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Induction as measurement omission of _properties_

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Concept formation involves measurement omission in relation to attributes of existents. Induction involves measurement omission in relation to the demonstrated inherent properties of the units of a concept, i.e., to that which these kind of existents can do, or have done.

Bill died at 97.

Gretchen died at 99.

David died at 102.

In forming the induction above, one asks: what actions have the entities taken? Answer: They died. They are mortal. The omitted measurement is the age of death in any given case.

Then: Is death inherent to the units subsumed by the concept? And the answer is, Yes, it is so. Their demonstrated capacity for death, for ending existence as a living being, is an inherent capacity given the nature of the units subsumed by the concept. Every entity thus subsumed can, in fact, die, as the three above demonstrate. It is not possible for a man to exist, and not be mortal. This is inherent to what he is, to what men are.

And thus the induction is valid. All Men are mortal. And Socrates, being a man, is mortal, as are all men.

Thoughts?

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Concept formation involves measurement omission in relation to attributes of existents. Induction involves measurement omission in relation to the demonstrated inherent properties of the units of a concept, i.e., to that which these kind of existents can do, or have done.

Bill died at 97.

Gretchen died at 99.

David died at 102.

In forming the induction above, one asks: what actions have the entities taken? Answer: They died. They are mortal. The omitted measurement is the age of death in any given case.

Then: Is death inherent to the units subsumed by the concept? And the answer is, Yes, it is so. Their demonstrated capacity for death, for ending existence as a living being, is an inherent capacity given the nature of the units subsumed by the concept. Every entity thus subsumed can, in fact, die, as the three above demonstrate. It is not possible for a man to exist, and not be mortal. This is inherent to what he is, to what men are.

And thus the induction is valid. All Men are mortal. And Socrates, being a man, is mortal, as are all men.

Thoughts?

That is not true. To show you why, I will change "died at age (number)" to "smoked (number) of cigarettes" and leave everything else the pretty much the same.

Bill smoked 97 cigarettes.

Gretchen smoked 99 cigarettes.

David smoked 102 cigarettes.

In forming the induction above, one asks: what actions have the entities taken? Answer: They smoked cigarettes. They are smokers. The omitted measurement is the number of cigarettes in any given case.

Then: Is smoking cigarettes inherent to the units subsumed by the concept? And the answer is, Yes, it is so. Their demonstrated capacity for smoking cigarettes, for lighting up and inhaling, is an inherent capacity given the nature of the units subsumed by the concept. Every entity thus subsumed can, in fact, smoke cigarettes, as the three above demonstrate. It is not possible for a man to exist, and not smoke cigarettes. This is inherent to what he is, to what men are.

And thus the induction is valid. All Men smoke cigarettes. And Socrates, being a man, smokes them too.

:wacko:

I don't think so.

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'Men smoke cigarettes' is not a valid induction. 'Some men smoke cigarettes' is true.

Why?

Because smoking cigarettes is not a property inherent to the concept's units.

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Concept formation involves measurement omission in relation to attributes of existents. Induction involves measurement omission in relation to the demonstrated inherent properties of the units of a concept, i.e., to that which these kind of existents can do, or have done.

Bill died at 97.

Gretchen died at 99.

David died at 102.

In forming the induction above, one asks: what actions have the entities taken? Answer: They died. They are mortal. The omitted measurement is the age of death in any given case.

I don't see where your inductive statement is. You cite 3 people who died at different ages. One could just a well claim that the common element is that all three of them lived at least 97 years. Is your induction going to be that all men live to be at least 97 years?

Then: Is death inherent to the units subsumed by the concept? And the answer is, Yes, it is so. Their demonstrated capacity for death, for ending existence as a living being, is an inherent capacity given the nature of the units subsumed by the concept. Every entity thus subsumed can, in fact, die, as the three above demonstrate. It is not possible for a man to exist, and not be mortal. This is inherent to what he is, to what men are.

And thus the induction is valid. All Men are mortal. And Socrates, being a man, is mortal, as are all men.

Thoughts?

How do you reach the conclusion that all men are mortal from citing 3 people who died?

