# A wonderful lecture by Lawrence Krauss

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In other words when an induction is right it is right an when it is wrong it is wrong.

It has been pointed out to you repeatedly on multiple threads that induction by enumeration is an invalid method since it fails to distinguish between causal/essential/necessary and accidental attributes. The example all swans have necks was provided to you as a valid induction. Your repeated refusal to acknowledge such corrections to your position is evasion. What is your motivation for refusing to listen to people who attempt to communicate with you and for insisting on attacking straw men? Fear? Laziness? The comfort of an easy target? You are moderately intelligent, Bob. Surely you could have something more interesting to say if you were to deal with the actual position being argued for rather than some silly bogeyman. Or no?

You still don't get it. Induction is NOT guaranteed to lead from true premises to a generally true conclusion. I have given one example after another to show that is the case. Induction is not a valid mode of inference, whereas deduction is. Unfortunately deduction does not tell us anything that wasn't already there (in the premises) whereas induction can lead out from a limited set of assertions to a general statement which sometimes is true and sometimes not. That is why we have to check the consequences of general principle derived by induction against empirical observations and measurement. It is experiment and measurement that keeps inductions honest. Sometimes it takes hundreds of years to show that a principle arrived at by induction is false. For example, Newton's Law of Gravitation. It is not generally true. In many cases it gives close to a right answer and in other cases not. Which is why it is not generally true. A generally true statement is never false under any circumstances.

Induction serves us in Discovery. It sometimes fails us in Justification.

Ba'al Chatzaf

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Induction is not a valid mode of inference, whereas deduction is.

Summary of his argument: In my vocabulary, induction is always invalid and can't be valid -- because it isn't deduction.

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In other words when an induction is right it is right an when it is wrong it is wrong.

It has been pointed out to you repeatedly on multiple threads that induction by enumeration is an invalid method since it fails to distinguish between causal/essential/necessary and accidental attributes. The example all swans have necks was provided to you as a valid induction. Your repeated refusal to acknowledge such corrections to your position is evasion. What is your motivation for refusing to listen to people who attempt to communicate with you and for insisting on attacking straw men? Fear? Laziness? The comfort of an easy target? You are moderately intelligent, Bob. Surely you could have something more interesting to say if you were to deal with the actual position being argued for rather than some silly bogeyman. Or no?

I gave an example of two inductions not of the enumerative type. One was the induction that lead to the theory of heat fluid or caloric and the other was the induction that lead to the idea of phlogiston. I further show that while initial evidence made both inductions reasonable later evidence showed that the conclusions to which they led were false. Two examples of perfectly good and kosher inductions which led to false general conclusions. How many more counter examples will you need to see that induction does not always get us to correct conclusions however auspicious the initial evidence is. How would I go about proving to you that a technique is not always successful except to point out the failures of the technique.

Ba'al Chatzaf

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I gave an example of two inductions not of the enumerative type. One was the induction that lead to the theory of heat fluid or caloric and the other was the induction that lead to the idea of phlogiston. I further show that while initial evidence made both inductions reasonable later evidence showed that the conclusions to which they led were false. Two examples of perfectly good and kosher inductions which led to false general conclusions. How many more counter examples will you need to see that induction does not always get us to correct conclusions however auspicious the initial evidence is. How would I go about proving to you that a technique is not always successful except to point out the failures of the technique.

Ba'al Chatzaf

The current theories of heat and oxidation are inductive generalizations. Are they invalid inductions?

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"Lawrence Krauss is the niftiest lecturer in physics since Richard Feynman. Have a look!"

He is certainly a much better lecturer in physics than anyone who would begin, "Okay, you dumb shmucks..."

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The current theories of heat and oxidation are inductive generalizations. Are they invalid inductions?

Some inductions work, some don't work. Deduction always works. Do a valid inference from true premises and you are bound to get a true conclusion. That is one of the differences between induction and deduction. Just because on induction fails does not mean they all fail.

Ba'al Chatzaf

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The current theories of heat and oxidation are inductive generalizations. Are they invalid inductions?

