New Developments re Harriman Induction book


9thdoctor

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> I take it, Phil, that, like Bob, you were unable to tell that I was joking about Peikoff? That's the second time. Is it possible you too may be an assburger?

Ted, I'm afraid I don't know what an assburger is. I may have to ask Cloris Leachman.

George, I'm afraid you will have to stay after class. Adam was at least clever enough to come up with a photo of a schoolmarm, not a strict nurse. My image here is of a schoolmarm, not a medical professional (or proctologist or sphincter analyst).

(Try to keep up.)

I tried but failed to find a picture of Nurse Diesel in her Nazi outfit.

Ghs

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> I take it, Phil, that, like Bob, you were unable to tell that I was joking about Peikoff? That's the second time. Is it possible you too may be an assburger?

Ted, I'm afraid I don't know what an assburger is. I may have to ask Cloris Leachman.

George, I'm afraid you will have to stay after class. Adam was at least clever enough to come up with a photo of a schoolmarm, not a strict nurse. My image here is of a schoolmarm, not a medical professional (or proctologist or sphincter analyst).

(Try to keep up.)

I tried but failed to find a picture of Nurse Diesel in her Nazi outfit.

Ghs

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I tried but failed to find a picture of Nurse Diesel in her Nazi outfit.

Time for some free association:

http://www.youtube.com/watch?v=0q3doiKoli0

Next up: Nurse Ratched.

Nominations remain open for the “What film character Phil most reminds you of: Female” poll.

Edited by Ninth Doctor
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Or, you can point out the vacuousness of Rand's ideas on patents (say), and you can point out the burden of proof principle in regards to government action against a 2nd inventor, and yet the Objectivist continues advocating patents anyway -- this is EVIL.

Shayne,

Not entirely sure what your full position on patents is.

My position is that we would be in huge trouble without them.

You'd end up with toxic secrecy, the return of the guild system, and scientific-industrial stagnation. I am an engineer who reads patents regularly at work and their value to civilization is inestimable.

Mike

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Ted,

You write:

You may recall the O J Simpson trial. I had not read OPAR when it was in progress. I screamed at the screen in disgust that the judge was allowing the defense to make arbitrary assertions that the evidence could have been tampered with or that there could have been some Colombian drug dealers involved without presenting any evidence to support their claims. There is no other way to criticize such claims except as arbitrary. Ito's allowing them was a miscarriage of justice and a betrayal of centuries of proper jurisprudence. Nothing is a more dramatic proof of the abomination of allowing such claims entrance in the realm of thought.

I think the problem here is that all the evidence pointed to Simpson's guilt and there was little or no exculpatory evidence. In addition, there was no reason to think that the evidence was tampered with. So Cochoran's claims weren't arbitrary, they were false.

However, what if we had no idea who killed Nicole and there was evidence that OJ was out of town? Would Cochoran's claims have been arbitrary? I don't think so.

-Neil Parille

Edited by Neil Parille
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Ted,

You write:

You may recall the O J Simpson trial. I had not read OPAR when it was in progress. I screamed at the screen in disgust that the judge was allowing the defense to make arbitrary assertions that the evidence could have been tampered with or that there could have been some Colombian drug dealers involved without presenting any evidence to support their claims. There is no other way to criticize such claims except as arbitrary. Ito's allowing them was a miscarriage of justice and a betrayal of centuries of proper jurisprudence. Nothing is a more dramatic proof of the abomination of allowing such claims entrance in the realm of thought.

I think the problem here is that all the evidence pointed to Simpson's guilty and there was little or no contrary evidence. In addition, there was no reason to think that the evidence was tampered with. So Cochoran's claims weren't arbitrary, they were false.

However, what if we had no idea who killed Nicole and there was evidence that OJ was out of town? Would Cochoran's claims have been arbitrary?

-Neil Parille

I was hoping Robert would answer my question on the honus of proof principle before I comment further - nudge me to answer this later if he hasn't responded.

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Ted,

I don't see what the concept of the arbitrary assertion adds to our logical and epistemological arsenal.

And it's used by Objectivists to prevent discussion on things they don't agree with. I find the evidence for ESP unpersuasive, but that doesn't mean the concept is arbitrary. Likewise, is it really arbitrary when Barbara writes in Passion that Rand was born in Russia, wrote Atlas Shrugged, or had anger problems? (Not that you agree with these uses of the arbitrary assertion doctrine.)

