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Is induction an axiomatic concept that does not require validation/?

In the manner you have been using the term, induction is a process of inference, describing how a conclusion/judgement/inference/generalization is made.

An axiomatic concept is conceptual representation of a primary, irreducible fact (I.e., a representation of a perceptually given self-evident fact.) such as existence, identity, consciousness, volition.

Induction qua concept does not qualify as axiomatic. Induction's genus is a process or a means, or a method, i.e., it describes "how" a certain effect is caused. A concept with a genus of method is not axiomatic.

Edited by phibetakappa
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Hume's problem of induction in part states that we need to use induction in order to validate induction as a correct method of reasoning.

I'm not sure this is precisely what Hume's problem of induction states.

Doesn't "validate" in this context mean deduce? Such that in order to make a syllogism we need a major premise, and that that major premise necessarily has to be formed via an induction.

For example:

(major premise) Men are mortal.

(Minor premise) Socrates is a Man

(Conclusion) Socrates is mortal.

The premise: "Men are mortal" is not the product of a deduction, it is a product of induction.

So, that deductions, which for Hume is synonymous with "validation" presuppose an induction.

However, in O'ist terms "validation" is a wider term describing the demonstration of a concept and/or conclusion's relationship to reality/fact.

In other words, "deduction" is not assumed as the only legitimate means of validation.

Properly done induction builds validation into the process. One starts with already validated facts and forms premises, conclusions, inferences, judgments and/or generalizations.

Induction is literally the process of predication and/or the process of judgement, i.e., it is starting with a given true subject and stating something true above it.

These judgement have a huge range of possible complexity: from the first predications a toddler makes, up to the thesis statement a doctoral candidate makes.

In the case of a toddler, he forms generalizations using observation of very simple primitive facts, which are very close to the perceptual level. For example: Balls roll. Blocks do not roll.

In the case of a doctoral student, it may take hundreds of pages of detailed evidence to demonstrate a valid connection to the facts of reality, which provides support for the truth of their predication, i.e., the conclusion of their thesis.

Edited by phibetakappa
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Hume's problem of induction in part states that we need to use induction in order to validate induction as a correct method of reasoning. Is this problem actually not a problem at all? Is induction an axiomatic concept that does not require validation/?

Why is it an epistemological problem to use something in order to validate it? Don't we use concepts to validate conceptual thinking? Isn't observation used to validate observed events? Isn't consciousness used to validate awareness of reality? The real issue is, what does "validation" consist of?

Edited by A is A
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Induction is not to be justified because it itself together with deduction are the means for justifying everything. The task is to explain how to perform induction.

Consider this validation Dr. Peikoff gives:

A generalization in essence is no more than a percept of cause and effect conceptualized.

Induction is measurement omission applied to causal connections.

Validation of first level generalizations:

Perception is self-evident.

Application of first level concepts is self-evident.

Therefore there lay at the base of all future inductions absolutely certain first level generalizations which extend beyond all possible perception and which follow self-evidently from man's highly limited perceptual experience as and when this is processed by his conceptual faculty.

This explanation takes for granted the Objectivist theory of concept-formation but that theory itself is a generalization, the result of Ayn Rand using induction on some of her own concepts to reach conclusions about all concepts. Forming the concept of 'concept' is an act of induction, and induction is applying a concept. This is not circular because there is no premise-conclusion structure, no logical priority of either idea before the other. It is tautological. Tautologies are valid.

The concept of 'concept' is not a self-evident irreducible primary so it is not axiomatic. It follows that induction is not axiomatic.

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Forming the concept of 'concept' is an act of induction, and induction is applying a concept.

Applying a concept is essentially a deductive process, not an inductive process. However, you are correct about forming a concept being essentially an inductive process.

"Thus the process of forming and applying concepts contains the essential pattern of two fundamental methods of cognition: induction and deduction.

The process of observing the facts of reality and of integrating them into concepts is, in essence, a process of induction.

The process of subsuming new instances under a known concept is, in essence, a process of deduction." (Intro to O'ist Epistemology, 27)

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Hume's problem of induction in part states that we need to use induction in order to validate induction as a correct method of reasoning. Is this problem actually not a problem at all? Is induction an axiomatic concept that does not require validation/?

Enumerative induction does not always produce true general (universally quantified) statements. European bird observers having seen nothing but white swans concluded that all swans were white. In Austrialia (or was it New Zealand?) black swans were found.

