The Logical Leap: Induction in Physics

[Dragonfly]

> It's not about calling him [Hume] a skeptic or an arch-skeptic (a very honorable viewpoint by the way), but about calling him [Kant] the most evil man in history

DF, I thought you could tell from the context of my post talking about philosophical viewpoints that I was talking about her being right in essentials ...about philosophers qua philosophers. Not her moral evaluation of them.

But I was talking about her cheap moral evaluation of them in a reaction to the discussion between Neil and Jim about her marginalia, so who is hijacking the discussion?

2> [Rand said] "observe what Bertrand Russell was able to perpetrate because people thought they “kinda knew” the meaning of the concept of “number” ..." (without any further clarification about what she meant with that murky and incomprehensible sentence).

She's talking about his philosophy of mathematics and about Principia Mathematica..."an attempt to derive all mathematical truths from a well-defined set of axioms and inference rules in symbolic logic" - which is absurd.

It turned out that this was not possible, but at the time it was certainly not an absurd idea. That would be like deriding Newton because his idea of an absolute time was absurd - easy to do now from your armchair, saying "observe what Newton was able to perpetrate, because he "kinda new" that time was absolute". It was Gödel who showed with his incompleteness theorems that such an undertaking by Russell and Whitehead was not possible, but Gödel was vilified by Objectivists like Peikoff exactly for that discovery, so Objectivists should be a bit more modest in their condemnations. Anyway, that was your interpretation of Rand's saying, but do you have any evidence to back up that claim? Rand wouldn't have understood one iota of Russell's mathematical ideas anyway. Nothing wrong with that in itself, nobody can specialize in every subject, but then she should also have refrained from judging those ideas.

> After quoting Emerson incorrectly, she called him "a very little mind"

Did you think he was a major, original philosopher? That transcendentalism makes sense or is original?

Do you think that justifies the nasty and contemptuous description of him being "a very little mind"? Is that the way a rational philosopher discusses colleagues? I think it's rather an indication that Rand herself was a very little mind.

[Dragonfly]

How much do you expect from a book on physics with only four equations?

One of which no doubt is A = A.

[James Heaps-Nelson]

> I don't know how people suddenly throw the switch where A is not A and suddenly everything they thought so fervently is now complete garbage. [Jim]

Because they never understood it in the first place. Never took the Oist courses or spent the years trying to think it through carefully.

Applying it in a Randroid way is only one form of that. That's why you see so many loud 'super-Objectivists' who accept everything unquestioningly and without integration, and in some cases defend opinion Rand ever had suddenly reject everything unquestioningly and without integration and in some cases conclude Rand was a monster.

I wish every Objectivist would get that the philosophy is first and foremost about your relationship to reality.

I think the problem is that after Rand opens up people's minds, gives them a hell of a lot of value and inspires them, they naturally put a lot of trust in her.

Then they step out into the real world, come face to face with people who are experts in the relevant fields that Rand never studied, or that she studied very little, and they discover that they were wrong to trust her. They've made loudmouthed fools of themselves by repeating some of her uninformed opinions as if they were brilliant new revelations of pure objective truth, and any value that they had hoped to share with others is then tainted. They don't know how to recover and explain that they and Rand are not complete idiots, and that there is value in her ideas, while people are laughing at them for having said something stupid (and having said it with an air of intellectual superiority).

I think it's understandable that those who have been burned by Rand are angry, and that they then go back and pick her ideas apart. It's really too bad that the anger has to be involved, but I think it's a natural reaction, and it's much more healthy than what True Objectivists do, which is to blind themselves to their and Rand's mistakes, and to condemn those who point them out.

To use the terrific Northwestern motto Quaecumque sunt vera, whatsoever things are true. If you disagree with something, think about it and speak up. It is through this process of engagement that your understanding will deepen.

