William W. Kaufmann

Induction

12 posts in this topic

I am interested in the question whether a formal system of induction is possible. Aristotle devised a formal deductive system, in which syllogism is the foundation of all deductive logic. What is the parallel system, if any, for induction? Putting it more succinctly, what IS "inductive logic", and how does one systematically make precise inductive inferences?

One hint here is that concept formation is inductive. Hence, do we have to have a formal system of concept formation first?

I have a number of answers, but would like to hear from knowledgeable students and professionals.

William W. Kaufmann

(I am a semi-retired Professor of Law, Lawyer, and Pro tem judge. I plan a book on legal philosophy, in which I intend to address the issues of induction and causation in the social sciences. and the fact that there is no science, including law, without precise induction).

Share this post


Link to post
Share on other sites

I am interested in the question whether a formal system of induction is possible.

Aristotle devised a formal deductive system, in which syllogism is the foundation of all deductive logic. What is the parallel system, if any, for induction? Putting it more succinctly, what IS "inductive logic", and how does one systematically make precise inductive inferences?

That depends on what you mean by a "formal system." If you mean a cut and dried procedure that applies in all contexts, like format deductive logic does, then no. Induction is very context dependent. There are, however, rules and standards for informal logic, informal fallacies, etc. that can be applied to inductive reasoning.

One hint here is that concept formation is inductive. Hence, do we have to have a formal system of concept formation first?

I don't think so because concept formation, like all of induction, is so context dependent. Here again, it depends on what you you mean by a "formal system of concept formation."

I have a number of answers, but would like to hear from knowledgeable students and professionals.

I'd love to hear more about your thoughts on the subject.

Share this post


Link to post
Share on other sites

What I mean is exactly what I said: a formal method. Syllogism is formal. The various forms devised by Aristotle are indeed forms. Hence: formal. Application of syllogism requires induction. The art of logic is always contextual. Did I suggest it was not?

Concept formation to be correct is contextual. A concept valid in a narrower context than "all human knowledge" is still valid within its context AND if properly formed will NOT contradict the full context of human knowledge. That is dependent in forming a proper definition, setting the concept in a correct heirarchical position (genus: animal; ccd: "mobile conscious life" or "mammal" if you mean the general usage of the term;)

Hence: man is that animal which conceptualises/reasons. But in reasoning one might conceptualize "man" as "black two legged two armed animal" in the narrower context. From that alone you may induce that man cannot flap his arms and fly. Your definition correctly includes limbs but not wings.

Just some hints. Showing beginnings of how you get to formal inductive reasoning and how that depends on a formal method if concept formation.

For the record, calling induction "generalization" may be true, but the kind of induction I am talking about is how we get to the major premise of a syllogism: All A is B. the problem of induction claims that is impossible. "How do you claim all crows are black? What do you do if the next crow you see is white? This is a strawman argument. Universals are propositions directly taken from concept formation.

William Kaufmann (this formulation is copyrighted by me 2012)

Edited by Betsy Speicher

Share this post


Link to post
Share on other sites

IMO, one way to validly claim All A is B is when B is causally related to the identity or nature of A. All atoms are matter; all men are mortal, etc. If one says that All crows are black, one is on shaky ground because color associated with most objects varies significantly for many reasons. Simply observing All A is B without causality is not going to get you there.

Share this post


Link to post
Share on other sites

Quite right.

But the cause you need to prove the universal induction has to be universally found in every concrete. That is, here, every crow . So the problem is pushed back to : how do you know every crow has the causal factor that you need to prove the next one wlll be black? Is it that the blackness can only be caused by such a factor? If you can show that scientifically, why then the white crow just can't have that causal factor. Right? Nice question begging in that case Now what?

You actually almost have the answer. At least as far as i have it. For a hint look at IOE on essential characteristics and omitted measurement.

Another hint is: the question as posed is a l

The problemis solvable based on IOE but partly only b y Aristotle.

William W Kaufmann. .

Share this post


Link to post
Share on other sites

Missing line: the problem is a logical error. A trap. The problem of induction is solved in concept formation. Even scientific induction. The real problem us in the minor premise, not the major u iversal one

Share this post


Link to post
Share on other sites

But in reasoning one might conceptualize "man" as "black two legged two armed animal" in the narrower context. From that alone you may induce that man cannot flap his arms and fly. Your definition correctly includes limbs but not wings.

The description is a possible definition delimiting man from other entities at a very early, beginning stage of knowledge. It implies nothing about an impossibility of flying. The meaning of a concept is its referents, known and unknown; past, present and future. The definition is not the meaning, may change with expanding knowledge, and need not include all known or unknown essential characteristics subsumed, explicitly or implicitly, by the concept.

For the record, calling induction "generalization" may be true, but the kind of induction I am talking about is how we get to the major premise of a syllogism: All A is B. the problem of deduction claims that is impossible. "How do you claim all crows are black? What do you do if the next crow you see is white? This is a strawman argument. Universals are propositions directly taken from concept formation.

Ayn Rand discussed the problem of induction at the workshops on epistemology, where she explained that concept formation is an inductive process, but is not the same inductive process as formulating and validating general propositions. She emphatically rejected the idea that her theory of concept formation solves the 'problem of induction' for general propositions, heading off a fallacy that arose decades ago and which has resurfaced several times since, including as an element in Leonard Peikoff's claimed solution to the problem of induction a few year ago and re-published in David Harriman's The Logical Leap (which despite that and some other problems, is a valuable work).

