# How can induction be valid?

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### #1 BaalChatzaf

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Posted 11 September 2010 - 03:30 PM

How can induction be valid? Even if all of a large set of instances are true, the general conclusion is not guaranteed to be true. The usual example: One billion black crows leads to the conclusion that all crows are black, and then someone finds a white crow (the do exist because of the gene for albinism).

Several scientific theories based on induction turned out to be false. For example the inductive conclusion that heat is a fluid (caloric) was falsified by Wm. Thompson (Lord Kelvin).

Inductive arguments are not guaranteed to turn out true conclusions even if all the premises are true. Whereas valid deductive arguments are guaranteed to produce true conclusions if the premises are true.

The best an induction can produces is a reasonable probability or possibility that the conclusion is true. Which is not an argument against using induction. It is the only way we can go from a finite set of observations to a general statement or a law.

Ba'al Chatzaf

Edited by BaalChatzaf, 11 September 2010 - 03:32 PM.

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### #2 George H. Smith

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Posted 11 September 2010 - 07:23 PM

How can induction be valid? Even if all of a large set of instances are true, the general conclusion is not guaranteed to be true. The usual example: One billion black crows leads to the conclusion that all crows are black, and then someone finds a white crow (the do exist because of the gene for albinism).

Several scientific theories based on induction turned out to be false. For example the inductive conclusion that heat is a fluid (caloric) was falsified by Wm. Thompson (Lord Kelvin).

Inductive arguments are not guaranteed to turn out true conclusions even if all the premises are true. Whereas valid deductive arguments are guaranteed to produce true conclusions if the premises are true.

The best an induction can produces is a reasonable probability or possibility that the conclusion is true. Which is not an argument against using induction. It is the only way we can go from a finite set of observations to a general statement or a law.

Ba'al Chatzaf

Suppose I conclude, based on past experiences, that I will get burned if I light a blowtorch, point it five inches away from my bare hand, and keep it there for ten minutes. Would you say that my conclusion is merely probable, not certain?

Really?

If you confine the term "valid" to deductive syllogisms, then of course inductive reasoning will not be "valid." This merely says that induction is not deduction. We knew that already.

The pertinent question is whether inductive reasoning can produce reliable knowledge. The answer is Yes.

Ghs

### #3 BaalChatzaf

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Posted 11 September 2010 - 07:28 PM

<br>The pertinent question is whether inductive reasoning can produce <i>reliable knowledge.</i> The answer is Yes.<br><br>Ghs<br>

<br><br>Not always, as the caloric example shows.&nbsp;&nbsp;Deduction works 100 percent of the time.&nbsp;&nbsp;Start with true premises and you ALWAYS get true conclusions if the deduction has a valid form.&nbsp;&nbsp;Every single time in every situation.&nbsp;&nbsp;Deduction is the Gold Standard of Arguments.&nbsp;&nbsp;Mathematics is based on deduction.&nbsp;&nbsp;Logic is based on deduction.&nbsp;&nbsp;<br><br>Induction does not always work, as shown by various examples. <br><br>The induction of the burning hand just happens to be right.&nbsp;&nbsp;The induction leading to caloric and aether are both wrong.&nbsp; Newton's induction leading to the inverse square law for gravitation is also wrong.&nbsp; Newton's law does not correctly predict the precession of the perihelion of Mercury, for example. <br><br>Some inductions are right,&nbsp; others are wrong.&nbsp; All deductions starting from true premises are right,&nbsp; every single time.<br><br>Ba'al Chatzaf

Edited by BaalChatzaf, 11 September 2010 - 07:31 PM.

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### #4 George H. Smith

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Posted 11 September 2010 - 10:27 PM

<br>The pertinent question is whether inductive reasoning can produce <i>reliable knowledge.</i> The answer is Yes.<br><br>Ghs<br>

<br><br>Not always, as the caloric example shows.&nbsp;&nbsp;Deduction works 100 percent of the time.&nbsp;&nbsp;Start with true premises and you ALWAYS get true conclusions if the deduction has a valid form.&nbsp;&nbsp;Every single time in every situation.&nbsp;&nbsp;Deduction is the Gold Standard of Arguments.&nbsp;&nbsp;Mathematics is based on deduction.&nbsp;&nbsp;Logic is based on deduction.&nbsp;&nbsp;<br><br>Induction does not always work, as shown by various examples. <br><br>The induction of the burning hand just happens to be right.&nbsp;&nbsp;The induction leading to caloric and aether are both wrong.&nbsp; Newton's induction leading to the inverse square law for gravitation is also wrong.&nbsp; Newton's law does not correctly predict the precession of the perihelion of Mercury, for example. <br><br>Some inductions are right,&nbsp; others are wrong.&nbsp; All deductions starting from true premises are right,&nbsp; every single time.<br><br>Ba'al Chatzaf

Deduction will give you a true conclusion provided the premises are true, but it won't give you new knowledge. Induction does, and it provides the major premise of a deductive syllogism.

