# SCORECARD! Can't tell the players without a scorecard!

## 333 posts in this topic

Bob,

So you are saying that it might be possible to have a counterexample and still not disprove something? Or does the counterexample disprove in all cases "universally quantified over an infinite domain"?

Michael

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Bob,

So you are saying that it might be possible to have a counterexample and still not disprove something? Or does the counterexample disprove in all cases "universally quantified over an infinite domain"?

Michael

Sigh! Counterexample IS disproof. Have you ever had a course in logic. I mean *real* logic, the kind they teach in universities, not Rand's caricature of logic?

The negation of for all x P(x) is there exists x such that -P(x). So if you come up with a specific instance n such that -P(n) then you have proven for all x P(x) is false.

Ba'al Chatzaf

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Bob,

So you are saying that because we know individual cases of logic and they have held, they are true in all future cases?

How do you know that? Can you prove it?

Michael

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Bob,

So you are saying that because we know individual cases of logic and they have held, they are true in all future cases?

How do you know that? Can you prove it?

Michael

I say no such thing. Puhleeeeze, learn some logic. Get a textbook on logic and learn something about first order predicate logic. Apparently what you "know" of logic is Rand's distorted and incorrect assertions about logic. If you want to learn medicine you go to a doctor for lessons, not a novelist. If you want to learn logic you go to a logician for lessons, not a novelist.

You can get Copi's textbook on logic pretty cheap at www.abebooks.com or borrow a copy from you local library. His textbook is not the very best or latest but it is solid enough for the non-specialist in logic to learn the basics. You don't even need the latest edition. You can get one or two editions back for cheap.

Ba'al Chatzaf

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Bob,

Can you prove that logic is always right about the falsity of something? I am asking for a reason. Trying to sidestep about my level of education is not an answer.

Michael

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Bob,

Can you prove that logic is always right about the falsity of something? I am asking for a reason. Trying to sidestep about my level of education is not an answer.

Michael

Logic is about the validity of inference, not the truth or falsity of premises. It deals with the issue: does the conclusion follow from the premises. Puhleeze, learn some logic.

Ba'al Chatzaf

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Bob,

Come on. You're sidestepping. If something does not follow from the premises, the formulation is false. Call it by any name you want, illogical, wrong, whatever.

What I am asking is how can you prove that logic will work in every instance of disproving a proposition by presenting one exception (or more). I thought that was calling the proposition false in any case.

But back to the question. Are you sure such logic will work every time? If you are sure, why are you sure?

We are discussing a process that is "universally quantified over an infinite domain."

Michael

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Michael,

On some issues, we all ought be bugging Bob K. This, however, is definitely not one of them. Though I have some disagreements with Bob K's philosophy of logic, none of them is relevant here.

Formal logic is the study of valid and invalid forms of argument.

Formal logic tells us the following:

A. A universal generalization (e.g., "All swans are white") is falsified (proven false) by one counterexample (e.g., "Swan#9867 is black"). If "Swan#9867 is black" is true, then "Some swans are black" has to be true, as does "Some swans are not white," so "All swans are white" has to be false.

B. Contrariwise, you can pile up true statements about this particular swan and that particular swan as high as you like, but from

"Swan#1 is white"

"Swan#2 is white"

"Swan#3 is white"

.

.

.

"Swan#9866 is white"

it does not validly follow that

"All swans are white"

These premises could all be true, yet the conclusion could still be false--for instance, because "Swan#9867 is black" is also true.

You can't take data statements about this swan and that swan and so on and use them to verify a universal conclusion. In slightly different words, you can't prove a generalization about all swans on the basis of data about particular swans.

By the way, this particular point can be made just as easily with ancient formal logic (the kind that Aristotle and the Stoics and the Medievals used) as with modern symbolic logic (the kind that was introduced by Gottlob Frege with the initial goal of making mathematical proofs more rigorous). Modern logic is necessary for some purposes, but not for all.

Because of this basic point I am confident that Leonard Peikoff has not presented a "solution to the problem of induction," in those lectures that ARI is selling for \$205 a pop. He may have done some other things, and these might be valuable. But the likelihood that Dr. Peikoff has come up with logically valid inductive argument forms is, well, the same as the likelihood that his favorite gremlins are holding a conference on Venus.

Robert Campbell

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Robert:

>Because of this basic point I am confident that Leonard Peikoff has not presented a "solution to the problem of induction"...

Yes.

