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organon1973

Induction

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This is a paper of mine on the subject of induction; I welcome your thoughts.

 

--

 

The problem of induction asks, “How does one infer a general truth relating to a concept as such from the observation of a number of particular instances?” How does one establish that a property (by which I mean an attribute or causal implication of an attribute) is something all units of a concept have in common, or share, by virtue of their inclusion in the concept? How can one know that “Men are rational beings” — “Men are mortal” — “Men require self-esteem in order to live”?

 

All of these statements are inductive truths, i.e. truths that assign a property to all units of a concept. An inductive truth is applicable universally to all units of that concept. But how does one determine that something is true of all instances of a concept based on a limited number of observations?

 

There are two types of valid induction, that I will designate as ‘simple’ and ‘relational’.

 

The first type, ‘simple’ induction, identifies a property that the units of a concept share by virtue of that which gave rise to the concept, i.e. the concept’s differentia. This type of induction involves an identification of a property of a concept informed by that which serves as the basis of the concept’s identity; it requires no further work than to look to the identification from which the concept was generated. “Spiders have eight legs”; “water has the chemical formula H2O”; “man is the rational animal”; are examples.

 

Any organism one identifies as a spider will have eight legs; this is mandated in order for it to be identified as a ‘spider’. Any water will have the chemical formula H2O; this is mandated in order for it to be identified as ‘water’. Any man will have the capacity of reason; this is mandated in order for him to be identified as a man. In all cases, to identify a thing as a unit of the concept, is to identify that it possesses the attributes that were isolated and integrated when the concept was formed.

 

The second form of induction I designate as ‘relational’ induction. This is the identification of a property that belongs to all units of a concept, not by virtue of the differentia, but by virtue of the nature of a wider group to which the concept belongs. The nature of the wider group informs the property for the narrower concept; it serves as an umbrella that informs the property for all that which comes within its scope.

 

The famous relational inductive truth we will explore below is that which Aristotle applied to the case of Socrates, namely, “All men are mortal.”

 

 

Relational’ induction begins with the observation that some units of a concept demonstrate a property and that the property cannot be established to characterize the units of the concept by virtue of the nature of the concept’s differentia – i.e., ‘simple’ induction is insufficient.

 

Are men mortal? Let us consider the process of a hypothetical thinker.

 

What are Men? Men are living beings whose distinct means of survival is rational thought.

 

That they are beings of thought is the key differentia of the concept of man in relation to living things, and were I called upon to validate the induction, ‘Man is the rational animal,’ I could look to this. I can thus easily make the simple induction that all men are beings with the capacity of reason, for this is true on the basis of what is involved in identifying man as man. But this is wholly unrelated to the mortality of men. Is there any other aspect of man that as such can be related to the fact that men have the capacity of dying? What can I look to?

 

As the differentia is not helpful, let me then look to a genus of man, and see if that will help.

 

What is the genus of ‘Man’ related to the context here? Is there a genus of man relevant to the fact of mortality?

 

What is ‘mortality’? It is the capacity for the life of a living thing to end. Perhaps help can be found here. Is there something in the nature of life that implies mortality?

 

Life (I have observed) is a conditional state of self-generated, self-sustaining action. For all living things, a certain course must be pursued for life to continue, this course dictated by the nature of the living thing. It is conditional on following such a course of action, which one must pursue. An organism has no alternative. If it does not follow that course, its life will not continue.

 

Thus the key identification here in relation to ‘living thing’, the genus of ‘man’ I am investigating, is that it is conditional, and does not necessarily endure. Should a living thing not engage in the requirements of life dictated by its nature, its life in all cases will end.

 

Does this characterize life as such? Yes, it does. It is true of any living thing. The continued life of a living thing depends upon meeting the requirements of its existence in reality, these requirements dictated by its nature.

 

So then.

 

Living things are mortal.

 

All living things are mortal, by the nature of life. Men are living things. The syllogism is clear. Men are mortal.”

 

What has our thinker done here?

 

He has established (by means of independent thought) a quality relating to the nature of a wider group within which men are a narrower, valid grouping, that informs that quality for the narrower concept. Men are living things, and, by virtue of the nature of living things as such, men are mortal. And this quality is applicable to all men, as well as all valid narrower groupings within the concept ‘organism’ (i.e., that which subsumes living things). Everything that is alive is mortal – men, and dogs, and dolphins, and birds, and insects.