-Neil Parille

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Or, you can point out the vacuousness of Rand's ideas on patents (say), and you can point out the burden of proof principle in regards to government action against a 2nd inventor, and yet the Objectivist continues advocating patents anyway -- this is EVIL.

Shayne,

Not entirely sure what your full position on patents is.

My position is that we would be in huge trouble without them.

You'd end up with toxic secrecy, the return of the guild system, and scientific-industrial stagnation. I am an engineer who reads patents regularly at work and their value to civilization is inestimable.

Mike

The government created the Internet, and its value to civilization is inestimable. Therefore we need to steal your money to keep funding government R&D projects.

The problem with patents (as you understand them) is that they blatantly and obviously violate individual rights, namely, my right to use my own brain to create my own ideas and transform my property in accordance with them. No one has ever provided nor can one anyone provide a justification "but I thought of it first!" as a reason to come take my property. But certainly, the pragmatist argument you provide is the best possible defense, the problem is that it is a viciously amoral argument. You want to have you cake and eat it too. You want to claim to be for individual rights, and you want to wave guns around for the "good" of civilization. This is why Objectivists have no credibility, this is why Murray Rothbard wins over Rand.

Now, patents in a limited form can be saved, but only by reconceptualizing in other areas Objectivists refuse to tread, which brings up another way Rothbard has won. It is not fair to say I am totally against patents. What I am against is a form of them that violates individual rights.

Shayne

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Wow. The internet was legitimate defense infrastructure that justified the taxes it consumed. Project Apollo was also a key part of the USA's defense apparatus.

How do you propose to invent anything after the exchange of information has ceased. Only protecting the 1st inventor will induce him to divulge the very information that subsequent inventors depend heavily on. I dispute that you would succeed in using your brain and your property as you imagine. Now a guild system certainly does violate individual rights. How is my argument amoral again?

I hope you are joking about Rothbard.

Warm regards,

Mike

The government created the Internet, and its value to civilization is inestimable. Therefore we need to steal your money to keep funding government R&D projects.

The problem with patents (as you understand them) is that they blatantly and obviously violate individual rights, namely, my right to use my own brain to create my own ideas and transform my property in accordance with them. No one has ever provided nor can one anyone provide a justification "but I thought of it first!" as a reason to come take my property. But certainly, the pragmatist argument you provide is the best possible defense, the problem is that it is a viciously amoral argument. You want to have you cake and eat it too. You want to claim to be for individual rights, and you want to wave guns around for the "good" of civilization. This is why Objectivists have no credibility, this is why Murray Rothbard wins over Rand.

Now, patents in a limited form can be saved, but only by reconceptualizing in other areas Objectivists refuse to tread, which brings up another way Rothbard has won. It is not fair to say I am totally against patents. What I am against is a form of them that violates individual rights.

Shayne

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Ted,

I don't see what the concept of the arbitrary assertion adds to our logical and epistemological arsenal.

And it's used by Objectivists to prevent discussion on things they don't agree with. I find the evidence for ESP unpersuasive, but that doesn't mean the concept is arbitrary. Likewise, is it really arbitrary when Barbara writes in Passion that Rand was born in Russia, wrote Atlas Shrugged, or had anger problems? (Not that you agree with these uses of the arbitrary assertion doctrine.)

-Neil Parille

Yes, you said this already. Like I said, I would like to see Robert's response to my question on the honus of proof principle before I answer you.

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Given the lack of comment, can I assume I pass muster on understanding Goedel?

Ted,

You seem to be adopting one of Jim Valliant's procedures, wherein the lack of an instant answer is presumed to prove that the critic has "conceded" Valliant's point.

It won't replace Hofstadter's exposition, or Nagel and Newman's, but I recommend consulting this Wikipedia article:

http://en.wikipedia....eteness_theorem

specifically, the sections on "Relation to the liar paradox" and "Examples of undecidable statements."

Note that the Gödel sentence G says "G is not provable in theory T."

It does not say, "G is false."

Further note that from the employment of a trick sentence or question ("G is not provable in T," or its computational analogue, "Will program P halt?') to prove the result we are discussing, it doesn't follow that only trick sentences are true but not provable within a system, or only trick questions include uncomputable predicates.

