Two Kinds of "Induction": Important similarities and trivial differences

[Michael Stuart Kelly]

Dragonfly,

In my world, I only define something so I can use the information or use the referent. I hold very little value for defining things as some kind of game or crossword puzzle.

The act of pointing at something correctly defines it for my use (for simple things) when no words are possible. It even does so often when words are possible.

Michael

[Roger Bissell]

Dragonfly,

In my world, I only define something so I can use the information or use the referent. I hold very little value for defining things as some kind of game or crossword puzzle.

The act of pointing at something correctly defines it for my use (for simple things) when no words are possible. It even does so often when words are possible.

Michael

Dammit, Mike, some of us need the exercise! I do crosswords, crytoquotes, and Sudoku every day. It's my first line of defense against dementia. The second line is to take a break from OL every now and then. :-) (I'm in the airport in Phoenix, taking advantage of the free high-speed internet access, perhaps my last for 5 days or so.)

I think that definitions are good not only for use, but also for efficient storage. Concept hierarchies, complete with genus-differentia definitions and lots of cross-links, are just neater ways of holding conceptual knowledge than just throwing your concepts into a verbal junkbox in your brain! (As some people apparently would have us do.)

Any concept whose class is both the genus for narrower classes or individuals and the species of a broader class can be defined by genus-differentia principles. Classes of things that are concretes and thus subsume no narrower groups cannot be so defined and thus have to be defined ostensively. Classes of things that are most abstract and thus are subsumed by no wider group also have to be defined in this manner. "Cherry red" and "existent" are two good examples.

Some concepts are correlatives and have to be defined as a pair, such as "part" and "whole" or "entity" and "attribute." All of these, however, are existents, kinds of things that exist. You can't define "existent." You can just say "something that exists" and point to or refer to as many different kinds of things as you can, then sweep your hand around and say "any of those things is an existent."

Rand covered most of this in ITOE. It's amazing that there is all this discussion and controversy over something that makes complete and utterly common sense. Of course, part of it is probably explained by the fact that some of the discussants appear to have a cursory acquaintance at best with Rand's epistemology and/or are looking at it through the lens of their own philosophical preconceptions. If the shoe fits...

REB

[tjohnson]

Rand covered most of this in ITOE. It's amazing that there is all this discussion and controversy over something that makes complete and utterly common sense. Of course, part of it is probably explained by the fact that some of the discussants appear to have a cursory acquaintance at best with Rand's epistemology and/or are looking at it through the lens of their own philosophical preconceptions. If the shoe fits...

REB

That is precisely what common sense is for, to be jarred into uncommon sense. One of the chief

services which mathematics has rendered the human race in the past century is to put ‘common

sense’ where it belongs, on the topmost shelf next to the dusty canister labeled ‘discarded nonsense.’

Unfortunately, it appears Rand did not realize the existence of undefined terms (something Bob says has been known since Aristotle ), something that is of tremendous importance for human agreement. Undefined terms are equivalent to assumptions and I want to identify what assumptions are implicit in Objectivism. You have stated "All of these, however, are existents, kinds of things that exist. You can't define "existent."" so it seems you accept 'existent' as undefined? I don't think I could.

[Michael Stuart Kelly]

GS,

I keep seeing you lecture us on how Objectivist epistemology is all wrong, but show clearly that you have no notion of what Objectivist epistemology is (or ethics, for that matter). Please learn it, then criticize it. I don't mind if you disagree, but at least you will be talking about the ideas that exist. I get the feeling from your posts that you are discussing with blinders on, saying the world to the side doesn't exist, only what is in front of you does.

The beauty of Objectivism is that the basics are really easy to learn, even if you disagree with them.

Michael

[tjohnson]

GS,

I keep seeing you lecture us on how Objectivist epistemology is all wrong, but show clearly that you have no notion of what Objectivist epistemology is (or ethics, for that matter). Please learn it, then criticize it. I don't mind if you disagree, but at least you will be talking about the ideas that exist. I get the feeling from your posts that you are discussing with blinders on, saying the world to the side doesn't exist, only what is in front of you does.

The beauty of Objectivism is that the basics are really easy to learn, even if you disagree with them.

Michael

I would NEVER say it was ALL wrong!

