Three Axioms or More?

[BrandonMV]

*** Mod's note: Split from another topic - sN ***

I hope this isn't getting too off-topic, but...

A minor correction. There are four axioms (validity of the senses being the last one) with three corollaries (entity and causality [in that order] stemming from identity, and volition stemming from consciousness).

It was my understanding that there are only three basic axioms: Existence, Consciousness, and Identity. And so I was confused when I read in the first chapter of David Kelley's The Logical Structure of Objectivism where he says, "Objectivism is founded on the axioms of Existence, Identity, Consciousness, and Causality." After seeing this repeated in the above post, I decided to see what OPAR had to say on this issue. It seems that Dr. Peikoff contests this point in the first chapter of OPAR, where, under the heading of "Causality as a Corollary of Identity," he says, "Causality is best classified as a corollary of identity. A "corollary" is a self-evident implication of already established knowledge. A corollary of an axiom is not itself an axiom; it is not self-evident apart from the principle(s) at its root (an axiom, by contrast, does not depend on an antecedent context)."

On this point, I agree with Dr. Peikoff, and others may wish to disagree (which would probably be more appropriate in another thread), but I just wanted to note that this is not an uncontested tenet of Objectivism.

Edited June 15, 2008 by softwareNerd
Added 'split-topic' notice

[Benpercent]

And so I was confused when I read in the first chapter of David Kelley's The Logical Structure of Objectivism where he says, "Objectivism is founded on the axioms of Existence, Identity, Consciousness, and Causality."

An axiomatic concept is a corollary of an axiom, and cannot be an axiom itself because it is self-evident, but not independently as it depends on other axioms as its antecedent. Causality does not have primacy, and is therefore not an axiom.

Cause and effect (causality) is an axiomatic concept because there are no floating actions (e.g. no punching without hands, no balls rolling without balls, etc.). It depends on another axiomatic concept: entity. An entity is that which acts, so it has primacy above causality (a thing that acts comes before the initial action). The axiom of identity has primacy over both of these because it must be present first before these are even possible (a thing that acts must be something before it can act).

There are three essential attributes of axioms that makes them axioms:

1. They only exist within the branch of metaphysics.
   
2. They presuppose *all* knowledge, and are therefore unprovable, but there is no need to prove them. The only way to prove something is to show how you derived a conclusion from antecedent knowledge, and axioms have no antecedents.
   
3. They are self-evident independently, that is, without any antecedent knowledge. If prior learning is required to grasp an "axiom" (implicitly, not explicitly) then it is not an axiom.
   

An interesting implication is that attacking the axioms engages in the fallacy of the stolen concept, which is when one uses a concept in the process of denying it. You have to exist and have an identity before you can say you don't exist and that the law of identity is invalid.

One last thing to know about axioms is that they do have an order according to primacy*. One cannot just list out the axioms randomly. Take for instance putting the consciousness axiom before the existence one. That is a contradiction, as there can be no consciousness without existence.

And to answer the thread question, there are four axioms. The final axiom is the validity of the senses. Our senses just do what they do, with no power to do otherwise, so it is self-evident that they are valid. To say otherwise is to give a self-refuting argument. In the words of Leonard Peikoff: "If seeing is not believing, then thinking is worthless as well." If the senses do not give us true evidence of existence, then our own conceptual knowledge is bumpkus, and all arguments for anything are invalid. An argument against the senses automatically collapses.

* The axioms [and their corollaries] in order are: Existence/identity [entity, causality] > consciousness [volition] > validity of the senses. Note that existence and identity cannot be separated.

[Plasmatic]

One last thing to know about axioms is that they do have an order according to primacy*. One cannot just list out the axioms randomly. Take for instance putting the consciousness axiom before the existence one. That is a contradiction, as there can be no consciousness without existence.

Like Galt said. " I am therfore Ill think... My favorite quote.

[BrandonMV]

Thanks, Benpercent. I suppose question (for me) now is: What makes something a basic axiom as opposed to just an axiom?

Dr. Peikoff notes that the validity of the senses is an axiom, but he does not seem to regard it as a basic axiom. He states, "The validity of the senses is not an independent axiom; it is a corollary of the fact of consciousness." Thoughts?

[Benpercent]

Thanks, Benpercent. I suppose question (for me) now is: What makes something a basic axiom as opposed to just an axiom?

Dr. Peikoff notes that the validity of the senses is an axiom, but he does not seem to regard it as a basic axiom. He states, "The validity of the senses is not an independent axiom; it is a corollary of the fact of consciousness." Thoughts?

Silly me. You're right. I have my copy of OPAR on my lap, and I should have underlined that specific line. What Peikoff means is that the validity of the senses is axiomatic instead of an axiom. I need to edit my working notes, then.

As far as I think, validity of the senses would come before volition, as one needs to have mental contents before he can contemplate them. Consciousness holds primacy because one needs to be aware before one can extrospect.

