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

[Ellen Stuttle]

Roger,

Does Peikoff give a definition of what he means by "induction"? [Edit: He gives a statement which sounds like a definition in the quote from him below. However, I'm not seeing how that definition would produce reflections on the kinds of scientific issues hinted at in your post.] From what you describe in your post #115, it sounds to me as if what he's talking about is what I'd call theory formation and testing rather than the traditional meaning of making a universally quantized statement (an "all") statement on the basis of a group of uniform observations (I've observed X number, all of which have had a particular quality).

In regard to the point 2 you listed:

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

Am I correct in thinking that he's making the claim that we perceive causal connection? That was my understanding of his claim in a statement I've given a couple times, which I take to be his 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.

___

Edited September 15, 2007 by Ellen Stuttle

[John Dailey]

GenSem:

~ In other words (re your post #120), as Rand pointed out, *we*, for inter-communicative purposes with others, before we get into 'linguistic definitionalizing' with them, must start with 'ostensive'...labeling...as primitive 'definitions'? --- Like, being washed up on a desert island with a 'foreigner', and working out a basis for communicating?

LLAP

J:D

Edited September 15, 2007 by John Dailey

[John Dailey]

~ FWIW:

~ I think we should all be careful about using the term definition (of 'X'), as if once given the def is presumed to foreverafter have some kind of cosmic, 'absolutistic', a-contextual, and non-finesseable meaning across all uses (even by the same person) of the term 'X.'

~ Rand 'defined' rights metaphysically.

~ Rand 'defined' rights ethically.

~ Rand 'defined' rights politically.

~ The contexts' defs are not identical.

~ All defs of 'X' (whether 'rights', 'deduction', 'logic', 'proposition-types') should be regarded as pertinent only to the subject/context being debated, and not mixed up with each other. Elsewise, all arguments thereof result in nothing more than circle-jerking...and this is worse than circular-defining because one doesn't see that one's involved in it.

~ Just thought I'd point this out.

LLAP

J:D

Edited September 15, 2007 by John Dailey

[John Dailey]

GenSem:

~ You say (in post #120)...

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.

~ Interesting assertion. Technically, 'true' empirically (probably!) But, your 'experiment' follow-up illustration establishes nothing, really, other than you can't think of anything relevent here other than pickiness. I mean, Einstein improved the 'rules' of Newton; clearly, improvement is needed for Einstein's views. So? Abstractedly, maybe Rand's 'rules' can be 'improved' upon; care to (unlike too many others) get up to the plate? Or are you saying that no 'rules' can encompass more than hers already has?

~ MSK is correct: you really should 'read' (not just look at the words) ITOE.

LLAP

J:D

Edited September 15, 2007 by John Dailey

[John Dailey]

GenSem:

~ You say (again, in post #120)...

...there need not be any word-experience relationship in math, the definition is all we have.

~ I ask: and...the 'truth' of this supposed 'definition' is accepted from where, who, and, upon what justification (aka 'why')? Like, the bible? Because it's written in some books by, maybe, 'mathematical'...astrologers?

LLAP

J:D

[BaalChatzaf]

GenSem:

~ You say (again, in post #120)...

...there need not be any word-experience relationship in math, the definition is all we have.

~ I ask: and...the 'truth' of this supposed 'definition' is accepted from where, who, and, upon what justification (aka 'why')? Like, the bible? Because it's written in some books by, maybe, 'mathematical'...astrologers?

LLAP

J:D

Definitions in mathematics are conventions. They are NOT Metaphysical Truths. People accept conventions for pretty much the same reason they accept game rules. They all want to play together.

In addition some of the conventions lead to useful results in the sciences. For example calculus produced a precise quantitative grasp of motion. Indeed, calculus was invented precisely for that purpose. Even so, the basic "rules of the game" took over 150 years to develop. The limit concept, which is key to doing calculus and differential equations did not assume its current rigorous form until around 1850 (give or take).

Strictly speaking definitions are neither true nor false. They are conventions that reflect usage. There sometimes are conventions that affect usage as well. I understand that in Objectivist circles definitions assume some kind of ontological status. That somehow they reflect what Is Really Out There. What is Really Out There is really out there whether we have a word or phrase for it or not. Again, this definition fetish reflects a confusion between the Word and the Thing, the Description and the Thing Described, the Map and the Territory. To the extent that such confusion exists, Korzybsky (the inventor of General Semantics) was right.

