What, if anything, did Rand write on Mathematics?

Science & Technology Physics and Mathematics
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I seem to remember Ayn Rand stating somewhere in ITOE that a consistent Philosophy of Mathematics had never been developed; I also vaguely remember her saying that she intended to undertake such a study someday. My questions are as follows:

Am I remembering correctly, or did I make all of that up?

If yes, did she ever get around to such a study before her death?

If not by her, has a study been undertaken by any other Objectivist Philosopher and where can I find it? Any rational study will fit the bill here; it doesn’t necessarily have to have been done by an Objectivist.

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I seem to remember Ayn Rand stating somewhere in ITOE that a consistent Philosophy of Mathematics had never been developed; I also vaguely remember her saying that she intended to undertake such a study someday. My questions are as follows:

Am I remembering correctly, or did I make all of that up?

If yes, did she ever get around to such a study before her death?

If not by her, has a study been undertaken by any other Objectivist Philosopher and where can I find it? Any rational study will fit the bill here; it doesn’t necessarily have to have been done by an Objectivist.

I didn’t read ITOE, but is it possible that she was talking about Mathematics of Philosophy rather than Philosophy of Mathematics?

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I didn’t read ITOE, […]

Philosophically speaking, Ayn Rand’s Introduction to Objectivist Epistemology is the single-most important work that she published. It provides the foundation for all of her other philosophical views. Serious study of Objectivism requires familiarity with ITOE.

[…]but is it possible that she was talking about Mathematics of Philosophy rather than Philosophy of Mathematics?

What is “Mathematics of Philosophy”?

The phrase “philosophy of …” refers to foundations of specialized sciences. Thus, “philosophy of physics” refers to a set of principles which are the foundation of the specialized science of physics, but not necessarily of other specialized sciences such as biology, history, or law.

“Philosophy of …” is a phrase by analogy. Philosophy, properly, is the universal science, but by analogy, we can speak of the “philosophy” (fundamentals) of particular sections of knowledge. See ITOE, p. 289, for a chapter entitled, “Philosophy of Science.” Likewise, Ayn Rand, ITOE, p. 304, speaks even more narrowly of the “epistemology of science.”

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I seem to remember Ayn Rand stating somewhere in ITOE that a consistent Philosophy of Mathematics had never been developed; I also vaguely remember her saying […]

Did you look up “Mathematics” in the index to ITOE?

If not by her, has a study been undertaken by any other Objectivist Philosopher and where can I find it?

There was an excellent two-part article on mathematics as inductive, in The Intellectual Activist, years ago. Search TIA’s list of articles and buy those two issues.

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Pat Corvini taught an absolutely fascinating course to this effect at last year’s summer confence. You can buy it here.

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Thanks, guys.

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Philosophically speaking, Ayn Rand’s Introduction to Objectivist Epistemology is the single-most important work that she published. It provides the foundation for all of her other philosophical views. Serious study of Objectivism requires familiarity with ITOE.

I think I have made my position clear in this thread, of which book is more important/fundamental in the studies of philosophy of Objectivism. I know that ITOE too is important, but I have no time to read it right now. I’m not into “serious study” of Objectivism, right now I only need to know its applications in real life, and that will suffice during my college years.

What is “Mathematics of Philosophy”?

(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.”)

That is where I first thought that dondigitalia saw the phrase, but had it mixed up with something else.

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Ayn Rand did intend to look into the philosophy of mathematics, and she did study advanced mathematics in her final years.

Unfortunately she died before she could leave any valuable writing on the subject.

I don’t know about other philosophers taking this challenge up, but I’d be very interested in seeing it done in my lifetime.

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I think I have made my position clear in this thread, of which book is more important/fundamental in the studies of philosophy of Objectivism. I know that ITOE too is important, but I have no time to read it right now. I’m not into “serious study” of Objectivism, right now I only need to know its applications in real life, and that will suffice during my college years.

I’m a bit confused by this… I certainly don’t think that you should engage in a study of something that is of no interest to you, or that you don’t think will be of value to you. But, I must point out that Ayn Rand’s revolutionary Epistemology (along with the Metaphysics that accompany it) is the foundation of Objectivism; all other areas are drawn from its application to reality. How would you propose to apply something to real life without first understanding the principles you are applying?

I skimmed the thread you linked, and did not see where you made it clear which book is more fundamental than ITOE. Perhaps I missed it. I can only assume that, since you’re interests lie in the application of Objectivism to your own life, you meant VOS, Ayn Rand’s work on ethics.

