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Thoughts on my view of induction and deduction?

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... [my professor] buys into the argument that because induction can't "predict the future" (which is a claim induction REALLY doesn't make), induction is a system of probabilities.

I see two possible ways that a version of Induction could be justified. Both of them involve probabilities.

1. You could base it on my version of the Law of Causality:

The same causes produce the same {probability distribution over possible} effects [regardless of when the event occurs, or where, or in what orientation, or how fast it is moving (below light-speed), or in which direction it is moving].

So, if you repeat the same experiment enough times then the relative frequencies of the outcomes should approach limits which are the true probabilities of the outcomes.

2. You could base it on Bayes' Theorem:

http://en.wikipedia.org/wiki/Bayes%27_theorem

Suppose you plan to do an experiment and partition the possible outcomes into N sets (events) numbered: 1, 2, 3, ..., N. And assume that any unexpected outcomes are thrown into event N.

Before executing the experiment, you estimate how likely each event is. Setting: E1 = estimated probability of event 1; ..., EN = estimated probability of event N. Also choose a maximum acceptable risk R that you will make an incorrect "induction".

Now you do the experiment and get event K as the outcome.

Then combining Bayes' theorem and a worst-case analysis, you can conclude that the true probability of event K was greater than or equal to:

R*EK/(1 - EK + R*EK)

(I can provide the calculation, if anyone is interested.)

Much better lower bounds on the true probability may be obtainable, if you can use knowledge specific to the problem and thus improve on the worst-case analysis.

Edited by Free Thinker
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1. You could base it on my version of the Law of Causality:

The same causes produce the same {probability distribution over possible} effects [regardless of when the event occurs, or where, or in what orientation, or how fast it is moving (below light-speed), or in which direction it is moving].

So, if you repeat the same experiment enough times then the relative frequencies of the outcomes should approach limits which are the true probabilities of the outcomes.

This is more or less the right approach, except (1) Speed matters and (2) You should not make these other variables axiomatic -- i.e. if it turns out that there is a fact of existence that depends on the location of the event, you should not put that fact utterly out of the reach of empirical study.
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As to the elevator button, suppose one has knowledge of the causal connection, then is the inference inductive? Also, (1) what is your definition of 'causal connection'? and (2) Would one avoid having made an unwarranted inference just by supposing that there is some causal connection without specifying what it is?
Let me address this by reviewing the basics of my understanding of induction as explained in Peikoff’s lectures titled, “Induction in Philosophy and Physics” (of which I have completed only about 20%). I stress that this is my understanding only. Obviously, I am not speaking for Peikoff or Objectivism.

Forgive the redundancy. I know much of this has been covered, but to get to point 8, I really don't want to leave anything out.

1) Induction is the process of reaching generalizations. It is the process of moving from the observed to the unobserved, of making inferences from some members of a class to all. It is the primary means of moving past the perceptual stage to the conceptual stage. As such, it is the essence of human cognition.

We need not look for a justification for induction any more than we need a justification for reason. The validity of both is a given. What we need to know is the proper method.

2) A generalization is a proposition that ascribes a characteristic to every member of an unlimited class, however it is positioned in space and time. It is of the form, “All S is P”.

3) Generalizations, like knowledge in general, are hierarchical. Some are more advanced and depend on earlier, simpler generalizations.

The simplest generalizations, called first level generalizations, are derived directly from perceptual observations and are self-evident. Here is a crucial point: As a child, you first grasped the concept of cause through your own efficacy and direct experience.

For instance, as a child, you learned by direct perception that if you push a ball on a flat surface, it will roll. You formed the first-level generalization that pushed balls will roll on flat surfaces.

4) There are many such first-level generalizations, and they form the foundation for all of our science. All other generalizations must be reducible to the first-level generalizations that are self-evident through perception.

5) To reach a valid generalization, one must identify the causal connection that accounts for the fact that “all S is P”. A causal connection is an instance of the law of causality, i.e. it is an instance of observing how the identity of an entity causes it to behave in a certain fashion or possess certain characteristics.

In the case of a pushed ball, it is self-evident why the ball rolls: it is inherent in the identity of the ball and the flat surface.

6) Knowledge acquired by induction is always limited but nonetheless real. Limited means: capable of being further qualified. For instance, one may confront a surface so rough and a ball so heavy that one cannot cause it to roll by pushing; a greater force is required than an unassisted human can provide. This does not invalidate the earlier generalization; it merely qualifies it.

7) As another example of valid and invalid generalization, consider the white swan problem. Merely observing that all swans within one’s purview are white does not permit us to conclude that all swans everywhere are white. Since we do not know the relevance of the color of the swan’s feathers, we do not know that all other swans are white.

Contrast this with the observation that the bones of all the swans we have dissected (unfortunate swans) are hollow. If we study the aerodynamics of birds in flight, and if we understand the limitations that must exist on the weight of a swan for it to fly, we may be justified in generalizing that all Swans will have hollow bones – quite possibly based on a single dissection – because we have identified a causal connection.

8) Peikoff identifies the essence of induction as follows: Induction is measurement-omission applied to causal connections. A valid generalization is no more than the perception of cause & effect conceptualized. To solve the problem of induction, we need only grasp Rand's theory of concepts.

To answer the original question: Is the following induction: “The next time I push the button, the elevator will stop at my floor”. This becomes the question: Did you discover and identify the causal connections responsible for the elevator’s behavior and have you reduced them back to first-level generalizations? Or, as Doug suggested, are you accepting this knowledge deductively?