Ba'al Chatzaf

[John Dailey]

~ Interesting question Ellen Stuttle brings up.

~ I've not heard the lecture, but, as she quotes, I definitely see a difference in the set of quotes.

~ As Peikoff is quoted, he 1st refers to what I'd call an 'impression' of an appearance of 'causality' (akin to Piaget's studies of children post-'object-permanence.') I think this is where Hume stops. --- Anyhoo, an impression/appearance of 'X' of course is not a rational ('logical'?) determination of its actuality. Peikoff's 2nd quote, unfortunately, doesn't make a direct connection to such perceptuality, but clearly adds in Rand's ITOE view of 'measurement-omission' as relevent to ('mentally'?) 'seeing' causality therein. Indeed, 'seeing' here, might be a term that has near, but not totally, metaphorical meaning; I think this is what Rand was referring to re a 'missing link.'

LLAP

J:D

Edited September 15, 2007 by John Dailey

[Michael Stuart Kelly]

Definitions in mathematics are conventions. They are NOT Metaphysical Truths.

Bob,

Wanna bet? Try doing math without the Law of Identity. Suddenly it would be a game with constantly changing rules and values with no connection to reality.

Math rests on Metaphysical Truth.

Michael

[John Dailey]

MSK:

~ Obviously, not for some.

LLAP

J:D

[tjohnson]

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.

OK, this is not so different from what I said - you can define with words no further.

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

Michael

I don't understand this statement. If I define a linear function as "a function that can be written in the form y=mx+b", there is nothing we can observe and say "I mean that".

[Michael Stuart Kelly]

If I define a linear function as "a function that can be written in the form y=mx+b", there is nothing we can observe and say "I mean that".

GS,

Sure there is. Each symbol has its own identity (even if it is simply a portion of another), there are relationships established, and even a proposition with them. For example, if you convert this into numbers for a specific equation, you cannot make "b" mean any old number. It has to stay true to its identity.

All this rests on an axiomatic proposition: 1 is 1. (For logic, Rand says A is A.) Then by extension, you can say, therefore 1=1. Everything else flows from this starting point.

Michael

[tjohnson]

Sure there is. Each symbol has its own identity (even if it is simply a portion of another), there are relationships established, and even a proposition with them. For example, if you convert this into numbers for a specific equation, you cannot make "b" mean any old number. It has to stay true to its identity.

Michael

???

[tjohnson]

Wanna bet? Try doing math without the Law of Identity. Suddenly it would be a game with constantly changing rules and values with no connection to reality.

Micheal, mathematics is the ONLY language where the law of identity works.

[tjohnson]

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."

Michael

Let us look at an example. Suppose, as in my "experiment" above, we accept that we can't define 'point' any further and that we trust we both know what 'point' means in some context. In a natural language we would imagine the 'point' of a needle or tool, for example. In mathematics we also used "undefined" terms in our definitions like "a circle is the locus of points equidistant from a point called the center". The difference is that the mathematical point has no physical referent like the needle point. We can see and feel points. They have dimension, some are sharper than others, etc. Not so in mathematics. The mathematical point, even though similar to the idea of a physical point cannot be sensed, has no dimensions and has existence only in our nervous systems. This is what we mean when we say "all particulars are included in the definitions" in mathematics because the undefined terms refer to imaginary entities that are stripped of their physical properties and no other characteristics are allowed.

This is why deductions work absolutely in mathematics but only relatively in natural language. Imagine trying to discover the value of pi using a string and a ruler. You might get close, you might get 3.14, but you are constrained by the "thickness" of your line and your approximate measurements with the ruler so you can only ever get an approximate answer.

To sum up, natural language is an imperfect language in which we can speak about everything and mathematics is a perfect language in which we can only speak about limited things.

[Michael Stuart Kelly]

GS,

Once again, you are using different meanings than Objectivists do. You keep missing the point about essentials (identification) when you get to integration of perceptual input (concepts). You have no problem once the perceptual input has been resolved in infancy, as in math. That is why you did not understand my comment about pointing to the symbol. (Distance in time does not mean that something did not exist. It only means that it is easy to ignore.)

btw - I certainly hope the Law of Identity works for you if someone yells for you to get out of the way of "that speeding car." If it doesn't, the Law of Identity will work anyway and the phrase "that speeding car" will correctly and perfectly indicate the entity with identity that ran you over.