When, by extension, Leonard Peikoff or any other Objectivist, can demonstrate how to validly derive universal laws from existential (or observation) statements - no matter how numerous - then they can claim to have solved the problem of induction.

Further, even if he has come up with some solution, wrapped up somewhere in one of his 137-cassette-series lectures, this solution cannot be part of official Objectivism.

Why? Because Ayn Rand didn't think of it. As I've noted before, on pages 304/5 of the ITOE she plainly admits she does not know the answer to this famous problem, and has never even thought seriously about it.

As she didn't think of it, even if this fantastic creature exists, it cannot be part of (official) Objectivism.

The fact that many Objectivists appear to believe she did solve Hume's problem is just due to years of propaganda from various sources hyping her as having solved all the major philosophical issues etc. They took it on trust that this was the case, but unfortunately there is absolutely no evidence that she or her successors have done anything of the sort. None, zero, zip, nada.

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Because of this basic point I am confident that Leonard Peikoff has not presented a "solution to the problem of induction," in those lectures that ARI is selling for \$205 a pop. He may have done some other things, and these might be valuable. But the likelihood that Dr. Peikoff has come up with logically valid inductive argument forms is, well, the same as the likelihood that his favorite gremlins are holding a conference on Venus.

Thank you, Robert. I'd been debating whether to try to pose a question to Roger about just what Peikoff claims to have demonstrated in those lectures. But since I'm not feeling well enough for sustaining dialogue, I hesitated to ask. You've provided enough groundwork, maybe I can frame this succinctly:

Roger, does Peikoff actually claim to have solved "the problem of induction"? If so, how is he defining "induction"? What is he thinking the problem is? I did hear a lecture which I think was from the IPP series (via a friend who has the tapes). What I understood Peikoff to be trying to do was to demonstrate that you can get causal necessity from experience. He was claiming (with an assist from a clue provided by Greg Salmieri [sp]) that we get our first knowledge of necessary cause from our own direct experience of being able to move our own bodies. But even granting this point, how would it solve the problem of induction? I realize I might be asking something more complicated than you can explain easily, or than you have time to explain. But I and probably others here too would welcome any clues you can provide on Peikoff's argument.

Ellen

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Robert,

I am not defending Peikoff. Also, we have discussed induction, etc., ad nauseum in the is-ought problem.

I am having a small bit of trouble with the mind-body dichotomy of saying that something "in here" (like the methodology of logic) is knowledge that can be "universally quantified over an infinite domain," while the moment this methodology is used with data from "out there," this is held as some kind of proof that knowledge is not really possible except as speculation (some more reliable than other).

I have been doing a bit of reading on experiments with subitizing (embedded in other studies) and what I have read show that this mental mechanism is remarkably consistent with many different people and for all five senses. Perception problems only start when the mind starts processing information that goes beyond a subitizing threshold (2 to 7, depending on the sense and object and arrangement) and only then can speculation be said to enter cognitive processing. Up to that threshold, people manage to repeat tests over and over and over and over without error.

Subitizing and counting (Wikipedia article)

The Magical Number Seven by George Miller

The Brain’s Innate Arithmetic from Where Mathematics Comes From by George Lakoff and Rafael E. Núñez

There is much more (thank goodness for Google) but the words are big and my time is not eternal and many of the articles need to be purchased (however I am doing more and more reading on this because it is fascinating me).

The accuracy or certainty of knowledge from subitizing depends on the health of the person, but I also claim that the use of logic depends on the same. Without a brain there is no logic and a brain can be unhealthy.

On the swan thing, here is what I wrote in a previous discussion:

The more I see this problem discussed, the more I become convinced that there is an axiom about entities that has not been properly included. I wrote about this once, see below (I highlighted the axiom part):
I am starting to believe that induction is the identification of an entity (or other existent) as a member of a group. I think I mentioned this before, but the more I ponder on this, the more I see that inductive reasoning is this process (identifying an existent as a unit). And I am beginning to see some holes in normal arguments against induction.

By going from observing a sample to projecting a truth about a group, one does not make a statement about contradicting a proposition, other than a proposition about the existence of the group itself. A person only makes a statement about creating a mental category of existents that, in fact, actually exist with such differences and similarities as observed.

In the classic example: "I have observed several white swans, therefore all swans are white," is a misuse of induction. The correct use is: "I have observed several white swans, therefore white swans exist as a category of reality." This implies that other white swans exist and rests on an axiom (one I have not seen anywhere in my reading, yet) that if two or more existents are observed and identified as a group, other unobserved members of that group exist. Science actually rests on this axiom in addition to deduction.

