# Induction, generalizations, and causality

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Can you give an example(s) of that? What about proving a generalization? Does that not also come under the process of forming the generalization? Does the proof come after or before the formation of the generalization? Is proof part of the process of induction? Forming and proving generalizations would seem to be two distinct but related fields and both come under induction, no?

Answering those questions in full would require a whole book -- which I am writing right now. Here's a little taste of my approach and my views.

We act to gain and keep values in order to live. Achieving values is causally related to the actions we take. Therefore, we need to understand causes in order to gain and keep values in order to live. Induction is the process of identifying causes.

In order to identify a cause we need to identify the causal entity and the causal properties of that entity which give rise to the action or characteristic which is the effect. There are several methods we can use to test reality to find specific causal entities and causal attributes. If we find similar causes having similar effects, we may summarize that fact into a generalization to save "crow space." A generalization is the conceptualization of a causal inference.

We can prove that something really is a cause, with certainty, if it reduces the causal statement or generalization to a statement of identity. Until we can find the cause that passes that Identity Test, we have various degrees of uncertainty with an as yet unproven hypothesis.

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Betsy wrote:

The fact is, the inductive process does not start with generalizations. It starts with propositions which we may or may not conceptualize into generalizations. A generalization, if and when we form one, is the last and not the first, step in the process of induction.

I think the inductive process starts with the formation of concepts. That is the first time we move from particulars to the general. AR made the point that concept-formation is the pattern of the inductive process and to my observation it is also the beginning. That is why The Logical Leap has made such a hash of things. With a head start like AR's theory of concepts, more progress should have been made.

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Can you give an example(s) of that? What about proving a generalization? Does that not also come under the process of forming the generalization? Does the proof come after or before the formation of the generalization? Is proof part of the process of induction? Forming and proving generalizations would seem to be two distinct but related fields and both come under induction, no?

Answering those questions in full would require a whole book -- which I am writing right now. Here's a little taste of my approach and my views.

We act to gain and keep values in order to live. Achieving values is causally related to the actions we take. Therefore, we need to understand causes in order to gain and keep values in order to live. Induction is the process of identifying causes.

In order to identify a cause we need to identify the causal entity and the causal properties of that entity which give rise to the action or characteristic which is the effect. There are several methods we can use to test reality to find specific causal entities and causal attributes. If we find similar causes having similar effects, we may summarize that fact into a generalization to save "crow space." A generalization is the conceptualization of a causal inference.

We can prove that something really is a cause, with certainty, if it reduces the causal statement or generalization to a statement of identity. Until we can find the cause that passes that Identity Test, we have various degrees of uncertainty with an as yet unproven hypothesis.

I think Betsy has some brilliant insights into causation here. Far more on the money than the Peikoff Harriman thesis.

That said, after reflection I'd say induction is a wider process than establishing causation. It also applies to the formation of any general conclusion from particular data. "All swans are white" is a generalization arrived at by induction, but it is not a statement of causality. It is also an example of an error that was corrected by being open to new evidence. The question of how you validate a general conclusion so as to avoid such errors is a worthwhile subject.

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That said, after reflection I'd say induction is a wider process than establishing causation. It also applies to the formation of any general conclusion from particular data. "All swans are white" is a generalization arrived at by induction, but it is not a statement of causality.

But if it were true, wouldn't it necessarily be a statement of causality? There would have to be something in the identity of swans which led to them having white feathers. How about: All swans have wings? Or: All swans have heads? It would violate the fundamental nature of a swan to not have either of those. And that nature is actually a result of development following a genetically driven "program", causally. Change the DNA enough and you get a different sort of entity - because you will have changed a fundamental cause.

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Several fallacies continue to be repeated here despite previous discussion. Generalization is not the process of identifying causes. Identifying a specific cause in an instance of it is not a generalization. The claim that generalization is the equivalent of identifying a cause or the identity of something in particular obliterates though an invalid linguistic manipulation changing the use of words to avoid discussion of the process and validity of generalizing.