Empirical Induction (I am using the term "empirical induction" to distinguish it from arithmetic or mathematical induction) is used to predict the future from the past. For example if whenever condition A (A is a Type) has been observed condition B collaterally holds or follows. This is the well known case of predicting the future from the past. At a certain scale of beings (man-size scale) this holds often enough to be a useful heuristic. In fact this is how we learn. But is it a generally valid mode of inference?

Let me give you an example. If electrons are shot through the magnetic field of a Stern-Gerlach magnet oriented horizontally, half the electrons have up-spin, the other half down-spin. Now take the stream of up-spin electrons and put them through a Stern-Gerlach magnet oriented vertically. Half of those electrons will have left-spin and half right-spin. Now take the stream of right-spin electrons (which started out as up spin electrons from the first magnet), and put them through another horizontally oriented Stern-Gerlach magnet. Intuitively one might think that all will be up-spin electrons. Not so. Half are up-spin and half are down-spin. In short the previous condition of being up-spin did not predict the final up or down spin states. One's common sense expectations simply are not fulfilled in this example.

In this case we cannot predict the future from the past. The best we can predict are the odds or frequency of outputs.

Bob Kolker

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Thanks for the responses guys.

I was hoping you could confirm my supposition about Hume's argument. What gave rise to your question?

I'm having a trouble locating where Hume states his case in the way you've stated it. It's been a very long time since I dealt with Hume, but I remember part of Hume's case as you've stated.

For example on Wikipedia they give 2 points related to the so-called "problem of induction," but they are typical skeptic angles:

"Hume's argument is that we cannot rationally justify the claim that nature will continue to be uniform, as justification comes in only two varieties, and both of these are inadequate. The two sorts are: (1) demonstrative reasoning, and (2) probable reasoning.[29] With regard to (1), Hume argues that the uniformity principle cannot be demonstrated, as it is "consistent and conceivable" that nature might stop being regular.[30] Turning to (2), Hume argues that we cannot hold that nature will continue to be uniform because it has been in the past, as this is using the very sort of reasoning (induction) that is under question: it would be circular reasoning.[31] Thus no form of justification will rationally warrant our inductive inferences."

**I suppose point #2 is at the root of your question?

I'd greatly appreciate if you could point me to where Hume states your thesis. And I'll keep look too.

Edited by phibetakappa
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I was hoping you could confirm my supposition about Hume's argument. What gave rise to your question?

I'm having a trouble locating where Hume states his case in the way you've stated it. It's been a very long time since I dealt with Hume, but I remember part of Hume's case as you've stated.

For example on Wikipedia they give 2 points related to the so-called "problem of induction," but they are typical skeptic angles:

**I suppose point #2 is at the root of your question?

I'd greatly appreciate if you could point me to where Hume states your thesis. And I'll keep look too.

It is in the Wikipedia article, and what gave rise to my question was an ongoing debate in a comment section on youtube actually. Your responses were more that sufficient for me to iron out the flaws in my current thinking, so thanks for that.

Here is the wikie entry about that piece of Hume's argument:

"If all matters of fact are based on causal relations, and all causal relations are found by induction, then induction must be shown to be valid somehow. He uses the fact that induction assumes a valid connection between the proposition "I have found that such an object has always been attended with such an effect" and the proposition "I foresee that other objects which are in appearance similar will be attended with similar effects."[8] One connects these two propositions not by reason, but by induction. This claim is supported by the same reasoning as that for causal relations above, and by the observation that even rationally inexperienced or inferior people can infer, for example, that touching fire causes pain. Hume challenges other philosophers to come up with a (deductive) reason for the connection. If he is right, then the justification of induction can be only inductive. But this begs the question; as induction is based on an assumption of the connection, it cannot itself explain the connection."

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Great thanks.

Yeah, this (below) reasoning is just wrong, as-wells-as based on false assumptions what "causality" is and how people know it.

"Hume challenges other philosophers to come up with a (deductive) reason for the connection. If he is right, then the justification of induction can be only inductive. But this begs the question; as induction is based on an assumption of the connection, it cannot itself explain the connection."
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Hume's problem of induction in part states that we need to use induction in order to validate induction as a correct method of reasoning. Is this problem actually not a problem at all? Is induction an axiomatic concept that does not require validation/?

Induction is a prerequisite for all validation.

The process behind induction must be identified, not "validated".

Since you already have a theory of concepts, your next step is to understand propositions and the process that gives rise to them.

Then you need to identify the process that produces a descriptive statement.

Finally, you identify the process that produces a descriptive generalization, i.e. one that accounts for several descriptive statements.

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I'm not sure this is precisely what Hume's problem of induction states.

