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What is induction?

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Hume claimed that we only ever witness 2 events happening in sequence, and never the 'necessary connection' between them, therefore we cannot logically justify the claim that these events will always occur together in the future.

Hume has an incorrect view of causality. He sees causality as a relationship between EVENTS.

The Objectivist/Aristotelian view is that causality is the Law of Identity with regard to action. It states that an entity acts in accordance with its nature. Therefore, it is a relationship between an ENTITY and its actions, not a relationship between actions.

Betsy, as I understand her, is claiming that causation _is_ this necessary connection, and that once we have grasped this cause we are then entirely justified in claiming that these events will always occur together, due to the law of identity.
What I am saying is that there is a necessary connection between what an entity IS and how it acts. It can only -- and MUST -- act in accordance with its nature.

I'm not entirely sure what "grasping this cause" consists of however, since we technically haven't grasped the cause of why apples fall to the ground, or the cause of the majority of things which we witness in daily life.

We may not know the ultimate cause of gravity yet, but we do know the nature of many, many things in a way that accounts for their actions.

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We may not know the ultimate cause of gravity yet, but we do know the nature of many, many things in a way that accounts for their actions.

Yeah, I agree that this is the best way to approach induction ('probabilistic truth until cause has been discovered'), I was just wondering how you would handle a few concrete cases. Thanks.

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It is not a matter of omitted measurements but of causal characteristics.  Proper induction requires identifying the characteristics of entities that cause their properties and actions.

Even if you establish that a particular behavior will follow from a given attribute don't you still have to show that all members of the concept will have that attribute?

To do that you would need to show that your subconscious will not dredge up the word "table" unless the object in front of you has that attribute. So you need to introspect to find out what it is doing - you need to know what attributes are triggering the word "table" are what are being omitted and therefore not.

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Even if you establish that a particular behavior will follow from a given attribute don't you still have to show that all members of the concept will have that attribute?

Yes. You have to show, in the case of generalizations, that all units of the concept have that attribute. If it is an essential attribute that is required to be a member of the class, that is no problem. For instance, the fact that men are rational animals means that they ALL have certain biological properties.

To do that you would need to show that your subconscious will not dredge up the word "table" unless the object in front of you has that attribute. So you need to introspect to find out what it is doing - you need to know what attributes are triggering the word "table" are what are being omitted and therefore not.

I don't accept your notion that a concept is something your subsconscious creates, somehow, automatically.

The only thing that would remotely resemble such a process is the automatic process of perceptual association. This is the process by which a perceptual creature, like a dog, comes to associate a word ("Come" "Sit") with an entity or an action. Many people use words that way INSTEAD of forming concepts, but that is NOT induction -- valid or otherwise.

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My question was how to know whether the conditions and characteristics one has identified are sufficient to explain a phenomenon.

Betsy said:

In my view of induction, in order to show causality, you have to be able to state the generalization as an identity or as a chain of identities.

In your example of Darwin, you use two facts to define the concept of natural selection and proceed to subsume species-variation under that concept.

Thus, your answer to my question seems to be: They are sufficient when they define a concept which subsumes the phenomenon.

This is fine if there is only one possible conception of the cause, as was the case with natural selection and bacterial resistance.

Unfortunately, the same phenomenon can often be conceptualized in multiple, equally acceptable ways. For example, there are a number of equally acceptable interpretations of quantum strangeness--equally acceptable in terms of predictive power.

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Thus, your answer to my question seems to be:  They are sufficient when they define a concept which subsumes the phenomenon.

NO, they are sufficient when they reduce to an identity -- when the actual characteristics of the units of the concept are the SAME as the phenomena.

This is fine if there is only one possible conception of the cause, as was the case with natural selection and bacterial resistance.
It as nothing to do with a "conception of the cause" but with actual, perceivable, provable identities.

Unfortunately, the same phenomenon can often be conceptualized in multiple, equally acceptable ways.  For example, there are a number of equally acceptable interpretations of quantum strangeness--equally acceptable in terms of predictive power.

I reject the whole notion of predictability as the standard of inductive validity. Predictability only describes what has happened. What we need for inductive certainty is knowledge of the NATURE of the entities that act so that we know WHY they act as they do and not just that they have acted that way in the past.

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Tom: Thus, your answer to my question seems to be:  They are sufficient when they define a concept which subsumes the phenomenon.
Betsy:

NO, they are sufficient when they reduce to an identity -- when the actual characteristics of the units of the concept are the SAME as the phenomena.

Tom:  This is fine if there is only one possible conception of the cause, as was the case with natural selection and bacterial resistance.

Betsy: It as nothing to do with a "conception of the cause" but with actual, perceivable, provable identities.