Unfortunately, that's not the mindset of Objectivists in general. Disagreeing, thinking and speaking up is often not tolerated. I've been banned from SOLOP and placed on moderation at RoR and for doing it. I've been asked not to do it at Noodlefood. Multiple times I've been censored at OO for doing it (sometimes for simply and politely reporting what Rand's actual view was on a position that those at OO were mistakenly opposing). OL is the first forum that I'm aware of which bills itself as Objectivist and actually encourages independent thinking.

J

Jonathan,

I don't disagree that these things are problems. As David Kelley says, many people want to slam the system down on arguments that should be addressed head on. There is no substitute for studying a subject if you want to render an informed opinion on it. If Michael Prescott or Neil Parille isn't satisfied with Rand's atheism, Objectivist Living's own George H Smith has a good book on the subject and I have been enjoying his prolific posting here.

Jim

[dan2100]

How much do you expect from a book on physics with only four equations?

One of which no doubt is A = A.

Seriously, what are the four equations?

Has anyone here, aside from me, read Penrose's massive tome -- the one abounding in equations, the one that might as function as a grand tour of mathematics?

[James Heaps-Nelson]

How much do you expect from a book on physics with only four equations?

One of which no doubt is A = A.

Seriously, what are the four equations?

Has anyone here, aside from me, read Penrose's massive tome -- the one abounding in equations, the one that might as function as a grand tour of mathematics?

I'll put in a bet for F=ma as one of them. Dan, if you're talking about the Road to Reality I'm impressed. I've picked at it here and there, but no I haven't read it.

Jim

[dan2100]

How much do you expect from a book on physics with only four equations?

One of which no doubt is A = A.

Seriously, what are the four equations?

Has anyone here, aside from me, read Penrose's massive tome -- the one abounding in equations, the one that might as function as a grand tour of mathematics?

I'll put in a bet for F=ma as one of them.

I bet you're right. I did listen to an excerpt from the audiobook version and it was praising Newton as the seal of the prophets for physics. (Actually, not that I'd disagree: Newton was brilliant and probably had the major impact on physics for the new few centuries if not up until today.)

Dan, if you're talking about the Road to Reality I'm impressed. I've picked at it here and there, but no I haven't read it.

Jim

Yes, The Road to Reality. I think it's a fairly good mathematical introduction to physics, including some recent theories (he doesn't just end with "and them came quantum weirdness"). I recommend it, but one has to be willing to put in the effort to understand the math.

[George H. Smith]

[Rand] doesn't deal with - and for her purposes doesn't have to - the occasions where the thinker said something contrary to or inconsistent with his main position. For example, Hume was a classical liberal. But that is a claim of certainty inconsistent with his withering skepticism.

Why do you persist in making statements like this when you obviously don't know what you are talking about? If you knew anything about "moral certainty," as this notion was understood by 18th century philosophers, and if you had actually read some Hume, you would know that he did not repudiate this kind of certainty. On the contrary, Hume defended moral certainty -- which is essentially the highest level of probability in matters pertaining to human action -- against skeptical objections.

This is not to say that I agree with Hume. On the contrary, some aspects of his epistemology are so crude as to leave us wondering how a thinker of Hume's brilliance could have seriously defended them. (Locke is generally much better.) But an accurate criticism of Hume's ideas presupposes an accurate understanding of what those ideas are.

And, no, I don't want to swat down -- yet again -- all the claims that she got Kant's fundamental philosophy wrong. See my past posts on this...or, better, go read a good history of philosophy source.

And, no, you don't have to read the entirety of Kant in the original or spend a month with the Critique of Pure Reason. The basic worldviews of Kant, Hume, Plato, Atistotle -- what their views are -- are essentially uncontroversial in the field of philosophy or to those who, like myself, spent a lot of years studying the subject .

Those appear to have been wasted years. When it comes to understanding past philosophers, you couldn't swat a dead fly.

Suppose someone asked you about Rand's ideas. Would you advise him to read a secondary source about Rand? Or, knowing that commentators on Rand are often inaccurate, would you recommend that he read her first hand?

