What Problem?

[Jonathan David Leavitt]

to validate induction is to validate reason and vice versa

What cognitive tool does one use to validate reason? It can't be reason, obviously, because reason is what is being validated.

[kiaer.ts]

Why? Because no matter how many instances of the universal are shown to be true, one might eventually run into an instance which is false.

How do you know this, if not by induction, Bob?

Truly sad.

Stop the nonsense. I have already provided an example of induction leading to a false generalization. This a a logical falsification of the general proposition that induction always leads to true generalizations. To falsify a universal proposition (x)P(x) one needs only a single instance f, such that -P(f). This is logic 101. A single false induction is sufficient to show induction starting with true premises does not necessarily lead to true conclusions. As a mode of inference, induction is not valid. As a mode of generating general (i.e. universally quantified statements) is a powerful heuristic. Learning by trial and error is a form of induction. But sometimes trials lead to errors so trial and error is not guaranteed to work in every instance.

Pointing to a singular true statement is not induction. Induction is going from the conjunction of singular propositions to a universally quantified proposition.

Ba'al Chatzaf

No one has claimed that every attempt at induction succeeds.

You mention premises but not method. Of course, with an invalid method, one can both induce and deduce a false conclusion from true premises. I do not hear you saying deduction is invalid because it can be improperly carried out.

"As a mode of inference, induction is not valid." - yet another induction on your part.

For all your claims of expertise and sarcastic references to logic 101 you are a sophomore.

Edited November 18, 2010 by Ted Keer

[Jonathan David Leavitt]

Prof. M: The question is: when does one stop? When does one decide that enough confirming evidence exists? Is that in the province of the issue of induction?

One decides based on the context. IMO it doesn't matter if one or more black swans exist, but the discussion and validation of Rand's ideas does matter on this forum, and to me.

There seem to be three positions:

1. "Enough of Ayn Rand's statements are true to validate the proposition that all of her statements are true." (Could this be the ARI position? Was it the position alleged to have been held by the original NBI?)

2. "Enough of Ayn Rand's statements are false to validate the proposition that all of her statements are false."

3. "Enough of Ayn Rand's statements are true to validate the proposition that all of her statements deserve consideration, or at least a second look." (My position.)

All of these assertions rely on an inductive process, but where one stops relies on one's personal context.

[Jonathan David Leavitt]

...] the failure of philosophers to offer a solution to what has been called 'the problem of induction.' Induction is the process of inferring generalizations from particular instances. [....] The primary process of gaining knowledge that goes beyond perceptual data is induction. Generalization -- the inference from some members of a class to all -- is the essence of human cognition.

Rand, according to Peikoff, appears to be asserting that philosophers have failed to solve a problem. Just because she said that, and Peikoff quoted it, however, doesn't mean that a problem exists.

However, if one believes the generalization, which I consider erroneous,

"Enough of Ayn Rand's statements are true to validate the proposition that all of her statements are true."

Then the "problem" exists.

[Brant Gaede]

Leonard Peikoff obviously doesn't care about the ARI if it doesn't inform his ego, which will go down with his ship, perhaps taking ARI with it.

--Brant

[BaalChatzaf]

2. "Enough of Ayn Rand's statements are false to validate the proposition that all of her statements are false."

All it takes is on.

One negative instance negates a universally quantified proposition. One fact contrary to a prediction without out any thing in the theory to explain the divergence brings a theory down. That is why the anomalous precession of the planet Mercury indicates Newton's gravitational theory is in error. There is no closer planet to the sun to explain the anomaly. (there is also another reason: According to Newton's theory, gravitational interaction is instantaneous which means information can be transferred at greater than light speed).

Ba'al Chatzaf

[anthony]

Ba'al: "All it takes is one."

I find this concretist in the extreme. Would 98% of rectitude not satisfy you? 89%?

On your basis, I'd be too scared to get out of bed in the morning, and for sure, mankind would not have left the caves.

In my own "sophomoric" way, my view is that seeking truth has no guarantees, and often only a partial truth, or finding the right direction to it, is a significant step towards it.