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'Men smoke cigarettes' is not a valid induction. 'Some men smoke cigarettes' is true.

Why?

Because smoking cigarettes is not a property inherent to the concept's units.

Solving the problem of induction requires proving that a property is inherent to all the concept's units. My version fails because it does not prove that all men smoke cigarettes but merely asserts it.

Likewise, your assertion, as presented, also fails to prove that all men are mortal but merely asserts it. Just because three men died proves nothing about all men nor that mortality is inherent in being a unit of the concept "man."

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I agree completely that three concrete confirmatory instances fall far short of establishing a valid inductive generalization as sweeping as "all men are mortal." There are some further issues to consider, also, such as the following (not necessarily an exhaustive list):

1. How many more confirmatory instances might be needed?

2. Should we look for any contrary instances? If so, how hard should we look, especially if we can't seem to find any?

3. Do we need to look for, and find, any underlying causal mechanisms?

These issues fall under the general topic of "the problem of induction." As far as I know, no one has yet solved that problem (except in the special case of forming concepts). At one time, Leonard Peikoff and David Harriman were working on a book on induction (in addition to Dr. Peikoff's book on DIM). As I recall, the task rapidly grew beyond the scope of a single chapter in the DIM book and needed to become a book on its own, which David Harriman took on the main task of writing (with at least one or two key chapters to be contributed by Dr. Peikoff). Others may be able to provide a more definitive update on this project. It's been a long time since I heard anything about it.

Also, if I recall correctly (although I haven't been able to confirm where), Ayn Rand once said (or was reported by Dr. Peikoff to have said) that "all men are mortal" would be far less believable if there wasn't a process of aging observable in all men (and, indeed, in all living things). The process of aging probably would fall under topic #3 above. There is a good discussion of induction in ITOE, pp. 295-304.

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I agree completely that three concrete confirmatory instances fall far short of establishing a valid inductive generalization as sweeping as "all men are mortal." There are some further issues to consider, also, such as the following (not necessarily an exhaustive list):

1. How many more confirmatory instances might be needed?

2. Should we look for any contrary instances? If so, how hard should we look, especially if we can't seem to find any?

3. Do we need to look for, and find, any underlying causal mechanisms?

In my view, only #3 is necessary and sufficient to solve the Problem of Induction.

As I have written elsewhere:

The "Problem of Induction" concerns how we can be certain our

generalizations are true. How much is enough evidence? One

observation? A million? A particular kind of observation? What

kind?

All generalizations involve either a relationship between members of a

class and their properties ("All men are mortal.") or between members

of a class and their actions ("Acorns grow into oak trees.") Because

of this, all generalizations depend on the truth of a causal

relationship.

A cause is that aspect of an entity's identity which accounts for the

entity's properties and actions. As Ayn Rand expressed it in Galt's

Speech:

"The law of causality is the law of identity applied to action.

All actions are caused by entities. The nature of an action is caused

and determined by the nature of the entities that act ..."

Let's take the proposition "All men are mortal." Another way of

saying this is that there is something about being a man which causes

all men to eventually die.

We know that all men have certain biological characteristics in common

with all other men (and all higher animals): we are composed of

cells which can die or malfunction, our bodies consist of complex

interrelated systems with some vital, irreplaceable components and

moving parts which wear out with time and use, etc., etc.

Once we know enough about what we are, we know how what we are

causes our mortality. Since causality is the law of identity

applied to actions, we have established a relationship of identity

between humanity and mortality. The characteristics which make an

entity human are the same characteristics which make him mortal.

This is the source of inductive certainty. If and when you can find a

cause which reduces a generalization about a thing and its properties

or actions to an identity, then your generalization is as certain as

A is A.

Sometimes you can reach inductive certainty after only one

observation. After introspecting just once on how she formed the

concept of "rose," Ayn Rand was able to discover that measurement-

omission is the key to concept-formation. Sometimes it takes a long

time. Roark spent many years trying to understand the "principle

behind the Dean" before he could identify it as cognitive second-

handedness.

The search for inductive certainty is the search for causes.