[Daniel Barnes]

Roger kindly restates the Objectivist principles for attaining a "true induction" here:

As for "rules" of induction, I've already stated them, but here they are again, as Peikoff states them in Induction in Physics and Philosophy: (1) valid concept-formation, (2) reduction of concepts and propositions to a base in observed reality, (3) Mills Methods of Agreement and Difference, and (4) integration of one's inductive conclusion with other, established knowledge. (Use of mathematics, where measurement and experimentation is necessary, is a fifth principle of induction.)

Now when we examine them, the problem becomes obvious. All we need do is take the first principle:

1)Valid concept formation.

What are Rand's criteria for a concept's "validity'? Two things. It must be both

a. precise - in fact, it must possess "the most rigorous mathematical precision."

b. true - for "the truth or falsehood of all of man's conclusions, inferences, thought and knowledge rests on the truth or falsehood of his definitions."

Yet it is exactly these two qualities that logic tells us cannot be fulfilled. For the attempt to make words precise through exact definition leads logically nowhere; likewise, and even more importantly, there is no way to logically establish the truth or falsity of definitions - that, say, my definition of "democracy", or "justice" or "selfish" or even "puppy" is the "true" one, and yours isn't. Only mutual agreement as to meaning can let dialogue usefully begin (i.e. convention)

So the principles of "true induction" have fallen at the first fence. We may look at the rest later in some detail - Roger's 2), for example, appears to be merely a restatement of 1) - but already the problems are quite obvious and, I think, fatal.

Edited September 26, 2007 by Daniel Barnes

[Michael Stuart Kelly]

Daniel,

We could use Kelley and Thomas's version here:

Induction is the process of drawing general conclusions from the observation of particular cases.

Of course, their contention is that both induction and deduction are needed for knowledge and I don't think that argument should interest you too much, given Popper's denial of induction.

Also, your post shows you didn't understood what Rand meant my "mathematical precision" within the context of concept formation.

Once again... measurement.

Michael

[tjohnson]

Yet it is exactly these two qualities that logic tells us cannot be fulfilled. For the attempt to make words precise through exact definition leads logically nowhere

Not sure about 'logically' but in fact it leads nowhere, this is demonstrable.

likewise, and even more importantly, there is no way to logically establish the truth or falsity of definitions

Agreed, how can a definition be "true"? It makes no sense. An assertion may be "true", or at least somewhat true (I cringe when I use the word), but not a definition.

[Daniel Barnes]

GS:

Not sure about 'logically' but in fact it leads nowhere, this is demonstrable.

If it is applied non-arbitrarily it leads to a logically infinite regress of definitions.

[Michael Stuart Kelly]

GS:

Not sure about 'logically' but in fact it leads nowhere, this is demonstrable.

If it is applied non-arbitrarily it leads to a logically infinite regress of definitions.

That's Popper's view. If you base definitions on concept formation as given in Objectivism, however, this does not hold at all. I am not even convinced that it holds as given by Popper. His argument failed to convince me.

Michael

[Daniel Barnes]

DB:

If it is applied non-arbitrarily it leads to a logically infinite regress of definitions.

Mike:

That's Popper's view. If you base definitions on concept formation as given in Objectivism, however, this does not hold at all.

Sayin' ain't showin'.

I am not even convinced that it holds as given by Popper.

Sayin' ain't showin'.

His argument failed to convince me.

Interestingly, there's psychological research that shows logical arguments are the ones least likely to persuade. This is case in point, it seems.

Or if you think there's a logical error in Popper's presentation, what is it?

[tjohnson]

GS:

If it is applied non-arbitrarily it leads to a logically infinite regress of definitions.

Well, the way I see it the process doesn't continue indefinitely, unless you count going in circles as an infinite regress. Korzybski's description of this was that you reach a point where you start using the same words over and over, which can be seen in practice. There doesn't seem to be much point in continuing after that, but as I said, in theory one could indefinitely.

[tjohnson]

For the record, here is how Korzybski describes this.

We begin by asking the ‘meaning’ of every word uttered, being satisfied for this

purpose with the roughest definitions; then we ask the ‘meaning’ of the words used in the definitions, and this process is continued usually for no more than ten to fifteen minutes, until the victim begins to speak in circles—as, for instance, defining ‘space’ by ‘length’ and ‘length’ by ‘space’. When this stage is reached, we have come usually to the undefined terms of a given individual. If we still press, no matter how gently, for definitions, a most interesting fact occurs. Sooner or later, signs of affective disturbances appear. Often the face reddens; there is a bodily restlessness; sweat appears—symptoms quite similar to those seen in a schoolboy who has forgotten his lesson, which he ‘knows but cannot tell’. If the partner in the experiment is capable of self-observation, he invariably finds that he feels an internal affective pressure, connected, perhaps, with the rush of blood to the brain and probably best expressed in some such words as ‘what he “knows” but cannot tell’, or the like. Here we have reached the bottom and the foundation of all non-elementalistic meanings—the meanings of undefined terms, which we ‘know’ somehow, but cannot tell.