Generalization also cannot be passed off as forming a concept of a particular type of cause. That reverses the process. Ayn Rand emphasized the importance of proving the correctness of definitions, i.e., of demonstrating that one has in fact identified the proper genus and differentia, that one is in fact stating the proper essential characteristics. We can form an abstract concept of a cause after we have the knowledge to do so by identifying and validating the generalization, not the other way around. Conceptualization is a form of inductive generalization, but all such generalization cannot be reduced to conceptualization alone. We think in terms of concepts; we do not get automatic knowledge of generalizations by appealing to concepts with no justification for the generalization entailed in forming it. We do not validate Newton's Second Law by appealing to a "concept" of it. Furthermore, many generalizations are stated in terms of concepts in which the statement is not about the CCD, but some other qualified aspect.

The attempt to reduce generalizations to concept formation as such as if it meant appealing to the essence of the meaning of the concept -- or its equivalent by simply noting similarities and differences, a role of measurements, etc. as described by Leonard Peikoff -- is one of the fallacies in his approach and is thoroughly rationalistic on principle. We do not get valid generalizations from classification alone. We think about things in terms of concepts; our abstract knowledge is not derived from them and nothing else. We must properly form the classifications and use them correctly as part of the process of generalizing. The attempt to reduce generalizations in science to conceptual classification without a philosophy of how to make the required generalizations inherent in the "conceptualization" of general causes sweeps the whole problem under the rug and begs the question.

Generalizations are not necessarily statements of causality. Causality is implicit in generalizations, but need not be the explicit meaning of the statement. Generalizations require the law of identity and its corollary causality -- the law of identity applied to action -- without which the consistency of the universe could not be counted on at all, but generalizations need not state the presence and nature of a cause. There are many laws of physics that are not statements of causality, such as the great Conservation Laws of mass, energy, momentum and charge, plus many other such principles.

For example, you can prove the law of conservation of energy in basic mechanics, limited for example, to kinetic and gravitational potential energy being constant, by integrating the work done during motion under gravity and forming the proper concept of kinetic energy so you are identifying the right measure of motion (KE = Â½ mvÂ²) to make the equation quantifying the conservation of kinetic and potential energy work out (KE + PE = Â½ mvÂ² + mgh = constant). But that principle does not state a causal principle even though it relies on the nature of gravitational attraction and the consequent dynamic behavior of objects as an underlying cause. Furthermore, the more general law of conservation of energy is built up in steps from many different mechanisms and accumulating concepts of different forms of energy, but the most general form of the law is broader than the sum of the mechanisms for which this has been done (as used, for example, in formulating Schrodinger's equation on the basis of conservation of energy and operator formulations of different forms of energy).

Ayn Rand emphasized that concepts are the basis of all propositions and all knowledge beyond the perceptual level, and that our knowledge rises or falls on the validity of our concepts. The role of concepts and the role of the law of identity are crucial to forming generalizations in scientific theory. The Objectivist formulation of these is an aspect of the approach to the problem that appears to be unique to Objectivism in thinking about philosophy of science (and is not new to any one who has read and understood IOE for the last almost half century), but the problem of validating generalizations in science cannot be addressed by a mere direct "application of Objectivism" attempting to reduce the whole problem to relying on conceptual classification alone, as if no fundamentally new thinking out of the box were required and as if this whole issue of philosophy of science could be derived and formulated as a generality from general philosophy without regard to the specific nature of the concepts, theories and subject matter of specific special sciences and the philosophy of each such subject.

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Betsy wrote:
The fact is, the inductive process does not start with generalizations. It starts with propositions which we may or may not conceptualize into generalizations. A generalization, if and when we form one, is the last and not the first, step in the process of induction.

I think the inductive process starts with the formation of concepts. That is the first time we move from particulars to the general. AR made the point that concept-formation is the pattern of the inductive process and to my observation it is also the beginning. That is why The Logical Leap has made such a hash of things. With a head start like AR's theory of concepts, more progress should have been made.