TOM:

For the actual characteristics of the units of the concept to be the same as the phenomenon, you must have some conception of the causal mechanism.

Which brings me to your dismissal of predictive power:

Both quantum wholeness and QED can be expressed as chains of identities, the former resting on propositions about pilot waves and the latter resting on propositions about the relationships between photons and time-traveling electrons.

Both match reality by every standard we have--except predictive power. QED is *slightly* better in terms of predictive power.

If we toss out predictive power, how will we decide between quantum wholeness and QED?

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Both quantum wholeness and QED can be expressed as chains of identities, the former resting on propositions about pilot waves and the latter resting on propositions about the relationships between photons and time-traveling electrons.

This is almost completely devoid of actual physics content. I suspect you are reading too much in the way of popularizations, and not nearly enough in the way of actual physics.

Both match reality by every standard we have--except predictive power.  QED is *slightly* better in terms of predictive power.
"*slightly* better"???? Bohm's theory was a dead end, for christ sake. It wasn't even relativistic! QED is one of the most precise experimental predictors in the entire history of science, in areas not even dreamed of by "quantum wholeness."

If we toss out predictive power, how will we decide between quantum wholeness and QED?

Well, to begin with, "quantum wholeness" was experimentally disproved almost two years ago. See "Experimental realization of a first test of de Broglie-Bohm theory," G. Brida et al., _Journal of Physics B-Atomic Molecular and Optical Physics_, 35 (22): pp. 4751-4756, Nov 28 2002.

But, to address the general point of how we decide between theories that make the exact same experimental predictions, the answer was/is contained in the preceding posts: A proper physics theory identifies the causal mechanisms that explain physically deterministic behavior. If such a theory contradicts fundamental philosophical principles, then that theory can be safely discarded.

For instance, Bohm's theory is explicitly nonlocal, as expressed in the instantaneous connection between quantum particles through the wavefunction and Bohm's "quantum potential." Bohm has simply replaced the standard theory's nonlocal "collapse" of the wavefunction with a quantum potential performing the same instantaneous action. Any theory which posits nonlocality as a fundamental, is fatally flawed, and such is the state of Bohmian theory. As far as proper philosophy and proper physics is concerned, case closed.

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This is almost completely devoid of actual physics content. I suspect you are reading too much in the way of popularizations, and not nearly enough in the way of actual physics.
I am merely pointing out the practical consequences of Betsy's position.

QED is one of the most precise experimental predictors in the entire history of science, in areas not even dreamed of by "quantum wholeness."

But Betsy rejects predictive power as a criterion for evaluating theories.

See her earlier post.

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But Betsy rejects predictive power as a criterion for evaluating theories.

Read what she actually wrote:

"I reject the whole notion of predictability as the standard of inductive validity. Predictability only describes what has happened. What we need for inductive certainty is knowledge of the NATURE of the entities that act so that we know WHY they act as they do and not just that they have acted that way in the past."

Predictability is NOT "the STANDARD of inductive validity." (Emphasis added.) In a true scientific theory predicability becomes a consequence of properly identifying the causal mechanisms that explain the physically deterministic behavior of entities. IF the theory is true, then its predictions MUST correspond to experimental facts. But, unfortunately, there are plenty of WRONG theories around that make accurate predictions. It is not too difficult to concoct a theory that lives within the error bars of experiment, but that does not make such a theory valid.

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points of agreement:

* causality is entity-based

* the end result of induction is knowledge of the nature of entities

* such knowledge can be summarized by chains of identities

* causal reasoning plays an important role in induction

* predictive power is a consequence of how well the theory corresponds to the facts of reality

* predictive power is insufficient for induction

points of disagreement:

* whether only one chain of identities is possible given the same set of facts

* the exact role of predictive power in inductive certainty

points to reflect on:

* For man's knowledge to be fully integrated, the conclusion of an induction must logically follow from wider generaliztions. If it does not, then either the wider generalization is wrong or the induction is wrong. But inductions can't be wrong, so the wider generalization must be missing a condition. Thus, a chain of identities might very well be the end product of a particular induction, but by no means should we treat such a chain as the first cause. For example, consider how the 19th century notion of magnetic vortices was subsumed by wider generalizations regarding electrons.

* There is a trend of simpler theories replacing more complicated, last-ditch efforts at salvaging older theories. That trend doesn't happen without new conceptualizations of the phenomena. Thus, the increasing complexity of a math-heavy scientific theory is often symptomatic of the end of the theory as the best theory, and fertilizer for the formation of a new concept.

* When building chains of identities, care must be taken so that they are truly connected (i.e. not mere tautologies).