Some inductions work, some don't work. Deduction always works. Do a valid inference from true premises and you are bound to get a true conclusion. That is one of the differences between induction and deduction. Just because on induction fails does not mean they all fail.

You are quite the word gamesman. An induction can not work, fail, and be invalid. On the other hand, it can work, or not fail, but it can not be valid.

Summarizing your argument again: In your vocabulary, induction is always invalid and can't be valid -- because it isn't deduction.

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Summarizing your argument again: In your vocabulary, induction is always invalid and can't be valid -- because it isn't deduction.

That is right. An induction starting with true premises can produce a false general conclusion. I have given several examples of this. On the other hand, every last deduction ever made and that will be made applied to true premises will produce a true conclusion. That is as certain as the principle of non-contradiction.

Ba'al Chatzaf

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Summarizing your argument again: In your vocabulary, induction is always invalid and can't be valid -- because it isn't deduction.

You know you can write a grammatical sentence that is nevertheless nonsensical. Chomsky’s classic Colorless green ideas sleep furiously is a good case in point. Does this invalidate grammar?

Reason can be attacked the same way. In fact, wasn’t the root of Hume’s problem with induction the fact that it’s validation is circular? Same with Reason, how do you validate Reason except by means of Reason? What a sophomoric waste of time. Anyway, there’s yet another Lawrence Krauss lecture out there, not on YouTube though:

http://www.q2cfestival.com/play.php?lecture_id=7742

It won't embed, I give up. It’s pretty similar to the other one, but different enough to be worth the time.

Edited by Ninth Doctor
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I gave an example of two inductions not of the enumerative type. One was the induction that lead to the theory of heat fluid or caloric and the other was the induction that lead to the idea of phlogiston. I further show that while initial evidence made both inductions reasonable later evidence showed that the conclusions to which they led were false. Two examples of perfectly good and kosher inductions which led to false general conclusions. How many more counter examples will you need to see that induction does not always get us to correct conclusions however auspicious the initial evidence is. How would I go about proving to you that a technique is not always successful except to point out the failures of the technique.

Ba'al Chatzaf

The current theories of heat and oxidation are inductive generalizations. Are they invalid inductions?

Every single concept Bob (almost) grasps is an induction. Although his supreme personal confusion does actually argue for the broad failure of induction, at least in his case.

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Every single concept Bob (almost) grasps is an induction. Although his supreme personal confusion does actually argue for the broad failure of induction, at least in his case.

Sigh. Some inductions from true premises produce true conclusion, some do not. I have given specific examples of the latter. Valid deductions always and forever produce true conclusions from true premises. Always. I have given counter examples to the assertion that ALL inductions from true premises produce true generalization. Giving counter examples is NOT an instance of induction because there is no generalization to a universally quantified proposition.

You seem to exhibit a lack of understanding of what a counter example to a universal generalization is.

Have you ever had a course in formal or mathematical logic? If you have, you seem to have forgotten the material.

Ba'al Chatzaf

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Valid deductions always and forever produce true conclusions from true premises. Always.

You seem to have unlimited confidence in this assertion, so let's put it to the test.

Induction: All humans are less than 9 feet tall.

Deduction:

P1. All human beings are less than 9 feet tall.

P2. X is a human being.

C. X is less than 9 feet tall.

Why should anybody be more confident about this deduction than this induction? Such a reply would be questionable given your use of "always" twice and "forever", but suppose you reply that your assertion does not apply to this case if and when a human is found to be 9 feet tall or more, i.e. P1 is no longer a true premise.

It seems to me the the validity of the above pair stand and fall together.

Edited by Merlin Jetton
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Valid deductions always and forever produce true conclusions from true premises. Always.

You seem to have unlimited confidence in this assertion, so let's put it to the test.

As much confidence as I have in the principle of non-contradiction.

And you happen to have presented an induction on the height of humans that has not yet been falsified. There is no logical or physical reason why humans cannot be nine feet tall although there are compelling physical and biological reasons why humans cannot be one hundred feet tall. Our bones are made of calcium, not titanium or some other very strong material that could bear a 1000 times the weight of calcium bone. Perhaps on the Moon there could be 100 feet tall humans or on some asteroid with very low mass.