So that means I have to edit my little axiom chain: Existence/Identity [entity, causality], consciousness [validity of the senses, volition].

[Olex]

Some minor corrections that I think you should be careful of.

Cause and effect (causality) is an axiomatic concept because there are no floating actions (e.g. no punching without hands, no balls rolling without balls, etc.).

Be careful here. It's certainly true that there are no "floating" (i.e. cause-less) actions, and that's a decent start for induction to arrive at the principle of causality. But the final argument shouldn't be using that.

Causality is really an extension or specification of principle of Identity. In short: if a thing is what it is, then it will act according to what it is as well. Once you say that, then in your argument you ought to provide some concrete examples to illustrate what you mean in reality. So "balls" should go here.

It depends on another axiomatic concept: entity. An entity is that which acts, so it has primacy above causality (a thing that acts comes before the initial action). The axiom of identity has primacy over both of these because it must be present first before these are even possible (a thing that acts must be something before it can act).

I don't think I would use "primacy" in this context, b/c it seems to mean metaphysical primacy. It's not as if first an entity comes into existence, and then a split second later, its actions and properties come in with appropriate causes and effects. In reality, it's all happens at the same time, and it's indivisible.

However, when we think of this, we have to break it up into parts, and when building the argument, one part certainly has to come first (entity and its identity) and then show the second (cause and effect). But that's not what "primacy" means.

As far as I have seen "primacy" in Objectivism only refers to metaphysical primacy. For example, existence over consciousness. But in this case, it is so b/c consciousness is subject to existence in many ways.

There are three essential attributes of axioms that makes them axioms: ... 2. They presuppose *all* knowledge ...

#2 is correct, however, the more essential statement is that knowledge requires a foundation. So, it's not that we happen to assume certain things when we think but rather that our knowledge is hierarchical and requires a base, a first step - and that's what axioms are.

#1. They only exist within the branch of metaphysics.

To be honest, I'm not sure why you have to outline things about axioms. It's not like you have to constantly be on lookout for axioms in philosophy. There are only 3 of them after all.

But given that, how would you defend that all axioms MUST be metaphysical?

3. They are self-evident independently, that is, without any antecedent knowledge. If prior learning is required to grasp an "axiom" (implicitly, not explicitly) then it is not an axiom.

I have doubts over this. For example, a child wouldn't be able to grasp an axiom. He would have a ton of work ahead of him. While axioms are the basis of knowledge, they are not "easy" to grasp. Another example is that a child goes through bunch of work being able to separate between existence and consciousness.

Keep in mind that "existence" and "consciousness" are very 'fat' concepts. They include a lot of concretes and involve a long road from 'table' to 'existence' for example.

I'd suggest you pick a different verb for "grasp."

[Benpercent]

As far as I have seen "primacy" in Objectivism only refers to metaphysical primacy.

Then what term would you use? I still think it's appropriate, as you have to have the entity before you have the action. So technically, entities do have metaphysical primacy to actions. Again, just switch them around and you'll find a contradiction.

To be honest, I'm not sure why you have to outline things about axioms. It's not like you have to constantly be on lookout for axioms in philosophy. There are only 3 of them after all.

There are plenty of "axioms" in philosophy I'm sure, but I wanted to show why only so few of them are valid.

But given that, how would you defend that all axioms MUST be metaphysical?

Since axioms have no antecedents, metaphysics are the only place they can belong, as every other branch in philosophy has antecedents, that is, they can be traced backwards. Plus, reality is the only thing that is truly self-evident.

I have doubts over this. For example, a child wouldn't be able to grasp an axiom. He would have a ton of work ahead of him. While axioms are the basis of knowledge, they are not "easy" to grasp. Another example is that a child goes through bunch of work being able to separate between existence and consciousness.

Keep in mind that I said "implicitly." If a child did not implicitly grasp the axiom of existence, then he would not act and would die. Since he does act after he is born, it is obvious he has at least one of the axioms down. Of course, they don't all develop simultaneously, but as time goes on.

Of course, now that I think of it, I should edit #3: Explicit prior learning may not be required, but prior mental processes are.

[Olex]

Then what term would you use? I still think it's appropriate, as you have to have the entity before you have the action. So technically, entities do have metaphysical primacy to actions. Again, just switch them around and you'll find a contradiction.

I don't see it. Entities and their actions are inseparable. So this primacy only exists in your mind when you break them into parts. But in reality it's one whole. So I don't see your point.

There are plenty of "axioms" in philosophy I'm sure, but I wanted to show why only so few of them are valid.

I don't know what you mean here.

Since axioms have no antecedents, metaphysics are the only place they can belong, as every other branch in philosophy has antecedents, that is, they can be traced backwards. Plus, reality is the only thing that is truly self-evident.

Actually, epistemology is in the same position as metaphysics is. So why are you separating metaphysics only?

Keep in mind that I said "implicitly." If a child did not implicitly grasp the axiom of existence, then he would not act and would die. Since he does act after he is born, it is obvious he has at least one of the axioms down. Of course, they don't all develop simultaneously, but as time goes on.