Lastly, any Philosophy is an immensely co of value to you. But, I must point out that Ayn Rand’s revolutionary Epistemology (along with the Metaphysics that accompany it) is the foundation of Objectivism; all other areas are drawn from its application to reality. How would you propose to apply something to real life without first understanding the principles you are applying?

I skimmed the thread you linked, and did not see where you made it clear which book is more fundamental than ITOE. Perhaps I missed it. I can only assume that, since you’re interests lie in the application of Objectivism to your own life, you meant VOS, Ayn Rand’s work on ethics.

Lastly, any Philosophy is an immensely complex subject which requires “serious study” to have any sort of complete understanding of its applications to your life. If you don’t wish to undertake such a study, that is your prerogitave, but I must advise you that it is hardly the way to go about finding Objectivism’s applications in real life. These applications deal almost entirely with abstractions. How would you propose to deal with these abstractions in reality without a proper method of relating them to reality?

Eran: Thanks for your input on my original question. I, too, would love to see such a study undertaken within my lifetime. Perhaps, after I have finished my education (or when I have gathered enough knowledge to make such a study worthwhile), I will delve into it myself.

Edited for punctuation. I really am a horrible proofreader. :wink:

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I’m a bit confused by this… I certainly don’t think that you should engage in a study of something that is of no interest to you, or that you don’t think will be of value to you. But, I must point out that Ayn Rand’s revolutionary Epistemology (along with the Metaphysics that accompany it) is the foundation of Objectivism; all other areas are drawn from its application to reality. How would you propose to apply something to real life without first understanding the principles you are applying?

First of all, I don’t know how what you are talking about in your first sentence. Second, it is not Epistemology, it is Metaphysics that is the foundation of Objectivism. Ayn Rand speaks of this in her early entries in her journal (moreover, in the exact paragraph I quoted), and Peikoff has structured OPAR in such a way as to show how other branches of philosophy are actually conceptually built upon the Metaphysical foundations. Not to mention that he says so at the very beginning of the book.

I skimmed the thread you linked, and did not see where you made it clear which book is more fundamental than ITOE. Perhaps I missed it. I can only assume that, since you’re interests lie in the application of Objectivism to your own life, you meant VOS, Ayn Rand’s work on ethics.

Sorry, that was a wrong thread. I’ll just quote what I wrote in another thread to avoid mistakes this time:

For that, I suggest OPAR - the rest of the ARL can be read later. When I started reading OPAR, I thought “THIS is the proper way to begin explaining a science - from its fundamentals, then build upon them.” And this is exactly the reason why I suggest OPAR to any beginner in Objectivism.

Correct me if I’m wrong, but you seem to have barged into the field of Objectivism at some random point. Maybe it was ITOE, or VOS, I don’t know. If you did, however, you are making exactly the mistake that Peikoff was warning about at the beginning of OPAR (paragraph on p.2-3). If you didn’t then I can’t see how you could have said I was talking about VOS.

Lastly, any Philosophy is an immensely complex subject which requires “serious study” to have any sort of complete understanding of its applications to your life. If you don’t wish to undertake such a study, that is your prerogitave, but I must advise you that it is hardly the way to go about finding Objectivism’s applications in real life. These applications deal almost entirely with abstractions. How would you propose to deal with these abstractions in reality without a proper method of relating them to reality?

To me, “serious study” means getting your hands on everything you can find on a certain topic, read it, make notes while reading it, and learn everything about it. At this point, I’m not interested in knowing EVERYTHING about Objectivism - I’m only interested in knowing its basics, which happen to be so brilliantly laid out in OPAR. As I read through it, I can see the interconnections between the branches of philosophy without having to make extensive notes. My primary study is not that of philosophy, but of engineering, and as much as I would like, I don’t have the time to do a “serious study” of Objectivism.

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First of all, I don’t know how what you are talking about in your first sentence.

I was responding to this: “I know that ITOE too is important, but I have no time to read it right now. I’m not into “serious study” of Objectivism, right now I only need to know its applications in real life, and that will suffice during my college years.”

Second, it is not Epistemology, it is Metaphysics that is the foundation of Objectivism.

I noted Metaphysics as well. The two subjects are so closely related that it is extremely difficult (in my experience) to separate one from the other. They are two separate branches, but they go hand-in-hand. While I have never read any statement of hers supporting this, I would suspect this is the reason why Miss Rand covered both subjects in one book.

Sorry, that was a wrong thread. I’ll just quote what I wrote in another thread to avoid mistakes this time:

Understood.

To me, “serious study” means getting your hands on everything you can find on a certain topic, read it, make notes while reading it, and learn everything about it … My primary study is not that of philosophy, but of engineering, and as much as I would like, I don’t have the time to do a “serious study” of Objectivism.