The next thing is to try to substantiate that Newton made not the slightest furtherance to human knowledge.

Is that your position and intention?

Here's a general query: is not the 'self-evident' a form of induction?

Tony

[Brant Gaede]

An inductive proof? Good luck with that. If it doesn't improve standard scientific methodologies, what good would that be? A "proof" is just a way to win an argument and for the intelligentsia to go out and kill people.

--Brant

[BaalChatzaf]

Ba'al: "All it takes is one."

I find this concretist in the extreme. Would 98% of rectitude not satisfy you? 89%?

On your basis, I'd be too scared to get out of bed in the morning, and for sure, mankind would not have left the caves.

In my own "sophomoric" way, my view is that seeking truth has no guarantees, and often only a partial truth, or finding the right direction to it, is a significant step towards it.

The next thing is to try to substantiate that Newton made not the slightest furtherance to human knowledge.

Is that your position and intention?

Here's a general query: is not the 'self-evident' a form of induction?

Tony

-[(x)Px] == Ex[-Px]

I cannot make it plainer.

A theory that makes predictions refuted by experiment is an incorrect theory. The theory might still be useful as a heuristic. For example Newton's theory of gravitation. It is both incorrect and useful. We use it to send probes to the outer planets. Classical mechanics is still useful for a large class of problems where masses are not too great and velocities are small compared to the speed of light. Also the mathematical techniques are still as useful as even in both quantum physics and relativity theory.

And the truth of scientific "truth" is contingent, provisional and only as good as the experiments say it is. Calling something correct when it is partially incorrect is not useful. Putting something incorrect to good use is useful. We do it all the time.

Ba'al Chatzaf

[bmacwilliam]

Ba'al: "All it takes is one."

I find this concretist in the extreme. Would 98% of rectitude not satisfy you? 89%?

On your basis, I'd be too scared to get out of bed in the morning, and for sure, mankind would not have left the caves.

In my own "sophomoric" way, my view is that seeking truth has no guarantees, and often only a partial truth, or finding the right direction to it, is a significant step towards it.

The next thing is to try to substantiate that Newton made not the slightest furtherance to human knowledge.

Is that your position and intention?

Here's a general query: is not the 'self-evident' a form of induction?

Tony

"I find this concretist in the extreme. "

No, this is the truth. The is the basis of the power of science and the measure of a good theory.

One fossil record that doesn't fit, ONE AND ONLY ONE contrary fossil would destroy the theory of evolution - poof - gone! That is indeed why it is powerful.

Bob

[anthony]

Ba'al: "All it takes is one."

I find this concretist in the extreme. Would 98% of rectitude not satisfy you? 89%?

On your basis, I'd be too scared to get out of bed in the morning, and for sure, mankind would not have left the caves.

In my own "sophomoric" way, my view is that seeking truth has no guarantees, and often only a partial truth, or finding the right direction to it, is a significant step towards it.

The next thing is to try to substantiate that Newton made not the slightest furtherance to human knowledge.

Is that your position and intention?

Here's a general query: is not the 'self-evident' a form of induction?

Tony

"I find this concretist in the extreme. "

No, this is the truth. The is the basis of the power of science and the measure of a good theory.

One fossil record that doesn't fit, ONE AND ONLY ONE contrary fossil would destroy the theory of evolution - poof - gone! That is indeed why it is powerful.

Bob

In which case one would look back on the newly refuted Theory of Evolution, and say it made good sense at the time, and that it was a necessary step on the path to knowledge.

The alternative, is to deny one's own innate and inductive ability to observe, generalize, and correlate.

The sun will keep rising, until it doesn't, which is a 100% certainty, ONE day. However, that it will rise tomorrow, is 99.999...etc.% certain. I'll take those odds.

Tony

[Brant Gaede]

Ba'al: "All it takes is one."

I find this concretist in the extreme. Would 98% of rectitude not satisfy you? 89%?

On your basis, I'd be too scared to get out of bed in the morning, and for sure, mankind would not have left the caves.