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Let me address this by reviewing the basics of my understanding of induction as explained in Peikoff's lectures titled, "Induction in Philosophy and Physics" (of which I have completed only about 20%).
I don't know his lectures, so I can't address how accurately you have represented Peikoff's position. I do know, however, that you've given an excellent summary of induction. Point 7 is particularly important. One point deserves a bit of amplification:
In the case of a pushed ball, it is self-evident why the ball rolls: it is inherent in the identity of the ball and the flat surface.
In addition, you can expand on that nature, by looking at notions such as "force", "gravity", "friction" and so on -- the search for "why" doesn't have to stop with the observation that it is in the nature of the ball.
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8) Peikoff identifies the essence of induction as follows: Induction is measurement-omission applied to causal connections. A valid generalization is no more than the perception of cause & effect conceptualized. To solve the problem of induction, we need only grasp Rand's theory of concepts.

As David said, this is an excellent summary of induction overall. You clearly understand this better than I do. Also, I really like point 8--there's an intriguing simplicity to the notion that induction is measurement-omission applied to causal connections.

To answer the original question: Is the following induction: “The next time I push the button, the elevator will stop at my floor”.

Strictly speaking, I would say that "The next time I push the button, the elevator will stop at my floor" is not a pure example of an inductive inference. It is a combination of a generalization ("every time I push the button, the elevator stops at that floor," or, better, "pushing the button causes the elevator to stop"), and a deduction ("thereffore, the elevator will arrive for this next push"). Compare with the equivalent, "The next baby to be born will die at some point" (which I tried to make fit your form as closely as possible). In one sense, this is just a way to state the induction that "All men are mortal." In another sense, it is deduction: "All men are mortal. The next baby born is a man. Therefore, the next baby born will die." Thus I would say that in this context, principles should not be stated as if-then clauses, because it can lead to confusion.

I say this not to nitpick or to insult your intelligence, but because I think the deductive element can easily mislead people who see the syllogism and think that induction is just another type of deduction. Also, I was motivated to explain that because it will help me understand the next part:

This becomes the question: Did you discover and identify the causal connections responsible for the elevator’s behavior and have you reduced them back to first-level generalizations? Or, as Doug suggested, are you accepting this knowledge deductively?

I agree that the first possibility is that has one identified the causal connections responsible (and traced them back to first-level generalizations, which is a useful addition to what I said). But I don't understand your alternative of "are you accepting this knowledge deductively," and I don't know how I suggested that. Could you elaborate?

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I agree that the first possibility is that has one identified the causal connections responsible (and traced them back to first-level generalizations, which is a useful addition to what I said). But I don't understand your alternative of "are you accepting this knowledge deductively," and I don't know how I suggested that. Could you elaborate?
I was referring to what you said in post 59, :

2) One need not know the particular mechanism if one knows that other humans have set up that mechanism. In that case, the conclusion that the elevator will come is based on a deduction of the form: 1) People have the ability to establish "causal connections" that serve some purpose, and 2) a person put this button in for the purpose of making the elevator arrive, therefore 3) this button causes the elevator to arrive. Of course, one would have to inductively validate the premise that "people have the ability to establish causal connections," but this is pretty easily shown (and is independent of elevators).
It was sloppy wording on my part to refer to this as "accepting this knowledge deductively". As your analysis shows, there is a combination of induction and deduction -- and I agree with your analysis of which statements belong to which processes.

Also, I really like point 8--there's an intriguing simplicity to the notion that induction is measurement-omission applied to causal connections.
I thought it was a brilliant identification on Peikoff's part.
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I was referring to what you said in post 59:

Ah, I see now. I thought you were making a distinction between valid, first-hand induction vs. invalid generalization based on correlation, when in fact you were referring to the distinction between valid, first-hand induction about elevator mechanisms vs. valid deduction from the well-known principle that buttons are designed to cause things to happen when you push them.

On rereading your post, I can say I was being obtuse. :D

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Don't worry, I'll limit my speech to goldfish size. [Thanks :D] In your example, you start with the universal in one form ("all dogs") and apply a form change to reach another universal ("any particular dog").

The first part ("all dogs") is a universal and false statement and the conclusion ("a particular dog") is also a universal and false statement.

My bad: I should have stated it as such:

[i have two dogs.]

If all of my dogs are fish, then all dogs ( mine or others' ) I come across are fish.

As I stated it originally, it didn't show a statement about my dogs leading to a statement about all [mine and others'] dogs. Restated, I believe that "all of my dogs" is specific compared to "all [mine and others'] dogs."

7) As another example of valid and invalid generalization, consider the white swan problem. Merely observing that all swans within one’s purview are white does not permit us to conclude that all swans everywhere are white. Since we do not know the relevance of the color of the swan’s feathers, we do not know that all other swans are white.

Contrast this with the observation that the bones of all the swans we have dissected (unfortunate swans) are hollow. If we study the aerodynamics of birds in flight, and if we understand the limitations that must exist on the weight of a swan for it to fly, we may be justified in generalizing that all Swans will have hollow bones – quite possibly based on a single dissection – because we have identified a causal connection.

I have a question about this part. The two examples seem highly similar to me. The first observes a trait common to all known swans, as does the second. It seems to me that both would be valid inductions, though their conclusions may or may not be correct.

My question is: does the second really identify a causal relationship any more than the first? The bones example does show why having hollow bones would be beneficial to swans, but it doesn't seem to say why having hollow bones is a necessary effect of being a swan. A valid generalization, as used here, also requires a vast amount of knowledge; valid inductions would thus be impossible to cavemen - how would they gain knowledge?