This relies on the common definition of induction that it is the process of going from the particular to the general. I am, personally, defining induction differently -- as the process of identifying causes.

I define it this way in order to deal with why we form propositions and generalizations which is essential to actually understanding and doing induction.

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I'd say induction is a wider process than establishing causation. It also applies to the formation of any general conclusion from particular data. "All swans are white" is a generalization arrived at by induction, but it is not a statement of causality.

I would say that, properly understood, it is a statement of causality.

"All swans are white" really means that there is something about being a swan - which applies to any and all swans -- that causes it to be white. If you can identify what that cause is -- maybe a certain gene sequence -- then you can be sure that all swans are white.

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I'd say induction is a wider process than establishing causation. It also applies to the formation of any general conclusion from particular data. "All swans are white" is a generalization arrived at by induction, but it is not a statement of causality.

I would say that, properly understood, it is a statement of causality.

"All swans are white" really means that there is something about being a swan - which applies to any and all swans -- that causes it to be white. If you can identify what that cause is -- maybe a certain gene sequence -- then you can be sure that all swans are white.

If the statement were accurately stated as "some swans are white" doesn't that constitute the causal connection you are referring to? Even saying "this swan is white" (if true) implies some causality. Else what would the correspondence between entity and attribute mean if it was uncaused?

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Several fallacies continue to be repeated here despite previous discussion. Generalization is not the process of identifying causes.

If this is in response to me, then I do not define generalization as the process of identifying causes. I am defining induction as the process of identifying causes. Generalizing is the process of conceptualizing causal identifications.

Identifying a specific cause in an instance of it is not a generalization. The claim that generalization is the equivalent of identifying a cause or the identity of something in particular obliterates though an invalid linguistic manipulation changing the use of words to avoid discussion of the process and validity of generalizing.

That is not my view. There are propositions about the particular causes of the particular actions and attributes of a particular entity, but a generalization is a proposition about the actions and attributes of all units of a class of entities.

Generalization also cannot be passed off as forming a concept of a particular type of cause. That reverses the process. Ayn Rand emphasized the importance of proving the correctness of definitions, i.e., of demonstrating that one has in fact identified the proper genus and differentia, that one is in fact stating the proper essential characteristics.

But, according to AR, that requires understanding the causal characteristics of the units of the class:

When a given group of existents has more than one characteristic distinguishing it from other existents, man must observe the relationships among these various characteristics and discover the one on which all the others (or the greatest number of others) depend, i.e., the fundamental characteristic without which the others would not be possible. This fundamental characteristic is the essential distinguishing characteristic of the existents involved, and the proper defining characteristic of the concept.

Metaphysically, a fundamental characteristic is that distinctive characteristic which makes the greatest number of others possible; epistemologically, it is the one that explains the greatest number of others.

In other words, a fundamental characteristic causes, and is the (causal) explanation of, the greatest number of other characteristics. Therefore, one has to understand the nature of the units causally in order to define them in terms of essentials.

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Generalizations are not necessarily statements of causality. Causality is implicit in generalizations, but need not be the explicit meaning of the statement. Generalizations require the law of identity and its corollary causality -- the law of identity applied to action -- without which the consistency of the universe could not be counted on at all, but generalizations need not state the presence and nature of a cause. There are many laws of physics that are not statements of causality, such as the great Conservation Laws of mass, energy, momentum and charge, plus many other such principles.

What do you say to this thought: that the laws of physics can be characterized as generalizations about the identity of the universe?

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We can form an abstract concept of a cause after we have the knowledge to do so by identifying and validating the generalization, not the other way around.

We don't5 start with a generalization which we then validate. Rather, we start with the pursuit of a value and a cognitive need to cause whatever will gain and keep that value such as getting food when hungry. That leads us to find causes. Some causes are generalizable and it is cognitively useful to do so. That way you don't have to enumerate each of thousands of supermarkets when you want to buy food. You just generalize that supermarkets sell food.