Obviously induction can be used to speculate, so the classic swan problem qua speculation is not a misuse of induction. But I am using induction here to mean a form of reasoning (or logic) for identification, i.e., for gaining knowledge. As a form of using induction for gaining knowledge qua knowledge, the classic problem as stated is a misuse of induction.

Finding a black swan does not disprove the knowledge of white swans gained by induction, because finding a black swan does not contradict the validity of the category. It only contradicts a proposition of closing the category off to new knowledge of the type of entity (closing swans off to any other color than white). In fact, a black swan causes the category of swan to be divided into two subcategories: white swans and black swans (more precisely, at that point, the categories are white swans and at least one black swan, and this will only become "white swans and black swans" when more than one black swan is observed).

When this kind of reasoning is applied to the is/ought problem (along with deduction), it becomes very easy to derive ought from is. One does not close the categories involved. One merely makes a statement about the categories that have already been identified.

In fact, there can be no deduction without categories. Induction is nothing more than volitional concept formation.

I have not had time to do the heavy reading on all this that I need to, but I do think this axiom needs to be included in the reasoning process of the "are you sure you can't be sure?" type.

By accepting the following axiom from above:

When two or more existents are observed and identified as a group, other unobserved members of that group exist,

one can be sure (or certain) that other individual examples of that group are out there somewhere. We cannot be sure that members with variations do not exist (in fact we can almost be sure that they do because the universe is so big). As an aside, we also can be sure that we can break individual existents (in any group) down into components that will form new groups. Reductionism is predicated on this premise.

The axiom above is kind of like an axiom of identity for groups. If applying this to inanimate matter bothers people, at least we can easily observe that with living entities, species do exist in reality. They may be made up of individual entities, but they also exist with group characteristics that do not apply to other groups (especially reproduction).

I would refine parts of the above (and certainly shorten it), but nothing essential. I was challenged on this by saying that in Objectivism, an axiom needs to be used in the very process needed to deny it—and this does not apply to the axiom: When two or more existents are observed and identified as a group, other unobserved members of that group exist. However, this can be stated in another way: All things exist in a form that can be categorized and the human mind exists in a form able to categorize them. In this case, this works as an axiom. In order to deny that all things can be categorized by the human mind, we have to categorize everything we use to deny it. (I.e., use concepts.)

In my present thinking, I consider that one of the best parts of Objectivist epistemology is tying concept formation critically to logic—i.e., no concept, no logic. I am not in full agreement with some details on how this has been developed, but the essential tie-in is absolutely correct. Most of the things I have read on logic so far take concept formation as an undefined given.

I have much more to say on this, but I hope that this shows that my questions to Bob are not simple teenage Randroid baiting. He insists on keeping things simple by repeating simple formulations over and over (sometimes accompanied with long marginally related technical tangents), so I decided to cut my questions down to the bone to see if he would actually ask me to learn about logic. After all, he participated in many discussions with me on epistemology. Well, he did.

My premise is that if the functioning of the brain results in one kind of absolute knowledge (methodology of logic) and the brain is organic, there is no reason on earth to claim that extensions of the brain to outer reality result in speculation only. If, according to this argument, sense organs are limited to providing speculation only because physiological conditions exist that govern them, this same standard must also be applied to the brain. If not, why isn't it? Just because? Is the brain suddenly inorganic?

If all observed knowledge is falsifiable, and the reason is because of the imperfection of the organs processing that knowledge, then the method itself must be governed by the same standard. This means that logic itself is falsifiable and only relatively reliable because of the imperfection of the brain. Or does logic exist independently of brains? If there were no brain anywhere in the world, could logic even exist?

Obviously, I do not hold to the "knowledge as speculation only except for some strictly mental operations" theory. I am merely pointing out that the inconsistency runs deeper than it appears.

Michael

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Mike's axiom:

>When two or more existents are observed and identified as a group, other unobserved members of that group exist.

False. There are only two cookies of my special chocolate chip cookies left in the jar. No more exist.

Or: the final pair of any endangered species.

Or...numerous other examples.

This axiom needs to be a little more axiomatic...;-)

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There are only two cookies of my special chocolate chip cookies left in the jar. No more exist.

Daniel,

Do you mean that there are no more chocolate cookies in the world? Not even the special type? This type of food has ceased to exist and cannot be remade?

Dayaamm!

(Incidentally, a chocolate cookie is more than an object. It is a man-made object. This information is included in the category. You just did a stolen concept thingie.)