Similarly, would the white swan example be valid if someone observed that white swans camouflaged better in a snowy environment - avoiding predators?

Couldn't it at least be said that the white swan example is valid within a particular context of knowledge?

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[i have two dogs.]

If all of my dogs are fish, then all dogs ( mine or others' ) I come across are fish.

Yes, with that change that would have an inductive form. (I hesitate to call it induction since your initial observation doesn't even hold for the specific instances, but it does go from specific to general.)

My question is: does the second really identify a causal relationship any more than the first? The bones example does show why having hollow bones would be beneficial to swans, but it doesn't seem to say why having hollow bones is a necessary effect of being a swan.

Well, in AisA's defense, he did refer to "the limitations that must exist on the weight of a swan for it to fly." A solid understanding of the immense benefit of hollow bones, coupled with the knowledge that only the fittest animals survive, allows one to generalize about all swans, since any swan with solid bones would be decidedly outcompeted, and thus would not have passed on its genes.

A valid generalization, as used here, also requires a vast amount of knowledge; valid inductions would thus be impossible to cavemen - how would they gain knowledge?
Well, the context required depends on how far from a first-level induction it is. First-level inductions (pushing a ball makes it roll, fire is hot, rain makes you wet) can grasped implicitly. Animals do, for instance. This is why Pavlov's dogs salivated--they learned that a bell ringing causes food, within the limits of their understanding.

Similarly, would the white swan example be valid if someone observed that white swans camouflaged better in a snowy environment - avoiding predators? Couldn't it at least be said that the white swan example is valid within a particular context of knowledge?

Possibly--for instance, that is why it is reasonable to say all polar bears are white. We know why the dark ones don't exist. (Note that the conclusion would be therefore implicitly qualified with, "in the north pole" even if they weren't called polar bears.) However, unless you could show that swans only lived where it was predominantly white, that would not be justified. (Pepper moths, for instance, are known to be two different colors for exactly this reason.)

One broad point: just because there are some instances in which induction is certain doesn't mean there can't be inductive conclusions that are tentative. Some of these examples might be in that stage for a while, as the possible contravening causes get eliminated one by one. Without the explanation of evolution, for instance, the mere fact of hollow bones in some swans would not justify the conclusion that all swans have hollow bones (but I am not a biologist, either).

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The bones example does show why having hollow bones would be beneficial to swans, but it doesn't seem to say why having hollow bones is a necessary effect of being a swan.
I think a more elaborate account is necessary. There is a known basis for the fact that swans have physical similarities, which is that they have a particular genetic makeup which is the physical vector of swan-identity. That is why when two swans mate, the offspring is a swan and not a bear. Someone else can elaborate on the details of how a particular gene sequence causes the creation of certain proteins in an animal's development, and what that has to do with tails, scales and color: the point is, there's no divine intervention, and the best physical explanation for the nature of swans is based on something about DNA. Then you have to ask why swan DNA is the way it is, with respect to hollow bones and color. Color is something that varies a lot across animals, and is widely associated with species. That's something that's in our knowledge context -- don't leap to hasty generalizations about color. Heck, look at elephants -- only two species of elephant, and they're different colors. Having hollow bones is a fundamental evolutionary fact about birds, so you will not find some species of swan that suddenly develops big blocky cow bones. That doesn't mean that a remote descendant of a swan couldn't have such a mutation, some 50 million years in the future -- but that would not be a swan. A more detailed study of how color vs. bone thickness is controlled at the genetic level would no doubt shed great light on why animals can change their color more easily than they can change whether they have tails or scales.
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Color is something that varies a lot across animals, and is widely associated with species. That's something that's in our knowledge context -- don't leap to hasty generalizations about color.

This is an excellent point, one I had thought of earlier (but not with nearly David's clarity here). Not only is there little evidence to suggest all swans are white because some are, it also contradicts everything we know about animals, in that color can vary wildly across species, and even within a species (dogs or cats, for instance). You can't drop all the context and declare, with no evidence, that swans are an exception to that.

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... regardless of when the event occurs, or where, or in what orientation, or how fast it is moving (below light-speed), or in which direction it is moving.

This part of the Law of Causality is also known as the Principle of Special Relativity. Each part of it strengthens the Law of Causality when used as a means of performing Induction:

"when the event occurs" allows you to generalize from observations at one time to situations which might arise at another time.

"where" allows you to generalize from observations at one place to situations at another place.

"in what orientation" allows you to generalize from observations with the apparatus pointing North (for example) to situations with the apparatus pointing Southeast (say).

"how fast it is moving (below light-speed)" allows you to generalize from observations done on Earth to situations on a spacecraft traveling to Mars at a high speed.

"in which direction it is moving" allows you to generalize from observations done on a spacecraft moving toward the Sun (say) to situations on a spacecraft moving away from the Sun.

The Principle of Special Relativity (due to Albert Einstein) is one of the greatest results of induction ever achieved. In my opinion, it is the culmination of informal induction; and it provides the postulate from which formalized induction can henceforth proceed.

... except (1) Speed matters and (2) You should not make these other variables axiomatic -- i.e. if it turns out that there is a fact of existence that depends on the location of the event, you should not put that fact utterly out of the reach of empirical study.

It is interesting that you who purport to be a proponent of induction would deny the result of such a great induction without any evidence whatever.

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... regardless of when the event occurs, or where, or in what orientation, or how fast it is moving (below light-speed), or in which direction it is moving.