We start by finding a cause and then may or may not generalize it similar to the way we can perceive an entity and then may or may not conceptualize that entity as a unit of a class of similar entities.

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Generalizations are not necessarily statements of causality. Causality is implicit in generalizations, but need not be the explicit meaning of the statement.

Causality is always contained, implicitly or explicitly, in every statement whether a statement about a concrete thing or a generalization about members of a class of things.

Every statement has a subject and a predicate. The subject is the entity we are discussing and the predicate is an action or attribute of that entity. The actions of an entity are caused by what the entity is and the attributes of an entity are also caused by what the entity is.

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If the statement were accurately stated as "some swans are white" doesn't that constitute the causal connection you are referring to? Even saying "this swan is white" (if true) implies some causality. Else what would the correspondence between entity and attribute mean if it was uncaused?

Exactly. Every statement, is implicitly or explicitly, a statement of causality. The difference between "this swan," "some swans," and "all swans" pertains only to how many entities the statement is making a causal claim about.

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I'd say induction is a wider process than establishing causation. It also applies to the formation of any general conclusion from particular data. "All swans are white" is a generalization arrived at by induction, but it is not a statement of causality.

I would say that, properly understood, it is a statement of causality.

"All swans are white" really means that there is something about being a swan - which applies to any and all swans -- that causes it to be white. If you can identify what that cause is -- maybe a certain gene sequence -- then you can be sure that all swans are white.

If we reword a proposition like "All swans are white" to say it really means "there is something about being swan that causes it to be white" aren't we just adding a needless layer of complexity? Why introduce causality on top of identity? Why not skip causality and simply say "the identity of a swan is such that it includes whiteness as one of its attributes?"

My problem with this approach is: how you know it? What process do you go through to verify your knowledge? Clearly those who induced the generalization "All swans are white" thought they had established that whiteness is an invariable characteristic of all swans. They were wrong and they had a good reason (in an advanced civilization) to know they could have been wrong. How could they have established the correct generalization?

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That said, after reflection I'd say induction is a wider process than establishing causation. It also applies to the formation of any general conclusion from particular data. "All swans are white" is a generalization arrived at by induction, but it is not a statement of causality.

But if it were true, wouldn't it necessarily be a statement of causality? There would have to be something in the identity of swans which led to them having white feathers. How about: All swans have wings? Or: All swans have heads? It would violate the fundamental nature of a swan to not have either of those. And that nature is actually a result of development following a genetically driven "program", causally. Change the DNA enough and you get a different sort of entity - because you will have changed a fundamental cause.

Why stop at DNA though? What causes DNA? In the end all things come back to the law of identity. It underlies causality. What causes identity? The question is back to front. Causality is an effect of identity.

I think there's a valid subject of induction and it's wider than isolating causes.

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That said, after reflection I'd say induction is a wider process than establishing causation. It also applies to the formation of any general conclusion from particular data. "All swans are white" is a generalization arrived at by induction, but it is not a statement of causality.

But if it were true, wouldn't it necessarily be a statement of causality? There would have to be something in the identity of swans which led to them having white feathers. How about: All swans have wings? Or: All swans have heads? It would violate the fundamental nature of a swan to not have either of those. And that nature is actually a result of development following a genetically driven "program", causally. Change the DNA enough and you get a different sort of entity - because you will have changed a fundamental cause.

Why stop at DNA though? What causes DNA? In the end all things come back to the law of identity. It underlies causality. What causes identity? The question is back to front. Causality is an effect of identity.

I think there's a valid subject of induction and it's wider than isolating causes.

As a further thought: we can induce true generalizations without reference to causality. We can say "All reds contrast with greens" long before we know red and green have different wavelengths or, to use Betsy's terms, are caused by them having different wavelengths.

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I'd say induction is a wider process than establishing causation. It also applies to the formation of any general conclusion from particular data. "All swans are white" is a generalization arrived at by induction, but it is not a statement of causality.