© 1997 Betsy Speicher

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3. Do we need to look for, and find, any underlying causal mechanisms?
In my view, only #3 is necessary and sufficient to solve the Problem of Induction.
But doesn't finding a causal mechanism itself require an induction? For example: If we want to reach the generalization "all men are mortal" then how do we solve this problem by seeking to reach the generalization "all men consist of biological cells"? The latter generalization would have to be reached by induction, too. Don't get me wrong, discovering a causal mechanism is great and it's a lot better than attempting to induce by enumeration. But in my opinion this approach shifts the problem to another place without solving it.

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If we want to reach the generalization "all men are mortal" then how do we solve this problem by seeking to reach the generalization "all men consist of biological cells"?
And to take it one step further: How do you induce the law of causality? How do you prove that every entity acts in accordance with its identity?

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If we want to reach the generalization "all men are mortal" then how do we solve this problem by seeking to reach the generalization "all men consist of biological cells"?
And to take it one step further: How do you induce the law of causality? How do you prove that every entity acts in accordance with its identity?

When you never find a single instance of one that doesn't, and understand why. B)

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If we want to reach the generalization "all men are mortal" then how do we solve this problem by seeking to reach the generalization "all men consist of biological cells"?
And to take it one step further: How do you induce the law of causality? How do you prove that every entity acts in accordance with its identity?

The Law of Causality states that all actions are actions of entities. The Law of Identity holds that a thing is what it is. The statement that "every entity acts in accordance with its identity" is an application or integration of the Law of Identity to the Law of Causality. One induces both Laws by conceptualizing what is available to one's consciousness. One does not need to perceive everything in existence. One does not prove either Law: proof presupposes such laws. Thus, but studying one man, if one can determine that a specific property, such as consisting of biological cells, is related to his identity (qua biological man as opposed to this particular man) then such a statement is true of all men. A particular man may or may not eat apples, but all men eat food.

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3. Do we need to look for, and find, any underlying causal mechanisms?
In my view, only #3 is necessary and sufficient to solve the Problem of Induction.
But doesn't finding a causal mechanism itself require an induction?

Finding a causal mechanism requires observation (and investigation). Whether that causal mechanism is operative in all instances requires an induction.

For example: If we want to reach the generalization "all men are mortal" then how do we solve this problem by seeking to reach the generalization "all men consist of biological cells"?

One does not solve the problem that way. One solves the problem by tracing each generalization back to perceptual observation. One observes that men are alive, that other living organisms are alive, and that all known things that have died were once alive. That men consist of biological cells is a scientific discovery that provides additional supporting evidence that can be used to support the generalization.

The latter generalization would have to be reached by induction, too. Don't get me wrong, discovering a causal mechanism is great and it's a lot better than attempting to induce by enumeration. But in my opinion this approach shifts the problem to another place without solving it.

I disagree. Betsy's analysis solves it beautifully by tracing induction back to generalizations tied to the Law of Identity, the Law of Causality, and perceptual observation: "This is the source of inductive certainty. If and when you can find a cause which reduces a generalization about a thing and its properties or actions to an identity, then your generalization is as certain as A is A."

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3. Do we need to look for, and find, any underlying causal mechanisms?

In my view, only #3 is necessary and sufficient to solve the Problem of Induction.

But doesn't finding a causal mechanism itself require an induction? For example: If we want to reach the generalization "all men are mortal" then how do we solve this problem by seeking to reach the generalization "all men consist of biological cells"? The latter generalization would have to be reached by induction, too. Don't get me wrong, discovering a causal mechanism is great and it's a lot better than attempting to induce by enumeration. But in my opinion this approach shifts the problem to another place without solving it.

We don't do induction in order to "reach a generalization." We do induction to discover and identify causes. Identifying causes is the purpose of induction.

The process of finding causal mechanisms is the process of induction.

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3. Do we need to look for, and find, any underlying causal mechanisms?

In my view, only #3 is necessary and sufficient to solve the Problem of Induction.