Doesn't "validate" in this context mean deduce? Such that in order to make a syllogism we need a major premise, and that that major premise necessarily has to be formed via an induction.

For example:

(major premise) Men are mortal.

(Minor premise) Socrates is a Man

(Conclusion) Socrates is mortal.

The premise: "Men are mortal" is not the product of a deduction, it is a product of induction.

So, that deductions, which for Hume is synonymous with "validation" presuppose an induction.

However, in O'ist terms "validation" is a wider term describing the demonstration of a concept and/or conclusion's relationship to reality/fact.

In other words, "deduction" is not assumed as the only legitimate means of validation.

Properly done induction builds validation into the process. One starts with already validated facts and forms premises, conclusions, inferences, judgments and/or generalizations.

Induction is literally the process of predication and/or the process of judgement, i.e., it is starting with a given true subject and stating something true above it.

These judgement have a huge range of possible complexity: from the first predications a toddler makes, up to the thesis statement a doctoral candidate makes.

In the case of a toddler, he forms generalizations using observation of very simple primitive facts, which are very close to the perceptual level. For example: Balls roll. Blocks do not roll.

In the case of a doctoral student, it may take hundreds of pages of detailed evidence to demonstrate a valid connection to the facts of reality, which provides support for the truth of their predication, i.e., the conclusion of their thesis.

Perhaps my understanding of induction is off kilter, but i was taught that induction was a form of logic by which one made predictions, not truth statements? if this is not the case please explain it so that i will understand the discussion

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Perhaps my understanding of induction is off kilter, but i was taught that induction was a form of logic by which one made predictions, not truth statements? if this is not the case please explain it so that i will understand the discussion

Here you go:

Notes on "Induction in Physics and Philosophy" Lecture 1

Not a transcript. These notes paraphrase the speaker's points and are not accurate quotes unless in quote tags. {Curly brackets denote my comments}

Generalization - The inference of some member of a class to all. The inference moves from

from the observed to the unobserved

from the past to the future

from here to everywhere

Generalizing is the essence of human cognition and distinguishing feature of man from the animal.

Induction is the primary process of gaining knowledge that goes beyond perception. Deduction also moves beyond perception but presupposes premises; therefore is not primary.

Definition of Generalization - a proposition that ascribes a characteristic to every member of an unlimited class, however a member is placed in time and space. Format: "All S is P"

'unlimited' is in the definition to rule out simple inventory as an induction. Example: Inspecting every marble in a bag of marbles, seeing they are all red, then stating "All the marble in this bag are red" is not an induction despite the universal format. {this is not an open-ended universal}

side note - metaphysical axioms are not inductive generalizations. 'A is A' is not 'All S is P'.

Generalizations are made possible by man's conceptual faculty. S and P are concepts. {Definition of concept from the Lexicon}

Concepts are tools of knowledge, file-folders. They are not the claims to knowledge, they organize it and integrate it. Higher level concepts can presuppose knowledge but themselves state nothing.

'Table' is not true or false but valid or invalid.

'All S is P' is true or false and belongs in the S file-folder

Rand formulated rules for concept formation.

Aristotle formulated the rules of deduction.

This course formulates the rules for induction.

Statement of the "Problem of Induction"

Man is neither omniscient nor infallible. His generalizations are therefore not automatically correct. Thus the question: How can man know, across the whole scale of time and space, facts which he does not and can never perceive?"

Importance: false generalizations are contradictions in thought and a clash with reality in action

Motivational statement for students of philosophy: Except for a few axioms all the crucial principles of philosophy are reached and validated by induction.

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Here you go:

Notes on "Induction in Physics and Philosophy" Lecture 1

Not a transcript. These notes paraphrase the speaker's points and are not accurate quotes unless in quote tags. {Curly brackets denote my comments}

Generalization - The inference of some member of a class to all. The inference moves from

from the observed to the unobserved

from the past to the future

from here to everywhere

Generalizing is the essence of human cognition and distinguishing feature of man from the animal.

Induction is the primary process of gaining knowledge that goes beyond perception. Deduction also moves beyond perception but presupposes premises; therefore is not primary.

Definition of Generalization - a proposition that ascribes a characteristic to every member of an unlimited class, however a member is placed in time and space. Format: "All S is P"

'unlimited' is in the definition to rule out simple inventory as an induction. Example: Inspecting every marble in a bag of marbles, seeing they are all red, then stating "All the marble in this bag are red" is not an induction despite the universal format. {this is not an open-ended universal}

side note - metaphysical axioms are not inductive generalizations. 'A is A' is not 'All S is P'.