In my own "sophomoric" way, my view is that seeking truth has no guarantees, and often only a partial truth, or finding the right direction to it, is a significant step towards it.

The next thing is to try to substantiate that Newton made not the slightest furtherance to human knowledge.

Is that your position and intention?

Here's a general query: is not the 'self-evident' a form of induction?

Tony

"I find this concretist in the extreme. "

No, this is the truth. The is the basis of the power of science and the measure of a good theory.

One fossil record that doesn't fit, ONE AND ONLY ONE contrary fossil would destroy the theory of evolution - poof - gone! That is indeed why it is powerful.

Bob

In which case one would look back on the newly refuted Theory of Evolution, and say it made good sense at the time, and that it was a necessary step on the path to knowledge.

The alternative, is to deny one's own innate and inductive ability to observe, generalize, and correlate.

The sun will keep rising, until it doesn't, which is a 100% certainty, ONE day. However, that it will rise tomorrow, is 99.999...etc.% certain. I'll take those odds.

Tony

I'll take that bet.

--Brant

[BaalChatzaf]

In which case one would look back on the newly refuted Theory of Evolution, and say it made good sense at the time, and that it was a necessary step on the path to knowledge.

The alternative, is to deny one's own innate and inductive ability to observe, generalize, and correlate.

Which theory of evolution? The theory of descent with modification as Darwin stated it has been modified and expanded to take into account the machinery of iheritance, to wit, the genetic theory. When Darwin hit on Natural Selection he did not know how those characteristics promoting reproductive success were transmitted to the next generations. Now we have a rather good (although not complete) theory of how this happens. The molecular biochemistry of genes was merged with the theory of natural selection in the 1940's and was nailed by Watson and Crick when they figured out the basic chemistry of inheritance by way of DNA and RNA. Darwin's hypothesis of natural selection corresponds roughly to what Mendele'ev did for chemistry. Mendele'ev did not have quantum theory (just as Darwin did not have genetics) but he understood that the structure of atoms could be ordered and sorted by valence. Darwin did not quite figure out how survival characteristics were handed down be he understood that a natural process weeded out those organisms which did not produce viable offspring in that the inheritance chain would be terminated for them. So called-survival of the fittest, actually the survival of the reproductively fit.

The current theory of biological inheritance and selection is still incomplete. It is part of a work in progress.

In the same way, physics is a work in progress. The physicists have not yet figured out how to unify the gravitational interaction with the other three know interactions.

All of our current physics theories are probably incorrect and they are certainly incomplete. As long as there are natural events and processes waiting to be explained there is work to be done.

Ba'al Chatzaf

[bmacwilliam]

Ba'al: "All it takes is one."

I find this concretist in the extreme. Would 98% of rectitude not satisfy you? 89%?

On your basis, I'd be too scared to get out of bed in the morning, and for sure, mankind would not have left the caves.

In my own "sophomoric" way, my view is that seeking truth has no guarantees, and often only a partial truth, or finding the right direction to it, is a significant step towards it.

The next thing is to try to substantiate that Newton made not the slightest furtherance to human knowledge.

Is that your position and intention?

Here's a general query: is not the 'self-evident' a form of induction?

Tony

"I find this concretist in the extreme. "

No, this is the truth. The is the basis of the power of science and the measure of a good theory.

One fossil record that doesn't fit, ONE AND ONLY ONE contrary fossil would destroy the theory of evolution - poof - gone! That is indeed why it is powerful.

Bob

In which case one would look back on the newly refuted Theory of Evolution, and say it made good sense at the time, and that it was a necessary step on the path to knowledge.

The alternative, is to deny one's own innate and inductive ability to observe, generalize, and correlate.

The sun will keep rising, until it doesn't, which is a 100% certainty, ONE day. However, that it will rise tomorrow, is 99.999...etc.% certain. I'll take those odds.

Tony

Sure, odds are good, and perhaps there is no disagreement here.

My point is that it is very necessary and very powerful that theories (even very useful ones that make sense at the time) can be shot down with one simple contrary example. This causes paradigm shifts and great leaps in knowledge. This is a good thing, and really should (or is) a characteristic of, dare I say, ANY good theory. Do you not agree?

