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

[Michael Stuart Kelly]

Are you simply saying that induction is not deduction, and that induction is not deductively valid? If so, Peikoff agrees with this, and he points out in his IPP lectures that one of the biggest mistakes theorists have made in trying to validate induction is to try to reduce it to a form of deductive logic.

Roger,

Thank you for that.

I jumped into discussions of epistemology in an attitude of "let's see what I can learn" back on SoloHQ and ever since then, all the way up to now, whenever I have come up against a wall where communication broke down (frequently and constantly), this has always been at the root.

I keep seeing induction being blamed for not being deduction (or using the methodology of deduction), and then the extension: induction is not reliable (or some variation of that, like not valid according to logic, etc.). Often this argument has gotten buried under a mountain of technical jargon to intimidate rather than explain, but I still kept seeing this problem.

When I came to Popper, I saw he went whole hog and denied the very existence of induction. However, his premise is that reality is absolute, so I think there might be more similarity to Objectivism than meets the eye once jargon issues and personal vanities have been set aside. (And these problems are as thick as thieves in politics.)

I might save my pennies and get that Peikoff course. It sounds interesting. I am especially interested on this self-correcting idea. Would you comment a bit on that?

Michael

[BaalChatzaf]

Bob K...in my post up-thread, I agreed with you that there are no valid argument forms in inductive logic. I.e., INDUCTIVE GENERALIZATION IS NOT LOGICALLY VALID.

Huh? Are you simply saying that induction is not deduction, and that induction is not deductively valid? If so, Peikoff agrees with this, and he points out in his IPP lectures that one of the biggest mistakes theorists have made in trying to validate induction is to try to reduce it to a form of deductive logic.

Deductive inferences are (by their nature and definition) truth preserving. If conclusion is deduced from -true- premises then the conclusion is bound to be true. Not so for Induction. One can have a set of true instances, but the generalization that is Induced might be false. The example of the black crows and the white swans shows this to be the case. There is no guarantee that the generalization drawn from the instances will be true.

The problem with induction and its associated problem of predicting the future from current and past events has been known since at least the time of Hume (and most likely before that). I am sure Aristotle would make the same point as did Hume.

Ba'al Chatzaf

[BaalChatzaf]

Huh? Are you simply saying that induction is not deduction, and that induction is not deductively valid? If so, Peikoff agrees with this, and he points out in his IPP lectures that one of the biggest mistakes theorists have made in trying to validate induction is to try to reduce it to a form of deductive logic.

Deductive inferences are (by their nature and definition) truth preserving. If conclusion is deduced from -true- premises then the conclusion is bound to be true. Not so for Induction. One can have a set of true instances, but the generalization that is Induced might be false. The example of the black crows and the white swans shows this to be the case. There is no guarantee that the generalization drawn from the instances will be true.

The problem with induction and its associated problem of predicting the future from current and past events has been known since at least the time of Hume (and most likely before that). I am sure Aristotle would make the same point as did Hume.

Be that as it may, Induction and Abduction (also known a Reduction) are ways of generating general suppositions from particular instances. They are not generally valid but they are the only way we have of getting beyond a limited set of particular propositions to general statements. Learning New Stuff requires Induction and Abduction.

Ba'al Chatzaf

Edited September 13, 2007 by BaalChatzaf

[Ellen Stuttle]

Induction is an extended form of concept-application by which we form more general propositions and argue for more general conclusions.

What Roger is saying there is, I believe, the central thesis of Leonard Peikoff's IPP course.

On the "Popper Talk" thread I quoted (See) what I take to be Peikoff's key contention relating concept formation and induction.

A generalization is no more than the perception of cause and effect conceptualized. [....] Induction is measurement-ommission applied to causal connection.

Ellen

___

[tjohnson]

All white swans are birds.

All non-white swans are birds.

Universally quantified and no exceptions. These statements are true for every single white and non-white swan observed in the past, present and includes all to be observed in the future.

My neighbor is a white person named Swan and he is not a bird, so much for no exceptions. Now what will you say? All white swan BIRDS are birds? Yes, I agree.