This is not the philosophical law of causality at all. For instance, why do you take into account the speed, but not the direction? Scientific reasons are irrelevant, since the law of causality is a philosophical principle, which by its nature precedes science and must not require specialized equipment. That's why the law of causality simply says that things must always and everywhere act in accordance with their nature.

Furthermore, we know that some causes are dependent on the location: the temperature at which water boils, for instance. The actions of a compass are dependent on orientation as well as location.

It is interesting that you who purport to be a proponent of induction would deny the result of such a great induction without any evidence whatever.

I don't think David doubts the result of special relativity (at any rate, I certainly don't). But regardless how valuable it has proved in science, it does not make it a philosophical claim.

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It is interesting that you who purport to be a proponent of induction would deny the result of such a great induction without any evidence whatever
In what way have I denied the results of "the world's (second) greatest induction"? If you're referring to part 1 of my statement, you've forgotten that time-dilation effects are empirically observed, at well below the speed of light (which is explained by the theory of relativity, thus I assume you simply misspoke). If you're referring to the second part, the theory of relativity does not address normative principle of the philosophy of science, so again you are way off the mark here. There are many facts which point to the conclusion that I offered. First, you would arrive at my conclusion by induction from other such relations, e.g. science does not state that a biological law pertaining to number of legs can never be overturned by observation; science does not state that a physical law pertaining to current flow cannot be empirically invalidated with a battery as the power source; ad nauseum. What you're advocating is the denial of the scientific method: you are saying that certain scientific theories are too good to be false, and that these principles are above refutation and scientific inquiry. Your claim reduces to saying that no matter what observation of reality is made, no matter how compelling that observation, if it contradicts your a priori presumption of time-invariance, the facts of reality must be denied because they would contradict what is for you the primary principle, a methodological supposition.

Second, it is not self-evident that physical laws are space/time-invariant and orientation-invariant. The concept of causation does not depend on those assumption, even if they turn out to be correct. In the conceptual hierarchy, these hypothesized restrictions on the nature of reality are higher order conclusions, one reached by first establishing the concept of causality (which is fundamental to science, inter alia). By elevating space-time invariance to the status of an undeniable absolute, your position claims that were solid experimental counterevidence uncovered, you would have to reject the concept of causality (or reject existence, but I assume you would take the less radical step). OTOH, if you consider principles such as space-time invariance to be empirical theories subject to testing and modification, then in the face of suitable evidence a counterexample would not force the rejection of causality, and would affirm that the fundamental goal of science is the explanation of the nature of reality.

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Hunterrose, did you understand the answers provided by Doug and David? They were excellent.

Valid generalizations beyond the first level do indeed require a vast amount of knowledge. Peikoff gives the example of what Galileo had to learn in order to induce that horizontal motion (of, say, a ball rolling on a flat surface) is constant while vertical (free fall) motion is accelerated. He had to grasp the concept of friction, what causes it, and how to minimize it in his experiments, which meant that he had to learn about surface textures and finishes; he had to develop the ability to push a ball with a repeatable force; he had to develop better ways of measuring distances and recording elapsed time. I don't recall the full list Peikoff came up with, but it clearly made the point.

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The same causes produce the same probability distribution over possible effects regardless of when the event occurs, or where, or in what orientation, or how FAST it is moving (below light-speed), or in which DIRECTION it is moving.

... why do you take into account the speed, but not the direction?

Hello, are you paying attention? I added emphasis on the words "FAST" and "DIRECTION" to aid the clueless.

Scientific reasons are irrelevant, since the law of causality is a philosophical principle, which by its nature precedes science and must not require specialized equipment. That's why the law of causality simply says that things must always and everywhere act in accordance with their nature.
I was under the impression that philosophy was supposed to apply to EVERYTHING. And last time I checked, everything includes science. Also notice that I did not say that specialized equipment was required for causality to apply.

And what do you mean by "always and everywhere", if not at all times, places, orientations, and velocities (as I said in different words)?

And what does it mean to "act in accordance with their nature", if not that it produces the same effects in the same circumstances (as I said in different words)?

The reason that I chose a different wording than the Objectivist tradition is that I was trying to be more precise and clear.

Furthermore, we know that some causes are dependent on the location: the temperature at which water boils, for instance. The actions of a compass are dependent on orientation as well as location.

The temperature at which water boils depends on the local pressure, not on the location. A compass responds to the local magnetic field, not to a particular orientation (direction) or location in space.

But regardless how valuable [special relativity]has proved in science, it does not make it a philosophical claim.

*I* am making the philosophical claim that to make sense of causality we must incorporate special relativity into it.

... except (1) Speed matters ...

In what way have I denied the results of "the world's (second) greatest induction"? If you're referring to part 1 of my statement, you've forgotten that time-dilation effects are empirically observed, at well below the speed of light (which is explained by the theory of relativity, thus I assume you simply misspoke).

Where did *I* say "the world's (second) greatest induction"? I only spoke of a great induction which was the culmination of informal induction and the basis of formalized induction. And what do you mean by "second"? And what is first?

Time dilation is not a violation of Relativity; it is a consequence of it. A co-moving observer does not see the time dilation; rather to him it appears that the things which are at rest (thus moving relative to him) are suffering time dilation. Those ignorant of Relativity think that this is a contradiction, but they are wrong. It would only be a contradiction IF the simultaneity of events were absolute, but it is not.

... except ... (2) You should not make these other variables axiomatic -- i.e. if it turns out that there is a fact of existence that depends on the location of the event, you should not put that fact utterly out of the reach of empirical study.