But doesn't finding a causal mechanism itself require an induction? For example: If we want to reach the generalization "all men are mortal" then how do we solve this problem by seeking to reach the generalization "all men consist of biological cells"? The latter generalization would have to be reached by induction, too. Don't get me wrong, discovering a causal mechanism is great and it's a lot better than attempting to induce by enumeration. But in my opinion this approach shifts the problem to another place without solving it.

We don't do induction in order to "reach a generalization." We do induction to discover and identify causes. Identifying causes is the purpose of induction.

The process of finding causal mechanisms is the process of induction.

I thought I understood what you stated in Post 7: "If and when you can find a cause which reduces a generalization about a thing and its properties or actions to an identity, then your generalization is as certain as A is A." But the last sentence above is not clear to me. Are you implying that there are valid generalizations that do not identify causal processes or that there are some generalizations that are not reached by induction?

If one billiard ball strikes another, I observe that the first billiard ball caused the second to move. The movement of the first is the cause of the movement of the second. What generalization have I used? What induction have I done here? The generalization would be "all billiard balls that collide with a stationary billiard ball will make them move." The generalization is a statement about the balls' properties and actions that pertain to the identity of the balls. Thus, the induction (how one arrived at the generalization) is valid.

Am I wrong?

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But doesn't finding a causal mechanism itself require an induction? For example: If we want to reach the generalization "all men are mortal" then how do we solve this problem by seeking to reach the generalization "all men consist of biological cells"? The latter generalization would have to be reached by induction, too. Don't get me wrong, discovering a causal mechanism is great and it's a lot better than attempting to induce by enumeration. But in my opinion this approach shifts the problem to another place without solving it.

We don't do induction in order to "reach a generalization." We do induction to discover and identify causes. Identifying causes is the purpose of induction.

The process of finding causal mechanisms is the process of induction.

I thought I understood what you stated in Post 7: "If and when you can find a cause which reduces a generalization about a thing and its properties or actions to an identity, then your generalization is as certain as A is A." But the last sentence above is not clear to me. Are you implying that there are valid generalizations that do not identify causal processes or that there are some generalizations that are not reached by induction?

No, I was challenging the common idea that the process of induction is performed in order to reach or validate generalizations. That only leads to a more fundamental issue: Why do we want to reach or prove generalizations?

Observe that we perform various actions of consciousness to in order to avoid dangers, gain values, and live. The purpose of perception is to identify the nature of particular entities. The purpose of concept formation is to identify the similar natures of similar things. The purpose of induction is to identify causes in individual concrete cases ("Why won't my car start?) and similar actions and states of similar things ("All men are mortal.")

I see a problem when someone thinks induction is about "reaching a generalization" and then wonders what causality has to do with it. He's focusing on one aspect of the process of induction without seeing why we engage in the process in the first place. In answer to that, I wrote what I wrote in order to restore the proper context for an understanding of what induction is and why we do it.

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If one billiard ball strikes another, I observe that the first billiard ball caused the second to move.

No you don't. You observe the first ball moving , then the balls touching, and then the second ball starting to move.

The movement of the first is the cause of the movement of the second.

No it's not. The cause of the movement of the second is the nature of the second ball which allows it to begin to move when it is struck with a certain force by the first ball. If the second ball were made of Jell-o or some other material that absorbed the force, it would not have moved. If it were made of fragile glass, it would have shattered.

The cause of an action is always the nature of the thing that acts. In the billiard ball case, we have two things acting and interacting, but the principle is the same.

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I see a problem when someone thinks induction is about "reaching a generalization" and then wonders what causality has to do with it. He's focusing on one aspect of the process of induction without seeing why we engage in the process in the first place. In answer to that, I wrote what I wrote in order to restore the proper context for an understanding of what induction is and why we do it.
I do not see "why we engage in the process in the first place" (emphasis mine). Different people can perform the same action for different reasons. I think it makes sense to explicitly distinguish between a process of consciousness and the product of such a process. In this context I would distinguish between the process of generalization ("generalization" being another word for "induction") and the generalization (i.e. a general statement such as "All men are mortal" or "2+2=4"). Are you claiming that one should perform each generalization for the purpose of identifying causes? What about a general statement like "2+2=4"?