I would say that, properly understood, it is a statement of causality.

"All swans are white" really means that there is something about being a swan - which applies to any and all swans -- that causes it to be white. If you can identify what that cause is -- maybe a certain gene sequence -- then you can be sure that all swans are white.

If the statement were accurately stated as "some swans are white" doesn't that constitute the causal connection you are referring to? Even saying "this swan is white" (if true) implies some causality. Else what would the correspondence between entity and attribute mean if it was uncaused?

Tom is correct that general statements are a broader class than statements identifying causality. Some of them have nothing to do with causality, some are explicit statements of some cause, and in some an underlying causal mechanism is only implicit in the statement -- which does not make it a statement about causality. (Mill gave several examples of the different categories.)

The statement "all swans are white" makes (whether true or not) a simple statement of fact about the color of swans and does not assert anything about causality. Implicit in any proposition is the law of identity and possibly its corollary form, the law of causality, pertaining to action. As Paul notes that is just as true for statements about "some" swans and "this" swan as for "all". And as Tom correctly states, that a generalization is arrived at by induction does not make it a statement of causality.

If someone wants to additionally state something about the cause of the color of swans or anything else he can say so by stating that directly, but simply stating the color of swans does not say that and is not the "real" meaning of the statement. The implicit, underlying presence of the law of identity in statements of fact does not make them statements about causality, i.e., about something other than what the statements say. Attributing such an additional intention as the "real" meaning of a simple statement about something else is (bad) psychology, not epistemology, and is not grounds to convert general statements of fact into alleged statements about causality as supposedly what they "really mean" as "properly understood". The person making the statement decides that in his choice of the words he uses in his own statement.

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My problem with this approach is: how you know it? What process do you go through to verify your knowledge? Clearly those who induced the generalization "All swans are white" thought they had established that whiteness is an invariable characteristic of all swans. They were wrong and they had a good reason (in an advanced civilization) to know they could have been wrong. How could they have established the correct generalization?

In principle, you investigate the nature of the entities until you find the cause that reduces "All swans are white" to a statement of identity. Here's a simple example of a similar generalization: All calico cats are female.

That was just an hypothesis until scientists studied cat genetics. They discovered that the gene for calico color was recessive and that unless the cat inherited a calico gene from both of its parents, it would not exhibit calico coloring. They also found that that particular gene was only found on the X chromosome. Female cats have two X chromosomes and male cats have one X chromosome and one Y chromosome.

Thus, "All calico cats are female" reduced to a statement of identity: All cats with two X chromosomes containing the calico gene (all calico cats) have two X chromosomes (are female). The cause that proves the generalization is having a recessive gene on the X chromosome.

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As a further thought: we can induce true generalizations without reference to causality. We can say "All reds contrast with greens" long before we know red and green have different wavelengths or, to use Betsy's terms, are caused by them having different wavelengths.

Having different wavelengths isn't THE cause of contrasting appearance. The perception of contrast can be causally explained on many levels depending on one's cognitive purpose and that is true of all causes.

If I want to know why my key didn't open my door, it might be sufficient to know that this was caused by trying to use the wrong key. But causes have causes and I could also inquire further as to WHY it was the wrong key by examining the inner workings of the lock, the shape of the key, etc., but what for? I found out enough about the cause to answer my question about why the key didn't work.

Likewise, simply seeing that red contrasts with green is sufficient if you want to weave a plaid or decorate a Christmas tree. You don't need to know about wavelengths of light.

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As a further thought: we can induce true generalizations without reference to causality.

What for?

If one's purpose is not to find or understand causes, why would you want to "induce true generalizations?"

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As a further thought: we can induce true generalizations without reference to causality.

What for?

If one's purpose is not to find or understand causes, why would you want to "induce true generalizations?"

To live. You might induce that the trains that run on a certain line are reliably on time. That helps you predict and arrive when you want to, even if you never find out what causes their punctuality.