It's not just that my blowtorch example happens to be right. We can know with certainty beforehand that we are right. This indicates that inductive reasoning per se is essentially sound.

The mistaken examples you gave are far more complex than my example. Mistakes in inductive reasoning occur in complicated cases because of the problem of isolating the relevant characteristics of the entities involved, as well as determining whether the circumstances are sufficiently similar. (Logicians sometimes call this the problem of sampling.) This is the reason that induction in some of the sciences is not sufficient. Inductive generalizations become "hypotheses" that need to be tested by experimental methods.

As I said, mistakes in inductive reasoning occur because of factual errors, not because of the form of inductive reasoning itself. The same is true of deductive reasoning: false premises will (usually) yield a false conclusion, even though the inference itself is formally valid.

Read almost any standard account of induction in science and you will learn that induction complements deduction; one is not a substitute for the other. The two methods work in tandem.

Ghs

### #5 Ted Keer

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Posted 11 September 2010 - 10:36 PM

How can induction be valid? Even if all of a large set of instances are true, the general conclusion is not guaranteed to be true. The usual example: One billion black crows leads to the conclusion that all crows are black, and then someone finds a white crow (the do exist because of the gene for albinism).

Several scientific theories based on induction turned out to be false. For example the inductive conclusion that heat is a fluid (caloric) was falsified by Wm. Thompson (Lord Kelvin).

Inductive arguments are not guaranteed to turn out true conclusions even if all the premises are true. Whereas valid deductive arguments are guaranteed to produce true conclusions if the premises are true.

The best an induction can produces is a reasonable probability or possibility that the conclusion is true. Which is not an argument against using induction. It is the only way we can go from a finite set of observations to a general statement or a law.

Ba'al Chatzaf

What about crows makes you think blackness is essential to them? Does your induke not know anything about biology? About what species are? About variation? About the phenomenon of albinism? I mean, really, Bob. How do you take such examples seriously?

Confession is always weakness. The grave soul keeps its own secrets, and takes its own punishment in silence.

### #6 BaalChatzaf

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Posted 12 September 2010 - 12:49 AM

What about crows makes you think blackness is essential to them? Does your induke not know anything about biology? About what species are? About variation? About the phenomenon of albinism? I mean, really, Bob. How do you take such examples seriously?

You miss the point. Those who saw a zillion black crews leapt to the inductive conclusion that all crows are black. But it ain't so. It was their induction that was wrong, not the crows. Induction lead to a conclusion that happened to be false. Other inductions have lead to true conclusions. Which shows sometimes induction works and sometimes it doesn't. Whereas deduction ALWAYS produces a true conclusion from true premises. It never fails to do so. It can't fail to do so because the necessity is essentially the principle of non-contradiction.

We are forced to use induction because it is the only way to get from a set of particulars to a generality in the empirical domain. When we learn by doing or learn by skinning our knees we use induction. Sometimes we learn the right lessons, sometimes we don't.

And THAT is the problem of induction. Sometimes it works and sometimes it doesn't.

Whereas deduction from true premises is guaranteed to produce a true conclusion.

Ba'al Chatzaf
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### #7 George H. Smith

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Posted 12 September 2010 - 01:08 AM

Those who saw a zillion black crews leapt to the inductive conclusion that all crows are black. But it ain't so. It was their induction that was wrong, not the crows. Induction lead to a conclusion that happened to be false. Other inductions have lead to true conclusions. Which shows sometimes induction works and sometimes it doesn't.

People sometimes make mistakes in addition and other mathematical calculations. Would you therefore say that mathematics sometimes works and sometimes doesn't?

Ghs

### #8 BaalChatzaf

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Posted 12 September 2010 - 01:32 AM

Those who saw a zillion black crews leapt to the inductive conclusion that all crows are black. But it ain't so. It was their induction that was wrong, not the crows. Induction lead to a conclusion that happened to be false. Other inductions have lead to true conclusions. Which shows sometimes induction works and sometimes it doesn't.