In fact, we have reached the un-speakable level. This ‘knowledge’ is supplied by the lower nerve centres; it represents affective first order effects, and is interwoven and interlocked with other affective states, such as those called ‘wishes’,‘intentions’, ‘intuitions’, ‘evaluation’, and many others. It should be noticed that these first

order effects have an objective character, as they are un-speakable—are not words.

When He says 'lower nerve centres' he refers to perceptions, memories, experience, etc. This is not totally contrary to Objectivism's 'concept formation', I don't think. The thing is 'concepts' are non-verbal and live in the 'lower nerve centres' and the words for them live in the 'higher nerve centres', so to speak.

[Daniel Barnes]

GS:

Well, the way I see it the process doesn't continue indefinitely, unless you count going in circles as an infinite regress..

Hey, circles or infinite regresses, either way it's a bust...;-)

Edited September 26, 2007 by Daniel Barnes

[BaalChatzaf]

When He says 'lower nerve centres' he refers to perceptions, memories, experience, etc. This is not totally contrary to Objectivism's 'concept formation', I don't think. The thing is 'concepts' are non-verbal and live in the 'lower nerve centres' and the words for them live in the 'higher nerve centres', so to speak.

Count K's grasp of neural function and physiology was formulated in what amounted to a dark age. This was well before decent scanners and first rate electron microscopes (30's and 40's). Don't take Korzybski's pronouncements on these matters seriously. If you want to see up to date stuff read treatises by the Churchlands.

Ba'al Chatzaf

[Michael Stuart Kelly]

Or if you think there's a logical error in Popper's presentation, what is it?

Daniel,

That's easy. False premises.

Michael

[Daniel Barnes]

Mike:

That's easy. False premises.

Sayin' ain't showin'.

Please demonstrate.

[BaalChatzaf]

Or if you think there's a logical error in Popper's presentation, what is it?

Daniel,

That's easy. False premises.

Michael

Which premises. State them clearly. And make sure it is Popper who stated them, and not substitute a straw man. Quote material from Popper's writing and show where he is mistaken.

Ba'al Chatzaf

[Michael Stuart Kelly]

The problem is in the definition of definition. It's kinda vague with Popper...

Isn't infinite regress an non-vague causal connection?

(That's just one.)

Michael

[Daniel Barnes]

Mike:

The problem is in the definition of definition.

Classic! What more need I say?

(That's just one.)

Do they get better?

Edited September 27, 2007 by Daniel Barnes

[Michael Stuart Kelly]

Do they get better?

Daniel,

That's normative, not cognitive. But, to answer:

Q. Do they get better?

A. Not for you.

:devil:

Michael

[Ellen Stuttle]

A few points re definitions:

The problems of circularity and of infinite regress in defining terms are related in that both militate against precision, but they aren't identical.

Circularity occurs when a term is defined by using other terms which then in turn (possibly with additional steps in between) are defined by using the original term.

Infinite regress occurs because in order to define one term other terms have to be introduced, which in turn require definition introducing still other terms, which in turn... This isn't solved by the nesting of geni culminating with the genus "existence" to define which you sweep your arm and say "I mean that." For example, suppose you give the definition "rational animal" for "man." You then have the terms "rational" and "animal" to define. Suppose you give the broad definitions "type of cognition" for "rational" and "type of "organism" for "animal." You then have four additional terms to define: "type," "of," "cognition," and "organism." Etc.

Rand didn't mean that you have to use the equivalent of micrometers or electron microscopes when you define words. She meant that you have to use clear-cut principles that unambiguously link more general and more specific concepts together, and the whole shebang to perceptual reality, in the same way that you have to tie your premises and conclusions together when you do geometry, for instance, or build up more complex algebra formulas from more simple ones. This means simply that you have to keep your mind clear and not allow definitional/conceptual fuzziness to creep in. None of this, "yeah, I sort of know what I mean" business...