Now here is what Leonard Peikoff has said in print:

Even the professional mathematicians, the onetime guardians of the citadel of certainty and of logical consistency, caught the hang of the modern spirit. In 1931, they were apprised of the latest Viennese development in the field, Kurt Gödel's incompleteness theorem, according to which logical consistency (and therefore certainty) is precisely the attribute that no systems of mathematics can ever claim to possess" (The Ominous Parallels, p. 215)

Would you take this as evidence that Peikoff knows what he is talking about, on the subject under discussion?

Can you explain what you mean by the honus of proof principle, Robert?

The onus (burden) of proof principle says, for instance, that if you claim that gremlins are convening on Venus, the burden is on you to provide evidence that there are gremlins or reasons for believing there are gremlins, not on your critic to prove that there are no gremlins.

The onus of proof principle does not include such provisions as:

—Claims made in violation of the principle are neither true nor false

—Anyone who ever makes a claim in violation of the principle has instantly embraced a Zero, permanently rotted his mind, and temporarily made himself dumber than a parrot

—Claims made in violation of the principle cannot be cognitively processed; needn't be responded to; and must under no circumstances be responded to—all at once

Nor does it include such Peikovian embellishments as:

—Gremlins are nothing, and the nonexistence of nothing leaves no traces, therefore, if a claim about the existence or operations of gremlins were false, no consequences would follow on account of its being false.

Robert Campbell

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This is why Rothbard has won. All you are doing is repeating ad nauseam pragmatist arguments.

Have you been so divested of morality that you cannot see any issues of natural rights violation with regards to patents? It's not complicated: I think of something, I transform my property. You then whine that you "thought of it first" and put a gun to my head. It's "patently" obvious there's a problem here.

Shayne

Wow. The internet was legitimate defense infrastructure that justified the taxes it consumed. Project Apollo was also a key part of the USA's defense apparatus.

How do you propose to invent anything after the exchange of information has ceased. Only protecting the 1st inventor will induce him to divulge the very information that subsequent inventors depend heavily on. I dispute that you would succeed in using your brain and your property as you imagine. Now a guild system certainly does violate individual rights. How is my argument amoral again?

I hope you are joking about Rothbard.

Warm regards,

Mike

The government created the Internet, and its value to civilization is inestimable. Therefore we need to steal your money to keep funding government R&D projects.

The problem with patents (as you understand them) is that they blatantly and obviously violate individual rights, namely, my right to use my own brain to create my own ideas and transform my property in accordance with them. No one has ever provided nor can one anyone provide a justification "but I thought of it first!" as a reason to come take my property. But certainly, the pragmatist argument you provide is the best possible defense, the problem is that it is a viciously amoral argument. You want to have you cake and eat it too. You want to claim to be for individual rights, and you want to wave guns around for the "good" of civilization. This is why Objectivists have no credibility, this is why Murray Rothbard wins over Rand.

Now, patents in a limited form can be saved, but only by reconceptualizing in other areas Objectivists refuse to tread, which brings up another way Rothbard has won. It is not fair to say I am totally against patents. What I am against is a form of them that violates individual rights.

Shayne

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Given the lack of comment, can I assume I pass muster on understanding Goedel?

Ted,

You seem to be adopting one of Jim Valliant's procedures, wherein the lack of an instant answer is presumed to prove that the critic has "conceded" Valliant's point.

It won't replace Hofstadter's exposition, or Nagel and Newman's, but I recommend consulting this Wikipedia article:

http://en.wikipedia....eteness_theorem

specifically, the sections on "Relation to the liar paradox" and "Examples of undecidable statements."

Note that the Gödel sentence G says "G is not provable in theory T."

It does not say, "G is false."

Further note that from the employment of a trick sentence or question ("G is not provable in T," or its computational analogue, "Will program P halt?') to prove the result we are discussing, it doesn't follow that only trick sentences are true but not provable within a system, or only trick questions include uncomputable predicates.

Now here is what Leonard Peikoff has said in print:

Even the professional mathematicians, the onetime guardians of the citadel of certainty and of logical consistency, caught the hang of the modern spirit. In 1931, they were apprised of the latest Viennese development in the field, Kurt Gödel's incompleteness theorem, according to which logical consistency (and therefore certainty) is precisely the attribute that no systems of mathematics can ever claim to possess" (The Ominous Parallels, p. 215)

Would you take this as evidence that Peikoff knows what he is talking about, on the subject under discussion?