The answer, I think, is obvious. And this raises the question: Why the double standard?

Ghs

[George H. Smith]

Back to this thread's initial topic. I had heard that the Harriman book was promoted as containing groundbreaking new solutions to age-old philosophical problems. Was that total bullshit?

J

How much do you expect from a book on physics with only four equations?

Ba'al Chatzaf

Exactly how many equations are required for you to take a book seriously? Is there a minimum number?

I was under the impression that Harriman's book is about the philosophy of physics (and possibly the philosophy of science generally), in which case oodles of equations may or may not be relevant. In any case, I find it curious that people are so eager to dismiss a book that they haven't even looked at, much less read.

Ghs

[dan2100]

Back to this thread's initial topic. I had heard that the Harriman book was promoted as containing groundbreaking new solutions to age-old philosophical problems. Was that total bullshit?

J

How much do you expect from a book on physics with only four equations?

Ba'al Chatzaf

Exactly how many equations are required for you to take a book seriously? Is there a minimum number?

I was under the impression that Harriman's book is about the philosophy of physics (and possibly the philosophy of science generally), in which case oodles of equations may or may not be relevant. In any case, I find it curious that people are so eager to dismiss a book that they haven't even looked at, much less read.

Ghs

For the record, I'm not dismissing Harriman's book. I hope to at least listen to the audiobook version of it this summer.

I was merely curious about which four equations were in the book.

[Jonathan]

Back to this thread's initial topic. I had heard that the Harriman book was promoted as containing groundbreaking new solutions to age-old philosophical problems. Was that total bullshit?

J

How much do you expect from a book on physics with only four equations?

Ba'al Chatzaf

Exactly how many equations are required for you to take a book seriously? Is there a minimum number?

I was under the impression that Harriman's book is about the philosophy of physics (and possibly the philosophy of science generally), in which case oodles of equations may or may not be relevant. In any case, I find it curious that people are so eager to dismiss a book that they haven't even looked at, much less read.

Ghs

For the record, I'm not dismissing Harriman's book.

Nor am I. I'm simply curious if those who have read the book feel that it delivers anything new and earthshaking in the fields of physics and philosophy as I seem to remember its pre-production hype claiming that it would.

J

[Dragonfly]

equations may or may not be relevant. In any case, I find it curious that people are so eager to dismiss a book that they haven't even looked at, much less read.

That is probably because they're already acquainted with Harriman's idiotic ideas, some of which I've mentioned on this forum before, for example that Einstein's general theory of relativity is an "unphysical rationalistic floating abstraction" or that quantum mechanics "is not a physical theory" or that physicists with chaos theory "have given up causality" or speaking about the big bang: "I believe that theory came more from the metaphysics of Augustine than that it did from observational evidence". Well, we don't have to take such a fool seriously, do we? So even if I've not read his new book, I'm sure that it is not much better than what he's uttered before. I'd like to dissect the book if anyone sends me a free copy, but I'm certainly not going to waste my money on it.

[George H. Smith]

equations may or may not be relevant. In any case, I find it curious that people are so eager to dismiss a book that they haven't even looked at, much less read.

That is probably because they're already acquainted with Harriman's idiotic ideas, some of which I've mentioned on this forum before, for example that Einstein's general theory of relativity is an "unphysical rationalistic floating abstraction" or that quantum mechanics "is not a physical theory" or that physicists with chaos theory "have given up causality" or speaking about the big bang: "I believe that theory came more from the metaphysics of Augustine than that it did from observational evidence". Well, we don't have to take such a fool seriously, do we? So even if I've not read his new book, I'm sure that it is not much better than what he's uttered before. I'd like to dissect the book if anyone sends me a free copy, but I'm certainly not going to waste my money on it.

Good answer.

Ghs

[James Heaps-Nelson]

Back to this thread's initial topic. I had heard that the Harriman book was promoted as containing groundbreaking new solutions to age-old philosophical problems. Was that total bullshit?

J

How much do you expect from a book on physics with only four equations?