Michael

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When "the problem of induction" is solved what will we be able to do we cannot do now?

--Brant

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Brant,

It was resolved a long time ago. That's one of the reasons mankind has such produced wealth and this is growing.

The truth is that rational thought doesn't work without both induction and deduction (and some derivatives like abduction, etc., but I consider them to be variations). Induction is needed in the very process of identification (note similarities and differences of existents and integrate the information into a new mental unit). Without identification, there is no deduction.

Michael

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When "the problem of induction" is solved what will we be able to do we cannot do now?

--Brant

Not a blessed thing. Whether or not our inductive generalization are correct and whether or not our hypothesizing to probable causes is correct, we will keep on doing what we do. Why? Because it is the only lway we can learn new stuff and it is the only way we can get beyond a paltry list of particular observations. Without induction and abduction (however faulty) we have no science.

When little babies learn what is what and what is where and what is when they do it by induction. It is as natural to humans as breathing in and out. It is the way our brains and nervous systems work.

Ba'al Chatzaf

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Dayaamm!

I am in full agreement with Bob's post above...

(Something's wrong somewhere... maybe time to bet on the lottery... put snow tires on the car... something...)

Michael

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When "the problem of induction" is solved what will we be able to do we cannot do now?

--Brant

Not a blessed thing. Whether or not our inductive generalization are correct and whether or not our hypothesizing to probable causes is correct, we will keep on doing what we do. Why? Because it is the only lway we can learn new stuff and it is the only way we can get beyond a paltry list of particular observations. Without induction and abduction (however faulty) we have no science.

When little babies learn what is what and what is where and what is when they do it by induction. It is as natural to humans as breathing in and out. It is the way our brains and nervous systems work.

Ba'al Chatzaf

Then there is no problem. But what are those who think there is want to get out of solving this hypothetical, aside from ego food?

--Brant

Edited by Brant Gaede
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When "the problem of induction" is solved what will we be able to do we cannot do now?

--Brant

Not a blessed thing. Whether or not our inductive generalization are correct and whether or not our hypothesizing to probable causes is correct, we will keep on doing what we do. Why? Because it is the only lway we can learn new stuff and it is the only way we can get beyond a paltry list of particular observations. Without induction and abduction (however faulty) we have no science.

When little babies learn what is what and what is where and what is when they do it by induction. It is as natural to humans as breathing in and out. It is the way our brains and nervous systems work.

Ba'al Chatzaf

Then there is no problem. But what are those who think there is want to get out of solving this hypothetical, aside from ego food?

--Brant

Well, for one thing, the satisfaction of not leaving unanswered the smears against, and misconceptions of the relative worth and validity of, philosophy by those who think science (i.e., the physical sciences) is superior to philosophy. (Anyone here want to cop to this scientistic attitude? )

As Peikoff says in "Induction in Physics and Philosophy," don’t be taken in by people who tell you, in any variant, that quantitative statements are more reliable than qualitative ones. That very statement is qualitative. Most of the alleged compliments given to math by its admirers are just like this one. They’re nothing but smears against nonmathematical subjects, smears that arbitrarily equate math with reason, with precision, with science as such. Philosophy explains what numbers are and thereby mandates their formation and use. Philosophy explains the relation of math to reality and to our cognitive faculty and, thereby, shows the physicist that he must be mathematical and how he must use his mathematical tools, how he must rise from concrete measurements to experimental formulas to broader mathematically formulated principles, the climax of which is all-embracing, super-integrated equations. The physicist cannot know to do any of this, i.e., how to make the proper use of numbers, without philosophy. Thus, it can’t be said that philosophy is invalid or worthless because it doesn’t use numbers. Physics or mathematics is not the standard of philosophy. The reverse is true; philosophy is the standard of physics and math. Philosophy tells these concrete disciplines what they are, how they relate to each other and to reality, and therefore what they must do to achieve knowledge of reality. (This material has been "chewed," so it's partly quoted, partly paraphrased.)

Why is this relevant to the Problem of Induction? Because induction in physics and philosophy is essentially the same process, yet, the essential feature of induction in physics is its use of mathematics, while mathematics does not apply to philosophy. Because of this, it is alleged that philosophy cannot have be just as scientific or as inductive as physics, just as hard-headed and factual, just as objective, inescapable, and absolute. As Peikoff notes, philosophy does everything that inductive sciences do. The things they need numbers for, it does without numbers. Since philosophy defines and validates a scientific method and, therefore, guides and validates the science of physics, no inductions made by physicists can ever be better off than the inductions which lead to the principles of philosophy and especially of epistemology.the proper methods and standards of thought, the virtues and values leading to human survival in desert island or in society, the criteria of great art and literature, these are laws and facts as ruthlessly scientific as laws of Newton or Maxwell.