Bob

[Jonathan David Leavitt]

2. "Enough of Ayn Rand's statements are false to validate the proposition that all of her statements are false."

All it takes is on.

One negative instance negates a universally quantified proposition. One fact contrary to a prediction without out any thing in the theory to explain the divergence brings a theory down. That is why the anomalous precession of the planet Mercury indicates Newton's gravitational theory is in error. There is no closer planet to the sun to explain the anomaly. (there is also another reason: According to Newton's theory, gravitational interaction is instantaneous which means information can be transferred at greater than light speed).

Ba'al Chatzaf

I am confused. Are you asserting that Rand's false statement that no woman is qualified to be President validates the the proposition that all of her statements are false, including, "A is A"?

[BaalChatzaf]

I am confused. Are you asserting that Rand's false statement that no woman is qualified to be President validates the the proposition that all of her statements are false, including, "A is A"?

No. What makes you think that ridiculous assertion about women presidents follows from the logical law of identity?

I was asserting two things.

1. How to negate a universally quantified formula in first order logic. Produce a counter example

2. Modus Tolens. if P implies Q and Q is false then so is P.

In the case of a scientific theory if a prediction is show to be false empirically and the reason for the falsity is not explained by the theory (for example a boundary condition is violated) then at least on of the assumptions underlying the theory is false. Rand said it herself. Remember all the business about "check your premises"? That was Modus Tolens, Rand style.

Ba'al Chatzaf

[Jonathan David Leavitt]

I am confused. Are you asserting that Rand's false statement that no woman is qualified to be President validates the the proposition that all of her statements are false, including, "A is A"?

No. What makes you think that ridiculous assertion about women presidents follows from the logical law of identity?

I was asserting two things.

1. How to negate a universally quantified formula in first order logic. Produce a counter example

2. Modus Tolens. if P implies Q and Q is false then so is P.

In the case of a scientific theory if a prediction is show to be false empirically and the reason for the falsity is not explained by the theory (for example a boundary condition is violated) then at least on of the assumptions underlying the theory is false. Rand said it herself. Remember all the business about "check your premises"? That was Modus Tolens, Rand style.

Ba'al Chatzaf

Got it. I looked up modus tollens.

The statement about Rand can be falsified. It is IMO a common logical error made by Rand haters.

Restating it:

If any of Rand's assertions are false, they all are false.

Rand asserted that A is A.

But the Law of Identity is true.

Therefore not all of Rand's statements are false

.

If I am correct, the foregoing was an example of both modus tollens and falsification.

Edited November 19, 2010 by Jonathan David Leavitt

[Ellen Stuttle]

Why? Because no matter how many instances of the universal are shown to be true, one might eventually run into an instance which is false.

How do you know this, if not by induction, Bob?

Truly sad.

Stop the nonsense. I have already provided an example of induction leading to a false generalization. This a a logical falsification of the general proposition that induction always leads to true generalizations. To falsify a universal proposition (x)P(x) one needs only a single instance f, such that -P(f). This is logic 101. A single false induction is sufficient to show induction starting with true premises does not necessarily lead to true conclusions. As a mode of inference, induction is not valid. As a mode of generating general (i.e. universally quantified statements) is a powerful heuristic. Learning by trial and error is a form of induction. But sometimes trials lead to errors so trial and error is not guaranteed to work in every instance.

Pointing to a singular true statement is not induction. Induction is going from the conjunction of singular propositions to a universally quantified proposition.

Ba'al Chatzaf

No one has claimed that every attempt at induction succeeds.

You mention premises but not method. Of course, with an invalid method, one can both induce and deduce a false conclusion from true premises. I do not hear you saying deduction is invalid because it can be improperly carried out.

"As a mode of inference, induction is not valid." - yet another induction on your part.

For all your claims of expertise and sarcastic references to logic 101 you are a sophomore.

Ted, what do you mean by "valid"? Clearly what Bob means is logically valid -- i.e., an argument form such that the truth of the premises guarantees the truth of the conclusion.