Ba'al Chatzaf

Exactly how many equations are required for you to take a book seriously? Is there a minimum number?

I was under the impression that Harriman's book is about the philosophy of physics (and possibly the philosophy of science generally), in which case oodles of equations may or may not be relevant. In any case, I find it curious that people are so eager to dismiss a book that they haven't even looked at, much less read.

Ghs

George,

It would depend on the subject. For a book touting an airtight defense of induction in physics, I would expect that it would present the Schrodinger Wave Equation or some quantum mechanical simile, maybe some field equations from Einsteins general theory of relativity, an equation representing radioactive decay and some equations dealing with chaotic dynamics. I would expect this in Harriman's case because he's spent a great deal of space writing to Objectivist audiences about how corrupt modern physics is. He has also endorsed and retracted said endorsement about a Theory of Elementary Waves, which no credible physicist holds and for which online refutations have been posted by Objectivist physicists, here's one by Tom Radcliffe:

http://enlightenment.supersaturated.com/essays/text/tomradcliffe/tew.html

Jim

Edited July 14, 2010 by James Heaps-Nelson

[BaalChatzaf]

How much do you expect from a book on physics with only four equations?

One of which no doubt is A = A.

Seriously, what are the four equations?

Has anyone here, aside from me, read Penrose's massive tome -- the one abounding in equations, the one that might as function as a grand tour of mathematics?

I read the Big Penrose Book. It is loaded to the gills with equations some of them involving tensors and other linear forms.

I would expect a book which dealt with the inductive/abductive aspects of physics to include the Maxwell Equations for electrodynamics, some of the equations of classical mechanics derived from the action principle. That would include D'Alemberts equations for virtual work, the Euler-Langrange equations. I would expect some of the basic equations from relativity theory (special relativity) and of course the Schroedinger wave equations and related stuff. And at least a passing reference to Noether's theorem and the relation between the symmetries and conservation laws.

Ba'al Chatzaf

Edited July 14, 2010 by BaalChatzaf

[James Heaps-Nelson]

How much do you expect from a book on physics with only four equations?

One of which no doubt is A = A.

Seriously, what are the four equations?

Has anyone here, aside from me, read Penrose's massive tome -- the one abounding in equations, the one that might as function as a grand tour of mathematics?

I read the Big Penrose Book. It is loaded to the gills with equations some of them involving tensors and other linear forms.

I would expect a book which dealt with the inductive/abductive aspects of physics to include the Maxwell Equations for electrodynamics, some of the equations of classical mechanics derived from the action principle. That would include D'Alemberts equations for virtual work, the Euler-Langrange equations. I would expect some of the basic equations from relativity theory (special relativity) and of course the Schroedinger wave equations and related stuff. And at least a passing reference to Noether's theorem and the relation between the symmetries and conservation laws.

Ba'al Chatzaf

Good, post Bob! A book like that would deal with induction in physics rather than "perceived philosophical problems with physics".

Jim

[dan2100]

How much do you expect from a book on physics with only four equations?

One of which no doubt is A = A.

Seriously, what are the four equations?

Has anyone here, aside from me, read Penrose's massive tome -- the one abounding in equations, the one that might as function as a grand tour of mathematics?

I read the Big Penrose Book. It is loaded to the gills with equations some of them involving tensors and other linear forms.

Yes, but he works up to those in a way that I think the diligent reader might be able to handle.

I would expect a book which dealt with the inductive/abductive aspects of physics to include the Maxwell Equations for electrodynamics, some of the equations of classical mechanics derived from the action principle. That would include D'Alemberts equations for virtual work, the Euler-Langrange equations. I would expect some of the basic equations from relativity theory (special relativity) and of course the Schroedinger wave equations and related stuff. And at least a passing reference to Noether's theorem and the relation between the symmetries and conservation laws.

