Tautologies

[stephen_speicher]

And once again you manage to misinterpret what I say.

Yes, once again you are absolutely correct. I applaud your insightful identifications. For some strange reason, whenever I read writings that are as clear and precise as yours, I seem to jumble the ideas and wind up with a big hodgepodge. Mea culpa. And permit me to thank you again for so clearly identifying all of my faults. Due to your insights I will now definitely work harder to understand the obviously brilliant concepts that emanate from you. In fact, as soon as I am done with this post I am going to make copies of all of your posts in this thread and distribute them to my friends and colleagues so that others too can benefit from all that I learned from your crystal clear presentations.

[source]

Before I start, I'd like to suggest reading this post completely. This will be my last attempt to getting things I talked about clearer to you and frankly I don't think you read my posts entirely.

One of the reasons we don't understand each other is because I have no idea what you are asking of me. You told me you want me to show how "combining tautologies and axioms" works in real science. The ONLY possible way I could actually show you their combination is strictly by using a mathematical theorem. Just as axioms are a bunch of abstractions, so are their combinations. They offer no reference to the real world; they aren't concretized; in other words, they have no content.

The way the most basic axioms and the less-basic tautologies are related to reality is the same way that a simple mathematical formula is related to reality. Physics does that - it describes the world using mathematical formulas. If a mathematical formula is an abstraction, how does physics describe concretes with them? Exactly by giving them content - by concretizing them; by establishing experimentally that a certain mathematical formula can be used to describe a concrete phenomenon. This isn't done by merely "combining tautologies and axioms," it is done by observing these concrete phenomena, then by generating a formula which best approximates the results of the observations. Such formula is by itself an abstract formula which has no particular meaning. However, physics concretizes it by saying that this formula describes this particular phenomenon.

Do you now understand why I cannot understand your request? I can show you how to get the formulas which describe Kepler's laws using mathematical tools only, but in order to be able to do that, I MUST concretize some abstractions. I must tie them down to something concrete; I must first tell you that I consider m to represent mass and that s represents distance and that t represents time. And there is no other way; I can't concretize an abstraction by combining it with yet another abstraction. And that, it seems to me, is what you ask of me to do.

If I don't concretize, meaning if I don't say that t is time and so on, I can then type out a bunch of formulas and you'd have nothing clever to say but that they look very nice. But if I give them content, some meaning and show what I'm referring to by typing out some symbol, then you can actually understand me.

Which brings me back to my first post in this thread. I bothered to give some examples (however silly they may be), in order to somehow concretize this abstraction I'm telling you about.

All that we have been discussing, however, is already well known. Physicists are concretizing abstract mathematical formulas all the time. What I intended to do with this thread was tho show that the same tautologies that work in mathematics, also work in metaphysics. Ayn Rand said it in her journal and she even wanted to study higher mathematics to use it as a model for her metaphysics, but as she herself also said, she wasn't very good at higher mathematics.

Finally, my question to steven_speicher is this: You asked of me to explain some things to you. I did not understand your request because of the reasons I mentioned above. Do you want now to elaborate more clearly on what it is you wanted me to explain to you, or will you continue with your childish remarks and unnecessary sarcasm?

[stephen_speicher]

What I intended to do with this thread was tho show that the same tautologies that work in mathematics, also work in metaphysics. Ayn Rand said it in her journal and she even wanted to study higher mathematics to use it as a model for her metaphysics ...

You have claimed in several posts that myself and others have "misunderstood" you, and have "misinterpreted" your words. Since these problems of understanding are not yours, but rather mine and others, I am sure you will have no difficulty in providing an exact quote from Ayn Rand's Journals that supports your understanding of what you claim she wrote. (Hint: try 1934.)

[source]

In her first philosophic journal, read entry from May 15, 1934. No hints are necessary, steven.

I only saw afterwards that you need an "exact quote," so here it is:

(All these things are only for my own use. They are pretty disjointed and not in any logical sequence. But what will [ultimately] come out of this is an arrangement of the whole in a logical system, proceeding from a few axioms in a succession of logical theorems. The axioms will be necessary - even mathematics has them - [because] you can't build something on nothing. The end result will be my "Mathematics of Philosophy.")