Can you provide an inductive argument form in which this condition is met?

Ellen

[Ellen Stuttle]

Prof. M: The question is: when does one stop? When does one decide that enough confirming evidence exists? Is that in the province of the issue of induction?

One decides based on the context. IMO it doesn't matter if one or more black swans exist, but the discussion and validation of Rand's ideas does matter on this forum, and to me.

There seem to be three positions:

1. "Enough of Ayn Rand's statements are true to validate the proposition that all of her statements are true." (Could this be the ARI position? Was it the position alleged to have been held by the original NBI?)

2. "Enough of Ayn Rand's statements are false to validate the proposition that all of her statements are false."

3. "Enough of Ayn Rand's statements are true to validate the proposition that all of her statements deserve consideration, or at least a second look." (My position.)

All of these assertions rely on an inductive process, but where one stops relies on one's personal context.

No, where one stops, in the sense meant, isn't where one feels satisfied, it's where one can demonstrate a guaranteed-true conclusion. That Socrates is mortal if it's true that all men are mortal and Socrates is a man is guaranteed to be true by the form of the argument. Each of the three options you presented is a personal opinion. None is a valid (logic meaning) argument.

Ellen

[Ellen Stuttle]

...] the failure of philosophers to offer a solution to what has been called 'the problem of induction.' Induction is the process of inferring generalizations from particular instances. [....] The primary process of gaining knowledge that goes beyond perceptual data is induction. Generalization -- the inference from some members of a class to all -- is the essence of human cognition.

Rand, according to Peikoff, appears to be asserting that philosophers have failed to solve a problem. Just because she said that, and Peikoff quoted it, however, doesn't mean that a problem exists.

[....]

Rand didn't say that. Peikoff said that. He is not quoting from Rand. Nor is he inventing what philosophers have called "the problem of induction." Awareness of the problem goes back at least to Aristotle.

Re Peikoff's supposed solution supposedly based on Rand's theory of concepts, maybe the worst result of this book, imo, is that Objectivism and Rand will be blamed for Peikoff's errors -- people other than the true-believers are believing that the book really does, as advertised, extend Rand's theories. I like to think that Rand herself would have screamed bloody murder (as the saying goes) if she'd been around to hear preliminary talk of the project. (There is the unfortunate fact that she sanctioned The Ominous Parallels. Nonetheless, I like to think that she'd have upbraided Peikoff royally for illogic before the course on which the first chapter of this book is based was ever given.)

Ellen

[kiaer.ts]

Why? Because no matter how many instances of the universal are shown to be true, one might eventually run into an instance which is false.

How do you know this, if not by induction, Bob?

Truly sad.

Stop the nonsense. I have already provided an example of induction leading to a false generalization. This a a logical falsification of the general proposition that induction always leads to true generalizations. To falsify a universal proposition (x)P(x) one needs only a single instance f, such that -P(f). This is logic 101. A single false induction is sufficient to show induction starting with true premises does not necessarily lead to true conclusions. As a mode of inference, induction is not valid. As a mode of generating general (i.e. universally quantified statements) is a powerful heuristic. Learning by trial and error is a form of induction. But sometimes trials lead to errors so trial and error is not guaranteed to work in every instance.

Pointing to a singular true statement is not induction. Induction is going from the conjunction of singular propositions to a universally quantified proposition.

Ba'al Chatzaf

No one has claimed that every attempt at induction succeeds.

You mention premises but not method. Of course, with an invalid method, one can both induce and deduce a false conclusion from true premises. I do not hear you saying deduction is invalid because it can be improperly carried out.

"As a mode of inference, induction is not valid." - yet another induction on your part.

For all your claims of expertise and sarcastic references to logic 101 you are a sophomore.

Ted, what do you mean by "valid"? Clearly what Bob means is logically valid -- i.e., an argument form such that the truth of the premises guarantees the truth of the conclusion.

Can you provide an inductive argument form in which this condition is met?

Ellen

Your question is unclear to me, Ellen.

