When examining a new idea, you first check whether it complies with the axioms. When you establish that it does (in the opposite case, the idea should be dismissed, so I won't discuss that case), then you work on integrating it into the rest of your knowledge. That is done, as you said, by looking at reality, or by looking at concepts, ideas and knowledge you already posess, for which you have already established that they (knowledge, ideas and concepts) are valid. If at any point you encounter a contradiction, then there are several possibilities:

1. the new idea is false

2. the old idea is false

3. the old idea is true but in your evaluation of the new idea you are using it out of its context (which is inconclusive in regard to the validity of the new idea)

4. the new idea is true but in your integration you are using it out of context

5. both ideas are false

6. both ideas are true, but only within their context, which you are dropping in your integration

("your" above does not refer to you).

I can't give exact guidelines of what to do in each of these cases, but the general rule is "Check your premises."

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1. When you quote someone -- fictional or not -- please specify the exact source so that your readers can go back to the original (for example, to see the context).
Sorry, I got it from the John Galt speech in Atlas Shrugged.

2. You might approach your problem initially by reviewing what you know about the key concepts of your question. For example, what do you mean by axiom, metaphysics, and epistemology? Answers to these questions might help you identify gaps or contradictions in your thinking -- which is what your "confused" smiley face suggests. Of course, here, Ayn Rand has already cleary explained the meaning of "axiom."
Yes, allow me to divulge my premises.

Premises:

1. Epistemology is the philosophical field of knowledge, whose basis is determined by axioms.

2. Ayn Rand used axioms in metaphysics

3. Epistemology is not Metaphysics

Conclusion: How can one use an axioms in metaphysics?

Definitions:

Epistemology - All ready defined (premise 1)

Metaphysics - One of the 4 principal philosophical fields, it includes the fields of cosmology, ontology, and theology. It deals with the concepts of being, existence, universal, property, relation, causation, space, time, event, etc.

Axiom - a self-evident truth upon which other knowledge must rest, from which other knowledge is built up

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First, Plato, do you own a copy of The Ayn Rand Lexicon? It is the single-most important, single-volume work for the study of Objectivism. If you don't own a copy -- and use it -- you aren't serious about the study of Objectvism. And if you aren't serious about studying Objectivism, why on earth are you here in this forum?

Sorry, I got it from the John Galt speech in Atlas Shrugged.

Yes, but where in Galt's Speech? Please provide a specific reference so that readers can go directly to that page.

Yes, allow me to divulge my premises.

Premises:

Please reread my post. I asked for the meaning of the concepts, not your premises. (If you don't have strong, abstract-integrative reading skills, I highly recommend Dr. Edwin Locke's Study Methods and Motivations, from The Ayn Rand Bookstore. It has been one of the perhaps 20 most important books in my life.)

1. Epistemology is the philosophical field of knowledge, whose basis is determined by axioms.
No, this is not a definition of epistemology, even informally. The genus is branch of knowledge. The differentia, in essence, is that it answers the question, "How do we know?" (Metaphysics is the branch that answers the question, "What exits?"

By the way, have you studied the section on definitions in Ayn Rand's Introduction to Objectivist Epistemology?

2. Ayn Rand used axioms in metaphysics

This is misleading, though not by intention. What is an axiom's role in the whole of knowledge?

3. Epistemology is not Metaphysics
Yes, each branch is itself, not another branch.

Conclusion: How can one use an axioms in metaphysics?

How can a question be the conclusion of an argument as you have presented it? Have you studied logic? I highly recommend Dr. Peikoff's lecture series, Introduction to Logic.

Definitions:

[...]

Metaphysics - One of the 4 principal philosophical fields, it includes the fields of cosmology, ontology, and theology. It deals with the concepts of being, existence, universal, property, relation, causation, space, time, event, etc.

[...]

Where did you get this description of metaphysics? It is not Objectivist and it is not accurate.

Plato, what is your purpose in being in this forum? You have been here quite a while, yet you seem to know almost nothing about Objectivism and you seem not to have studied it. Why are you here?

Did you choose the screen name "Plato" as a sign of contempt for Objectivism?

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An axiom is an item of knowledge that identifies, in very broad terms, a fundamental fact about reality or our perception of it.

As an item of knowledge, an axiom serves an epistemological role as a uniter of all our knowledge. Therefore, an axiom specifies an item of knowledge that is epistemologically prior (in some sense) to a big chunk of our other specific knowledge of the world.

In a metaphysical sense, however, 'A is A"'has no extra "factuality" than "Water boils, in most contexts, at 100 degrees centigrade". All facts, whether identified by axioms or by the most high-falutin' abstraction are metaphysically simulataneous.

So, the way I understand things...Axioms are principles that serve a particular role in our knowledge (that of being fundamental and all-encompassing) but the facts axioms point to have no more metaphysical priority than any garden-variety "empirical" observation (assuming it's a valid one).

Axioms are epistemological, in that they point out which knowledge "comes before" (a notion deserving a whole separate discussion) the rest of our knowledge, and the facts that axioms point out (plus some of their immediate corollaries) comprise the field of metaphysics.

So, axioms are both metaphysical and epistemological in the senses specified above.

(Note: In the above, by "axiom" I mean "philosophical axiom", as opposed to the axioms of various sub-fields of knowledge, the axioms of which, within the context of any given discipline are considered "the given" but which in the broader context of knowledge definitely require outside validation...but that's just nitpicking.)

That's my understanding anyway, for what it's worth.

P.S. I know that my first sentence is not a definition of 'axiom'. Rather it is a true characterization of axioms slanted to set up my elaboration. I very well familar with her definition and believe that the above is implied by it and included in it.