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If one billiard ball strikes another, I observe that the first billiard ball caused the second to move.

No you don't. You observe the first ball moving , then the balls touching, and then the second ball starting to move.

The movement of the first is the cause of the movement of the second.

No it's not. The cause of the movement of the second is the nature of the second ball which allows it to begin to move when it is struck with a certain force by the first ball. If the second ball were made of Jell-o or some other material that absorbed the force, it would not have moved. If it were made of fragile glass, it would have shattered.

The cause of an action is always the nature of the thing that acts. In the billiard ball case, we have two things acting and interacting, but the principle is the same.

Thanks for clarifying that. It's a point I should have grasped. My statement above amounted to stating that actions cause actions.

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I see a problem when someone thinks induction is about "reaching a generalization" and then wonders what causality has to do with it. He's focusing on one aspect of the process of induction without seeing why we engage in the process in the first place. In answer to that, I wrote what I wrote in order to restore the proper context for an understanding of what induction is and why we do it.

I do not see "why we engage in the process in the first place" (emphasis mine). Different people can perform the same action for different reasons. I think it makes sense to explicitly distinguish between a process of consciousness and the product of such a process. In this context I would distinguish between the process of generalization ("generalization" being another word for "induction") ...

That's what I'm objecting to. Generalization is not synonymous with induction and assuming it is leads to some serious errors.

To indicate why, compare the linguistic analysis approach to understanding concepts to Ayn Rand's. The Linguistic analysts hold that concept formation is using words and then proceeed to look at how people use words. Ayn Rand's approach to was investigate what concepts are and the function they serve in human life. The result is an understanding of the nature of concepts and why we form them as well as a validation of the process of concept formation.

If we are ever going to understand induction, we have to understand what the process of induction is, why we do it, and the human need it serves. Until we do that, we cannot validate the process and solve the Problem of Induction. All we do is play games with generalizations just as the linguistic analysts play games with words.

and the generalization (i.e. a general statement such as "All men are mortal" or "2+2=4"). Are you claiming that one should perform each generalization for the purpose of identifying causes?

It is not an issue of "should." Identifying causes is the essence of the process of induction and the only valid reason for ever doing induction.

What about a general statement like "2+2=4"?

That's a causal statement. It says that adding two units of a concept to another two units of a concept causes you to have four units of the concept. It's an answer to questions like "How come I have four rabbits? All I used to have were two: a male and a female."

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What about a general statement like "2+2=4"?

That's a causal statement. It says that adding two units of a concept to another two units of a concept causes you to have four units of the concept. It's an answer to questions like "How come I have four rabbits? All I used to have were two: a male and a female."

Yes, but the cause of the additional rabbits is different than "2 billiard balls + 2 billiard balls = 4 billiard balls." I know this; I've tried it... and the billiard balls just lie there.

By "cause," you're saying that the cause of your counting 5 units is the addition of 3 units to your original stack of 2 units, right? Not the specific cause of procreation in rabbits, vs. carrying in and dropping billiard balls on the table next to the the initial set of billiard balls. So the "cause" you're talking about is what you induce when you observe the result of the addition of y units to an existing set of x units. N'est-ce pas? Because I think that some people (ok, me, on occasion) are misunderstanding which "cause" you are talking about. It's the cause of the inductive statement: "2+2=4," "a car won't run without gas," "people who live in glass houses shouldn't throw stones... or walk around in the nude," "licking a frozen flagpole is a really bad idea."

Right? I think that the clear definition of what you mean by "cause" and "causality," in this context, is critical. In the blood type example, it's not which saccharides are on the end of the sugar molecule that turns out to be the cause of a red blood cell being classified as Type A, but the observed cause that adding a second blood sample to the first we're calling "Type A" results in clumping, so we call it "Type B." We get a consistent result even if we don't yet know exactly why; what it is in the blood that makes it react this way.

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What about a general statement like "2+2=4"?

That's a causal statement. It says that adding two units of a concept to another two units of a concept causes you to have four units of the concept. It's an answer to questions like "How come I have four rabbits? All I used to have were two: a male and a female."