If you are asking for an example of an induction from true premises to a false conclusion due to an faulty method, the black swan example is perfect. The induction that all swans are white is invalid because it makes no causal connection. There is nothing inherent in swanness that requires them as swans to have to be white. It amounts to an accident so far as the rest of their physiology.

[Xray]

[bolding mine]

I have already provided an example of induction leading to a false generalization. This a [sic] a logical falsification of the general proposition that induction always leads to true generalizations.

But who would be so naive as to claim that induction always leads to true generalizations?

[replying to Ba'al Chatzaf]:

"As a mode of inference, induction is not valid." - yet another induction on your part.

Ted, what do you mean by "valid"? Clearly what Bob means is logically valid -- i.e., an argument form such that the truth of the premises guarantees the truth of the conclusion.

Can you provide an inductive argument form in which this condition is met?

Your question is unclear to me, Ellen.

If you are asking for an example of an induction from true premises to a false conclusion due to an faulty method, the black swan example is perfect.

Ted,

I think Ellen asked you if you can provide an inductive argument form where the truth of the premises guarantess the truth of the conclusion (which is impossible).

But while induction cannot guarantee the truth of generalizations, mankind could not have survived if not for performing inductive reasoning countless times (with errors included, and then corrected).

In fact a person unable to perform inductive reasoning would be mentally impaired.

As for Harriman, while he does not claim that induction always leads to true generalizations, he seems to believe that there does exist a method of valid induction that can prove the geralizations to which it leads.

David Harriman, The Logical Leap, p. 7:

"When and why is the inference from "some" to "all" legitimate? What is the method of valid induction that can prove the generalization to which it leads?" (end quote)

But how is Harriman going to prove the truth of a generalization reached by a "method of valid induction"?

Edited November 21, 2010 by Xray

[Starbuckle]

This thread is a good source for random babbling. For example, if one needed some verisimilitudinous random babbling for a character in a novel, one could adapt some of the opinings uttered herein.

[BaalChatzaf]

Your question is unclear to me, Ellen.

If you are asking for an example of an induction from true premises to a false conclusion due to an faulty method, the black swan example is perfect. The induction that all swans are white is invalid because it makes no causal connection.

And sometime hypothetical causal connections turn out to be wrong. For example heat. For some time, heat was assumed to be a fluid. Heat got from Here to There because it was a fluid that moved (flowed) from Here to There. But that turned out to be wrong. It was discovered that heat is the average energy in the motion of molecules of a substance and not a substantial fluid* Ironically Sadi Carnot came up with the first good statement of the second law of thermodynamics based on the disproved hypothesis that heat was a fluid (caloric).

Another example: for some time it was presumed that light was the undulation of a very light substance (aether) which fills space. That is how a light beam gets from Here to There. Pretty much like ripple spreading out on the surface of a pond. The Michelson Morley experiment produced a negative result which shot down the aether hypothesis. Aether is not the means by which light gets from Here to There. There is no aether.

If you take Hume seriously (which I do) causality is hypothetical based on the repeated occurance of event-type pairs. Whenever type A event happens then type B event is observed. When Type A does not happen then Type B does not happen. Conclusion Type A event causes Type B event. It is the elevation of an accidental to a substantial hypothesis. Causality is an itch we cannot scratch. We find it difficult to think of something happening without something before (or at the same time) causing it. Unfortunately, this insistence leads us to infinite regress. It is Turtles all the way down. The good news is that causality is often a good heuristic for making correct predictions. Causality, along with induction is the basis for learning at human scale. We find causes all the time and we seem happy with the results. The bad news is that it does not always work at all scales. What is the cause of spin in some orientation of an electron?

Ba'al Chatzaf

*Count Rumford found that heat was motion of the molecules of material. He got that from studying the heat generated when canon barrels were bored.

[Jonathan David Leavitt]

No, where one stops, in the sense meant, isn't where one feels satisfied, it's where one can demonstrate a guaranteed-true conclusion..

Ellen

It seems to me that demonstration of a guaranteed-true conclusion is impossible using induction. Is that, then, the problem?