People sometimes make mistakes in addition and other mathematical calculations. Would you therefore say that mathematics sometimes works and sometimes doesn't?

Ghs

No. Math always works if you do the proofs right. The problem is that the method of induction sometimes yields true conclusions and sometimes not. The method is the same in both the instances that are true and the instances that are false. The real problem is that induction won't work generally until one has the Last Fact and that won't happen.

But that is no basis for bad mouthing induction. Induction is how we learn to ride bicycles and wipe our tushies. It is the only way to get from a finite collection of particular assertions to a general proposition. But sometimes the general proposition is wrong.

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### #9 George H. Smith

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Posted 12 September 2010 - 02:51 AM

Those who saw a zillion black crews leapt to the inductive conclusion that all crows are black. But it ain't so. It was their induction that was wrong, not the crows. Induction lead to a conclusion that happened to be false. Other inductions have lead to true conclusions. Which shows sometimes induction works and sometimes it doesn't.

People sometimes make mistakes in addition and other mathematical calculations. Would you therefore say that mathematics sometimes works and sometimes doesn't?

Ghs

No. Math always works if you do the proofs right.

This is like saying that induction always works if you don't make any mistakes.

The basic point, which I discussed two posts up, is this: From the fact that people sometimes make mistakes when employing a method of reasoning (including mathematics), it does not follow that the method itself is flawed, inadequate, or unreliable. If you have ever taken a college course on traditional logic, you will know that students frequently err in matters of deductive logic. If this were not the case, all students would score 100 percent on their exams.

The problem is that the method of induction sometimes yields true conclusions and sometimes not. The method is the same in both the instances that are true and the instances that are false.

No. The people who engage in inductive reasoning sometimes come up with true conclusions and sometimes not. The same is true in mathematics and deductive logic. The inductive method, properly applied, will not result in false conclusions. Again, the same is true in mathematics and deductive logic. The man is not the method.

Having said this, I freely acknowledge that it is far easier to make mistakes when reasoning inductively than when reasoning deductively. Errors will be more common in inductive reasoning. But this is not owing to the method itself. It is because of the complexities of the facts with which it deals.

The real problem is that induction won't work generally until one has the Last Fact and that won't happen.

So-called complete (or perfect) enumeration is a completely different method than the one I have been discussing on various OL threads. As H.W.B. Joseph explains in An Introduction to Logic (p. 504):

[T]he reasoning which infers general truths from the analysis of a limited number of particulars does not rely on enumeration, and is not an operation of the same kind as that which proceeds by complete enumeration. Though the one may therefore cite every instance, and the other not, yet they are not to be contrasted as if they were operations of the same kind, differing only in that respect. They are operations of different kinds; and their other differences are more fundamental than the difference in the completeness or incompleteness of the enumeration they involve.

Ghs

### #10 Dennis Hardin

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Posted 12 September 2010 - 03:33 AM

How can induction be valid? Even if all of a large set of instances are true, the general conclusion is not guaranteed to be true. The usual example: One billion black crows leads to the conclusion that all crows are black, and then someone finds a white crow (the do exist because of the gene for albinism).

Several scientific theories based on induction turned out to be false. For example the inductive conclusion that heat is a fluid (caloric) was falsified by Wm. Thompson (Lord Kelvin).

Inductive arguments are not guaranteed to turn out true conclusions even if all the premises are true. Whereas valid deductive arguments are guaranteed to produce true conclusions if the premises are true.

The best an induction can produces is a reasonable probability or possibility that the conclusion is true. Which is not an argument against using induction. It is the only way we can go from a finite set of observations to a general statement or a law.

Ba'al Chatzaf

Induction is the process of inferring conclusions based on observation. Deduction is the process of deriving new conclusions from existing knowledge. Induction is like earning money; deduction is like spending it. You cannot have deduction without induction.

Induction is simply an observation of a causal connection. The law of causality has two aspects: (1) An event is determined by the circumstances in which it occurs, including the nature of the entities involved, and (2) the same cause has the same effect. Hume’s assault on induction was really an attack on causality.

Hume’s mistake was to see sensation, rather than perception, as the base of all knowledge. On the level of sensations, we only have momentary awareness of disparate qualities. He saw entities as constructed inventions of the mind, and events as autonomous occurrences disconnected from the entities that act. This is the basis for suggesting that establishing inductive connections involves finding more and more instances of that connection. This is how induction gets confused with probability theory.