... you ... deny the result of such a great induction without any evidence whatever.

What you're advocating is the denial of the scientific method: you are saying that certain scientific theories are too good to be false, and that these principles are above refutation and scientific inquiry. Your claim reduces to saying that no matter what observation of reality is made, no matter how compelling that observation, if it contradicts your a priori presumption of time-invariance, the facts of reality must be denied because they would contradict what is for you the primary principle, a methodological supposition.

If your denial of the Principle of Special Relativity were based on evidence, then it would make sense to consider it. But since your denial is ARBITRARY, good Objectivists must disregard it.

Second, it is not self-evident that physical laws are space/time-invariant and orientation-invariant. The concept of causation does not depend on those assumption, even if they turn out to be correct.

I did not say that it was self-evident. Nevertheless, it is true and one of the greatest inductions.

If you merely said "The same causes produce the same effects." without qualification, then someone could interpret this as a mere tautology lacking any meaning because only one event of causation would be encompassed by it.

The clause "regardless of when the event occurs, or where, or in what orientation, or how fast it is moving (below light-speed), or in which direction it is moving" identifies a ten-parameter family of events for which the same effects will result, if the same causes are present. This gives the Law of Causality a real meaning.

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Where did *I* say "the world's (second) greatest induction"? I only spoke of a great induction which was the culmination of informal induction and the basis of formalized induction.
That's right: if you disagree with the ranking, that's fine and really not important to the point.
And what do you mean by "second"?
"Second" refers to a point on some scale, which has discrete values. You might be more familiar with the mathematical expression "number 2".
And what is first?
Newton's laws of mechanics.
Time dilation is not a violation of Relativity; it is a consequence of it.
Indeed, I said that. Speed matters. You are still wrong about speed not mattering.
If your denial of the Principle of Special Relativity were based on evidence, then it would make sense to consider it. But since your denial is ARBITRARY, good Objectivists must disregard it.
You are on the verge of foaming: please stop. Try looking for the place where I denied the theory of special relativity. It will be an infinite, pointless search, since I said no such thing. Stop trying to change the topic.
I did not say that it was self-evident. Nevertheless, it is true and one of the greatest inductions.
Then why are you unwilling to leave the truth of space-time invariance to be a testable hypothesis?
The clause "regardless of when the event occurs, or where, or in what orientation, or how fast it is moving (below light-speed), or in which direction it is moving" identifies a ten-parameter family of events for which the same effects will result, if the same causes are present. This gives the Law of Causality a real meaning.
I don't see how. Taking space-time invariance to be an absolute and therefore unrefutable axiom means that if some facts were to disprove an aspect of that hypothesis, you would have to reject causality (by positing that the event had no cause, for example it was only a coincidence that there was some apparent cause) or reject reality (it didn't really happen).
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Hello, are you paying attention? I added emphasis on the words "FAST" and "DIRECTION" to aid the clueless.

Unfortunately, jrs has decided that he is exempt from the rules of debate etiquette, and that he is free to substitute sarcasm and insult for reason. Since I find can nothing offensive in my post to him, nor any of my posts (some to people more knowledgeable than me, and some to less knowledgeable) that would warrant this type of response, I will no longer respond to him.

Because others reading this thread may have disagreed with my dismissal of jrs' Law of Causality, or wondered why I said what I did, I will expand on my critique of it in a later post.

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In my previous post, I promised to follow up on why I disagree with jrs' preferred formulation of the Law of Causality. It naturally appeals to scientists because it states a truism they would agree with--in fact, when I first read it back in April, I agreed with it myself. It is only recently that I have begun to appreciate the subtle error in it.

This is his formulation of the Law of Causality:

The same causes produce the same probability distribution over possible effects regardless of when the event occurs, or where, or in what orientation, or how FAST it is moving (below light-speed), or in which DIRECTION it is moving.

This is mistaken on two major points: first, that causes produce a "probability distribution" of possible effects, and second, because it states invariance under time, place, speed, orientation, and direction. I will leave disagreement with the first for later, and concentrate on the second.

Since the law of causality is pre-science, it cannot involve or make reference to scientifically discovered principles. For instance, how do we know, as philosophers, that causes are time-invariant, or direction-of-travel-invariant? This is armchair-philosophizing--dictating to the universe what circumstances may and may not be relevant. To illustrate this, consider a person who had decided on jrs' law of causality, but had not yet discovered any modern science. First, he heats some water over a two-log fire for 5 minutes, and it boils. "A-ha!" he says. "Since I know that the same causes produce the same effects regardless of where it is, I know this water will boil with the same amount of heat no matter where it is." Then when his friend on the mountain can't get the water to boil, he is forced to reject his friend's result because that would violate his law of causality. However, a scientist operating under the correct formulation, which does not make conclusions about location, would realize the same causes must not be in effect, would explore these new causes, and would discover the principle of atmospheric pressure and the role it plays in boiling water.

You can construct a similar scenario for a compass, which is affected by orientation (in fact, that is its whole purpose). At this point, you might be inclined to conclude that my examples are silly, but there is a more real-world example in jrs' formulation: the explicit accounting for relativistic effects. If jrs lived in the nineteenth century, his version would necessarily not contain any qualification about "below light speed." Thus when relativistic effects were proposed and then verified, he would have to either 1) reject them outright, or 2) modify his statement. (DavidOdden's post is an excellent summary of this point.) A properly formulated metaphysical principle is timeless, and does not need qualification as science develops.