 

To review:

 

Induction is the process of identifying a truth relating to a concept. It identifies a property (whether an attribute or a causal implication of an attribute) that all units of a concept have in common, or share, by virtue of their inclusion in the concept. For example: “Men are rational beings” – “Men are mortal” – “Men require self-esteem in order to live.”

 

There are two types of induction, ‘simple’ and ‘relational’.

 

Simple’ induction identifies a truth informed by an attribute true by virtue of the concept’s differentia. It relates to that which was isolated and integrated when the concept was formed.

 

Relational’ induction identifies a property shared by all units of a concept, not deriving from the concept’s differentia, but instead from a wider group to which the concept belongs, the nature of which informs that property for the narrower group. And it is a property shown by all things that come within its scope of the wider group.

 

Thus a truth common to all units of a concept thus derives either (1) from the nature of the the concept qua the concept, i.e. by reference to the concept’s differentia, or (2) from a wider group, the nature of which informs the property for the narrower subgroup.

 

Note that the units of a concept retain all of the properties of all of the wider groups to which the concept belongs.

 

Again: Are all Men Mortal?

 

Men are living things. All living things have the capacity of dying (this follows from the nature of life – see above). Therefore, men have the capacity of dying. Thus all men are mortal. As are all living things.

 

And once we establish with certainty that all Men are Mortal, then given that we know (as Aristotle wrote) that Socrates is a Man, we can say with certainty that Socrates is mortal. This is the process of deduction – the application of an inductive truth to a given unit of the concept identified in that truth, establishing a property of that unit.

 

Why is Socrates mortal? Because Men are mortal.

 

Why are Men mortal? Because living things are mortal, by virtue of the nature of living things, a wider group within which men are contained.

 

And a man stops here, once he, by means of his own reason, establishes that living things are mortal. And he is certain of his related convictions on every level from the point of the validated induction forward.

 

Two final notes:

 

(1) The widest categories – the Phyla, if you would, of the kingdom of reality – are existence and consciousness. All properties identified as belonging to each of these apply to all narrower categories within these groups.

 

(2) In pursuit of an inductive truth, one first identifies that the units of a concept demonstrate a certain property. One can then look to the differentia of the concept, and see if the induction can be validated there (‘simple’ induction). If this offers no assistance, one then seeks the path of relational induction, and begins with the goal of identifying the relevant wider group the nature of which informs the property. How? There are two ways.

 

First, to seek the relevant genus by seeking a genus that relates in some way logically to the attribute. E.g., if the issue is that of mortality, we can consider looking to the nature of life, for mortality is the capacity for life to end. Thus, perhaps there is something in the nature of life that causes life to the have the capacity of ending.

 

Second, if we have no guidance from the first method, we can look for other concepts that share the attribute (e.g. mortality is shared by dolphins and men), then seek for a common, wider group they share to investigate. One then can inquire into the nature of that genus, and if all goes well establish the truth on its foundation (“Living things are mortal”). One can then go forward again, now with the confidence of certainty, and let that inductive truth inform all narrower concepts within that genus (“All men are mortal”, “All dolphins are mortal”, “Ants are mortal”), and all units of those concepts (“Socrates is mortal”, “This dolphin is mortal”, “This ant is mortal”).

 

Also note that no matter how many instances of a given quality you witness, i.e. no matter how many men you see die, or apples you see fall, you do not achieve the certain belief that “All men are mortal” or that “All apples fall” until you yourself validate the induction by one of the two above described methods.

Edited by organon1973

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Two final notes:

 

(1) The widest categories – the Phyla, if you would, of the kingdom of reality, are existence and consciousness. All properties identified as belonging to each of these apply to all narrower categories within these groups.

 

Consider:

"There is only one fundamental alternative in the universe: existence or non-existence—and it pertains to a single class of entities: to living organisms. The existence of inanimate matter is unconditional, the existence of life is not; it depends on a specific course of action.

The widest categories of the kingdom of reality would be matter, inanimate and animate. Not all life is conscious.

Is this paper for a school class?

Edited by dream_weaver

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Could one first divide existence into matter and energy?

Edited by organon1973

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I don't really see the benefit of trying to do so here, in the context of this paper as written..

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Any water will have the chemical formula H2O; this is mandated in order for it to be identified as ‘water’.

It's more work than that. The attributes that lead you to first differentiate a set of existents are by necessity not based on an advanced knowledge of them; that has to come later. At first, the most you could say is that all water looks alike.