If "logic" is about forms and devoid of content then it must be mathematics, you can't have it both ways. You can't make statements about ALL things because you can't perceive all things. Not so in mathematics. Let A be the set of real numbers in the interval 0<x<1. Then for ALL x in A, x<1.

[Michael Stuart Kelly]

You can't make statements about ALL things because you can't perceive all things.

GS,

Sure you can. You just cannot perceive them all at the same time. (I am talking within the context of restricting the referents as concept formation does.)

To be clear, if I say "all white swans are birds," I assure you that I am able to perceive all white swans and even verify that they are birds. All one has to do is cross my visual range and I can perceive it. There is no such thing as an invisible white swan, nor even an invisible swan. I can perceive all of them. If they exist, I can perceive them.

To go for overkill on this idea, if a white swan crosses my visual field and my eyes are healthy and I am looking at the swan, I cannot not perceive it. I have to perceive it. Perception is automatic. This hold true for all white swans.

If you want to go all the way down and talk about ALL THINGS that exist, haven't you already included them within the concept just by naming it? That is not math, but the concept denoted by the phrase ALL THINGS is a symbol that denotes, er... all things. And one cannot perceive many of them at all, even with specialized instruments.

As to your friend named Swan, in Objectivism there is a strong distinction between a mental unit of thought called a concept and the word for it. Context is always a big factor in determining what the referent is. If we were talking in Portuguese and discussing cisnes, your friend would not even enter the picture, yet we would be talking about the same referents as "swan" in English.

Michael

[tjohnson]

As to your friend named Swan, in Objectivism there is a strong distinction between a mental unit of thought called a concept and the word for it. Context is always a big factor in determining what the referent is.

Michael

This is true in all natural languages, which was my point - and O'ism falls into the category of natural languages. Of course I knew exactly what you meant yet one cannot always be sure that is the case, unlike in mathematics where we can be sure EXACTLY what is meant. You cannot remove ambiguity from natural languages, if you succeed you are in the realm of mathematics.

[Robert Campbell]

Roger,

What does Leonard Peikoff say in his IPP course about the structure or formation of propositions?

Does he offer a theory of propositions?

Is his account of induction adequate, by his own criteria, if he doesn't offer such a theory?

Robert Campbell

[John Dailey]

~ Baal says...

Deductive inferences are (by their nature and definition) truth preserving.

~ Am unclear what 'by their nature' empirically, observationally, analytically, synthetically, or even deductively means here, and...am not aware that they are even 'definitionally' so. Indeed, the most accurate 'definition' I can find is "inference in which the conclusion is of no greater generality than the premises." (check Wiki)

~ I have no argument with the description, as such (other than what 'nature' means in this abstract territory); but, such is its definition? Depends on one's argumentative context I guess.

~ Be such as such may, my question still remains as to whether such a statement is 'definitionally' true (presumably in the ASD view of definitions)...or...observationally ('empirically'?) induced; such a question I already implied in my last post and it is quite noteworthy all responses are ignoring (avoiding?) it.

LLAP

J:D

[John Dailey]

~ Strictly speaking, to even speak about 'abstractions', of whatever level (from percepts or abstracted 'abstractions'...such as the process of deduction), is not one already talking about a result/consequence from using INDUCTION?

~ I mean, whenever one uses the term 'abstraction', can one be meaningfully talking about something that did not require INDUCTION? If so...how? How does one acquire a worthwhile, useful 'abstraction' without using the process of INDUCTION?

LLAP

J:D

[John Dailey]

~ Take the subject of 'Deduction' itself. It's considered as (ahem!) always ('inherently'?) 'truth-preserving', correct?

~ HOW is this determined as being 'true'? Merely 'analytically' (aka, 'by definition')?

~ If so, this has then, in reality, nothing to do with if it'll empirically/synthetically be seen as 'true' next time it's used...by someone else, on some other subject.

~ If not, then...what criteria of 'truth' can be applied to this idea besides 'analytical'? 'Empirical'? If so, then...what about 'next time' this process is used, (like Russell's prob with the sun rising tomorrow)?