Roger,

That might be a reasonable synopsis of what she meant. (In the next post I'll type in a passage from her "Definitions" chapter which I think exhibits considerable fuzziness in her own presentation.) But just taking your statement as written, I think it's stating an unachievable goal, that of (my emphasis) "unambiguously link[ing] more general and more specific concepts together, and the whole shebang to perceptual reality, in the same way that you have to tie your premises and conclusions together when you do geometry, for instance, or build up more complex algebra formulas from more simple ones"

Consider, just to cite one example but an important one, the category "existent" of which you said in a subsequent post:

Any concept whose class is both the genus for narrower classes or individuals and the species of a broader class can be defined by genus-differentia principles. Classes of things that are concretes and thus subsume no narrower groups cannot be so defined and thus have to be defined ostensively. Classes of things that are most abstract and thus are subsumed by no wider group also have to be defined in this manner. "Cherry red" and "existent" are two good examples.

Some concepts are correlatives and have to be defined as a pair, such as "part" and "whole" or "entity" and "attribute." All of these, however, are existents, kinds of things that exist. You can't define "existent." You can just say "something that exists" and point to or refer to as many different kinds of things as you can, then sweep your hand around and say "any of those things is an existent."

Is an idea an "existent"? Is a "part" of speech? Is an "attribute" of a story? Is an imaginary number? I don't think you can get any unambiguous answers to these sorts of questions, and certainly not just by sweeping your hand around and saying "any of those things" is what I mean.

Ellen

___

[Brant Gaede]

All definitions end in circularity because concepts don't exist "out there," only their referents or ultimate referents. All definitions are concepts!

--Brant

[Ellen Stuttle]

Roger kindly restates the Objectivist principles for attaining a "true induction" here:

As for "rules" of induction, I've already stated them, but here they are again, as Peikoff states them in Induction in Physics and Philosophy: (1) valid concept-formation, (2) reduction of concepts and propositions to a base in observed reality, (3) Mills Methods of Agreement and Difference, and (4) integration of one's inductive conclusion with other, established knowledge. (Use of mathematics, where measurement and experimentation is necessary, is a fifth principle of induction.)

Now when we examine them, the problem becomes obvious. All we need do is take the first principle:

1)Valid concept formation.

What are Rand's criteria for a concept's "validity'? Two things. It must be both

a. precise - in fact, it must possess "the most rigorous mathematical precision."

b. true - for "the truth or falsehood of all of man's conclusions, inferences, thought and knowledge rests on the truth or falsehood of his definitions."

Daniel,

Some dwelling on what Rand meant by "valid concept formation" is in order. Something to keep in mind is a point I've made in a previous post (I've forgotten where), that Rand's view of the nature of concepts includes three layers: (1) the units, the "somethings" categorized, which are the referents of the concept; (2) the concept, which is a "mental integration"; and (3) the word, the audio-visual symbol which labels the concept. (Eventually, I want to get back to layer (2), since I think there isn't such a "something" as she describes.)

She writes:

pg. 10, Expanded 2nd Edition, ITOE

A concept is a mental integration of two or more units which are isolated according to a specific characteristic(s) and united by a specific definition.

Of definitions, she writes:

pg. 40, Expanded 2nd Edition, ITOE

A definition is a statement that identifies the nature of the units subsumed under a concept.

It is often said that definitions state the meaning of words. This is true, but it is not exact. A word is merely a visual-auditory symbol used to represent a concept; a word has no meaning other than that of the concept it symbolizes, and the meaning of a concept consists of its units. It is not words, but concepts that man defines--by specifying their referents.

The purpose of a definition is to distinguish a concept from all other concepts and thus to keep its units differentiated from all other existents.

There's no specific entry for "Valid concept" in the Index of ITOE; however a passage in the "Definitions" chapter, the passage in which the statement you quote in point "b." occurs, provides indications of a circularity involved in her idea of "valid concept."

Note as you read: She says that concepts are organized into propositions, and then, in the next paragraph, that every concept "stands for a number of propositions."

pp. 48-49, Expanded 2nd Edition, ITOE

(All italics in the original.)

Truth is the product of the recognition (i.e., identification) of the facts of reality. Man identifies and integrates the facts of reality by means of concepts. He retains concepts in his mind by means of definitions. He organizes concepts into propositions--and the truth or falsehood of his propositions rests, not only on their relation to the facts he asserts, but also on the truth or falsehood of the definitions of the concepts he uses to assert them, which rests on the truth or falsehood of his designations of essential characteristics.