Inductive work is done from there. "Simple" induction can't account for the discovery of the chemical formula.

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I read this last night, but I didn't trust myself to give a proper response because I was tired. I read it again this morning. I think you have a valuable point here, and I will try to integrate it with my understanding of Aristotle's logic.

If I understand you correctly, your point is that an inductive argument has to be either simple, proceeding from the differentia of the category, or relational, proceeding from a broader genus that the category belongs to. A particularly clear illustration of what I take to be your point here might be found in geometry. I can demonstrate that a right triangle obeys the Pythagorean theorem by reference to the differentia of a right triangle, but to demonstrate that the angles of a right triangle add up to 180 degrees I need to move up to the genus "triangle" and demonstrate the point of all triangles.

This insight is related to the concept of a property in Aristotle's logic. According to Aristotle, a property is a predicate that holds of all and only the subject and is not contained in its definition. If the predicate holds of all instances of the subject category but holds of other instances outside the subject category as well, it is not a property of the subject category but of some broader category that contains the subject category. For example, mortality is a property of living things, not of animals or human beings, even though all animals and human beings are mortal.

Now, my suggestion about your theory is that it should be presented as a theory of deduction, not induction. This is for two reasons. First, it applies to fields that are entirely deductive, like geometry in my example above. Second, the processes of simple induction and relational induction as you describe them do not seem to involve drawing inferences from any fresh observations, since the reasoning you describe is all done within the context of a previously established conceptual framework.

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Two final notes:

 

(1) The widest categories – the Phyla, if you would, of the kingdom of reality, are existence and consciousness. All properties identified as belonging to each of these apply to all narrower categories within these groups.

 

Consider:

"There is only one fundamental alternative in the universe: existence or non-existence—and it pertains to a single class of entities: to living organisms. The existence of inanimate matter is unconditional, the existence of life is not; it depends on a specific course of action.

The widest categories of the kingdom of reality would be matter, inanimate and animate. Not all life is conscious.

Is this paper for a school class?

This assumes that materialism is true, and as far as I know there is no evidence that Rand was a materialist. She laid down some constraints on a valid solution to the mind body problem, but she didn't take a specific position like materialism.

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This assumes that materialism is true, and as far as I know there is no evidence that Rand was a materialist. She laid down some constraints on a valid solution to the mind body problem, but she didn't take a specific position like materialism.

Not really.  It merely repudiates the supernatural.

Recognizing the fact that all things may be disintegrated into matter and energy, and all things may be integrated from matter and energy does not imply materialism, it merely recognizes for example before "you", there was ONLY matter and energy which came together in a certain manner to make "you", and after "you", ALL that will be left is matter and energy.

Perhaps you could characterize this as application of identity to naturalism... but certainly not materialism, unless you define materialism as the rejection of supernaturalism. 

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Not really.  It merely repudiates the supernatural.

Recognizing the fact that all things may be disintegrated into matter and energy, and all things may be integrated from matter and energy does not imply materialism, it merely recognizes for example before "you", there was ONLY matter and energy which came together in a certain manner to make "you", and after "you", ALL that will be left is matter and energy.

Perhaps you could characterize this as application of identity to naturalism... but certainly not materialism, unless you define materialism as the rejection of supernaturalism. 

Yes, well, this is a description of materialism. Materialism is the claim that everything is composed of matter, including consciousness, and that is what you wrote here nearly word for word.

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Ms. Rand only ever seemed to have referred to materialism as the denial of consciousness. (Eliminative materialism) She did not seem to make any wider distinctions on materialism. The definition of physics being "matter AND energy" presupposes the philosophy of physics that upholds the substantival interpretation of energy, which is not a given. Most Physicist don't even care to answer these ontological questions. Dr. Peikoff and Ms. Rand held that "energy" had not yet been defined in a way that would allow it to be considered an entity. It certainly did not begin that way in the history of science. Also the Oist view that entities are the only metaphysical primaries is technically a species of materialism.

Feynman said:

It is important to realize that in physics today, we have no knowledge of what energy is. We do not have a picture that energy comes in little blobs of a definite amount. It is not that way. However, there are formulas for calculating some numerical quantity and when we add it together it gives “28″—always the same number. It is an abstract thing in that it does not tell us the mechanisms or the reasons for the various formulas.