I on the other hand presented three inductions that have been falsified proving that sometimes induction goes from true statements to false generalities. SOMETIMES. Whereas deduction NEVER goes from true premises to false conclusions. NEVER EVER. That is as sure a thing as the principle of non-contradiction.

What you do not appear to comprehend is this: Induction as a method of reasoning or inference is NOT guaranteed to produce true generalizations from true premises. That does not mean there are no true inductions; there are. It means that there are false inductions, not that all inductions are false. Can you grasp that? Come on now, try! I know you can do it.

Ba'al Chatzaf

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I on the other hand presented three inductions that have been falsified proving that sometimes induction goes from true statements to false generalities. SOMETIMES. Whereas deduction NEVER goes from true premises to false conclusions. NEVER EVER. That is as sure a thing as the principle of non-contradiction.

In formal terms deduction never goes from true premises to false conclusions. What I have tried to address is applying the formalism to empirical reality, which you have so far failed to grasp. The principle of non-contradiction is also a formalism, which we try to apply to empirical reality.

In post #22 above you told the story about the phlogiston theory. Before fault was found with it, there were many who applied the theory deductively, thinking they had true premises and finding only true conclusions. They were not aware of the contradiction, which Lavoissier found, hidden within it. Do you now see the distinction between a formalism and applying the formalism to empirical reality?

What you do not appear to comprehend is this: Induction as a method of reasoning or inference is NOT guaranteed to produce true generalizations from true premises. That does not mean there are no true inductions; there are. It means that there are false inductions, not that all inductions are false. Can you grasp that? Come on now, try! I know you can do it.

Your psychologizing is far amiss and unwarranted. I wish I were as confident about you grasping the distinction between a formalism and applying the formalism to empirical reality. In post #37 I tried to get you to address applying deduction to empirical reality, and your response was to repeat the formalism.

Edited by Merlin Jetton
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Valid deductions always and forever produce true conclusions from true premises. Always.

You seem to have unlimited confidence in this assertion, so let's put it to the test.

Induction: All humans are less than 9 feet tall.

Deduction:

P1. All human beings are less than 9 feet tall.

P2. X is a human being.

C. X is less than 9 feet tall.

Why should anybody be more confident about this deduction than this induction? Such a reply would be questionable given your use of "always" twice and "forever", but suppose you reply that your assertion does not apply to this case if and when a human is found to be 9 feet tall or more, i.e. P1 is no longer a true premise.

It seems to me the the validity of the above pair stand and fall together.

The Deduction you give remains valid if P1 turns out to be false and (in that case) whether C is true or false. A valid deduction guarantees a true conclusion from true premises. It doesn't guarantee the truth of the premises. It might also produce a false conclusion if one or more of the premises is false, or a true conclusion if one or more of the premises is false. What it doesn't produce is a false conclusion from true premises. IF all humans are less than 9 feet tall and if X is a human, then X is less than 9 feet tall. Guaranteed by non-contradiction. Were the conclusion of the deduction instead "X is more than 9 feet tall," then the deduction would be invalid, since in that case if the premises are true, the conclusion, which contradicts the premises, would necessarily be false.

{I don't understand what you're trying to get at, in your post #39, which continues from this one.)

Ellen

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Every single concept Bob (almost) grasps is an induction. Although his supreme personal confusion does actually argue for the broad failure of induction, at least in his case.

Sigh. Some inductions from true premises produce true conclusion, some do not. I have given specific examples of the latter. Valid deductions always and forever produce true conclusions from true premises. Always. I have given counter examples to the assertion that ALL inductions from true premises produce true generalization. Giving counter examples is NOT an instance of induction because there is no generalization to a universally quantified proposition.

You seem to exhibit a lack of understanding of what a counter example to a universal generalization is.

Have you ever had a course in formal or mathematical logic? If you have, you seem to have forgotten the material.

Ba'al Chatzaf

"Sigh"?

I don't know if that's worse than a lisp or a fart.