This topic has been discussed extensively in previous threads on the Forum, although there is more to say. (In my case I didn't have the time to complete and submit every post I began working on, partly because of diversions over alternate theories such as claims by one Forum member that concepts are evolutionary, in contrast to Ayn Rand's epistemology.)

Share this post


Link to post
Share on other sites
The description is a possible definition delimiting man from other entities at a very early, beginning stage of knowledge. It implies nothing about an impossibility of flying. The meaning of a concept is its referents, known and unknown; past, present and future. The definition is not the meaning, may change with expanding knowledge, and need not include all known or unknown essential characteristics subsumed, explicitly or implicitly, by the concept.

You did not read what I said. The narrower primitive concept does not contradict the appropriate conclusion of other referents. Eg white ones. What may I ask implies in the concept that the entity in question can fly by flapping his arms. The evidence is contrary and the burden of proof on he who asserts it should be included, since in the "primitive" observers context, only winged beings fly.

I really dont care to have a lecture on what I have known for decades. And why do you claim I say the meaning of a concept is its definition. Read what I said. I said "definition" to simplify the issue. Would you understand better if I said the individual's concept of man was only those characteristics plus speech and thinking and a few other things? The meaning of a concept is a potential. It consists of an infinite number of entities with an infinite number of characteristics.

William W Kaufmann

Edited by Betsy Speicher

Share this post


Link to post
Share on other sites

You say:

"Ayn Rand discussed the problem of induction at the workshops on epistemology, where she explained that concept formation is an inductive process, but is not the same inductive process as formulating and validating general propositions.

She emphatically rejected the idea that her theory of concept formation solves the 'problem of induction' for general propositions, heading off a fallacy that arose decades ago and which has resurfaced several times since, including as an element in Leonard Peikoff's claimed solution to the problem of induction a few year ago and re-published in David Harriman's The Logical Leap (which despite that and some other problems, is a valuable work)."

Me: I have read all that. It has nothing to do with what I haven't even said yet. Consider first. : whether and how to create a formal method of concept formation That she said is an inductive process. So did I. I then said i think you can form a formal method of induction in science as well There are two inductive processes. Concept formation from which some additional ste

You:

"This topic has been discussed extensively in previous threads on the Forum, although there is more to say. (In my case I didn't have the time to complete and submit every post I began working on, partly because of diversions over alternate theories such as claims by one Forum member that concepts are evolutionary, in contrast to Ayn Rand's epistemology.)"

And this says simply

Share this post


Link to post
Share on other sites

Concept formation sets the stage. Propositions are made up of concepts. Universals cannot necessarily be drawn out of concepts alone. But definitions are universals I am considering the formal process of concept formation. . If then you add a few other steps you will have a formal process of of forming universal propositions. Scientific induction is another step yet. Harriman's book doesn't come close to dealing with any of this. And if this had been discussed already it surely hasn't the way I am doing so. Someone's claim about concepts as evolutionary means nothing to me, nor is the claim relevant (or even understandable since you don't explain it ) Nor can I reply to your implication that you have all the answers but didn't have time to post them. When you post them I will consider them on their merits. I offered the discussion. Since you feel the topic is settled to your satisfaction, why waste your time with it. Write a definitive analysis why it is impossible. Prove the negative. Meantime I will prove it is. . .

William W Kaufmann

Share this post


Link to post
Share on other sites

Concept formation sets the stage. Propositions are made up of concepts. Universals cannot necessarily be drawn out of concepts alone. But definitions are universals I am considering the formal process of concept formation.

That assumes concept-formation is a formal process. Why do you think it is? As far as I know, it is not a step-by-step process with no options that you can program into a computer like you can with a deductive process. If it is a formal process, what are the steps? Can you give an example with a particular concept?

If then you add a few other steps you will have a formal process of of forming universal propositions.

Can you give a concrete example of doing this?

Share this post


Link to post
Share on other sites

Do you mean formal steps on concept formation? There are many kinds of induction. Concept formation is just one. Induction by enumeration us another. Scientific induction directly proceed from concept formation but it maybe similar. The purpose of this post/thread is to get intelligent input. As i said, causation is extremely important on s ientific induction. Note it is part of concept formation. I am not interested in being told that AR said it cant be done or its not relevant to concepts. IF she said it what were her reasons? And the writer should cite to the text

That being said what kind of example? We know from conceot formation that all men are mortal. The definition if man is rstionsl animal. Animality includes all the characteristics belonging to the concept. Animality is a set of characteristics of living things. All livin things die But thus approach tho correct is DEductive and deprnds on the validity of the concepts. So we ate back to formalizing the inductive orocess which AR did not do. Nor did she say it us not possibke to do so. She did give any number if indications.

Scientific induction involve the formation of universal laws by isolating a context SIMILARLY to concept formation. Hence back to looking for a formally exact account of it.

Take the classic billiard ball question. How do you know what will happen the next time the balls collide! That redts on a certain view of concepts and their formation PLUS knowing how to cirrectly state the problem ! It isnt just hypothesis first. It is observation, isolation and grasp of the causal aspects if formation of concepts. Ie induction. Only then are you on track to formulate a law. .

Sorry I went so far afield but the answer is to work our formal induction in concept formation first. . .

William W. Kaufmann

Share this post


Link to post
Share on other sites