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Axioms are the basis of knowledge. They only come up when one attempts to think conceptually. But their referents include everything in reality (the metaphysical axioms) or every conceptual identification thereof (the epistemological axioms). And the axioms are all implicit in every single act of conscious awareness.

Indeed, axioms are items of knowledge. Like all items of knowledge, they refer to facts of reality. The referents of axioms are either all facts of reality or all knowledge of facts of reality. All axioms are implicit in all knowledge of facts of reality.

For example, the axiom of identity refers to every single fact in reality and is implicit in every single act of conscious awareness, while the axiom of the validity of the senses refers to and is implicit in every single act of conscious awareness.

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Source, in addition to what others have said here, I'd like you to explain why

I will make my explanation as brief as I can. If in my attempt to do so I leave some point unexplained or unclear, do say so.

The axioms of metaphysics state: existence exists, a is a, and consciousness is conscious (of something). Metaphysics thus states that existence (reality) is knowable, because - if you observe the axiom of consciousness, it states that consciousness is conscious of things that exist, and only of things that exist; and things that exist have identity, i.e. they are what they are and they cannot violate their own nature.

Epistemology, on the other hand, studies man's means of grasping reality - reason. Reason presupposes consciousness. Consciousness perceives facts (existents) and reason integrates them into concepts. Reason is, therefore, capable of identifying objects it perceives (because they indeed have identity). You can see already the interrelation between metaphysics and epistemology - just try for example denying the validity of the axiom of identity (for the sake of the argument, regardless of the contradictions it will invoke), and see what happens to epistemology - suddenly, reason is no longer the right means to perceive reality, because existents have no identity; suddenly, by negating the axiom of identity, a ball can start bouncing all by itself for no reason whatsoever, or turn into a brick, then a needle and back into a ball (in Heraclitus' formulation "one cannot step into the same river twice"). When identity is "reinstated" such apparent possibilities are elliminated.

Ethics recognizes that man's standard of value is life. Therefore, he must act to sustain it. One thing required to do so is to gather food. To man, this does not come instinctively - he must use his mind, i.e. his faculty of reason; and reason, in epistemology, is man's means of grasping that which is, and that which is - metaphysics tells us - is existence. Existents have identity. Some existents are nutritious, some aren't and some are poisonous. Man must, by using his faculty of reason, establish which is which, i.e. he must identify existents by their nutritional value. When this is done, he must pursue these existents to fulfill his basic need for survival. (I am deliberately using here the terminology such as "existent" and "identify" to show the most direct link to metaphysics, and I use reason to point to epistemology, which again points to metaphysics. I could have easily said, for example "Man must know which is which, i.e. he must figure out what is edible and what isn't" but then I am not showing that "knowing" requires reason, that "figuring out" requires reason, and the axiom of identity is only indirectly visible.) Every virtue of man is ultimately a virtue of survival, each one of them requires a process of reason, and such process is impossible if the mind contains no "data" to process. This data is collected by observing reality, i.e. that which exists. "Observing" something (whatever that might mean in the context of this sentence) that doesn't exist, is fatal for a man who is trying to be virtuous. Think for example of the idea of god. God doesn't exist, yet many men worship "him." If you tried for even a fragment of a second to accept the idea of god, you would be accepting as true something that does not comply to any of the axioms. Does god exist? No. Does god have identity? No (even if you only judge by what others think of what god is, you will notice that they hold beliefs that are in many ways different, i.e. they do not give the idea any particular and consistent identity). Can you consciously be aware of god? No. What I just did was preform a test of the axioms on the idea of god. Obviously, such idea violates every axiom, therefore, according to metaphysics, this idea cannot be true. (By the way, the idea cannot be true even if it - on its face - violates only some of the axioms; a good example is the idea of the primacy of consciousness, although furhter analysis can show that it violates all the axioms - even consciousness - just like every other false idea.)

Moving finally on to politics, I can only say that a social structure should be based on reason and allow for every man to practice this faculty and all his virtues to the fullest extent. Things to identify here, have already been identified in ethics - virtues are the means to values which are the means to survival. What does man need to survive? That has already been answered.

As for art, I will only cite the definition quoted from Ayn Rand by Leonard Peikoff in OPAR. Everything else should become clear - if you have read carefully what I've written above - when you read the definition:

Art [...] is a selective re-creation of reality according to an artist's metaphysical value-judgements.

Edited to correct a spelling error.

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I usually write a conclusion at the end of my posts, but in my haste to complete this one, I forgot, so I'm writing it here.

You can see how good epistemology relies on good metaphysics, how good ethics relies on good epistemology, how good politics relies on good ethics. Change just one bit of metaphysics and see the effects on epistemology. I've made an example of denying identity and in epistemology this resulted in invalidating reason as man's proper means of perceiving reality. Going further to ethics, building it on the same error, what standard of value can you set? If you set life, without identity, how can you ask of a man whose mind is incompetent to grasp the world he lives in, to sustain that life? In fact, who is to say that ethics in this case would in fact come, hierarchically before politics? Perhaps then politics of a certain country would determine how a man should act - because man is incompetent to judge that for himself. Then again, who would devise the political system of a country? Some invisible force, god, the people or the ancestors? As for art - well, just what kind of recreation of reality could you make if reality is unknowable to you? Perhaps some of the modern works of abstract art which show absolutely nothing but random splashes of paint and of colors which make your eyes hurt? Truly, THAT then would be the proper expression of your metaphysical value-judgements.

Happily, we live in a world that is knowable, so we CAN judge for ourselves and we don't need the states and gods to "point us in the right direction." All we need to learn is to think.

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