Can you explain what you mean by the honus of proof principle, Robert?

The onus (burden) of proof principle says, for instance, that if you claim that gremlins are convening on Venus, the burden is on you to provide evidence that there are gremlins or reasons for believing there are gremlins, not on your critic to prove that there are no gremlins.

The onus of proof principle does not include such provisions as:

—Claims made in violation of the principle are neither true nor false

—Anyone who ever makes a claim in violation of the principle has instantly embraced a Zero, permanently rotted his mind, and temporarily made himself dumber than a parrot

—Claims made in violation of the principle cannot be cognitively processed; needn't be responded to; and must under no circumstances be responded to—all at once

Nor does it include such Peikovian embellishments as:

—Gremlins are nothing, and the nonexistence of nothing leaves no traces, therefore, if a claim about the existence or operations of gremlins were false, no consequences would follow on account of its being false.

Robert Campbell

Don't play the comparing me with Valiant game. I am not evading any direct questions. You raised the implicit challenge that I am not qualified to discuss Goedel, and I answered you, and wanted a recognition that I responded to you.

The reason that the truth of the Goedel statement can't be proven is that it implies an apparent contradiction, isn't it? What I have said above is essentially correct. Goedels' proof relies on the truth value of a sentence which, since it does note refer to anything outside itself, leads to an infinite regress of self-reference. You do not deny this, do you? All Goedel proves is that people can utter contradictions.

As for the "honus of proof principle", I expected an explanation in the context of the O J trial. Can you explain to me exactly where you think it was applicable? Who bore the burden of arguing what?

Edited by Ted Keer
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Rothbard hasn't won anything. Are you an AnCap, BTW?

Natural rights are violated by patents. There, happy?

Secure borders also violate natural rights. We could go on.

Patents violate natural rights less than any alternative, however.

Specifically, permitting the 2nd inventor to use the new idea,

without compensating the 1st inventor, will cause all invention

to be done in secret. Boy will natural rights be buggered then.

A USA (I am Canadian, BTW) without a patent system would have

lost the Cold War and we'd both be arguing in a Gulag about now.

Talk about having a gun to your head.

Rand was wrong about some things but this isn't one of them.

Mike

This is why Rothbard has won. All you are doing is repeating ad nauseam pragmatist arguments.

Have you been so divested of morality that you cannot see any issues of natural rights violation with regards to patents? It's not complicated: I think of something, I transform my property. You then whine that you "thought of it first" and put a gun to my head. It's "patently" obvious there's a problem here.

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The reason that the truth of the Goedel statement can't be proven is that it implies an apparent contradiction, isn't it?

No. For example, Goldbach's conjecture is true (there are no known exceptions), but not proven.

What I have said above is essentially correct. Goedels' proof relies on the truth value of a sentence which, since it does note refer to anything outside itself, leads to an infinite regress of self-reference. You do not deny this, do you? All Goedel proves is that people can utter contradictions.

What it proves is that all truths (known or not yet discovered) are not derivable from a given axiomatic system. What it shows is human creativity.

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The reason that the truth of the Goedel statement can't be proven is that it implies an apparent contradiction, isn't it?

No. For example, Goldbach's conjecture is true (there are no known exceptions), but not proven.

The Goldbach conjecture does not rely on an implied contradiction. I fail to see the relevance, and believe you have misunderstood me.

What I have said above is essentially correct. Goedels' proof relies on the truth value of a sentence which, since it does note refer to anything outside itself, leads to an infinite regress of self-reference. You do not deny this, do you? All Goedel proves is that people can utter contradictions.

What it proves is that all truths (known or not yet discovered) are not derivable from a given axiomatic system. What it shows is human creativity.

Be specific. Show me an example of one of these non demonstrable truths. I predict it will make an assertion about the truth value of a sentence which does not have a truth value because it has no non-recursive reference.

A consciousness conscious of only itself is a contradiction in terms.

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I fail to see the relevance, and believe you have misunderstood me.

The latter might be true. If you don't understand the relevance of Goldbach's conjecture, then you don't understand the Incompleteness Theorem.