Edited by Plasmatic

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William O said:

Now, my suggestion about your theory is that it should be presented as a theory of deduction, not induction. This is for two reasons. First, it applies to fields that are entirely deductive, like geometry in my example above. Second, the processes of simple induction and relational induction as you describe them do not seem to involve drawing inferences from any fresh observations, since the reasoning you describe is all done within the context of a previously established conceptual framework.

Aren't these both the same objection? The concepts in any deductive syllogism are inductively arrived at (the conceptual framework), in geometry or anywhere.

Edited by Plasmatic

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Two final notes:


(1) The widest categories – the Phyla, if you would, of the kingdom of reality, are existence and consciousness. All properties identified as belonging to each of these apply to all narrower categories within these groups.

This assumes that materialism is true, and as far as I know there is no evidence that Rand was a materialist. She laid down some constraints on a valid solution to the mind body problem, but she didn't take a specific position like materialism.

I was not thinking of it in that context. The paper started with consciousness, and used life as the fulcrum of assigning mortality to the class. What I thought was needed was to divide the kingdom of reality into two divisions, one of which is life, and preferably another term than existence, which is essentially the kingdom of reality.

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Yes, well, this is a description of materialism. Materialism is the claim that everything is composed of matter, including consciousness, and that is what you wrote here nearly word for word.

"nearly"...

 

No.

I spoke of, prior to you, and formation of you.. and after you.  You can still believe in a kind of "emergent" dualism or some-such of you like... but only during the time there exists a consciousness. 

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Ms. Rand only ever seemed to have referred to materialism as the denial of consciousness. (Eliminative materialism) She did not seem to make any wider distinctions on materialism. The definition of physics being "matter AND energy" presupposes the philosophy of physics that upholds the substantival interpretation of energy, which is not a given. Most Physicist don't even care to answer these ontological questions. Dr. Peikoff and Ms. Rand held that "energy" had not yet been defined in a way that would allow it to be considered an entity. It certainly did not begin that way in the history of science. Also the Oist view that entities are the only metaphysical primaries is technically a species of materialism.

Feynman said:

I think Feynman was speaking of "energy" here in its widest conception, including things like kinetic energy, potential energy, etc. 

Now with respect to fundamental particles, IF you take a photon to be "matter" then I suppose you could dispense with the term energy in "energy and matter" when speaking of existents, but if you take a photon not to be matter ... then it properly is a quanta of energy.

I assume you take the existence of photons as confirmed.

 

In any case, when I used the term "matter and energy" I mean to say constituents of natural existence, in any form. 

Whatever the number of categories of "natural stuffs" you or anyone wishes to come up with, none can contradict "identity" and "causality" in the Objectivist sense of those concepts.

Whether you call of these "natural stuffs" - "material"... or "immaterial"... or "nonmaterial" becomes a playing at words. 

Something you Plasmatic do not... but others do.

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Ms. Rand only ever seemed to have referred to materialism as the denial of consciousness. (Eliminative materialism) She did not seem to make any wider distinctions on materialism. The definition of physics being "matter AND energy" presupposes the philosophy of physics that upholds the substantival interpretation of energy, which is not a given. Most Physicist don't even care to answer these ontological questions. Dr. Peikoff and Ms. Rand held that "energy" had not yet been defined in a way that would allow it to be considered an entity. It certainly did not begin that way in the history of science. Also the Oist view that entities are the only metaphysical primaries is technically a species of materialism.

Feynman said:

I think Feynman was speaking of "energy" here in its widest conception, including things like kinetic energy, potential energy, etc. 

Now with respect to fundamental particles, IF you take a photon to be "matter" then I suppose you could dispense with the term energy in "energy and matter" when speaking of existents, but if you take a photon not to be matter ... then it properly is a quanta of energy.

I assume you take the existence of photons as confirmed.

 

In any case, when I used the term "matter and energy" I mean to say constituents of natural existence, in any form. 

Whatever the number of categories of "natural stuffs" you or anyone wishes to come up with, none can contradict "identity" and "causality" in the Objectivist sense of those concepts.

Whether you call of these "natural stuffs" - "material"... or "immaterial"... or "nonmaterial" becomes a playing at words. 

Something you Plasmatic do not... but others do.

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I assume you take the existence of photons as confirmed.

I would willingly be a "fly on the wall" witnessing you two parsing this one!

Edited by dream_weaver
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It's more work than that. The attributes that lead you to first differentiate a set of existents are by necessity not based on an advanced knowledge of them; that has to come later. At first, the most you could say is that all water looks alike.