In fact, the base of human knowledge is perception, which involves the direct awareness of entities, or objects as unified collections of properties. Actions depend on the nature of the entities that act. An entity with the same nature, under the same circumstances, will act in the same way. From this perspective, once a cause has been isolated, we can generalize on the base of one instance. Repetition plays no role in the reasoning process beyond replication as a test of accuracy.

We know that water freezes when the temperature gets sufficiently cool that the molecular movement slows down and the molecules stick to each other to form crystals. But how do we know that cooling temperatures caused this result and not some other factor, such as light or sound? We use Mill’s Methods: Agreement, Difference, Concomitant Variations, et. al. The Method of Agreement says: If two or more instances of the phenomenon under investigation have only one circumstance in common, the circumstance in which alone all the instances agree, is the cause (or effect) of the given phenomenon. Once you have isolated temperature as the cause of the slowing molecules under the microscope, the job is done.

The error in the Black Swans example consists in the conclusion that color is an essential attribute somehow connected to the nature of Swans. That is an inductive hypothesis based on enumeration, not an inductive inference based on an analysis of the nature of Swans.

### #11 BaalChatzaf

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Posted 12 September 2010 - 06:57 AM

The error in the Black Swans example consists in the conclusion that color is an essential attribute somehow connected to the nature of Swans. That is an inductive hypothesis based on enumeration, not an inductive inference based on an analysis of the nature of Swans.

But it is a generalization from a set of particulars to a universal. It happens to be an erroneous generalization. The induction by enumeration permits the assumption that color is a consequence of all the other identifiable characteristics of crows, swans and such like. And THAT is a problem. Also, inductions can be incomplete. There is always the possibility that a contrary fact will be found later one which destroys the generalization. Induction is guaranteed to work only after one has every last possible fact, which is something that is not going to happen. Induction is a perfect method for omnipotent folks, But for ordinary mortals knowing only some of the possible facts (but not all) it is not guaranteed to work. Sometimes it does, sometimes it doesn't.

Ask yourself what error Newton made when he arrived at his law of gravitation based on observation. His law is very intuitive (it has spherical symmetry, i.e. does not favor a particular direction; it fits many observed fact; it has lead to the discovery of hitherto unknown planets). But it is wrong. How do we know it is wrong? It does not correctly predict the precession of the perihelion of Mercury, for example. Also, in a deeper way it is wrong. It is assumes instantaneous action at a distance. Einstein's approach in General Theory of Relativity corrects this latter defect at the root and also makes better predictions than Newton's Law.

Newton acted in a perfect sane, reasonable, "logical" way in formulating his Law of Gravitation. He made sure it was consistent with Kepler's empirical laws of planetary motion. He assured its generality by checking to see that it applied to the Moon as well as it applied to falling fruit from a tree. For over two hundred years it checked with astronomical observations within all bounds of instrumental error. When anomalies were found they were resolved by finding new objects to which the Law applied. That is how Couch-Adams and Verrier found the planet Neptune which is too far away to be seen by naked eye and mankind had telescopes for too short a time for the planet to be seen right off. Its existence was inferred from observed anomalies in the motion of the planet Uranus. What did Newton do wrong? Nothing. His method of concluding his law of gravitation applied in the solar system simply did not take into account the motion of mercury correctly. The adverse fact he did not see and could not see was that the gravitational field itself, gravitates. That required another approach. The method of induction simply cannot prevent these contrary facts from creeping in. Like I said, it is not guaranteed to produce correct conclusions although it often does.

Going to causes and their enumeration, Mills method works very well in the macroscopic domain. The Mill approach simply cannot cope with the way the physical world operates at the subatomic level. Also the Mill approach assumes that one knows ahead of time which factors are relevant to the observation made. When a ball rolls down an inclined plane we assume its surface regularity and that of the plane are the relevant factors. What if some unseen force were operating other than gravity? As such a force been eliminated correctly? If it is undetected, it cannot be eliminated with certainty. Newtonian modeling for falling and rolling bodies works under the assumption that matter is distributed in a sufficiently uniform manner. A dropping experiment made near a very big mountain will actually produce initially unexpected deviations. One must remove tricky factors like mass distributions not uniform with the rest of the planet. Mills method is not guaranteed to spot such anomalous factors. Even so, Mills methods are perfectly fine first order procedures for starting an investigation.