Edited August 7, 2004 by source

[stephen_speicher]

In her first philosophic journal, read entry from May 15, 1934. No hints are necessary, steven.

I only saw afterwards that you need an "exact quote," so here it is:

And where in these words from Ayn Rand do you find her saying, as you claim, that she "wanted to study HIGHER MATHEMATICS to use it as a MODEL FOR HER METAPHYSICS?" [Emphasis added.]

[source]

And where in these words from Ayn Rand do you find her saying, as you claim,  that she "wanted to study HIGHER MATHEMATICS to use it as a MODEL FOR HER METAPHYSICS?" [Emphasis added.]

I don't, but I don't find her mentioning metaphysics at the beginning of the journal at all. My conclusion is thus that Ayn Rand then had no conscious concept of mtaphysics yet, so I assume that "Mathematics of Philosophy" is actually what she will later call metaphysics. Am I wrong to assume that? Why? What became of this "Mathematics of Philosophy" then? A project she abandoned? Or has it become something I never heard of? In the first case I am terribly wrong and logic has nothing to do with philosophy, or Ayn Rand has invented some new logic I don't know of. If it's the second case that's true, then I skipped somewhere an important part of her philosophy. I am only aware of 5 branches, which are metaphysics, epistemology, ethics, politics and aesthetics.

And when you ask me, I'll tell you that of these 5, only metaphysics qualifies as "mathematics of philosophy" as metaphysics is that which is based on the axiom that existence exists, that A is A. It deals with the most abstract questions of existence and doesn't go into the concretes, save to give an example.

[stephen_speicher]

I don't, but I don't find her mentioning metaphysics at the beginning of the journal at all.

You miss my point, just as you missed what Ayn Rand actually said in the quote. Once again: "The axioms will be necessary - even mathematics has them - [because] you can't build something on nothing." She is saying that, like mathematics, her philosophy will necessarily have axioms, not, as you claimed, that she wanted to use mathematics as a model for her metaphysics.

Don't you see the difference? That philosophy and mathematics have axioms does NOT mean that one must MODEL philosophy using mathematics. Those are two completely different statements.

[Ed from OC]

That philosophy and mathematics have axioms does NOT mean that one must MODEL philosophy using mathematics. Those are two completely different statements.

Also, the fact that both fields have axioms does not imply that they must have the same axioms.

[stephen_speicher]

Also, the fact that both fields have axioms does not imply that they must have the same axioms.

Good point!

And, of course, years after these early writings in her journal, Miss Rand did make an important connection between mathematics and philosophy, but that was in the field of epistemology. At the heart of ITOE is the identification of the process of concept formation as being "in large part, a mathematical process." The epistemological connection is mathematics as a science of measurement, and measurement omission being at the root of the whole process of abstraction.

But none of this is even remotely related to Source's "model for her metaphysics." Source has continued to make claims of myself and others "misunderstanding" and "misinterpreting" what he writes, but those claims are just projections of his own poor grasp of the written word, combined with the burden of a bevy of floating abstractions.

[source]

Don't you see the difference? That philosophy and mathematics have axioms does NOT mean that one must MODEL philosophy using mathematics. Those are two completely different statements.

Also, the fact that both fields have axioms does not imply that they must have the same axioms.

I didn't say that they should.

But tell me then, how is it that objectivists use these axioms? How do YOU use them? You have them and what do you do with them? From what I've seen on this board, all they have been used for is to show what's wrong with someone's claims.

Also, what is it that you want to tell me, in regard to the subject of the post? That the tautologies I mentioned make no difference to philosophy? That they are only some constructs, the validity of which is restricted to the area of mathematics and logic, but when it comes to philosophy they are suddenly irrelevant and should be avoided?