There’s no need to explain all of your specific reasons to me; the only person who needs to concern themselves with your reasons is you. Back to what I said at the very beginning, but I’ll rephrase a little bit: If you don’t think it will be of enough value to you to merit such a study, then you shouldn’t engage in one. The fact that you place something else higher up in your value structure is justification enough. The end.

It appears as though you are going on the defensive a bit (correct me if I’m wrong; it’s hard to tell when you aren’t face-to-face). There’s no need (Simma dah-na!). I was trying to help, not belittle. :slight_smile:

Edited to fix quotes.

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I have a question regarding this topic.

Can Objectivism be expressed in mathematical form due to its highly logical structure?

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I have a question regarding this topic.

Can Objectivism be expressed in mathematical form due to its highly logical structure?

No. Formal logic can be expressed algebraically, but it would be impossible to express an entire philosophy using symbols and numbers.

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I was responding to this: “I know that ITOE too is important, but I have no time to read it right now. I’m not into “serious study” of Objectivism, right now I only need to know its applications in real life, and that will suffice during my college years.”

…

There’s no need to explain all of your specific reasons to me; the only person who needs to concern themselves with your reasons is you. Back to what I said at the very beginning, but I’ll rephrase a little bit: If you don’t think it will be of enough value to you to merit such a study, then you shouldn’t engage in one. The fact that you place something else higher up in your value structure is justification enough. The end.

Yes, now I see what you were talking about. Thanks. :slight_smile:

I noted Metaphysics as well. The two subjects are so closely related that it is extremely difficult (in my experience) to separate one from the other. They are two separate branches, but they go hand-in-hand. While I have never read any statement of hers supporting this, I would suspect this is the reason why Miss Rand covered both subjects in one book.

Perhaps I see the distinction more clearly because I’ve been studying mostly the natural/mathematical sciences during my life. To explain this would require a whole new thread. However, for now, I will paraphrase one of my professors at college, who said that “…nobody knows why nature conforms to the laws of mathematics. Scientists just saw that explaining natural laws through mathematical formulae works, so they explained them in this manner. However, none of them was able to explain why.” He later promptly left the matter to philosophy. I think that the reason no one’s explained why this works, is because of lack of knowledge in regard to epistemology. This could be a lot of guesswork, but if mathematics is to natural sciences what metaphysics is to philosophy, then it is proper to conclude that answering my professor’s problem would require creating epistemology of science?

It appears as though you are going on the defensive a bit (correct me if I’m wrong; it’s hard to tell when you aren’t face-to-face). There’s no need (Simma dah-na!). I was trying to help, not belittle.  :wink:

I was trying to explain why I chose OPAR over ITOE. It has to do with how much I want to know about Objectivism at this time, but I’m not going further into this because, as you said, I don’t have to explain specific reasons to you.

Your posts have been enlightening. Thank you.

Edited for clarity.

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Can Objectivism be expressed in mathematical form due to its highly logical structure?

I don’t know the answer, but I see no purpose in doing that.

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“…nobody knows why nature conforms to the laws of mathematics. Scientists just saw that explaining natural laws through mathematical formulae works, so they explained them in this manner. However, none of them was able to explain why.” 

This would be because the laws of mathematics conform to nature. :slight_smile:

Introduction to Objectivist Epistemology is, well, an introductory work. Dr. Peikoff made extensive use of it in the Epistemology section of OPAR, so you don’t really HAVE to read both, although the one helps you understand the other and vice versa.

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Lastly, any Philosophy is an immensely co of value to you. But, I must point out that Ayn Rand’s revolutionary Epistemology (along with the Metaphysics that accompany it) is the foundation of Objectivism; all other areas are drawn from its application to reality. How would you propose to apply something to real life without first understanding the principles you are applying?

This is correct; specifically, Ayn Rand created an original solution to the “problem of universals” that prevented her philosophy from descending into the degenerate realms of subjectivism and intrinsicism. Her Metaphysics are in essence Aristotlean, though much clarified. It is the unique Epistemology that makes Objectivism so different from any other philosophy that came before.

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tommyedison,

Mathematics is completely deductive in its method (don’t let those “inductive proofs” fool you). Objectivism, on the other hand, is mostly inductive, that is derived from the observation of the world rather than some highest principles.

Therefore, an effort to derive the latter using the method of the former would be doomed to failure.

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Mathematics is completely deductive in its method (don’t let those “inductive proofs” fool you). Objectivism, on the other hand, is mostly inductive, that is derived from the observation of the world rather than some highest principles.

Could you define what exactly you mean by “deductive” and “inductive”?