My teeth and gums are worn out from chewing this stuff, so that will have to suffice as a teaser to convince you of the worth of Peikoff's IPP series (as more than just some kind of pompous ego trip) -- and to answer old Ba'al and his put-downs of philosophy. I'll try to answer Ellen's question in a separate post.

REB

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Because of this basic point I am confident that Leonard Peikoff has not presented a "solution to the problem of induction," in those lectures that ARI is selling for \$205 a pop. He may have done some other things, and these might be valuable. But the likelihood that Dr. Peikoff has come up with logically valid inductive argument forms is, well, the same as the likelihood that his favorite gremlins are holding a conference on Venus.

Thank you, Robert. I'd been debating whether to try to pose a question to Roger about just what Peikoff claims to have demonstrated in those lectures. But since I'm not feeling well enough for sustaining dialogue, I hesitated to ask. You've provided enough groundwork, maybe I can frame this succinctly:

Roger, does Peikoff actually claim to have solved "the problem of induction"? If so, how is he defining "induction"? What is he thinking the problem is? I did hear a lecture which I think was from the IPP series (via a friend who has the tapes). What I understood Peikoff to be trying to do was to demonstrate that you can get causal necessity from experience. He was claiming (with an assist from a clue provided by Greg Salmieri [sp]) that we get our first knowledge of necessary cause from our own direct experience of being able to move our own bodies. But even granting this point, how would it solve the problem of induction? I realize I might be asking something more complicated than you can explain easily, or than you have time to explain. But I and probably others here too would welcome any clues you can provide on Peikoff's argument.

Ellen

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Yes, Peikoff does claim to have solved the Problem of Induction, by which he means the problem of the validity of generalization, going from the more particular to the more general.

He maintains that all generalizations are a conceptual grasp of differences and similarities in a causal context, and that if one does this correctly, one can successfully generalize, often, on simply one case, while a whole raft of enumerated observations will not yield a successful generalization, if has not correctly noted the differences and similarities involved. In other words, Peikoff holds that all generalizations -- not only in physics but also in philosophy -- are implicitly or explicitly statements of causal connection, so all generalizations are ultimately reducible to a statement of that kind. (The exception is principles from metaphysics, which are basically the Law of Identity and its implications -- at least, as Rand and Peikoff in their more "minimalist" moments conceive metaphysics.)

Now, some would insist that a "solution" to the POI would have to include some infallible method of generating incorrigible truths, as though simple error would invalidate induction. But we don't invalidate deduction just because people plug in false premises; and we shouldn't invalidate induction because people over-generalize or commit other contextual errors. Peikoff holds that induction, when properly applied, is ultimately self-correcting, in both physics and philosophy, and he lays out five general rules for induction (including Rand's model of conceptualization, Mill's Methods of Difference and Agreement, and others I won't name here) that, when followed conscientiously/objectively, yield broader and broader valid generalizations.

I'll stop with that.

REB

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I spent over 30 years distant from the Objectivist culture and one of the reasons was so I could make sure I was worthy of interaction with these people when I finally met them. But when I finally jumped into the subculture, I found pettiness and schisms. Very little that was heroic or rational. It was a major disappointment. Big time.

Michael

Ditto and the lengths people will go to maintain appearances in the Objectivist movement is ridiculous. Solution: don't build your social network primarily on Objectivists, talk to everybody you can, read everything you can, discourage groupthink, slaughter sacred cows when they need to be slaughtered and be willing to associate with anybody you want to or wish to hear from on a given topic regardless of movement status. The sooner people exercise their prerogatives as individuals within the movement, the sooner the schism stuff will go away.

Jim

Edited by James Heaps-Nelson
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Now, some would insist that a "solution" to the POI would have to include some infallible method of generating incorrigible truths, as though simple error would invalidate induction. But we don't invalidate deduction just because people plug in false premises; and we shouldn't invalidate induction because people over-generalize or commit other contextual errors. Peikoff holds that induction, when properly applied, is ultimately self-correcting, in both physics and philosophy, and he lays out five general rules for induction (including Rand's model of conceptualization, Mill's Methods of Difference and Agreement, and others I won't name here) that, when followed conscientiously/objectively, yield broader and broader valid generalizations.