Mills methods did not lead Wolfgang Pauli to postulate the existence of neutrinos. It was the requirement of mathematical symmetry and the saving of conservation laws that did. Observed facts did not lead Maxwell to modify Ampere's equation by adding the displacement current term. It was a mathematical issue that lead to his modification of the equation.

In particular look at the section on History and Interpretation.

If Maxwell had reached Displacement Current based on observation he would have had to had in and some kind of electromagnetic transmission system that worked in free space. At the time no such systems understand to be electromagnetic waves in fields were known. It was from the notion of displacement current that the theory of traveling electromagnetic waves was born. First came the mathematical intuition, then came the hypothesis and latter came the verification by Hertz (Maxwell had died by this time).

I would love to see a Harriman type analysis of Maxwell's modification of Ampere's equation. For those who have read the book (I have not) is there such a portion?

Ba'al Chatzaf
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### #12 George H. Smith

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Posted 12 September 2010 - 08:31 AM

The error in the Black Swans example consists in the conclusion that color is an essential attribute somehow connected to the nature of Swans. That is an inductive hypothesis based on enumeration, not an inductive inference based on an analysis of the nature of Swans.

But it is a generalization from a set of particulars to a universal. It happens to be an erroneous generalization. The induction by enumeration permits the assumption that color is a consequence of all the other identifiable characteristics of crows, swans and such like.

We are not talking about induction by enumeration. Have you been reading any of my posts on this thread?

And even induction by enumeration does not permit the "assumption" you mention.

Not all generalizations are examples of inductive reasoning. Reasoning involves having plausible reasons for one's conclusions. If you once met a red-haired woman with a bad temper and concluded that all red-haired woman have bad tempers, you are guessing, not reasoning.

There are standards for inductive reasoning, just as there are standards for deductive reasoning and mathematics.

Ghs

### #13 Ted Keer

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Posted 12 September 2010 - 10:14 AM

What about crows makes you think blackness is essential to them? Does your induke not know anything about biology? About what species are? About variation? About the phenomenon of albinism? I mean, really, Bob. How do you take such examples seriously?

You miss the point. Those who saw a zillion black crews leapt to the inductive conclusion that all crows are black. But it ain't so. It was their induction that was wrong, not the crows. Induction lead to a conclusion that happened to be false. Other inductions have lead to true conclusions. Which shows sometimes induction works and sometimes it doesn't. Whereas deduction ALWAYS produces a true conclusion from true premises. It never fails to do so. It can't fail to do so because the necessity is essentially the principle of non-contradiction.

We are forced to use induction because it is the only way to get from a set of particulars to a generality in the empirical domain. When we learn by doing or learn by skinning our knees we use induction. Sometimes we learn the right lessons, sometimes we don't.

And THAT is the problem of induction. Sometimes it works and sometimes it doesn't.

Whereas deduction from true premises is guaranteed to produce a true conclusion.

Ba'al Chatzaf

There is nothing wrong with induction. The problem is with the indukes. Induction works when done properly. The fact that a million people draw a false conclusion is no more an indictment of [induction] than is malpractice an indictment of medicine or solecism an indictment of grammar or Peikoff an indictment of the primacy of existence.

The complaint that even we cannot be guaranteed ahead of time that we have not made a mistake is no different from the petulance you see in a child who, loosing unexpectedly against his friends, takes his game and goes home.

Edited by Ted Keer, 12 September 2010 - 10:32 AM.

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### #14 BaalChatzaf

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Posted 12 September 2010 - 10:15 AM

There are standards for inductive reasoning, just as there are standards for deductive reasoning and mathematics.

Ghs

Yes. There are inductive heuristics that are quite useful if not completely general. For example, Mills rules for isolating causes/effects. By the way, Mill's rules do not completely determine which is the cause and which is the effect.

Ba'al Chatzaf
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### #15 Ted Keer

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Posted 12 September 2010 - 10:16 AM

The error in the Black Swans example consists in the conclusion that color is an essential attribute somehow connected to the nature of Swans. That is an inductive hypothesis based on enumeration, not an inductive inference based on an analysis of the nature of Swans.

Didn't I just say that?

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### #16 George H. Smith

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Posted 12 September 2010 - 10:30 AM

There is nothing wrong with induction. The problem is with the indukes. Induction works when done properly. The fact that a million people draw a false conclusion is no more an indictment of grammar than is malpractice an indictment of medicine or solecism an indictment of grammar or Peikoff an indictment of the primacy of existence.