~ O-t-other-h, if 'empirical' is a base (and more than 'perception' oriented) for something else...'deduction' has a logically justifiable base for using beyond linguistic puzzles. --- My question is: what is this 'basis'?

LLAP

J:D

Edited September 14, 2007 by John Dailey

[John Dailey]

ADDENDUM:

~ I marvel at hearing about "The 'Problem' with Induction" with nary a word about "The 'Problem' with Deduction."

~ Deduction has no 'problem' some would say. That's because the prob's ignored.

~ What's it's problem? How about..."As useful in reality as it's been everywhere it's been used, how does one know that it will continue to be so...next time it's used?"

~ As far as I'm concerned, talk about a 'stolen concept'! Deduction's worthwhileness/usefulness depends upon INDUCTION.

LLAP

J:D

[Michael Stuart Kelly]

~ Deduction has no 'problem' some would say. That's because the prob's ignored.

~ What's it's problem? How about..."As useful in reality as it's been everywhere it's been used, how does one know that it will continue to be so...next time it's used?"

~ As far as I'm concerned, talk about a 'stolen concept'! Deduction's worthwhileness/usefulness depends upon INDUCTION.

John,

LOL...

Don't say that too loud. Some get real touchy about this.

Just for general purposes, in lay language, analytic is a purely mental system and if you follow the rules, this is called truth. Synthetic is a system where some kind of checking is needed to become true because reality starts entering the picture.

In other words, something can be unreal but can be true if it is analytic. If it has to correspond to reality to be true, that is synthetic.

Part of the whole controversy is how the rules for analytic are derived. Peikoff flat-out denies that there is a difference between the two and claims that those who accept it are intellectually poisoning their thinking. From what I have read so far, those who follow this distinction think that the rules for analytic systems like logic and math are innate and just kinda happen or develop that way.

Here is one hell of a good Wikipedia article that is simple enough for lay people to understand. (OK, it is a little boring, but you don't have to prop your eyes open with toothpicks to read it.) It deals with propositions in a very clear manner.

Analytic-synthetic distinction

It is interesting to note that one of Kant's core thoughts is explained in a brief simple manner—one of the best I have seen so far (with the caveat that I am relatively new to all this).

Michael

[John Dailey]

Mike:

~ Thanx for the response. Re some being 'touchy' on this...I'm quite aware...lately. I'm also quite aware about 'synthetic' and 'analytic' views, if I haven't made myself clear.

~ Ntl, 'touchiness' or non, my questions (especially on the worth/justification of 'deduction') remain unanswered.

~ Why do I suspect that my questions...might...get several 'responses', but, not get any relevent 'answers'?

LLAP

J:D

Edited September 14, 2007 by John Dailey

[Roger Bissell]

Are you simply saying that induction is not deduction, and that induction is not deductively valid? If so, Peikoff agrees with this, and he points out in his IPP lectures that one of the biggest mistakes theorists have made in trying to validate induction is to try to reduce it to a form of deductive logic.

Roger,

Thank you for that.

I jumped into discussions of epistemology in an attitude of "let's see what I can learn" back on SoloHQ and ever since then, all the way up to now, whenever I have come up against a wall where communication broke down (frequently and constantly), this has always been at the root.

I keep seeing induction being blamed for not being deduction (or using the methodology of deduction), and then the extension: induction is not reliable (or some variation of that, like not valid according to logic, etc.). Often this argument has gotten buried under a mountain of technical jargon to intimidate rather than explain, but I still kept seeing this problem.

When I came to Popper, I saw he went whole hog and denied the very existence of induction. However, his premise is that reality is absolute, so I think there might be more similarity to Objectivism than meets the eye once jargon issues and personal vanities have been set aside. (And these problems are as thick as thieves in politics.)

I might save my pennies and get that Peikoff course. It sounds interesting. I am especially interested on this self-correcting idea. Would you comment a bit on that?

Michael

Yes, but only a bit. I'm not going to make the entire case. I'll let Peikoff do that for you, if you're interested enough to follow up and get his IPP course. (I'd recommend that one -- more recent, tighter integration -- over the Objectivism through Induction course.)