The way I see it, without them, there can be no logical thread of thoughts; without them, your thoughts suddenly become disjointed, random flashes without beginning or end, without cause or consequence and they have nothing to do with what you do. And if without them, you want to remain logically consistent, your thread of thoughts must always go back to the very basics of the entire philosophy, all the way to its axioms.

Are you telling me that I cannot use completed constructs for which I already know they are true, in order to prove myself the validity and non-contradiction of some idea of mine without need to use the axioms directly?

Or is it that you just try to discredit everything I say (correct and incorrect) by taking the least relevant point of my post and showing that my assumption about it was incorrect and then accuse me of having poor grasp of written word and using floating abstractions? I may not know everything about Ayn Rand, since I haven't yet managed to read all her writing, or the writing of Leonard Peikoff. But you don't seem to understand that; you fail to acknowledge that in the process of learning something, one can make honest mistakes - the big ones and the small ones alike. And when one does make these mistakes, you don't even show enough integrity of your own to say "you're wrong, keep studying."

[Ed from OC]

But tell me then, how is it that objectivists use these axioms? How do YOU use them? You have them and what do you do with them? From what I've seen on this board, all they have been used for is to show what's wrong with someone's claims.

Please re-read my first two posts, where I directly answer this question. Also, see OPAR and ItOE discussions on axioms for more details.

Also, what is it that you want to tell me, in regard to the subject of the post? That the tautologies I mentioned make no difference to philosophy?

1. Axioms in the fields of metaphysics and logic do not have the same content or function. (See my prior posts for elaboration.)

2. AR didn't deduce Objectivism from 3 axioms, as you implied.

3. Rationalism is a not uncommon error in thinking among Objectivists, and my intent in posting here was primarily a caution against thinking that way.

The way I see it, without them, there can be no logical thread of thoughts; without them, your thoughts suddenly become disjointed, random flashes without beginning or end, without cause or consequence and they have nothing to do with what you do. And if without them, you want to remain logically consistent, your thread of thoughts must always go back to the very basics of the entire philosophy, all the way to its axioms.

The choices are not limited to, one the one hand, reducing every single conversation or thought to the axioms, or, on the other hand, abondoning logic. Thinking should be consistent with the axioms (and with the rest of one's knowledge), but that does not require re-inventing the wheel.

For instance, when ordering lunch at a restuarant, one's thoughts aren't: "A is A, therefore I'll have the salmon." That's bizarre. Likewise, one shouldn't order 10 servings of everything on the menu, just because you have the sudden urge to do so.

BTW, "Understanding Objectivism" has a great analysis of rationalism, which I highly recommend. Based on what you've posted on this thread, I'd bet you haven't heard it.

I may not know everything about Ayn Rand, since I haven't yet managed to read all her writing, or the writing of Leonard Peikoff. But you don't seem to understand that; you fail to acknowledge that in the process of learning something, one can make honest mistakes

If this is directly aimed at Stephen, I'll let him speak for himself. My comment to you is that while extra consideration to new students is warranted, it is not without limits. Frankly, your posts here have been confusing, with a lot of floating abstractions that are hard to understand (which is why Stephen asked for you to concretize.) You've said some things (such as your odd connection between tautalogies and science) that are unusual (if not bizarre), vague, and asserted without proof. These add up to make your posts unclear and confusing.

My point is that while a "newbie" deserves some extra consideration, it is also the newbie's responsibility to make the effort to listen to advice he asks for, and to be specific in his thoughts. This thread is going in circles, and it seems as though you don't grasp what I or Stephen or others have said.

[Betsy]

But tell me then, how is it that objectivists use these axioms? How do YOU use them? You have them and what do you do with them? From what I've seen on this board, all they have been used for is to show what's wrong with someone's claims.

That's right.

The basic axioms are implicit and always there in any interaction between existence and consciousness. We implicity assume that things are what they are, that we are conscious of it, the contradictions can't exist, that we can choose between truth and error, etc.

The only time it becomes an issue is when something goes wrong: when there is an apparent contradiction, when things are not as they appear to be, etc. Then the axioms are brought in explicitly. Axioms are "the rules of the game" of cognition and they are only made explicit when the rules need to be enforced.