Be specific. Show me an example of one of these non demonstrable truths.

I gave you one -- Goldbach's conjecture.

P.S. Regarding #218, I said "No. For example, ...", not you.

Edited by Merlin Jetton
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Be specific. Show me an example of one of these non demonstrable truths. I predict it will make an assertion about the truth value of a sentence which does not have a truth value because it has no non-recursive reference.

Ted,

Recursive reference does not require the presupposition of a mind conscious only of itself.

Here are a few examples of mathematical generalizations that are widely regarded as true but unprovable. They come from the Wikipedia article aforecited:

The combined work of Gödel and Paul Cohen has given two concrete examples of undecidable statements (in the first sense of the term [i.e., the one employed by Gödel]): The continuum hypothesis can neither be proved nor refuted in ZFC [Zermelo-Fraenkel with Choice] (the standard axiomatization of set theory), and the axiom of choice can neither be proved nor refuted in ZF (which is all the ZFC axioms except the axiom of choice). These results do not require the incompleteness theorem. Gödel proved in 1940 that neither of these statements could be disproved in ZF or ZFC set theory. In the 1960s, Cohen proved that neither is provable from ZF, and the continuum hypothesis cannot be proven from ZFC.

In 1973, the Whitehead problem in group theory was shown to be undecidable, in the first sense of the term, in standard set theory.

In 1977, Paris and Harrington proved that the Paris-Harrington principle, a version of the Ramsey theorem, is undecidable in the first-order axiomatization of arithmetic called Peano arithmetic, but can be proven to be true in the larger system of second-order arithmetic. Kirby and Paris later showed Goodstein's theorem, a statement about sequences of natural numbers somewhat simpler than the Paris-Harrington principle, to be undecidable in Peano arithmetic.

Kruskal's tree theorem, which has applications in computer science, is also undecidable from Peano arithmetic but provable in set theory. In fact Kruskal's tree theorem (or its finite form) is undecidable in a much stronger system codifying the principles acceptable on the basis of a philosophy of mathematics called predicativism. The related but more general graph minor theorem (2003) has consequences for computational complexity theory.

Gregory Chaitin produced undecidable statements in algorithmic information theory and proved another incompleteness theorem in that setting. Chaitin's theorem states that for any theory that can represent enough arithmetic, there is an upper bound c such that no specific number can be proven in that theory to have Kolmogorov complexity greater than c. While Gödel's theorem is related to the liar paradox, Chaitin's result is related to Berry's paradox.

Robert Campbell

PS. I won't assume that you've conceded anything, but you still haven't commented on what Peikoff said about Gödel.

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I am sorry, but I do not have Peikoff's opus available, and so cannot comment on his specific arguments. You can always quote him in a stand alone post and ask me if I object the way you do. I do remember thinking while reading him that while I understood what he wanted to say, he did not express himself well.

As for Goedel's theorem, there is an essential difference between an as yet unproven conjecture and a proposition which results directly in a contradiction unresolvable without infinite regress. Was my explanation correct or not? Did he not supposedly produce a recursive wff within an axiomatic system the truth of which could not be determined? Does his proof not require that one attach a truth value to such a recursive statement? If I deny that such a statement has a truth value, does my premise not, if accepted, invalidate his proof?

The consciousness conscious of itself statement was not an assertion that a self-referential wff requires such a conscious state, but rather an analogy, showing in parallel why a statement the truth of which depends on its own truth value is as invalid as a consciousness which is consciousness of itself.

Robert, if you haven't already done so in a cross post, could you please explain concretely where the honus of proof principle was applicable in the O J trial?

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Ted,

I'm not a legal expert, to put it mildly. In what follows, I'll be using the wrong vocabulary, if nothing else.

But in a criminal trial, the onus of proof is on the prosecution, as far as the elements of the crime are concerned. For instance, Marcia Clark et al. were obliged to prove that a particular knife was used to commit the murder (e.g., because, among other things, the victims were stabbed to death and the knife had the victims' blood on it) and that it was wielded by OJ Simpson (e.g., because it also had his blood on it). Etc.