Yes, but the cause of the additional rabbits is different than "2 billiard balls + 2 billiard balls = 4 billiard balls." I know this; I've tried it... and the billiard balls just lie there.

In one sense -- adding two additional units -- they are the same. In another sense -- how there came to be two additional units -- they are different. I just used the rabbit example to humorously make the point that "2 + 2 = 4," like all generalizations, is really a statement about causality. "2 + 2 = 4" means that if we have two units and add two units it causes us to have four units.

By "cause," you're saying that the cause of your counting 5 units is the addition of 3 units to your original stack of 2 units, right?

Right!

Not the specific cause of procreation in rabbits, vs. carrying in and dropping billiard balls on the table next to the the initial set of billiard balls. So the "cause" you're talking about is what you induce when you observe the result of the addition of y units to an existing set of x units.

Correct.

Because I think that some people (ok, me, on occasion) are misunderstanding which "cause" you are talking about. It's the cause of the inductive statement: "2+2=4," "a car won't run without gas," "people who live in glass houses shouldn't throw stones... or walk around in the nude," "licking a frozen flagpole is a really bad idea."

Right?

Right. (I should know. I do live in a glass house. B) )

I think that the clear definition of what you mean by "cause" and "causality," in this context, is critical. In the blood type example, it's not which saccharides are on the end of the sugar molecule that turns out to be the cause of a red blood cell being classified as Type A, but the observed cause that adding a second blood sample to the first we're calling "Type A" results in clumping, so we call it "Type B." We get a consistent result even if we don't yet know exactly why; what it is in the blood that makes it react this way.

It is important to realize that causes exist on many different levels. If we need to know why something happened, we do induction in order to find the cause. We can then continue the process by seeking the cause of the cause.

Why do we now have four rabbits? Because we added two rabbits. Where did the two new rabbits come from? .... etc.

or

Why was the transfusion fatal? Because the blood clumped. Why did the blood clump? Because when you combine certain different types of blood it clumps. What causes different types of blood to clump? An antigenic reaction. What causes the antigenic reaction? ...etc.

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"2 + 2 = 4" means that if we have two units and add two units it causes us to have four units.

I'm having difficulty reconciling "if we have two units and add two units it causes us to have four units" with the fact that entities and not actions are causes. If the "it" in your statement refers to the action "addition," then aren't you stating that the action is the cause? You seem to reinforce that here:

By "cause," you're saying that the cause of your counting 5 units is the addition of 3 units to your original stack of 2 units, right?

Right!

Again, addition being an action, you appear to be stating that an action, not an entity, is a cause.

Would it be correct to say that the nature of the (abstract) entity "number" causes there to be more units? Or is there something else I'm not grasping in this case? It was relatively easy for me to understand the billiard ball motion example; not so here.

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What about a general statement like "2+2=4"?

That's a causal statement. It says that adding two units of a concept to another two units of a concept causes you to have four units of the concept. It's an answer to questions like "How come I have four rabbits? All I used to have were two: a male and a female."

Yes, but the cause of the additional rabbits is different than "2 billiard balls + 2 billiard balls = 4 billiard balls." I know this; I've tried it... and the billiard balls just lie there.

------------

Have you checked to see if it's a female ball and a male ball? The rabbit example wouldn't add up with two males or two females.

B):)

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"2 + 2 = 4" means that if we have two units and add two units it causes us to have four units.

I'm having difficulty reconciling "if we have two units and add two units it causes us to have four units" with the fact that entities and not actions are causes. If the "it" in your statement refers to the action "addition," then aren't you stating that the action is the cause? You seem to reinforce that here:

By "cause," you're saying that the cause of your counting 5 units is the addition of 3 units to your original stack of 2 units, right?

Right!

Again, addition being an action, you appear to be stating that an action, not an entity, is a cause.

Would it be correct to say that the nature of the (abstract) entity "number" causes there to be more units? Or is there something else I'm not grasping in this case? It was relatively easy for me to understand the billiard ball motion example; not so here.

But wouldn't the fuller statment be---If I have two units (in a certain place) and I add two units (to that place), my adding (or putting in) is the cause of my having four units (in that place).

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