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My problem with this approach is: how you know it? What process do you go through to verify your knowledge? Clearly those who induced the generalization "All swans are white" thought they had established that whiteness is an invariable characteristic of all swans. They were wrong and they had a good reason (in an advanced civilization) to know they could have been wrong. How could they have established the correct generalization?

In principle, you investigate the nature of the entities until you find the cause that reduces "All swans are white" to a statement of identity. Here's a simple example of a similar generalization: All calico cats are female.

That was just an hypothesis until scientists studied cat genetics. They discovered that the gene for calico color was recessive and that unless the cat inherited a calico gene from both of its parents, it would not exhibit calico coloring. They also found that that particular gene was only found on the X chromosome. Female cats have two X chromosomes and male cats have one X chromosome and one Y chromosome.

Thus, "All calico cats are female" reduced to a statement of identity: All cats with two X chromosomes containing the calico gene (all calico cats) have two X chromosomes (are female). The cause that proves the generalization is having a recessive gene on the X chromosome.

That's the bit of your theory I like--and then some.

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That said, after reflection I'd say induction is a wider process than establishing causation. It also applies to the formation of any general conclusion from particular data. "All swans are white" is a generalization arrived at by induction, but it is not a statement of causality.

But if it were true, wouldn't it necessarily be a statement of causality? There would have to be something in the identity of swans which led to them having white feathers. How about: All swans have wings? Or: All swans have heads? It would violate the fundamental nature of a swan to not have either of those. And that nature is actually a result of development following a genetically driven "program", causally. Change the DNA enough and you get a different sort of entity - because you will have changed a fundamental cause.

The statement that all swans are white does not say anything about causality. It only says what their color is without regard to why or how it got that way. Implicit in that and every other such statement is the fact that things are what they are and act accordingly, but you don't keep repeating that in every statement you make and that is not the meaning of your statement -- your statements are intended to state something explicit by the words you choose; if you want to say something about causality then say that instead. You can observe that birds have the characteristics they do and state what you observe without knowing why it is the case and without making statements about causality at all. What you can't do is induce on the basis of limited observation and without further explanation the generality that all swans everywhere always have and always will be white. For that you need expanded knowledge. But the statement is meaningful as an hypothesis without that and does not require or mean anything beyond what it actually says.

Why stop at DNA though? What causes DNA? In the end all things come back to the law of identity. It underlies causality. What causes identity? The question is back to front. Causality is an effect of identity.

I think there's a valid subject of induction and it's wider than isolating causes.

As for the question about why stop at DNA to explain characteristic colors of birds, you don't stop there. The knowledge you form of DNA allows you to explain the resulting colors, but there is no reason not to look for further explanations of DNA and how it works, which increases your knowledge of both DNA and the resulting colors. (This is illustrated in LL for examples from physics.)

Obtaining more knowledge than you have at any stage increases your understanding of what you have previously observed and allows for further investigation to learn more, but does not require an infinite regress before you can claim to know anything. You can only know what you know in the context of observation of reality that you already have and the context of already developed knowledge and explanation. Knowledge does not require an impossible omniscience. Both IOE and LL also explain this. The finite stage of the pyramid of your knowledge always leaves more to be investigated, but does not preclude you from identifying and understanding causes in earlier levels of knowledge in terms of your relatively more advanced levels of knowledge.

As a further thought: we can induce true generalizations without reference to causality. We can say "All reds contrast with greens" long before we know red and green have different wavelengths or, to use Betsy's terms, are caused by them having different wavelengths.

The generalization inherent in forming the concepts of red and green consists of open-ended classification to form concepts, which is not the same thing as making general propositions. You observe similarities and differences in forming the concepts of the colors of entities by directly perceiving the attribute of color and recognizing that a color is a color of certain types of entities. The formation of such concepts does not require further explanation of why the attributes are different, only recognizing that they are. The generalization consists in the fact that the concepts refer to all instances of red or green, not a statement of why they are different in terms of wavelenghts, reflectivity and absorption, or anything else. From those concepts of color alone there is no prediction being made of what will turn out to be red or green and no necessity to explain it -- when you observe a new instance you perceive what it is similar to and therefore know which classification it belongs to. This is very different than formulating and justifying a general proposition about entities. So yes, there is more to the subject of inducing general propositions than identifying causation (or "conceptualizing" particular causations), but it is not in the distinction between statements and concepts.