Generalizations are made possible by man's conceptual faculty. S and P are concepts. {Definition of concept from the Lexicon}

Concepts are tools of knowledge, file-folders. They are not the claims to knowledge, they organize it and integrate it. Higher level concepts can presuppose knowledge but themselves state nothing.

'Table' is not true or false but valid or invalid.

'All S is P' is true or false and belongs in the S file-folder

Rand formulated rules for concept formation.

Aristotle formulated the rules of deduction.

This course formulates the rules for induction.

Statement of the "Problem of Induction"

Man is neither omniscient nor infallible. His generalizations are therefore not automatically correct. Thus the question: How can man know, across the whole scale of time and space, facts which he does not and can never perceive?"

Importance: false generalizations are contradictions in thought and a clash with reality in action

Motivational statement for students of philosophy: Except for a few axioms all the crucial principles of philosophy are reached and validated by induction.

So induction is merely a process by which people make generalizations that, while probably true, cannot realistically be validated in the same way that inductive logic can?

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Perhaps my understanding of induction is off kilter, but i was taught that induction was a form of logic by which one made predictions, not truth statements? if this is not the case please explain it so that i will understand the discussion
They are true predictive statements, because they say something that is true about concepts, and concepts are open-ended so you have not encountered every reference of the concept.

(I assume in the question about "validated in the same way that inductive logic can?", you mean ... "deductive logic"). Inductive logic is necessary to validate the premises of a deductive proof: a deductive proof is nothing more than saying "this is a specific instance of what we already know".

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Hi. You don't need to requote the entire post to which you reply. It is there by default for your convenience, but in the future please delete the parts not being referred to specifically.

No, induction is totally valid and required before there can be any deduction. If valid induction was not possible there would not be any valid deduction. Any contrary to what you have been taught, probability has nothing to do with induction. The possibility of being wrong undercuts the necessity required to prevent a conclusion from being a non sequitor, and would justify the skeptic's doubt about all claims to knowledge.

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No, induction is totally valid and required before there can be any deduction. If valid induction was not possible there would not be any valid deduction.

And contrary to what you have been taught, probability has nothing to do with induction.

im still not really convinced, i have looked into other sources and re-looked into my text and, again perhaps you're using an understanding of the term induction which i do not know, but the definition of "inductive reasoning" that i find anywhere i look is "a type of reasoning that involves moving from a set of specific facts to a general conclusion." but it also goes on to state that "The premises of an inductive logical argument indicate some degree of support (inductive probability) for the conclusion but do not entail it; i.e. they do not ensure its truth."

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... the definition of "inductive reasoning" that i find anywhere i look is ..

Oh yes, I believe you. Objectivism has its own take on induction which is an improvement on the conventional wisdom, resolving the "problem of induction". Altruism is no good as an ethical theory either.

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Oh yes, I believe you. Objectivism has its own take on induction which is an improvement on the conventional wisdom, resolving the "problem of induction". Altruism is no good as an ethical theory either.

ah i see, i guess i've yet to read the objectivist understanding of induction.. which book/essay does it appear in. i'll have to read it and at least understand it in order to stop looking like an idiot lol

also, i understand that not every theory which has been proposed has been the correct one, however i was not taught inductive reasoning in a philosophy class, merely in a logic class, so i took the professors words at face value... although i suppose it's entirely possible for him to be incorrect i wouldnt normally contradict a math teacher on the nature of advanced functions lol still an answer to the problem of induction would certainly be welcome

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ah i see, i guess i've yet to read the objectivist understanding of induction.. which book/essay does it appear in. i'll have to read it and at least understand it in order to stop looking like an idiot lol

It does not exist in that form, so it is effectively a secret. Dr. Peikoff explains his own progress on induction in a lecture series available on CD(s) from the Ayn Rand Bookstore for $205. David Harriman (Dr. Harriman I presume?) has a book on the topic derived from that lecture course titled The Logical Leap: Induction in Physics coming out this year (July 2010) for $10.95. You can get a sneak preview of what the theory is from my notes on Dr. Peikoff's course, follow the link to "Notes on Induction in Physics and Philosophy" in my sig.

The theory is an application of Rand's theory of concepts, so you need to know that. Since Rand's theory of concepts is the essence of Rand's method in every area of Objectivism, you should learn that anyway. Introduction to Objectivist Epistemology, 2nd edition by Ayn Rand herself is available in several bookstore chains as well as the Ayn Rand Bookstore.

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