Every concept stands for a number of propositions. A concept identifying perceptual concretes stands for some implicit propositions; but on the higher levels of abstraction, a concept stands for chains and paragraphs and pages of explicit propositions referring to complex factual data. A definition is the condensation of a vast body of observations--and stands or falls with the truth or falsehood of these observations. Let me repeat: a definition is a condensation. As a legal preamble (referring here to epistemological law), every definition begins with the implicit proposition: "After full consideration of all the known facts pertaining to this group of existents, the following has been demonstrated to be their essential, therefore defining, characteristic..."

[interjection re the following examples: I can almost guarantee she missed the point of the articles to which she refers. Her comments are examples of how non-evolutionary her way of thinking was.]

In the light of this fact, consider some modern examples of proposed definitions. A noted anthropologist, writing in a national magazine, suggests that man's essential distinction from all other animals, the essential characteristic responsible for his unique development and achievements, is the possession of a thumb. [That should be "opposable thumb."] (The same article asserts that the dinosaur also possessed [an opposable] thumb, but "somehow failed to develop.") What about man's type of consciousness? Blank out.

An article in a reputable encyclopedia suggests that man might be defined as "a language-having animal." Is "language-having" a primary characteristic, independent of any other characteristic or faculty? Does language consist of the ability to articulate sounds? If so, then parrots and myna-birds should be classified as men. If they should not, then what human faculty do they lack? Blank out.

There is no difference between such definitions and those chosen by individuals who define man as "a Christian (or Jewish or Mohammedan) animal" or "a white-skinned animal" or "an animal of exclusively Aryan descent," etc.--no difference in epistemological principle or in practical consequences (or in psychological motive).

The truth or falsehood of all of man's conclusions, inferences, thought and knowledge rests on the truth or falsehood of his definitions.

(The above applies only to valid concepts. There are such things as invalid concepts, i.e., words that represent attempts to integrate errors, contradictions or false propositions, such as concepts originating in mysticism--or words without specific definitions, without referents, which can mean anything to anyone, such as modern "anti-concepts." Invalid concepts appear occasionally in men's languages, but are usually--though not necessarily--short-lived, since they lead to cognitive dead-ends. An invalid concept invalidates every proposition or process of thought in which it is used as a cognitive assertion.)

___

Edited September 27, 2007 by Ellen Stuttle

[Daniel Barnes]

DB:

Roger kindly restates the Objectivist principles for attaining a "true induction" here:

As for "rules" of induction, I've already stated them, but here they are again, as Peikoff states them in Induction in Physics and Philosophy: (1) valid concept-formation, (2) reduction of concepts and propositions to a base in observed reality, (3) Mills Methods of Agreement and Difference, and (4) integration of one's inductive conclusion with other, established knowledge. (Use of mathematics, where measurement and experimentation is necessary, is a fifth principle of induction.)

Ellen:

Some dwelling on what Rand meant by "valid concept formation" is in order. Something to keep in mind is a point I've made in a previous post (I've forgotten where), that Rand's view of the nature of concepts includes three layers: (1) the units, the "somethings" categorized, which are the referents of the concept; (2) the concept, which is a "mental integration"; and (3) the word, the audio-visual symbol which labels the concept.

Agreed.

There's no specific entry for "Valid concept" in the Index of ITOE; however a passage in the "Definitions" chapter, the passage in which the statement you quote in point "b." occurs, provides indications of a circularity involved in her idea of "valid concept."

Note as you read: She says that concepts are organized into propositions, and then, in the next paragraph, that every concept "stands for a number of propositions."

Also agreed. The problem becomes evident with the "files and folders" analogy. For can we name a "file" which is not also a "folder"? I don't think so.

I could be wrong, but there appears to be an underlying circularity to Roger's presentation too. If concept formation is the whole point of human thought, what is the point of the process of "true induction" if not the forming of valid concepts? But we note that 1) a valid concept is a precondition for "true induction"...

At any rate, Roger may be able to clarify on his return.

Yes there is little detail on what constitutes a valid concept; but she talks a lot about how essential precise definitions are, and also true ones, so we may reasonably take these to be at least two key criteria.

Edited September 27, 2007 by Daniel Barnes