Michael

[Daniel Barnes]

REB:

>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.

Ok. So Peikoff is saying Hume is right after all, and that he solved the problem of induction correctly. Because the whole of Hume's argument is that attempting to predict future occurrences from past occurrences is deductively invalid. This is what is generally known as "the problem of induction."

With that conceded, Peikoff now has some other process, apparently, that he wants to call "induction." Well, let him. It makes no difference to the fact that what is usually called "induction" is deductively invalid, and everyone accepts that.

However, clearly calling two different things the same name will cause teminological confusion. So, I propose we christen Peikoff's new process "Obduction" to avoid confusion. Obduction has 5 points according to Roger's breakdown.

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

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

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

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

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

We can now discuss just how helpful or not obduction is to our search for truth. And best of all, we can now call "time" on Objectivistliving's regular debates on "the problem of induction" because everyone agrees the problem is solved, negatively, by Hume.

REB:

>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.

The counter argument to this is simple: that in fact such evidence is always available, and from a fully approved source - that is, our experience. For all of us have experienced times when we have no facts to suggest a generalisation is false; yet it nonetheless later turns out to be false for reasons we did not suspect. From this fact of our experience (and the similar experiences of all humankind) we may quite reasonably therefore doubt the validity of such generalisations in other situations.

Edited September 16, 2007 by Daniel Barnes

[Ellen Stuttle]

With that conceded, Peikoff now has some other process, apparently, that he wants to call "induction." Well, let him. It makes no difference to the fact that what is usually called "induction" is deductively invalid, and everyone accepts that.

I almost posted to exactly that effect yesterday, Daniel. The way I'd put it in my thoughts was like this:

Definition A is traditionally used for "induction."

Peikoff changes to definition B.

He concedes that "induction" defined by definition A is invalid.

He argues that "induction" defined by definition B is, on the other hand, valid.

But he doesn't mention the definitional substitution and instead claims to have solved "the problem of induction [definition A]."

This looks to me like it's what he's done.

Further issue, though, is whether he indeed is claiming that we perceive causality and that this perceiving provides an unassailable foundation (O'ist foundationalism) for inductive inferences.

Even if he is saying this, however, from the sound of Roger's description what Peikoff comes up with in practice is that our inductions (his definition) (what Popper would call "conjectures") can always turn out to be wrong. I.e., another case of calling uncertainty "certainty."

Ellen

___

[Daniel Barnes]

Ellen:

>This looks to me like it's what he's done.

Yep.

>Further issue, though, is whether he indeed is claiming that we perceive causality and that this perceiving provides an unassailable foundation (O'ist foundationalism) for inductive inferences.

If he is claiming we perceive something as complex as causality this would create any number of problems for him. It seems that we are hardwired to have causal expectations, if those experiments with babies are anything to go by. But this, in addition to being basically Kantian, is hardly the same as perceiving it. Besides, the babies' expectation of an object's cause of movement can also be wrong (this was Kant's mistake), as can all our causal hypotheses, hardwired or not.

>Even if he is saying this, however, from the sound of Roger's description what Peikoff comes up with in practice is that our inductions (his definition) (what Popper would call "conjectures") can always turn out to be wrong. I.e., another case of calling uncertainty "certainty."

Yes. We can know P, yet P may be false. As I have always argued, that is precisely where their theories come out at, even though they intended the reverse.

[Michael Stuart Kelly]

As I understand it, you guys are saying that (to replace by metaphor) the taste of an orange cannot be known by eating a banana. (In other words, induction and deduction are two different processes.) This has been Hume's great philosophical insight?

Dayaamm!

I could go deeper and say that the taste of the whipped cream on top cannot be known by eating the pie-crust underneath, since deduction rests on induction by default, but that would be repeating endless past discussions.

Michael

[Daniel Barnes]

Mike:

>As I understand it, you guys are saying that (to replace by metaphor) the taste of an orange cannot be known by eating a banana.

You don't understand it.

[Alfonso Jones]

Steve;

I hope that at least Objectivist Living is better than monks debating how many angels can dance on the head of a pin.