While the defense is not under a general obligation to prove that the defendant did not commit the crime—and it should not be, legally or logically—it does assume the burden of proof with regard to certain affirmative claims that it might want to make. For instance, if the defense wants to argue that evidence was planted in order to incriminate the defendant, it needs to provide reasons why anyone ought to believe that this piece of evidence was planted by some particular person in this case, in order to implicate this defendant. From a logical standpoint, it's not enough to argue that, in general, evidence can be planted (obviously true, but so what?).

Apparently, you think that the Peikovian doctrine of the arbitrary assertion is required, lest Judge Lance Ito and his counterparts allow Johnny Cochran and his counterparts to mount improper defenses in court.

Why do you think so?

I see the onus of proof (a logical principle of great antiquity) as sufficient, without any need to accept Peikoff's assimilation of it into his grand, confused scheme.

For what it's worth, while the judge did a poor job in the OJ case, there isn't a whole lot that any judge can do to prevent naked appeals to jury nullification, on racial or other political grounds, when the jury is receptive to them.

Robert Campbell

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While the defense is not under a general obligation to prove that the defendant did not commit the crime—and it should not be, legally or logically—it does assume the burden of proof with regard to certain affirmative claims that it might want to make. For instance, if the defense wants to argue that evidence was planted in order to incriminate the defendant, it needs to provide reasons why anyone ought to believe that this piece of evidence was planted by some particular person in this case, in order to implicate this defendant. From a logical standpoint, it's not enough to argue that, in general, evidence can be planted (obviously true, but so what?).

Yes—except for the final "so, what?"—this is exactly what I wanted to hear. Affirmative defenses made without evidence, i.e., based upon imagination, are a paradigm case of arbitrary assertions. Nothing better illustrates applied epistemology that rational rules of evidence. A jury is supposed to deliberate and make determinations of fact based on evidence. The judge's role is to exclude from consideration irrelevant matters such as prejudicial appeals to emotion and bald speculation—precisely because there is no way to weigh them objectively. The honus of proof principle, as you call it, does not enforce itself. It is upon precisely the criterion of arbitrariness (lawyers call it lack of evidence) which such judgments are made.

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I am sorry, but I do not have Peikoff's opus available, and so cannot comment on his specific arguments. You can always quote him in a stand alone post and ask me if I object the way you do. I do remember thinking while reading him that while I understood what he wanted to say, he did not express himself well.

Ted,

The principle of charity is a good thing. But reading into a philosopher's text what makes sense to you, the reader, is not a wise procedure. You may have ended up deciding that while you understood what you wanted to say, Leonard Peikoff wasn't expressing your intended meaning very well.

I've become convinced that, by and large, neither Peikoff's critics nor his supporters actually read what he says with much care.

It could well be that you have your own notion of arbitrariness that bears little relation to Peikoff's. In which case, you'll be doing yourself and the rest of us a service if you lay out the Keerian doctrine of the arbitrary, putting to the side for now whether it agrees with Peikoff's doctrine, or even whether it counts as some species of Objectivism.

As for Goedel's theorem, there is an essential difference between an as yet unproven conjecture and a proposition which results directly in a contradiction unresolvable without infinite regress. Was my explanation correct or not? Did he not supposedly produce a recursive wff within an axiomatic system the truth of which could not be determined? Does his proof not require that one attach a truth value to such a recursive statement? If I deny that such a statement has a truth value, does my premise not, if accepted, invalidate his proof?

Sorry, but I still think you're not getting what Gödel was doing.

His theorem pertains, not merely to the unproven, but to the unprovable.

There are mathematical truths that cannot be proved with the resources of a given formalized theory.

These mathematical truths are not all Gödel sentences.

If, contrary to appearances, you have in mind some other objection that goes to the core of what Gödel was doing, write a critique of his proof and submit it for publication.

Robert Campbell

PS. When I quoted The Ominous Parallels on Gödel, I provided as much context as Peikoff did.

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The principle of charity is a good thing. But reading into a philosopher's text what makes sense to you, the reader, is not a wise procedure. You may have ended up deciding that while you understood what you wanted to say, Leonard Peikoff wasn't expressing your intended meaning very well.

I've become convinced that, by and large, neither Peikoff's critics nor his supporters actually read what he says with much care.

I know that when I first read OPAR, I fell into this error. It wasn't until speaking with him in person that I realized that what he actually thought was quite different from what I had understood him to say, and that what he thought was bogus. It was a wakeup call about reading too charitably.

Shayne

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