[source]

The only time it becomes an issue is when something goes wrong:  when there is an apparent contradiction, when things are not as they appear to be, etc.  Then the axioms are brought in explicitly.  Axioms are "the rules of the game" of cognition and they are only made explicit when the rules need to be enforced.

My understanding of axioms is that of a mathematician. From A is A, the tautologies I listed above are built, after introducing certain symbols. Mathematicians "explore" the field of mathematics and they write the results of their exploring in form of a theorem. The theorem is then proved. It is either a logical consequence of some of the previous theorems, or it is built upon some additional definitions or the kind of statements which are considered true and cannot be proved. Whatever the case, the theorem is proved and just as you said, in this proof the axioms are implicitly used. The theorem is proved by means of one of the tautologies, which is a consequence or a combination of the axiom(s) (I can give an example if needed, as it is really hard to explain the principle in general). I think there was only one instance when we actually had to prove at college that something is wrong.

Therefore, since mathematics is built on certain axioms, when I saw Ayn Rand mentioning axioms for her pholosophy, upon which she will build her "Mathematics of Philosophy," I thought this is it - at least one part of philosophy will be learned the same way as Mathematics.

And when I see people here like DavidOdden who claim that further research in philosophy, is not needed because axioms are all that is required, I ask myself how is that possible? If mathematicians had the same stance, they'd still be arguing over whether 1 is greater, equal or smaller than 0, if they'd even get that far. Ayn Rand, on the other hand, came all the way to defining and explaining rational egoism, laissez-faire capitalism, individual rights, etc. And all of it is based on her axioms. Posting the tautologies here was my attempt to probe the underlying structure of these concepts; to see how she got all the way from her axioms to defining them. Ed from OC says it was done by induction; induction based on what? You need to observe some facts before you begin an induction and then the induction itself consists of deriving a general principle that guides those facts.

Induction exsists in mathematics too, but not all things are proved with induction. In fact, in mathematics, proof was required to show that the process of induction is valid.

And in this induction Ed mentions, I can see how the first and third axiom (existence exists and consciousness is conscious of something) can be implicitly used. But where is A is A? Forgotten?

Note also that not even mathematics is built strictly upon the axioms as Ed from OC suggested that I was suggesting. There are always some new definitions which often aren't proved and statements which are accepted generally without proof as are axioms. Directly using the law of identity, it is only the tautologies that can be proved, and even then only using symbolic representation of them. In order to get to number systems, it was needed to define them; in order to get to derivation, it was needed to define it; in order to get to integrals, it was needed to define them.

My thought was that philosophy of Objectivism was structured the same way: axioms - definitions - theorems - more definitions - more theorems... or at least that metaphysics would be structured this way, since epistemology deals with reason as man's tool of perceiving reality and ethics, politics and aesthetics deal with things way too concrete to be called "mathematics of philosophy." Hence my conviction that philosophy MUST be researched, just like mathematics. Mathematicians didn't even dream of a tool as powerful as integrals when they began their research. And my analogy was such - what tool of reason can we find by researching this "mathematics of philosophy?"

[source]

Please re-read my first two posts, where I directly answer this question.  Also, see OPAR and ItOE discussions on axioms for more details.

And what I find is this. Must have skipped this earlier.

"A is A" means something quite different from "x<=>x". "The 'identity' of an existent means that which it is, the sum of its attributes or characteristics." (OPAR, p6)

I still don't quite get it. If say x is then defined with x === P & Q, then x <=> P & Q is always true. P and Q could be characteristics of x. Logic therefore applies to (philosophical) A is A, and tautologies I mentioned still follow.

AR didn't deduce Objectivism from 3 axioms, as you implied.

If I implied that, I apologize. Read my reply to Betsy above for elaboration of what I wanted to say.

For instance, when ordering lunch at a restuarant, one's thoughts aren't: "A is A, therefore I'll have the salmon." That's bizarre. Likewise, one shouldn't order 10 servings of everything on the menu, just because you have the sudden urge to do so.