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points of disagreement:

* whether only one chain of identities is possible given the same set of facts

What does this mean? That there is only one way to reach a given inductive conclusion? I'd have to say that is false because reality is a non-contradictory whole and there may be several different routes to reach and prove the validity of the same causal conclusion or generalization.

* the exact role of predictive power in inductive certainty
The fact that an action always seems to occur in a given context is inductively significant. It provides the necessary evidence to establish a valid hypothesis.

The value of an hypothesis is that it indicates a possible causal connection and points to where the cause probably is to be found. A valid hypothesis serves as a guide to further examination of the entities and the context in a way most likely to lead to the discovery of the cause.

points to reflect on:

* For man's knowledge to be fully integrated, the conclusion of an induction must logically follow from wider generaliztions.  If it does not, then either the wider generalization is wrong or the induction is wrong.

;) What does this mean? I have discovered and validated many inductive conclusions in different areas of knowledge which are validated by their relationship to reality -- NOT because they "logically follow from wider generalizations."

But inductions can't be wrong, so the wider generalization must be missing a condition.

Inductions most certainly CAN be wrong and the whole area of logic dealing with informal fallacies shows many of the ways people can do induction wrong.

Thus, a chain of identities might very well be the end product of a particular induction, but by no means should we treat such a chain as the first cause.

Who is doing that? When people do induction, they are seeking the cause of a particular action which may or may not have wide-ranging applications. They may be asking, "Why won't my car start?" OR "What makes the Dean and Peter Keating act that way?"

* There is a trend of simpler theories replacing more complicated, last-ditch efforts at salvaging older theories.  That trend doesn't happen without new conceptualizations of the phenomena.  Thus, the increasing complexity of a math-heavy scientific theory is often symptomatic of the end of the theory as the best theory, and fertilizer for the formation of a new concept.
Here you are dealing with causal explanations that are still in the hypothesis / experiment stage and not an established inductive truth.

* When building chains of identities, care must be taken so that they are truly connected (i.e. not mere tautologies).

They must be connected to REALITY and NOT just to each other.

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Tom, I see Betsy has answered you and there is no point in me duplicating her arguments. For the record let me say that I completely agree with all of her criticism. However, there is one point that I want to highlight because I find it to be particularly noxious.

points of disagreement:

* whether only one chain of identities is possible given the same set of facts

There is only one reality and the very notion of "fact" is derived from that. Given any set of facts that are causally related there is one and one chain of identities which link those facts, and that chain is the one which actually occurred. To say otherwise is to deny the law of identity and the law of causality, not to mention casting aspersions on existence itself.

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What does this mean? That there is only one way to reach a given inductive

conclusion?

No, the question is whether there is only one possible interpretation of the same set of facts.

I would argue that as we know more and more about the identities involved, there will be fewer and fewer possible interpretations.

Tom: the exact role of predictive power in inductive certainty

Betsy: The fact that an action always seems to occur in a given context is inductively significant. It provides the necessary evidence to establish a valid hypothesis.

This is true, but it doesn't address the point. The predictive power of a hypothesis is established after the hypothesis has been formed.

Tom: For man's knowledge to be fully integrated, the conclusion of an induction must logically follow from wider generaliztions.  If it does not, then either the wider generalization is wrong or the induction is wrong. 

Betsy:  What does this mean? I have discovered and validated many inductive conclusions in different areas of knowledge which are validated by their relationship to reality -- NOT because they "logically follow from wider generalizations."

Of course they are validated by their relationship to reality.

But as you form more and more inductions, you will often find that two generalizations can be accounted for or expalined by a wider generalization subsuming the phenomena covered by the two generalizations (and even phenomena you haven't studied yet).

Consider the following phenomena:

* getting zapped by a doorknob after walking on carpeted floors with socks on

* lightning

* a spark jumping from your car battery to your jumper cable

They're all examples of voltage overcoming air-resistance.

Now consider the following classes of phenomena

* voltage overcoming air resistance

* induction of current by magnetic field

* light

They're all accounted for by a set of laws explaining the behavior of orbital shells.

All phenomena are validated by reference to reality, but they are explained by logically prior generalizations. If you find that the implication of a phenomenon defies a wider generalization, then something is wrong. Maybe your inference is bad. Maybe your generalization depends upon a condition which you hadn't known about. Maybe one of the assumptions behind your generalization is inapplicable to the particular phenomenon. But something is wrong.

This is why it is very important to organize your generalizations hierarchically.

Tom: There is a trend of simpler theories replacing more complicated, last-ditch efforts at salvaging older theories.  That trend doesn't happen without new conceptualizations of the phenomena.  Thus, the increasing complexity of a math-heavy scientific theory is often symptomatic of the end of the theory as the best theory, and fertilizer for the formation of a new concept.