I think you are taking this too far.

I'm pretty sure that many people today have a separation between action and thought. So they could act while denying the axiom.

Furthermore, they often mess themselves up so bad, that they can't even understand what "Existence exists" means. They begin to wonder in circles about second word having the same root as the first, etc.

Now, it's true that in order to properly claim any knowledge, one must build from those axioms. However, this only happens when one goes through the entire process correctly, of correctly building knowledge. A wrong example is a rationalist who says that one can't be certain that reality exists, since one can't prove it by deductive means.

How would you assess such case?

Of course, now that I think of it, I should edit #3: Explicit prior learning may not be required, but prior mental processes are.

That sounds too vague for me. In essence, you are saying that one needs a conscious and develop it somewhat to be able to grasp axioms consciously ?

EDIT: clarifications

Edited June 16, 2008 by Olex

[Benpercent]

I don't see it. Entities and their actions are inseparable. So this primacy only exists in your mind when you break them into parts. But in reality it's one whole. So I don't see your point.

I know they're inseparable, and that neither of them "came into existence" before one another (the concepts of the first two axioms, for certain, are eternal [have always been and will always be], but the consciousness one is debatable). What I'm saying is that entities have primacy hierarchy-wise. Switching around the positions of entity and causality in the hierarchy leads to a contradiction.

I don't know what you mean here.

In philosophy there are probably plenty of "axioms" being touted around, but they aren't actually axioms since they don't fit the definition of being self-evident. To use a pop culture example, for instance, I was listening to the television when a DVD commercial came on; one guy was complaining as to how everyone was after his treasure map, and the other guy say that "is the axiom of treasure hunting." This axiom isn't valid because it has antecedents, and isn't obvious until you've down a certain amount of learning, such as about pirates, the history of treasure found up to date, the fact that treasure maps even exist, etc.

(A silly example I know, but I couldn't remember the other one I heard in philosophy class)

Actually, epistemology is in the same position as metaphysics is. So why are you separating metaphysics only?

But epistemology *does* have an antecedent: metaphysics. In this context, having no antecedents means being irreducible, being unable to be broken into smaller facts. We can reduce epistemology. Before you can ask "How do we acquire knowledge and validate it?" one must ask "What is there to study?"

I'm pretty sure that many people today have a separation between action and thought. So they could act while denying the axiom.

They may consciously deny the axioms, but never subconsciously. Denying them consciously simply results in a contradiction and a case of hypocrisy. Take David Hume's epistemology of skepticism, which claims that we literally cannot know anything. Hume is being hypocritical because he's claiming knowledge that there is no knowledge. Skepticism is self-refuting.

In the case of denying your own existence, one would be hypocritical because actively denying it (either mentally, verbally, or on paper) would suggest that you have subconsciously accepted that you exist, and are thus acting.

Furthermore, they often mess themselves up so bad, that they can't even understand what "Existence exists" means. They begin to wonder in circles about second word having the same root as the first, etc.

I'm afraid I don't understand.

A wrong example is a rationalist who says that one can't be certain that reality exists, since one can't prove it by deductive means.

How would you assess such case?

By saying, of course, that one can't prove that reality exists at all, either by deductive or inductive means. It's self-evident, and by his acting we know that the rationalist has subconsciously accepted it.

That sounds too vague for me. In essence, you are saying that one needs a conscious and develop it somewhat to be able to grasp axioms consciously ?

What I'm saying is that a child needs to develop a certain amount before he can implicitly grasp the axioms. At birth existence is implicit. And a while after that, when he has been looking at blurs of color, identity becomes implicit. Once his eyes become focused, and he can see entities and not just patches of color, entities become implicit. And so on.

[y_feldblum]

My understanding is that there are five axioms. There are three axioms of metaphysics: existence, identity (from which we get the corollary: causality), and consciousness. There are two axioms of epistemology: the validity of the senses, and volition. The axioms of epistemology are not at the root of all of philosophy and are therefore not said to be among the axioms of philosophy.

[Benpercent]

I forgot to mention a question I have: Leonard Peikoff makes a distinction between an axiom and an axiomatic concept (this being a corollary). Later on he says that validity of the senses is an axiom, but not an independent one; it's a corollary of the consciousness axiom. By his priorly set guidelines, wouldn't that make this an axiomatic concept and not an axiom, and thus a contradiction within the writing?

[y_feldblum]

Consciousness is an axiom of metaphysics. The validity of the senses, a corollary of the metaphysical axiom of consciousness, is itself an axiom of epistemology.

[Benpercent]

Volition a corollary too, so would that just make it a dependent axiom?

[y_feldblum]

Volition a corollary too, so would that just make it a dependent axiom?

It is an axiom of epistemology, although not an axiom of metaphysics - in other words, one needs to go into detail to discover how volition is related to (knowledge of) every single fact, whereas it is self-evident how existence is part of the nature of every fact.