Understood, but denying the deductive process suggests to me that you do exactly that (theoretically).

BTW, "Understanding Objectivism" has a great analysis of rationalism, which I highly recommend. Based on what you've posted on this thread, I'd bet you haven't heard it.

Living where I live, objectivist lectures (I suppose that that's what it is, since you say that I haven't *heard* it), are not easy to come by. I doubt, in fact, that I can even get a recording of them, unless I ask someone who attends them to record them for me.

My point is that while a "newbie" deserves some extra consideration, it is also the newbie's responsibility to make the effort to listen to advice he asks for, and to be specific in his thoughts. This thread is going in circles, and it seems as though you don't grasp what I or Stephen or others have said.

Stephen began making a mockery ot of everything when I asked a simple question. As a result, I still don't know what he wanted me to explain. As for others who participated, the best advice I got was to read OPAR and ITOE. The only reason I haven't yet begun reading OPAR is because the book I have says it's volume 6 and I'm having troubles getting some of the previous volumes over Amazon. I always like to start from page 1. Anyway, to those who referred me to these books, thank you.

[stephen_speicher]

And when I see people here like DavidOdden who claim that further research in philosophy, is not needed because axioms are all that is required ...

It is because of tripe like this that I separate out those who are new to Objectivism, and interested in learning, from those who have some level of self-interest in distortion. It is impossible to communicate with someone who cannot separate reality from the way that they feel, and remarks such as these just further demonstrate your inability or your unwillingness to understand. God only knows how you justify in your own mind such a nonsensical comment about Dave Odden, but, like a great deal of what you think and say, it has nothing to do with reality.

[source]

It is because of tripe like this that I separate out those who are new to Objectivism, and interested in learning, from those who have some level of self-interest in distortion. It is impossible to communicate with someone who cannot separate reality from the way that they feel, and remarks such as these just further demonstrate your inability or your unwillingness to understand. God only knows how you justify in your own mind such a nonsensical comment about Dave Odden, but, like a great deal of what you think and say, it has nothing to do with reality.

Stephen, I need not justify anything in my mind. It's all right here in this thread. His "why bother listing it twice" I have no way of interpreting in any other way. His very first post begins with a statement that I don't need all those symbols I use. I could as well ask why then do we have so many buttons on a keyboard? We could post messages with only two buttons (1 and 0).

And when I answered his question, he said nothing.

As for your assumptions, I challenge you to answer this question; not necessarily on this board, but to yourself: On what basis did you make them? I've always had to explain my assumptions in this thread about everything. The trick is that I knew why I made them, and I still know, so if there was something wrong with the way I presented my ideas, you could have simply told me which of my assumptions is incorrect. Instead you told me stories about red bags and blue baloons and closets which were completely irrelevant to the thread topic.

And the only reason why this thread is still going on is exactly because I'm interested in learning objectivism. As you never tried to explain anything, there was nothing to understand.

[Ed from OC]

My understanding of axioms is that of a mathematician. From A is A, the tautologies I listed above are built, after introducing certain symbols. ...

Therefore, since mathematics is built on certain axioms, when I saw Ayn Rand mentioning axioms for her pholosophy, upon which she will build her "Mathematics of Philosophy," I thought this is it - at least one part of philosophy will be learned the same way as Mathematics. ...

My thought was that philosophy of Objectivism was structured the same way: axioms - definitions - theorems - more definitions - more theorems... or at least that metaphysics would be structured this way, ...

Look, you can't reduce philosophy to mathematics. Period. The content and structures of the fields are completely different.

AR did not structure Objectivism along the lines you describe.

I would suggest taking the time to read OPAR to at least get an overview of how the philosophy is structured. Yes, it is systematic, consistent, logical and true, but that does not imply a structure that matches that of mathematics.

It seems as though you're taking this "Mathematics of Philosophy" phrase out of context, dropping nearly 50 years of subsequent thought on AR's part from consideration. Don't do that. Look at what she actually said and wrote.