Basically, proof in either inductive or deductive logic rests on two essentials: integration and reduction. This, I take it, means that to be true, your ideas must not contradict one another (coherence) and must be based on reality (correspondence). How this works out in induction and deduction is different in each case...

In deduction, your premises have to be integrated in a certain way for the conclusion to be valid; and your premises have to be reducible to a basis in observable reality (i.e., true) for the conclusion to be necessarily true. (You can get a true conclusion, by accident, from one or more false premises: e.g., all cows are green, all green things are mammals, therefore all cows are mammals, which is the accidentally true conclusion of a valid syllogism -- as against all cows are mammals, all mammals are animals, therefore all cows are animals, which is the necessarily true conclusion of a valid syllogism using true premises.)

In induction, your generalizations have to derived from a base in observable reality, and they have to be formed step by step from this base using valid (reducible) concepts. Peikoff gives extended illustrations of this process in physics and philosophy, and he codifies the methodology with these points:

1. Valid concept-formation is essential at every stage of induction; valid concepts are the only "green light" to induction.

2. Induction begins with first-level, self-evidence generalizations to which all other generalizations must be ultimately reduced.

3. Inductive generalizations are essentially the identification of causal connections, using (Mill's) Methods of Agreement and Difference.

4. Induction requires integration of generalizations with one's other knowledge.

5. Physics, above the earlier stages of observation and generalization, require mathematics.

Peikoff concedes that it's possible to make honest errors in applying the methodology of induction. But as long as you know they explicitly and you conscientiously try to apply them, the errors will show up fairly quickly. And that is why he says that induction, by its nature, is self-corrective.

Sometimes we overlook the fact that our generalizations are limited to a specific context, and we over-generalize -- e.g., saying that all swans are white. Over-generalizations are soon enough shown to have exceptions in a new context. Peikoff gives some good examples of this from physics.

Sometimes we try to explain observations before we have enough information for a rational explanation of a phenomenon. Peikoff cites Kepler's attempt to explain his three laws of motion in terms of the Sun's supposed magnetic force on the planets, and how Newton supplied the correct alternative explanation in terms of gravity.

Peikoff gets a lot of mileage out of examples from the history of physics of how inductive methodology is self-correcting, and how rational conscientious thinkers will eventually correct their (or others') errors and find the truth about a situation. He says (and illustrates how) this also applies to philosophy.

He also has what I think is a crucial point about people who object to a well-integrated, well-founded generalization or principle, asking "what if tomorrow it's different?" You have to have some basis in evidence for doubting or questioning a generalization and the integrated body of observations and conclusions you have inductively formed. If there is no basis to a challenge, it is not rational to entertain it. Call it "arbitrary" or whatever you like, I think Peikoff is exactly correct about this kind of assertion by skeptics.

REB

[Roger Bissell]

ADDENDUM:

~ I marvel at hearing about "The 'Problem' with Induction" with nary a word about "The 'Problem' with Deduction."

~ Deduction has no 'problem' some would say. That's because the prob's ignored.

~ What's it's problem? How about..."As useful in reality as it's been everywhere it's been used, how does one know that it will continue to be so...next time it's used?"

~ As far as I'm concerned, talk about a 'stolen concept'! Deduction's worthwhileness/usefulness depends upon INDUCTION.

LLAP

J:D

Exactly so, John.

In his IPP lectures, Peikoff points out the parallel between induction and deduction, and he says that deduction is ~supposedly~ not a problem. "Nobody walks around holding their head in their hands and bewailing the Problem of Deduction." Yet, you can honestly make an error in deduction. But if you do, by conscientiously following the rules of deductive logic, you'll find the error soon enough.

Robert Campbell said that induction is not "logically valid." It appears that he simply means that there are no canonical forms of induction as there are for syllogisms in deductive logic. True, but there ~are~ rules or principles that must be followed in order to ensure that one is aimed at the truth, and I mentioned them in my preceding post.