The law of identity is implicit in all knowledge, and that includes the law of causality as the law of identity applied to action. But you don't reduce all knowledge to metaphysical axioms. You build your knowledge on observations of particulars, form concepts, apply your knowledge using concepts and further analysis and observation to form new concepts and theories, etc. as you identify the particular nature of things in ever increasing depth and breadth. That is not a reduction to metaphysical axioms. As important as the law of identity is as underlying everything we do, to try to explain induction as "reduction to identity" is vacuous and is not a theory of induction: it doesn't tell you anything about the methodology and validation of generalizations and doesn't distinguish reaching general statements from particulars from any other kind of statement or knowledge of causality or anything else. The law of identity is implicit in all of it and you are always identifying what things are in some respect. Restating that doesn't tell you anything new about induction.

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My problem with this approach is: how you know it? What process do you go through to verify your knowledge? Clearly those who induced the generalization "All swans are white" thought they had established that whiteness is an invariable characteristic of all swans. They were wrong and they had a good reason (in an advanced civilization) to know they could have been wrong. How could they have established the correct generalization?

...

Thus, "All calico cats are female" reduced to a statement of identity: All cats with two X chromosomes containing the calico gene (all calico cats) have two X chromosomes (are female). The cause that proves the generalization is having a recessive gene on the X chromosome.

That's the bit of your theory I like--and then some.

But it is a particular example from science, not a theory of induction, and is not new. As Ayn Rand (and almost everyone else) has observed, the problem of induction is knowing when sufficient observations of the right kind have been made to validate the generalization. Leonard Peikoff certainly hasn't answered that either, instead basing his theory on an alleged direct perception of causality as such in the infamous "first level generalizations", claims to have reduced generalities to the equivalent of conceptual classification, and a "unity" of knowledge providing "contextual certainty", a rationalistic approach that Ayn Rand explicitly rejected and which is more reminiscent of epistemological idealism cloaked in Objectivist terminology than Ayn Rand's always reality-based approach.

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We can form an abstract concept of a cause after we have the knowledge to do so by identifying and validating the generalization, not the other way around.

We don't5 start with a generalization which we then validate. Rather, we start with the pursuit of a value and a cognitive need to cause whatever will gain and keep that value such as getting food when hungry. That leads us to find causes. Some causes are generalizable and it is cognitively useful to do so. That way you don't have to enumerate each of thousands of supermarkets when you want to buy food. You just generalize that supermarkets sell food.

We start by finding a cause and then may or may not generalize it similar to the way we can perceive an entity and then may or may not conceptualize that entity as a unit of a class of similar entities.

Why are you addressing this to me? Neither I nor anyone else here has said that we "start" with generalizations that we then validate, and that is not what the snippet you quoted says. LL doesn't say that either. You are not addressing what I wrote.

Statements about "cognitive needs" and "pursuit of value" treated as epistemology of induction sound more like William James. But moving to the actual epistemological claims, we don't "start" by "finding a cause" and then generalizing the single instance into a concept, either. You don't know you have correctly identified a causal principle simply by treating it like a concept. One must validate the hypothesis. Applying Objectivism to the problem of induction does not mean equating general propositions with the equivalent of concepts. That is Leonard Peikoff's theory. The problem of induction is knowing when you have identified enough information of the right kind to generalize from particular observations so you know that you have in fact successfully identified an explanation and that it is true in general. Without that you don't know that a proposed explanation of even a single instance is valid, let alone a generalization of it. Induction is science is a lot more complicated than being told by your mother that supermarkets sell food.