For these reasons, the Objectivist law of causality simply states that actions are caused by entities, and the action is therefore determined solely by the nature of the entities involved. It does not specify which entities are involved in any given case, nor does it limit what the action can be or what it is affected by. And, of course, it applies equally below light speed and above it.

Edited by dougclayton
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You are still wrong about speed not mattering.

Can you describe an observation or experiment which would allow you to discover anything about your absolute speed (other than that it is below light-speed)?

Take, for example, the reciprocal electrodynamic action of a magnet and a conductor. The observable phenomenon here depends only on the relative motion of the conductor and the magnet, whereas the customary view draws a sharp distinction between the two cases in which either the one or the other of these bodies is in motion.

.....

Examples of this sort, together with the unsuccessful attempts to discover any motion of the earth relatively to the "light medium," suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest. They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the "Principle of Relativity") to the status of a postulate, ...

Try looking for the place where I denied the theory of special relativity.

Part of what Einstein is saying is that one's absolute speed does not matter. This contradicts what you said.

Then why are you unwilling to leave the truth of space-time invariance to be a testable hypothesis?
First, it has already been exhaustively tested. If you think that you have a counter-example, bring it forth.

Have you now changed your position to say that all inductions are to be taken as uncertain?

You also seem to be implying that anything which has been incorporated into the Objectivist axioms and their corollaries (such as the Law of Causality) is beyond the reach of reason and science. Is that what you mean?

Taking space-time invariance to be an absolute and therefore irrefutable axiom means that if some facts were to disprove an aspect of that hypothesis, you would have to reject causality (by positing that the event had no cause, for example it was only a coincidence that there was some apparent cause) or reject reality (it didn't really happen).

I did not say anything about it being irrefutable. I just said that it should be incorporated into the Law of Causality, because otherwise the Law of Causality is too vague to be meaningful.

... For instance, why do you take into account the speed, but not the direction?

Unfortunately, jrs has decided that he is exempt from the rules of debate etiquette, and that he is free to substitute sarcasm and insult for reason. Since I find can nothing offensive in my post to him, ... I will no longer respond to him.

I hope that you will appreciate that my lapse of good manners was caused by anger that you had accused me of not taking the direction of motion into account while your own quotation from me clearly shows that I DID take it into account.

And while we are talking about good manners -- Is it good manners to alter my name (to "jroberts", which is incorrect) in your quotation from me in your next post (#94)?

However, a scientist operating under the correct formulation, which does not make conclusions about location, would realize the same causes must not be in effect, would explore these new causes, and would discover the principle of atmospheric pressure and the role it plays in boiling water.

I think that you have this backward. If location does not matter, then one must search for another cause to explain the fact that water boils more readily in the mountains than at the sea shore. Searching, one may find out about atmospheric pressure.

If you think that location does matter, then you will rest content with the inexplicable "fact" that water boils at a lower temperature at some places than at others.

If jrs lived in the nineteenth century, his version would necessarily not contain any qualification about "below light speed."

Before Einstein, the laws of Electromagnetism were more complex and confused because they tried to account for the motion of the observer and substances (dielectrics and conductors) using the incorrect Galilean transformation instead of the Lorentz transformation.

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Can you describe an observation or experiment which would allow you to discover anything about your absolute speed (other than that it is below light-speed)?
Since you persist in ignoring what I actually said and also seem to have forgotten what you said regarding speed, I interpret this tangential question as a way of granting that your first statement about speed was in error, without explicitly saying "Oops, I meant something else". So the speed question is clearly closed.
First, it has already been exhaustively tested. If you think that you have a counter-example, bring it forth.

Have you now changed your position to say that all inductions are to be taken as uncertain?

The term "exhaustively" means "all cases": similarly, "This account exhausts the possibilities" means that all (which means all) of the possibilities have been checked. I dunno if you're aware of this, but it is not possible to exhaustively test all situations where space-time invariance might hold. Just as Newton's law of gravity was only empirically tested in a small range of cases (so, not in the range of the massively tiny or the range of the massively massive), space-time invariance has been tested empirically in a small range of the possible contexts. Within that context, it is well tested, but even then, not exhaustively. Perhaps "extensively" would be a better term. Or perhaps you were thinking that "exhaustively" means "so much that I would be exhausted if I had to do this myself".

I do not need to provide any counterexample to space-time invariance to know that it is epistemologically totally wrong to hold that it is the fundamental axiom, that it trumps existence. I would be quite happy if it turns out to be a fact; but unlike you, I am willing to take space-time invariance to be a scientific discovery that is subject to testing -- which means, possible falsification -- and I do not take it to be a rationalist's religious principle. If you were a Popperian, I would chide you for failing to remember that you are supposed to abjure untestable claims.

You also don't seem to understand what "certain" means. I will say, though, that Special Relativity does not rise to the status of "certain" precisely because it has not been tested at enough times (for example). The claim that physical law (the nature of the universe) is time invariant -- for example, conservation of charge -- has been widely tested and verified in the modern era, but remains (and will forever remain) untested for those first however-many nanoseconds of the universe. Since there are reasons to think that early time might matter, we cannot conclude that conservation of charge describes a fact of the universe at that times. See Peikoff's discussion of the relationship between "possibility of an alternative" in relation to "certainty".

I did not say anything about it being irrefutable.
You have a habit of not saying what you mean. By now, you have enough reasons to discard your statement of Causality. Space-time invariance is not part of the definition of the concept of causality. With that further bit of info, I think you ought be able to see how space-time invariance is conceptuallty related to causality.
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Hunterrose, did you understand the answers provided by Doug and David? They were excellent.