But such a comment by others often seems to contain an undercurrent (surely not part of Robert's own thinking) that induction is inferior because it is not infallible or automatically correct. Deduction is not infallible or automatically correct either! But that doesn't mean we have to entertain skeptical doubts or worry about some deep epistemological shortcoming about deduction. And the same is true for induction.

As Peikoff says, "There is no more Problem of Induction than there is a Problem of Deduction."

REB

[Roger Bissell]

Roger,

What does Leonard Peikoff say in his IPP course about the structure or formation of propositions?

Does he offer a theory of propositions?

Is his account of induction adequate, by his own criteria, if he doesn't offer such a theory?

Robert Campbell

Not much, not in IPP but in an earlier course, but probably so.

In re questions 1 and 2: I think that Peikoff is probably relying on the general knowledge people studying logic have about the structure of propositions. He laid this out fairly well in his 1974 course on logic, though I would have a lot to add (and some corrections) if I were presenting logic from concepts to propositions to deductive and inductive arguments.

In re question 3: you could argue that Peikoff's entire discussion is a gigantic floating abstraction, because he doesn't define "proposition." By the principle of charity, I would grant that he is assuming our general knowledge of what a proposition is and/or how he defined it in his logic lectures. But this whole "oral tradition" of Objectivism is a huge problem for scholarship, not to mention critical examination.

Putting aside my extreme aggravation that so much of Peikoff's thought is in aural/oral form and not easily critiqued, I have to say that I think his account of induction -- building on his account of propositions from 1974 -- is at least adequate. I am very glad to see the level of integration he has brought to the subject, tying induction and deduction together, tying math, science and philosophy together, etc.

I think there is even more one can say than he does in either his old logic lectures or his more recent induction lectures -- or than Kelley says, for that matter -- but that is something I will have to put aside for another time. I do intend to write on this some day, as a follow-up to the essay that is pending for the next issue of JARS on Rand's trichotomy. Just remember: unit-perspective and file-folders. That says it all for me.

REB

[tjohnson]

ADDENDUM:

~ I marvel at hearing about "The 'Problem' with Induction" with nary a word about "The 'Problem' with Deduction."

~ Deduction has no 'problem' some would say. That's because the prob's ignored.

~ What's it's problem? How about..."As useful in reality as it's been everywhere it's been used, how does one know that it will continue to be so...next time it's used?"

~ As far as I'm concerned, talk about a 'stolen concept'! Deduction's worthwhileness/usefulness depends upon INDUCTION.

LLAP

J:D

Yes John, there IS a problem with deduction. In any natural language deductions can only ever work relatively since we cannot include all particulars in our definitions. In mathematics they can work absolutely so long as we follow the rules of deduction.

[Michael Stuart Kelly]

GS,

I highly recommend you study ITOE a bit. Concept formation in Objectivism is based on identification (differentiation and integration) and essentials are used to establish hierarchies. In this sense, rules can be established like with math.

Michael

[tjohnson]

GS,

I highly recommend you study ITOE a bit. Concept formation in Objectivism is based on identification (differentiation and integration) and essentials are used to establish hierarchies. In this sense, rules can be established like with math.

Michael

It doesn't matter how many rules you establish you can't include all particulars in your definitions and so the rules may not always work. Here is an experiment; Take a word and define it then define a key word in your definition. Repeat this until you are defining in circles, for example defining 'point' with 'line' and 'line' with 'point', etc. You have reached the objective level and cannot define verbally anymore. Now we must have common experience-word relationships to communicate ie. I must trust that you understand what I mean by a certain term.

This differs highly with math because there need not be any word-experience relationship in math, the definition is all we have.

[BaalChatzaf]

GS,

I highly recommend you study ITOE a bit. Concept formation in Objectivism is based on identification (differentiation and integration) and essentials are used to establish hierarchies. In this sense, rules can be established like with math.