Ba'al Chatzaf

I'd expect some of this, but I don't think a heavy mathematical treatment is necessary. (In fact, much philosophy of physics avoids this -- even, in my opinion, excellent works such as those of Lawrence Sklar on spacetime stuff do, such as his classic Space, Time, and Spacetime.)

[Robert Campbell]

You don't consider "mental integration" a "real genus"? If not, is that because of the question of what on earth a "mental integration" *is* or from some other reason? I mean, couldn't there by other forms of "mental integration" with concepts being a sub-type?

I've been over this issue before, with that renowned epistemologist Lindsay Perigo.

But I've been long since banned from SOLOP, and after agitating for quite a few bannings herself, Ms. Stuttle has apparently found the pickings so slim as to voluntarily absent herself from Swami Perigonanda's ashram.

Ayn Rand does not really explain what a mental integration is, despite the importance of "integration" in her epistemology.

Nor does she mention any other varieties of mental integration besides concepts.

Why she didn't use "knowledge" or "means of cognition" as the genus, I really can't fathom.

Robert Campbell

[James Heaps-Nelson]

How much do you expect from a book on physics with only four equations?

One of which no doubt is A = A.

Seriously, what are the four equations?

Has anyone here, aside from me, read Penrose's massive tome -- the one abounding in equations, the one that might as function as a grand tour of mathematics?

I read the Big Penrose Book. It is loaded to the gills with equations some of them involving tensors and other linear forms.

Yes, but he works up to those in a way that I think the diligent reader might be able to handle.

I would expect a book which dealt with the inductive/abductive aspects of physics to include the Maxwell Equations for electrodynamics, some of the equations of classical mechanics derived from the action principle. That would include D'Alemberts equations for virtual work, the Euler-Langrange equations. I would expect some of the basic equations from relativity theory (special relativity) and of course the Schroedinger wave equations and related stuff. And at least a passing reference to Noether's theorem and the relation between the symmetries and conservation laws.

Ba'al Chatzaf

I'd expect some of this, but I don't think a heavy mathematical treatment is necessary. (In fact, much philosophy of physics avoids this -- even, in my opinion, excellent works such as those of Lawrence Sklar on spacetime stuff do, such as his classic Space, Time, and Spacetime.)

Dan,

Thanks for the Sklar reference, I'll look into that. I try to look at 1 or 2 philosophy of science books a year. Most recently, I read Gerald Edelman's Second Nature. I will give the Penrose book a concerted try. Advanced math doesn't scare me too much. I especially enjoyed Ilya Prigogine's The End of Certainty. One advantage with that book was that the math was right up my alley in thermodynamics as my graduate studies were in chemical engineering and dealt with really neat topics in far from equilibrium chemical reactions. I've been through a course in special relativity, although only about 2 weeks of looking at Einstein's General Theory and standard mechanics and E&M from Halliday and Resnick, although I'm weak on the E & M. Most of the quantum I learned was from a physical chemistry course so I still have a ways to go with that.

The physics book I usually recommend for laymen is Lisa Randall's Warped Passages. It's pretty equation sparse, but has footnotes for interested techies.

Jim

Edited July 14, 2010 by James Heaps-Nelson

[Michael Stuart Kelly]

Ayn Rand does not really explain what a mental integration is, despite the importance of "integration" in her epistemology.

Robert,

I noticed this also and at one time earlier, I actively sought it out. I don't have time to be thorough right right now, but I can provide some examples. Before that, though, I understand her use of "integration" basically to mean combining (or joining together) different things into a new whole, whether physical or abstract. It can be automatic or volitional.

For instance, integration is what happens to sensations in order to turn them into percepts. That part is automatic. And integration is what happens to percepts in order to turn them into concepts. Here she gets a little bit ambivalent, since sometimes she calls concept formation volitional only, but other times recognizes that there is an automatic process going on that can result in concepts (usually poor ones to her).

Doing a run of the CDROM, here are some quotes (I have bolded integration):

Galt's speech in Atlas Shrugged:

All thinking is a process of identification and integration.

. . .