P.S. "Understanding Objectivism" is a taped lecture course available at the Ayn Rand Bookstore.

That said, I'm done here. I'm tired of repeating myself.

[AndrewSternberg]

The only reason I haven't yet begun reading OPAR is because the book I have says it's volume 6 and I'm having troubles getting some of the previous volumes over Amazon. I always like to start from page 1. Anyway, to those who referred me to these books, thank you.

The 'Volume 6' that you mention means the 6th volume of 'The Ayn Rand Library'. There is only one OPAR book and 'page one' can be found inside.

Some of the other volumes in 'The Ayn Rand Library' include "The Voice of Reason" and "The Ayn Rand Lexicon".

[stephen_speicher]

Stephen, I need not justify anything in my mind. It's all right here in this thread. His "why bother listing it twice" I have no way of interpreting in any other way.

I believe you, and that is the problem. You interpret so many things in a way that seems so evident to you, but that is not the way that things really are. What you claimed Dave Odden to be saying was patently absurd.

And the only reason why this thread is still going on is exactly because I'm interested in learning objectivism. As you never tried to explain anything, there was nothing to understand.

Look, Nikola, I do not mean to be offensive to you, but you are a very difficult person to talk to about ideas. Dave Odden, Ed from Oc, and Ash Ryan all tried to explain some things to you right at the beginning, but you missed it all. It was then that I posted and said: "I think that at least one major reason I personally am having difficulty following you is that you speak so much in the abstract that I really have no idea how your words are connected to reality." I then asked you to make that connection to reality, and everything went downhill after that.

You started this whole thread with: "Ayn Rand limits her axioms to 3 in her philosophy, which makes it hard to logically reach other conclusions. However, by learning also the tautologies below, you can be faster about making your conclusions, not to mention that there's less margin for error." If you really do want to learn Objectivism then I would suggest that you stop trying to make Objectivism better and try harder to actually learn it instead. Leonard Peikoff's Objectivism: The Philosophy of Ayn Rand is an excellent systematic presentation of the philosophy. I would suggest reading that book from start to finish, giving it a lot of thought along the way.

And instead of posting your additions and expansions to Objectivism to this forum, ask questions you might have about the ideas that Peikoff presents. As I said in the beginning, your words are so abstract that I find it difficult to connect what you say to reality. Confine yourself to trying to to understand what Peikoff writes.

[source]

Look, you can't reduce philosophy to mathematics.  Period.  The content and structures of the fields are completely different.

AR did not structure Objectivism along the lines you describe.

All I needed to hear was that. I read the works of Ayn Rand and I can't help having a few ideas of my own. So I come here and make a post about it. If it's wrong, fine. I was once wrong about the structure of mathematics too.

[source]

The 'Volume 6' that you mention means the 6th volume of 'The Ayn Rand Library'.  There is only one OPAR book and 'page one' can be found inside.

Good. Then I'll start reading it immediately.

[source]

I believe you, and that is the problem. You interpret so many things in a way that seems so evident to you, but that is not the way that things really are. What you claimed Dave Odden to be saying was patently absurd.

Why?

If you really do want to learn Objectivism then I would suggest that you stop trying to make Objectivism better and try harder to actually learn it instead. Leonard Peikoff's Objectivism: The Philosophy of Ayn Rand is an excellent systematic presentation of the philosophy. I would suggest reading that book from start to finish, giving it a lot of thought along the way.

You can expect that I will question the validity of every sentence when I read it. Maybe I won't ask on the forum about it, but I WILL question it.

And instead of posting your additions and expansions to Objectivism to this forum, ask questions you might have about the ideas that Peikoff presents. As I said in the beginning, your words are so abstract that I find it difficult to connect what you say to reality. Confine yourself to trying to to understand what Peikoff writes.

Still I wonder whether anyone knows where my error was? I know I don't. I might figure it out reading OPAR, though. As for connecting what I said to reality - it already is. Look at natural sciences which use mathematics in describing reality. Why would a mathematician bother to define all those tautologies if none of them were used anywhere? They needed them. And there they are.