It is worth noting that a great many people have looked at and commented on Neil Pariell's discussion of Valliant's book My hope is that Neil's comments have saved people from reading Valliant's book.

Some of us read Valliant's book first. UUGGHH!!

I thought I would enjoy the snippets from the journals - but they were so edited (clips in the middle of sentences, ... as to have less than the expected value.

Alfonso

[Roger Bissell]

Some of you folks wanted to know Peikoff's definition of "induction"? It's interesting, how quickly you all galloped off to the races on the basis of what you ~thought~ you knew his definition was. Perhaps your instincts were correct. I'll let you all sort that out.

About 10 years ago, in "Objectivism Through Induction," Peikoff defined "induction" as: "the process of reaching principles from concretes...generalization from perception." (And he referred to the latter phrase as being the "dictionary definition" and that that was all he meant by the term.)

More recently, in "Induction in Physics and Philosophy," Peikoff said that the "essence of induction is the process of inferring generalizations from perceived instances." And he defines "generalization" as: "a proposition that ascribes a characteristic to every member of an unlimited class, however it is positioned in space and time." (In symbolic terms, this includes universal positive propositions like "All S is P" and universal negative propositions like "No S is P." Peikoff discussed these at some length in his 1974 lectures on logic.)

Also, some of you seem to think that Peikoff is doing a "bait and switch" on the nature of the Problem of Induction. Here is how he characterized it in lecture 1 of "Induction in Physics and Philosophy":

How can man know, across the whole scale of time and space, facts which he does not and can never perceive?...When and why is the inference from “some” to “all” legitimate? What is the method of valid induction, the rational method, which alone can prove the generalizations to which it leads? In short: how can man determine which generalizations are true, in other words, they correspond to reality, and which ones are false, they contradict reality?

In my opinion, Peikoff meets this challenge head-on and very successfully, especially in his more recent lecture series. I think that David Harriman's forthcoming book presenting Peikoff's theory of induction is going to put this controversy -- including all the vociferous attempts to continue stirring it and denigrating those who claim it has been solved -- to rest once and for all.

I say this, while having considerable reservations about Peikoff's overall achievement in philosophy. I think he has been very careless, both in presenting his own views and the views of others, in both Ominous Parallels and OPAR. However, in regard to the nature of induction, I think he has hit a bases-loaded home run.

Having said this, I am going to bow out of the rest of this discussion. There is way too much focus on defending and attacking thinkers, and way too little on addressing what they actually said. And that includes thinkers posting in this discussion.

REB

P.S. -- Whoever it was that said (in this thread?) that Rand's aesthetics views were based ?mainly/solely? on her personal artistic tastes, I suggest you read/re-read my essay "Art as Microcosm," posted here on Objectivist Living. I am sick to death of hearing this claim. Regardless of her various errors in stating, and misapplications of, her own theory, the theory itself is well enough grounded in her writings to allow for a conscientious thinker to see that it is far from a mere rationalization of her personal biases.

[Michael Stuart Kelly]

You don't understand it.

Daniel,

I am pretty sure I do. I disagree with the party line on rational grounds. That's all.

I am aghast that this thing prompted Kant's Critique of Pure Reason. From small seeds grow mighty weeds.

(Actually, I bounced around some Kant texts on the Internet and I was surprised that I agreed with some of the things I read. He certainly is organized. I think I will end up reading this book over time. btw - It was not the part about duty. )

Michael

[Daniel Barnes]

Mike:

>I am pretty sure I do. I disagree with the party line on rational grounds. That's all.

If you were sitting a question on the problem of induction at college and you gave your banana example to demonstrate your knowledge, you'd fail. It's not a question of a "party line," Mike.

Anyway, Peikoff has already agreed with Hume, so there the story ends. We can wrap this discussion up, and move on. If you want talk about Peikoff's theory of something else entirely, which I've called 'obduction,' Roger laid it out a while back:

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

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

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

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

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

[Michael Stuart Kelly]

Daniel,

You can try, but I doubt that "obduction" will take. It sounds klunky.

Induction will probably continue to be used in its broad meaning of finding universal principles and definitions from a limited number of samples. (One from the many, but applicable to all.)

But, hey. Give it a whirl. Who knows?

Michael