...somewhat :P

Well, the context required depends on how far from a first-level induction it is. First-level inductions (pushing a ball makes it roll, fire is hot, rain makes you wet) can grasped implicitly.

One question would be how can one know what level a desired induction is?

Taking the swan example, ancient people would have no way of knowing that "all swan are white" is an induction which they don't have the knowledge to make. All they would know is what they observe, and what they think is a cause-and-effect relationship... until something proves it wrong.

I'd grant that it's likely a person can figure out this isn't a first-level induction, but how would they know that their knowledge is insufficient to make a valid induction?

Then you have to ask why swan DNA is the way it is, with respect to hollow bones and color. Color is something that varies a lot across animals, and is widely associated with species. That's something that's in our knowledge context -- don't leap to hasty generalizations about color.

Granted, but they would have no reason to think that "white" is any less a trait of swans than "born from eggs" and "has feathers."

If they have a context of knowledge that suggests that color varies in organisms, okay. But does that mean that "all swans are white" is automatically not a valid induction? It would seem that it is a valid induction in at least some narrow context of knowledge - but that would suggest that it could be a valid (though not necessarily correct) induction in all contexts where all known swans were white.

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the difference between identifying the nature of something and forming a concept for it.
In Objectivist terms, having a nature is having attributes (and perhaps more fundamentally, the identity of a thing is the sum of its attributes). Thus, I would think, to identify the nature of something, one must identify its attributes. But attributes are identified by concept formation and concept definition. But to form a concept definition we must distinguish between essential properties and accidental ones. Thus, if causality is explained in terms of the natures of things, then this explanation requires a precise explanation of the distinction between the essential and the accidental. However, to avoid circularity, this distinction cannot revert to an appeal as to the natures of things, since the natures of things is explained by attributes which are identified by concepts which are formed with respect to the distinction between essential and accidental. Moreover, since the concepts essential and accidental are concepts, by Objectivism's own terms, they must be formed and defined by Objectivist concept formation and definition, and I wonder how this would avoid an infinite regress.

So let me answer your intent: combining a principle such as "the elevator will arrive whenever I push the button" with "I just pushed the button" to arrive at the conclusion "it will arrive" is entirely deductive, no matter what one knows about the elevator's mechanism.
But the example does not combine with the principle that the elevator will arrive whenever the button is pushed. That premise is not in the example. Again, the example is (with knowledge of the mechanism added):

(1) In every instance I have witnessed, the elevator arrives after pushing the button.

(2) I understand the causal relation by which the button causes the action of the arrival of the elevator.

(3) Therefore, the elevator will arrive after I push the button now.

If deduction is defined as inference to the particular, then the above is deduction. But if induction is understood as inference from causal relation, then the above is induction.

And whether the inference is valid is a separate question.

Moreover, there are not two combinations, but four:

Inference from general to specific.

Inference from general to general.

Inference from specific to general.

Inference from specific to specific.

Then what form of inference is the proof that, for all n, if n is a natural number, then there is a prime greater than n? The conclusion is general (it is a generalization about all n, or at least about all natural numbers) while the proof uses understanding of the nature of natural numbers (if this is not causal in an Objectivist sense, then why not?). So in both senses, for an Objectivist, the inference must be an inductive one, correct?

For instance, one can see that this particular item will roll because (loosely speaking) there are no flat surfaces it would tend to rest on, so there is nothing to stop it from moving. It is that aspect of its nature that causes it to roll when pushed. At this point, one can say this item will roll when pushed even if we don't have a concept for roundness yet. One cannot say, "round things will roll" because one doesn't have the concept of "round things" yet, but one can see why this item will roll. Once one sees that, it is straightforward to generalize to, "anything with the property of not having flat surfaces will roll," and that gives us the essential characteristic for a new concept. Thus in a sense it is the nature of the item (no flat surfaces) and the context (what happens when pushed) that gives us the essential.
If you say that things without flat surfaces roll whenever pushed because there's nothing stopping them from rolling, then what this seems to depend upon is that is in the nature of anything to move (whether by rolling or not) whenever pushed and not impeded. While I don't want to commit to a particular physics here, it seems that your explanation is made more clear by not casting it in the negative (the cause of the pen rolling is the lack of impediment) but rather in the positive (the cause of the pen rolling is that it is in the nature of things, all things, to continue in motion). Thus, this particular causality would be to explain not things moving but rather things stopping (the cause of the pen not rolling is that its surfaces are not round enough).

But neither this nor your own explanation avoid that it is not adequate just to say that something behaves in certain ways because it is the thing's nature to behave in those ways. That's pretty much question begging. But if one says that we observe the relation between the nature of an entity and its modes of action, then not only are we back to the problem of essentials, but we should ask what is the difference between saying that things are observed to act in certain ways and saying that things have modes of action? The former does not ascribe that there is a thing that is a mode, but just that there are observed actions. So if one declares that there is something else, not just observations, but a mode, then one needs to say what a mode is. And if things have these modes, independent of observation, then one needs to explain why that is not a form or realism (for that matter, one needs to explain why maintaining that things having properties that are independent of observation but only identified by observation and concept formation is not a form of realism). Presumably an Objectivist would deny that it is realism by reminding that these properties, modes, essences, accidentals, and relations among them do not exist independent of concretes. Fine, but then they still do exist independent even of human abstraction (since they are only identified by, but not dependent on, human abstraction), which is at least a form of moderate realism - one in which concretes exist along with their properties, modes, essences, accidentals, and relations, independent of human consciousness. It seems to me that by holding that the concept of induction is explained in terms of the concept of causality which is explained in terms of a concept of modes of action is to veer much closer to realism than an ostensible empiricist might want to do.