Michael

In addition to comparison and contrast, concepts can also be generated by analogy and metaphor. For example the -head- of the line. Lines do not literally have heads, but they have front ends and rear ends. For some reason the end of the line is not called the buttock or ass of the line. Structures can have feet or pediments as analogy to the feet of humans and animals. We also have tongues of fire because of the similarity of shape between the tongue (found in the mouth) and elongated jets of flame. Then there are the teeth of a storm. The part of the storm (the cold wind front which is biting cold) is analogized to teeth. And there are, of course, the jaws of death. or the jaws of defeat. He snatched victory from the jaws of defeat.

Rand was a word smith. It is strange that she did not dwell on metaphors, similes and analogies.

Ba'al Chatzaf

[Brant Gaede]

GS,

I highly recommend you study ITOE a bit. Concept formation in Objectivism is based on identification (differentiation and integration) and essentials are used to establish hierarchies. In this sense, rules can be established like with math.

Michael

It doesn't matter how many rules you establish you can't include all particulars in your definitions and so the rules may not always work. Here is an experiment; Take a word and define it then define a key word in your definition. Repeat this until you are defining in circles, for example defining 'point' with 'line' and 'line' with 'point', etc. You have reached the objective level and cannot define verbally anymore. Now we must have common experience-word relationships to communicate ie. I must trust that you understand what I mean by a certain term.

This differs highly with math because there need not be any word-experience relationship in math, the definition is all we have.

If we go with your position, can we say nonetheless that knowing and identifying logical fallacies has serious merit?

--Brant

[tjohnson]

If we go with your position, can we say nonetheless that knowing and identifying logical fallacies has serious merit?

--Brant

Don't get me wrong - I'm all for deductive and inductive reasoning, it's just that we need to realize the limitations of these methods in natural languages - when we speak about real, physical things, for lack of better terms.

See this excellent site for an exhaustive list of fallacies.

http://www.esgs.org/uk/logic.htm

I don't personally use them but they may help one look for "verbal tricks" and avoid common pitfalls in language use.

[Michael Stuart Kelly]

It doesn't matter how many rules you establish you can't include all particulars in your definitions and so the rules may not always work. Here is an experiment; Take a word and define it then define a key word in your definition. Repeat this until you are defining in circles, for example defining 'point' with 'line' and 'line' with 'point', etc. You have reached the objective level and cannot define verbally anymore. Now we must have common experience-word relationships to communicate ie. I must trust that you understand what I mean by a certain term.

This differs highly with math because there need not be any word-experience relationship in math, the definition is all we have.

GS,

I repeat, I highly recommend you study ITOE a bit. At least you will know whether or not a subject has been addressed if you have an objection.

The objection you just raised about going around in circles occurs when one eliminates hierarchy from concepts. This is the mistake Popper made with his view that defining terms leads to infinite regress (see "Two Kinds of Definition"—your have to scroll down, or see here, but you have to scroll down, too).

In Objectivism, as you define a concept, then define the concepts it is built on, then define those, you eventually get to a point of observation where the only thing you can do is indicate it somehow and say, "I mean that." This is called an "ostensive definition" and the fundamental axioms can only be defined that way.

This is not too different than math, where you look at the definition and say, "I mean that."

If the idea of direct observation seems too much a burden on this, we should keep in mind that sense organs are interrelated parts of the mind's apparatus. The brain itself is needed for math and, as stated earlier, sensory input is essential for the basic building blocks of math. In fact, I wonder what kind of math a human being who is born blind, deaf and highly deficient in other sense operations, but with a functioning mind, can develop.

Michael

[Brant Gaede]

If we go with your position, can we say nonetheless that knowing and identifying logical fallacies has serious merit?

--Brant

Don't get me wrong - I'm all for deductive and inductive reasoning, it's just that we need to realize the limitations of these methods in natural languages - when we speak about real, physical things, for lack of better terms.

See this excellent site for an exhaustive list of fallacies.

http://www.esgs.org/uk/logic.htm

I don't personally use them but they may help one look for "verbal tricks" and avoid common pitfalls in language use.

I think fallacies should be classified according to how common they generally are and learned that way. The site you linked to above is incredible, but it is only as the Merck Manual is to medicine: everything but the kitchen sink.

--Brant