In case your social disability leaves you clueless, no one wants to hear your bodily functions.

You have been told over and over that inductions with improper forms fail. Just like deductions with fallacious forms. Induction by enumeration is fallacious.

Newton's law of gravity was not an induction from unquestionable premises, he took the speed of light as instantaneous and did not take relativity into effect. That he found an approximation of the limiting case at low speeds and energies is not problematic.

You have not provided a single induction with true premises and proper form that fails.

Watch the effeminate noises crossed with the willful ignorance. You are becoming the Vancome lady of this website. La la la la la. La la la la la.

Edited by Ted Keer
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Summarizing your [ba'al's] argument again: In your vocabulary, induction is always invalid and can't be valid -- because it isn't deduction.

In mine, too. Or, precisely, there's no formality of induction guaranteed, if properly carried through, to produce true conclusions from true premises. This is a difference between induction and deduction which can't be gotten rid of, whatever word you use for the difference.

Even Peikoff/Harriman in Chapter 7 of The Logical Leap recognize that

pg. 235

[...] deductive validity is determined solely by the form of the argument, not by its content. Some forms are logically valid, i.e., the conclusion follows from the premises, no matter what the content; other forms are invalid--again, independent of content.

The next paragraph makes a horrendous gaffe I was amazed to read. See pp. 235-236. (Assignment, should you choose to accept it: state the gaffe.) Nonetheless, even the Peikoff/Harriman duo acknowledge the difference between induction and deduction.

If you (and Ted) want to use a definition of "valid" which includes both deductive and inductive reasoning, of course you can do that, but what you won't get rid of by defining the term "valid" differently from the way Ba'al uses it is the difference he's describing between the two methods.

You're stuck with that. (An attempt to produce a guaranteed inductive method is an attempt to find an algorithm which confers infallibility on a fallible being.)

Ellen

Edited by Ellen Stuttle
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An attempt to produce a guaranteed inductive method is an attempt to find an algorithm which confers infallibility on a fallible being.

What is this supposed to mean? That because humans make mistakes they will make mistakes?

Or that because we have no a priori guide to all truth, no algorithm that will mechanically spit out all discoverable truth, that we cannot achieve any truth at all?

Who denied that induction with its broad scope is more complicated than deduction with its three term arguments?

Bob keeps making absurd statements and acting as if the formal mistake behind enumerative inductions hasn't been found.

Not to mention the fact that there is no general algorithm for, say, finding the integral of any arbitrary term, or the fact that the accuracy of equations using infinitesimal series rests on the fact that we can always iterate our functions enough times to be guaranteed an answer that falls within whatever acceptable range of error we set. The results of such calculations and solutions are induced, but we don't here Bob complaining.

The fact remains that no one has produced an induction from unquestionably true premises which fails which cannot be explained as failing due to an invalidity of form.

Produce one.

Edited by Ted Keer
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Even Peikoff/Harriman in Chapter 7 of The Logical Leap recognize that

pg. 235

[...] deductive validity is determined solely by the form of the argument, not by its content. Some forms are logically valid, i.e., the conclusion follows from the premises, no matter what the content; other forms are invalid--again, independent of content.

Who denies it?

But the question is the truth of the conclusions, not their validity.

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Induction: All humans are less than 9 feet tall.

Deduction:

P1. All human beings are less than 9 feet tall.

P2. X is a human being.

C. X is less than 9 feet tall.

Why should anybody be more confident about this deduction than this induction? Such a reply would be questionable given your use of "always" twice and "forever", but suppose you reply that your assertion does not apply to this case if and when a human is found to be 9 feet tall or more, i.e. P1 is no longer a true premise.

It seems to me the the validity of the above pair stand and fall together.

The Deduction you give remains valid if P1 turns out to be false and (in that case) whether C is true or false. A valid deduction guarantees a true conclusion from true premises. It doesn't guarantee the truth of the premises. It might also produce a false conclusion if one or more of the premises is false, or a true conclusion if one or more of the premises is false. What it doesn't produce is a false conclusion from true premises. IF all humans are less than 9 feet tall and if X is a human, then X is less than 9 feet tall. Guaranteed by non-contradiction. Were the conclusion of the deduction instead "X is more than 9 feet tall," then the deduction would be invalid, since in that case if the premises are true, the conclusion, which contradicts the premises, would necessarily be false.