The complaint that even we cannot be guaranteed ahead of time that we have not made a mistake is no different from the petulance you see in a child who, loosing unexpectedly against his friends, takes his game and goes home.

In The Principles of Logic (vol. II, p. 572), the British Idealist F.H. Bradley has some very interesting remarks on this general topic:

We...may end our chapter with another word against the sceptic. We are bound to admit some degree of probability in favor of error of the badness of any one inference; and the sceptic once more may urge his objection. If every argument is probably false [i.e., if every argument has some probability of being false], how can any argument be certainly true? But the answer is simple. Considering my reasoning as a number of acts, I conclude that I am fallible throughout the series. But this chance is mere antecedent probability. It may become unmeaning when the instance is present and actually before us; as unmeaning as the chances against a die giving six, when the actual throw has been observed. And if so, the presumption of our fallibility may warrant a general feeling of diffidence; but it cannot affect any actual inference which has once been seen to exhibit the type required for demonstration. If in the present instance you can show me no ground which justifies doubt, your mere general probability is quite irrelevant. Whether it is true that in every case we have actual cause for hesitation, is a question of fact to be settled by itself.

Ghs

### #17 BaalChatzaf

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Posted 12 September 2010 - 10:34 AM

The complaint that even we cannot be guaranteed ahead of time that we have not made a mistake is no different from the petulance you see in a child who, loosing unexpectedly against his friends, takes his game and goes home.

Never the less a valid deduction from true premises guarantees the truth of the conclusion. For certain, for sure. Such certainty is not inherent in the inductive mode. Induction works often enough to be useful and fails often enough so that we should be cautious in its use.

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### #18 Ted Keer

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Posted 12 September 2010 - 10:35 AM

There is nothing wrong with induction. The problem is with the indukes. Induction works when done properly. The fact that a million people draw a false conclusion is no more an indictment of grammar than is malpractice an indictment of medicine or solecism an indictment of grammar or Peikoff an indictment of the primacy of existence.

The complaint that even we cannot be guaranteed ahead of time that we have not made a mistake is no different from the petulance you see in a child who, loosing unexpectedly against his friends, takes his game and goes home.

In The Principles of Logic (vol. II, p. 572), the British Idealist F.H. Bradley has some very interesting remarks on this general topic:

If in the present instance you can show me no ground which justifies doubt, your mere general probability is quite irrelevant.

Ghs

As a proof of fallibility in posting, where I first wrote "grammar" above I meant to say induction.

Do you recommend Bradley's Logic, George? Can you compare it in value to Joseph's?

Edited by Ted Keer, 12 September 2010 - 10:35 AM.

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### #19 George H. Smith

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Posted 12 September 2010 - 10:37 AM

There are standards for inductive reasoning, just as there are standards for deductive reasoning and mathematics.

Ghs

Yes. There are inductive heuristics that are quite useful if not completely general. For example, Mills rules for isolating causes/effects. By the way, Mill's rules do not completely determine which is the cause and which is the effect.

Ba'al Chatzaf

I have said before that in those cases where great precision is required, as in science, inductive reasoning may not be adequate by itself. This is where inductive conclusions become the hypotheses that are tested by experimental means, as in the hypothetico-deductive method that Daniel has mentioned on several occasions.

If if you are looking for infallibilty in any method of reasoning, you won't find it.

### #20 Brant Gaede

Brant Gaede

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Posted 12 September 2010 - 10:38 AM

It seems to me that the problem of induction is only epistemological tail chasing. If it could be solved how would it be generalized to other cases than those already addressed other than on a case by case basis solving this problem over and over again? This problem will never be solved--it's been designed not to be (no?)--for reasoning itself isn't really deficient save for lack of use and irrationality--deficiencies in teaching thinking in the first place. The real way to solve an artificial problem like this is to identify it as an artificial problem and chuck it. That's what needs work here, by me and thee. My basic position is that without deduction the problem cannot be solved if it can at all because that would require purely inductive reasoning--no? Since inductive reasoning itself is not invalid--if it was we wouldn't use it at all--it has to simply be taken as a part, but not the whole part, of reasoning, which as a practical matter of use is not dividable. Tentative generalization seems to be as far as we can go with pure induction; deduction tells us so.

--Brant

Rational Individualist, Rational self-interest, Individual Rights--Libertarian

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