Anyway, Objectivism recognizes that just observing balls roll and generalizing from this is not causal explanation. Objectivist causal explanation at least depends on identification of something more.

In the case of a pushed ball, it is self-evident why the ball rolls: it is inherent in the identity of the ball and the flat surface.
If it is a correct understanding of Objectivism, then it points to the lack of substance in the theory. Rather than explain even by reference to the specific properties of things like balls and surfaces, to say that balls roll on flat surfaces because that is inherent in the identity of balls and flat surfaces is just to gloss over an explanation. There is nothing in the explanation to preclude asserting self-evidence of explanation for any correlation, whether causal or not. If all the snails I ever observed were ones that I saw slithering toward stucco, then I could just as easily say it is self-evident that it is inherent in the nature of snails that they slither toward stucco. But it is not self-evident at all. What is self-evident is that I've observed snails slithering toward stucco and that balls roll on flat surfaces. The observations themselves are taken are "raw", as it were, givens. But the explanation as to "inherent in the identity" is self-evident only if it is so general that it not have explanatory value at all.

Merely observing that all swans within one's purview are white does not permit us to conclude that all swans everywhere are white. Since we do not know the relevance of the color of the swan's feathers, we do not know that all other swans are white.
Fair enough, but, as I mentioned above, if by just observing balls roll we can say it is self-evident that they roll on account of their nature, then, by this method, what precludes one from saying that swans are white due to their nature? I recognize that you mention that there are better explanations (the hollow bones example), but it is still not tenable that the mere "inherent in the identity" explanation is any decent explanation at all. Edited by LauricAcid
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Granted, but they would have no reason to think that "white" is any less a trait of swans than "born from eggs" and "has feathers."
I'll try not to repeat myself, but the point is that there is very good reason to separate color from such things as having feathers, live birth, contralaterality, or various other animal traits. If you just look at trait names, nothing in the names suggests any difference -- the suspicion comes from science, i.e. knowledge of biology.
If they have a context of knowledge that suggests that color varies in organisms, okay.
What's this if business? This is such a fundamental fact about reality on Earth that no normal adult human anywhere doubts that. Size and color are the two features that are the most robust basis for all biological taxonomies everywhere on Earth, meaning that they are the most obviously variable across species. So this is knowledge that you do not need to doubt in the slightest.
But does that mean that "all swans are white" is automatically not a valid induction? It would seem that it is a valid induction in at least some narrow context of knowledge - but that would suggest that it could be a valid (though not necessarily correct) induction in all contexts where all known swans were white.
I could describe an imaginary knowledge context where the universal swan whiteness conjecture would be valid, but it depends on pretty primitive science. You need to be certain that there is only one species of swan in the world. This works for polar bears, also lions (though by lion I mean "proper lion" and not that other species known as cougar aka mountain lion). White is the only possible candidate for universal color (given albinism). The problem is that, AFAIK, it was known that not all swans are white before the causal basis for the supposition was known.

Now, I have no idea what you mean by "automatically". If you mean, would a being with a conceptual faculty and no knowledge whatsoever instantly say "The proposition 'all swans are white' is invalid", then no. Such a being would not speak: you need knowledge to be able to speak. If you mean, given the knowledge that we have, would we apply that knowledge -- and require no further knowledge, even if the entire fraggin' southern hemisphere (where live the non-white swans) were blasted out of existence -- to derive reasonable doubt about the white swan song? Yes indeedy, we would.

It is really important to not get confused into thinking that induction is the same as mindless statistical correlation. Regression sucks, 'mkay? Inductive statements should, properly conceived, be expressed as causal relations. The other point to keep anchored to is that causation is not magical, and understanding causation takes a lot of work, so you should not get frustrated if you do not immediately see what causal mechanism underlies an observed correlation.

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This will have to be a brief response. I might have time to respond more fully later.

But attributes are identified by concept formation and concept definition.

No, this is a mistake. Observation of attributes (there is no other kind of observation) precedes concept formation. In fact, you've got it backwards: concept-formation is built on top of observation and identification of attributes (perceptual, at first), as well as actions and relationships. For instance, one can know a table has the attribute of a reddish color without having the slightest notion of "table" or even "red." Note that we have to distinguish between explicitly calling it "a table with a reddish color" (which a child could not do) and perceiving a thing's color (which a child can do).

I believe this eliminates the circularity you mentioned, but I am sure if I misinterpreted something you will correct me.

Rather than explain even by reference to the specific properties of things like balls and surfaces, to say that balls roll on flat surfaces because that is inherent in the identity of balls and flat surfaces is just to gloss over an explanation.

I believe AisA was summarizing the reason a ball rolls, rather than explaining what is its particular nature that makes it roll. It is true of all things to say that their actions are determined by their nature (indeed, this is just the law of causality). It is no shortcoming that it does not mention what particular facts about a ball makes it roll.

Furthermore, it is rather obvious what makes a ball roll. One can see this by inspecting a single ball and thinking about it. Nothing in the observation of snails says "they always slither towards stucco," like you point out, but it does say, "Snails move by sliding on their foot" (I guess--I am no biologist). Nothing in the observation of swans shows any connection between being a swan and being white, but there is plenty of connection between flapping wings and flying, for instance.

I hope this short reply was somewhat useful, even if only in convincing you I totally misunderstood your points. :worry: I appreciate your honesty and the chance to improve my own thinking.

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