I'll stop with that.

REB

Do you know what this sounds like? When an induction is correct it is correct and when it is not correct it can or ought to be corrected. I have waited all my life for this Profound Discovery. And how does one know if an inductive generalization is correct? I will tell you. One must check each and every instance of the inductive generalization empirically. As Master Yodah says: Hold not your breath until all cases are checked, else blue turn you will.

Yodah also says: Hold not your breath until L.P. publishes in a refereed journal, else blue turn you will.

Ba'al Chatzaf

Edited by BaalChatzaf
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When little babies learn what is what and what is where and what is when they do it by induction. It is as natural to humans as breathing in and out. It is the way our brains and nervous systems work.

That gives me a convenient opening for asking Daniel Barnes a question I've wanted to ask him: Am I correct in understanding that Popper argues that, no, we do NOT learn by induction? (Near as I've thus far understood his comments anti Hume's view on the psychological issue of induction, this is what he's arguing -- I'm doing some heavy mulling over on that issue, since I've always hated the description "trial and error," given my Behavorist college education, but Popper is leading me to think of "trail and error" in a different way than I ever have before -- and I'm doubting that "our brains and nervous sytems" do work by "induction.")

Ellen

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Yes, Peikoff does claim to have solved the Problem of Induction, by which he means the problem of the validity of generalization, going from the more particular to the more general.

He maintains that all generalizations are a conceptual grasp of differences and similarities in a causal context, and that if one does this correctly, one can successfully generalize, often, on simply one case, while a whole raft of enumerated observations will not yield a successful generalization, if has not correctly noted the differences and similarities involved. In other words, Peikoff holds that all generalizations -- not only in physics but also in philosophy -- are implicitly or explicitly statements of causal connection, so all generalizations are ultimately reducible to a statement of that kind. (The exception is principles from metaphysics, which are basically the Law of Identity and its implications -- at least, as Rand and Peikoff in their more "minimalist" moments conceive metaphysics.)

Roger, thank you for answering. That's what I thought he was trying to argue -- that generalizations "are implicitly or explicitly statements of causal connection." I don't myself see how this argument could be other than a huge "begging of the question." It does seem he's reducing science to being a type of concept formation (and I don't think AR's right anyway on her theories of how cognition works, but it seems that the way Peikoff is arguing one would have to assume she is right and then proceed from there).

Ellen

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Roger,

The more I think on all this, the more I discern a mind-body dichotomy and not mind-body difference. Here is how I see it:

Position 1 (mind-body difference only): The mind/brain is constructed according to the same laws that operate in the organization of the rest of reality, thus it is accurate in processing reality.

For instance, if proper differences and similarities are noted, a category (concept) can be formed because such differences and similarities actually exist. Also, the very act of mentally ("in here") integrating many small things into a single whole, and using such a whole as one of the "small things" that can be integrated into an even broader whole, reflects reality's nature ("out there"), i.e., the existence of entities, which are integrated wholes of many small things and can and usually do include a hierarchy of smaller wholes.

Thus the difference between the mind and body is in function, not essential nature organization-wise.

Position 2 (mind-body dichotomy): The mind/brain operates according to laws that are different organization-wise than the rest of reality, but there are some interconnections between the mind and reality.

So the mind is somewhat reliable in processing reality, but ultimately unreliable. It is entirely reliable in processing its own innate procedures when divorced from the rest of reality (I specifically mean the methodology of logic and math here).

A variation on this is that the mind is reliable when it takes entities apart, but is not reliable when it forms them from observations.

Then there is even another variation on this. The mind operates according to perfect methods of logic and math ("in here"). Reality ("out there") operates according to the perfect existence of separate non-related objects. As the two have different natures organization-wise, the interconnection is faulty. Since we are only aware of the interconnection on our side ("in here"), we presume that the brain is a faulty organ for interconnecting, although a perfect one for logic and math.

Thus the difference between the mind and body is in function (as with Position 1) but, also, in some parts, it is in their essential nature organization-wise. The mind ("in here") processes organization differently than the way things are organized ("out there"), although some things align.

I believe Peikoff would agree with Position 1 in essence, although I do not know if he has used this kind of terminology. Obviously, Position 1 is my position. Where I saw Peikoff go too far was in the DIM Hypothesis lectures. There he overemphasized integration and tried to use it to replace or govern deductive thinking. My position is that induction and deduction work together as essential and non-replaceable parts of rational thought. You need both, not just one. Thus one cannot be more important than the other.

Michael

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