Inductive work is done from there. "Simple" induction can't account for the discovery of the chemical formula.

Is the expansion of knowledge an inductive process?

Rand writes:

"All thinking is a process of identification and integration. Man perceives a blob a color; by integrating the evidence of his sight and his touch, he learns to identify it as a solid object; he learns to identify the object as a table; he learns that the table is made of wood; he learns that the wood consists of cells, that the cells consist of molecules, that the molecules consist of atoms...." (Galt's Speech)

Is this an inductive process? Certainly our knowledge of what a concept is can continually expand. But does induction relate instead (as described in the paper) to establishing the conceptual level at which a discovered property inheres (informing that property for all subconcepts), and achieving certainty that this property is demonstrated by the concept on this level by virtue of its nature (our grasp of which can continually grow)? 

Edited by organon1973

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On 11/20/2015, 10:41:36, organon1973 said:

Is the expansion of knowledge an inductive process?

Rand writes:

"All thinking is a process of identification and integration. Man perceives a blob a color; by integrating the evidence of his sight and his touch, he learns to identify it as a solid object; he learns to identify the object as a table; he learns that the table is made of wood; he learns that the wood consists of cells, that the cells consist of molecules, that the molecules consist of atoms...." (Galt's Speech)

Is this an inductive process? Certainly our knowledge of what a concept is can continually expand. But does induction relate instead (as described in the paper) to establishing the conceptual level at which a discovered property inheres (informing that property for all subconcepts), and achieving certainty that this property is demonstrated by the concept on this level by virtue of its nature (our grasp of which can continually grow)? 

When discovering some property of some concrete entity, to what category should we attribute it?

 

For example, suppose a team of biologists discovers X about some individual organism in their lab, and rightly infers X about that entire species. Should they then infer X about homo sapiens?

In reality, they might (tentatively) posit X about mankind if their specimen was a mouse or a chimpanzee, but not an amoeba or a tree. Why?

 

Each abstraction refers to a certain kind of entity, which has certain attributes. Every attribute - from "solid" to "made of wood" to "both a particle and a wave" - is either directly perceptible or inferred from some other basis (which must ultimately be directly perceptible).

 

An entity, apart from any of its attributes, isn't conceivable. Indeed, I think that entities are -in a sense- composed of their attributes. This isn't to say that they're the sum of their attributes, as if white+feathers+swimming=swan, but rather the integral B) of their attributes.

I may be wrong, of course, but that would make the whole thing an inductive sort of process (right down to the way we integrate sensations into percepts).

 

 Edit:

My point being that if an entity is a mental integration of its attributes, and if all attributes are inferred (directly or indirectly) from firsthand experience, then entities are mental groupings of our own observations; induction being the particular way we group them together.

I realize that this seems like "the meaning of 'Napoleon lost the battle of Waterloo' is your trip to the library where you read it", but it seems sound enough at the moment.

Edited by Harrison Danneskjold

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On 11/17/2015, 9:26:19, organon1973 said:

Could one first divide existence into matter and energy?

Actually, no, because concepts like matter and energy belong to the specific sciences, not philosophy.  Dealing with these terms in a philosophical treatise would be rampantly anti-hierarchical and produce nothing but confusion.

DonAthos likes this

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On 12/5/2015 at 5:15 PM, JMeganSnow said:

Actually, no, because concepts like matter and energy belong to the specific sciences, not philosophy.  Dealing with these terms in a philosophical treatise would be rampantly anti-hierarchical and produce nothing but confusion.

Here's a relevant quote from ITOE, from the appendix on philosophy of science:

Prof. B: Is the concept of "matter" a philosophical concept or a scientific one?

AR: In the way we are using it here, as a very broad abstraction, it is a philosophical concept. If by "matter" we mean "that of which all the things we perceive are made," that is a philosophical concept. But questions like: what are different things made of? what are the properties of matter? how can you break it down? etc. - those are scientific problems.

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On 12/4/2015 at 6:15 PM, JMeganSnow said:

Actually, no, because concepts like matter and energy belong to the specific sciences, not philosophy.  Dealing with these terms in a philosophical treatise would be rampantly anti-hierarchical and produce nothing but confusion.

Hmm. I was thinking that a general scientist in relation to existence might first divide existence into matter and energy (in a general sense, no equations needed : ) ) and then, of matter, into that which lives and that which does not. I need to consider further if this approach is fundamentally incorrect.

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