It is to a baby that the world appears as a blur of motion, without things that move—and the birth of his mind is the day when he grasps that the streak that keeps flickering past him is his mother and the whirl beyond her is a curtain, that the two are solid entities and neither can turn into the other, that they are what they are, that they exist. The day when he grasps that matter has no volition is the day when he grasps that he has—and this is his birth as a human being. The day when he grasps that the reflection he sees in a mirror is not a delusion, that it is real, but it is not himself, that the mirage he sees in a desert is not a delusion, that the air and the light rays that cause it are real, but it is not a city, it is a city's reflection—the day when he grasps that he is not a passive recipient of the sensations of any given moment, that his senses do not provide him with automatic knowledge in separate snatches independent of context, but only with the material of knowledge, which his mind must learn to integrate—the day when he grasps that his senses cannot deceive him, that physical objects cannot act without causes, that his organs of perception are physical and have no volition, no power to invent or to distort, that the evidence they give him is an absolute, but his mind must learn to understand it, his mind must discover the nature, the causes, the full context of his sensory material, his mind must identify the things that he perceives—that is the day of his birth as a thinker and scientist.

From her essay, "For The New Intellectual":

But to integrate perceptions into conceptions by a process of abstraction, is a feat that man alone has the power to perform—he has to perform it by choice.

From her essay, "Philosophy: Who Needs It"

You have no choice about the necessity to integrate your observations, your experiences, your knowledge into abstract ideas, i.e., into principles. Your only choice is whether these principles are true or false, whether they represent your conscious, rational convictions—or a grab-bag of notions snatched at random, whose sources, validity, context and consequences you do not know, notions which, more often than not, you would drop like a hot potato if you knew.

. . .

Your subconscious is like a computer—more complex a computer than men can build—and its main function is the integration of your ideas. Who programs it? Your conscious mind. If you default, if you don't reach any firm convictions, your subconscious is programmed by chance—and you deliver yourself into the power of ideas you do not know you have accepted.

Notice in this last that, to Rand, integration is something happening in the subconscious, and it happens with "ideas" (which I take to include concepts), but you can "program" it by conscious will.

Sometimes she used the term to mean "system building."

From her essay, "For The New Intellectual":

System-building—the integration of knowledge into a coherent sum and a consistent view of reality—is denounced by all the Attila-ists as irrational, mystical and unscientific.

From her essay, "The Cashing-In: The Student 'Rebellion'":

Add to this: the opposition to "system-building," i.e., to the integration of knowledge, with the result that the material taught in one class contradicts the material taught in the others, each subject hanging in a vacuum and to be accepted out of context, while any questions on how to integrate it are rejected, discredited, and discouraged.

In the following quote, Rand implies that integrate is the opposite of condense, or at least is very different from it.

From Chapter 4, "Concepts of Consciousness" in ITOE:

The purpose of conjunctions is verbal economy: they serve to integrate and/or condense the content of certain thoughts.

In the following quote, integration means tying an identification (a "differentiation") to a genus. In other words, as I understand it, making a category in system building.

From Chapter 5, "Definitions" in ITOE:

Thus a definition complies with the two essential functions of consciousness: differentiation and integration. The differentia isolates the units of a concept from all other existents; the genus indicates their connection to a wider group of existents.

Here's an interesting use, showing that, to her, integration does not involve differentiation, but needs to work in conjunction with it.

From "Appendix—Abstraction as Measurement-Omission" in ITOE:

Now, the essential thing there is that you cannot form a concept by integration alone or by differentiation alone. You need both, always.

This is fun and I believe there is more to be found, but I am out of time.

As one last thought, I have the same problem with her use of the term "abstraction."

Michael

[James Heaps-Nelson]

Dan,

Have you read Stuart Kauffman's At Home in the Universe? That book is currently on my list and my brother read it. Kauffman has a renegade theory that the autocatalytic reactions make the origin of life a much more statistically likely event. If I like that book, I'll proceed to his more mathematically intensive Origins of Order.