That's fine. And if you want to use the word valid exclusively with regard to deduction, that is your decision. Doing so, you cannot have a valid driver's license. In retrospect, "truth" would have been a better word than "validity" by me.

{I don't understand what you're trying to get at, in your post #39, which continues from this one.)

Then reread it. Throughout the course of this dialog, Ba'al has persistently criticized induction bringing up empirical examples of it failing. On the other hand, whenever somebody says something about problems encountered with the empirical use of deduction, he usually responds with a formal statement about deduction. My attempt above was one to compare induction and deduction on the same grounds, that of true conclusions.

Edited by Merlin Jetton
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Then reread it. Throughout the course of this dialog, Ba'al has persistently criticized induction bringing up empirical examples of it failing. On the other hand, whenever somebody says something about problems encountered with the empirical use of deduction, he usually responds with a formal statement about deduction. My attempt above was one to compare induction and deduction on the same grounds, that of true conclusions.

They cannot be compared on the same grounds. One (induction) is a set of rules for producing a general statement from a finite set of particulars. The other (deduction) is rule of inference such that when applied to true premises it is guaranteed to produce true conclusions. Roughly speaking, induction has a role in Discovery. Deduction has a role in Justification and Testing.

Ba'al Chatzaf

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• 4 months later...

This ought to be fun. I find William Lane Craig very annoying, I wonder how Krauss will do. Over 2 hours, damn it's long. This debate was about a month ago.

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... much easier to understand than Hawking. Apparently he doesn’t think much of string theory.

Funny you should mention it. We are fans of Big Bang Theory, the TV sitcom about physicists. I am not too invested in it, but I do enjoy it On one show, Leonard the experimental physicist disparages Sheldon's theories by pointing out the String Theory has nothing to commend it except mathematical symmetry. His actual lines sounded nearly verbatim from Harriman though lacking a Tartis, that would be impossible. This show is supported by a physics website, Big Blog Theory here http://thebigblogtheory.wordpress.com/. So, while I would not invest too much in a sitcom, it does support the view that String Theory is not strongly accepted. Hence, I am not surprised that Hawking has reservations.

(As for Big Bang Theory, I don't know how it plays where you are, but here in Ann Arbor, at the district library I was number 18 on the waiting list for Season 3 Disk 3. Two months later I am now 6 out of 24. Not only do people watch it, but they seem to be taking notes...)

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You have not provided a single induction with true premises and proper form that fails.

Your "definition" of a "proper form" induction is an induction that goes from a true premise to a true conclusion. I find your "definition" somewhat underwhelming.

Here is the bottom line. Induction is not and never was a valid form of inference. It is a heuristic for generating general statements from finite collections of particulars. And that is ALL induction is. Induction has a role in Discovery, i.e. generating general laws and hypotheses. Deduction has a role in Justification. It is used to derive particulars from general laws later to be tested by experiment or observation.

Now here is my challenge: State what a proper form induction is such that a computer program could be written to test whether a particular induction is "proper" or not. In short state a definite well defined rule for telling whether an induction is "proper" or not. Can you do that?

Ba'al Chatzaf

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Your "definition" of a "proper form" induction is an induction that goes from a true premise to a true conclusion. I find your "definition" somewhat underwhelming.

Here is the bottom line. Induction is not and never was a valid form of inference. It is a heuristic for generating general statements from finite collections of particulars. And that is ALL induction is. Induction has a role in Discovery, i.e. generating general laws and hypotheses. Deduction has a role in Justification. It is used to derive particulars from general laws later to be tested by experiment or observation.

Ba'al Chatzaf

Bob,

Those are excellent definitions - Discovery and Justification.

They are so good, you strengthen the inductivist position: a role in "generating general laws and hypotheses", is ALL induction is?

Sounds like plenty, to me.

Tony