Jim

[Philip Coates]

George H. Smith makes several silly statements in his last post: He claims to know that I have not read David Hume. He claims that Hume has a position in ethics he would call 'moral certainty'. And he apparently believes that if a philosopher (inconsistently) holds a strong view in ethics, that he can't be a skeptic in more fundamental ways.

George, try to stay out of fundamental philosophy. You obviously simply do not think in essentials in that area.

Just curious: Which if any of Peikoff's courses did you take? They would have helped you with that.

Edited July 15, 2010 by Philip Coates

[George H. Smith]

George H. Smith makes several silly statements in his last post: He claims to know that I have not read David Hume. He claims that Hume has a position in ethics he would call 'moral certainty'. And he apparently believes that if a philosopher (inconsistently) holds a strong view in ethics, that he can't be a skeptic in more fundamental ways.

George, try to stay out of fundamental philosophy. You obviously simply do not think in essentials in that area.

Just curious: Which if any of Peikoff's courses did you take? They would have helped you with that.

What can one do with an ignoramus of Phil's caliber? For all of his pretentious advice to other people, for all of his boasting, Phil doesn't show the least bit of respect for historical truth.

Never mind that Phil misrepresents Hume. Never mind that Phil substitutes fantasy for history when it comes to tracing the influence of Hume, Kant, and other philosophers in the Objectivist pantheon of villains. None of this matters, for Phil has mystical insight into the nature of "fundamentals." Phil has no evidence for any of this, but he doesn't need evidence. If Rand and/or Peikoff told Phil something, that's all he needs to know.

It is highly instructive to observe Phil's reaction when he is corrected about something -- even on a simple point that he could easily verify for himself. Does Phil concede that he might have made a mistake, even as an outside possibility? Of course not. Instead, he babbles something about "fundamentals," as if this is a magic word that will make all of his problems disappear.

Ghs

[James Heaps-Nelson]

How much do you expect from a book on physics with only four equations?

One of which no doubt is A = A.

Seriously, what are the four equations?

Has anyone here, aside from me, read Penrose's massive tome -- the one abounding in equations, the one that might as function as a grand tour of mathematics?

I read the Big Penrose Book. It is loaded to the gills with equations some of them involving tensors and other linear forms.

I would expect a book which dealt with the inductive/abductive aspects of physics to include the Maxwell Equations for electrodynamics, some of the equations of classical mechanics derived from the action principle. That would include D'Alemberts equations for virtual work, the Euler-Langrange equations. I would expect some of the basic equations from relativity theory (special relativity) and of course the Schroedinger wave equations and related stuff. And at least a passing reference to Noether's theorem and the relation between the symmetries and conservation laws.

Ba'al Chatzaf

Bob,

Your mention of D'Alembert and Euler-Lagrange makes me wish I had stretched to take a good course in theoretical mechanics. After seeing how Lagrange multipliers could be used in microeconomics in Debreu's set theory derivation of utility maximization, it's some of the prettiest math around.

Jim

[Brant Gaede]

George H. Smith makes several silly statements in his last post: He claims to know that I have not read David Hume. He claims that Hume has a position in ethics he would call 'moral certainty'. And he apparently believes that if a philosopher (inconsistently) holds a strong view in ethics, that he can't be a skeptic in more fundamental ways.

George, try to stay out of fundamental philosophy. You obviously simply do not think in essentials in that area.

Just curious: Which if any of Peikoff's courses did you take? They would have helped you with that.

Incredible. Phil, you are a great big fort!

--Brant

I mean fort!

[Alfonso Jones]

George, try to stay out of fundamental philosophy. You obviously simply do not think in essentials in that area.

Just curious: Which if any of Peikoff's courses did you take? They would have helped you with that.

Philip - - -

This post of yours is laughable. Do you really compare yourself favorably to GHS in philosophical acumen, in particular the area of thinking in essentials? What would be the objective basis of this judgment on your part?

Bill P