Betsy: Here you are dealing with causal explanations that are still in the hypothesis / experiment stage and not an established inductive truth.

But competing theories are reducible to sets of identities. If you're after a very small set of identities, then you're applying a principle subsuming Newton's rule of "necessary and sufficient" and Einstein's advice of "keep it as simple as possible but no simpler".

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This is true, but it doesn't address the point [of inductive certainty].  The predictive power of a hypothesis is established after the hypothesis has been formed.

As I indicated, predictive power can lead to a productive hypothesis, but 100% predictive success does NOT establish inductive certainty. It is not enough to know THAT certain effects occur. In order to be certain, we need to know WHY they occur. What is it about the particular ENTITIES which CAUSE the characteristic or action?

For man's knowledge to be fully integrated, the conclusion of an induction must logically follow from wider generalizations.  If it does not, then either the wider generalization is wrong or the induction is wrong.

Later you wrote:

Of course they are validated by their relationship to reality.

But as you form more and more inductions, you will often find that two generalizations can be accounted for or explained by a wider generalization subsuming the phenomena covered by the two generalizations (and even phenomena you haven't studied yet).

Those are two very different statements.

It is definitely true that you often find a common cause that applies to the similar actions of more than one class of entities, but the conclusion follows from the facts of reality when you observe that the fact is true of more than one class of entities. It does NOT "logically follow from wider generalizations." To the contrary, wider generalizations follow from wider knowledge of the entities.

I also question the idea that a man's knowledge should be fully integrated. What for? Isn't it quite sufficient to understand the particular things one deals with in one's life?

All phenomena are validated by reference to reality, but they are explained by logically prior generalizations.
No, they are not. They are explained AND validated by reference to reality ... only.

If you find that the implication of a phenomenon defies a wider generalization, then something is wrong.  Maybe your inference is bad.  Maybe your generalization depends upon a condition which you hadn't known about.  Maybe one of the assumptions behind your generalization is inapplicable to the particular phenomenon.  But something is wrong.

This is why it is very important to organize your generalizations hierarchically.

No, this is why it is necessary to tie your generalizations to REALITY -- to the real properties of the entities referenced in the generalization. If your generalization identifies the causal properties of those entities, it is valid. Period.

But competing theories are reducible to sets of identities.  If you're after a very small set of identities, then you're applying a principle subsuming Newton's rule of "necessary and sufficient" and Einstein's advice of "keep it as simple as possible but no simpler".

Valid induction is not a matter of reducing theories to an identity, but of FINDING the identity between the entity and it's characteristics and/or actions -- in REALITY.

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Tom: whether only one chain of identities is possible given the same set of facts

Stephen: There is only one reality and the very notion of "fact" is derived from that.  Given any set of facts that are causally related there is one and one chain of identities which link those facts, and that chain is the one which actually occurred. To say otherwise is to deny the law of identity and the law of causality, not to mention casting aspersions on existence itself.

We seem to be talking passed each other.

There is often more than one set of rational, explanatory, apparently tautological propositions possible given the same set of facts. At that point, you should regard those sets as tentative--as probable but not certain.

But even if you settle on one set of propositions, you still still face the problem of bridging the gap between abduction and induction. At what point should you regard the set of propositions as a recognition of the chain of identities? Should you just add the qualifier "within the context of my knowledge" and leave it at that? If so, how do you reconcile your view with the necessity of proof? If not, how do you reconcile your view with the contextual nature of knowledge?

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It is definitely true that you often find a common cause that applies to the similar actions of more than one class of entities,
That's all I meant.

I also question the idea that a man's knowledge should be fully integrated. What for? Isn't it quite sufficient to understand the particular things one deals with in one's life?

In order to understand the particular things one deals with in one's life, it is necessary to apprehend the relationships between things.

If some of your generalizations lead to A and other generalizations lead to NOT-A, it is to your benefit that you resolve the apparent contradiction.

Tom: All phenomena are validated by reference to reality, but they are explained by logically prior generalizations.

Betsy: No, they are not. They are explained AND validated by reference to reality ... only.

How can you do that without showing how the nature of the thing causes the action?

Tom: If you find that the implication of a phenomenon defies a wider generalization, then something is wrong.  Maybe your inference is bad.  Maybe your generalization depends upon a condition which you hadn't known about.  Maybe one of the assumptions behind your generalization is inapplicable to the particular phenomenon.  But something is wrong.

This is why it is very important to organize your generalizations hierarchically.

Betsy: No, this is why it is necessary to tie your generalizations to REALITY -- to the real properties of the entities referenced in the generalization. If your generalization identifies the causal properties of those entities, it is valid. Period.

If two of your generalizations contradict, you've screwed up. Period. If further investigation tells you that a certain causal inference is wrong, you did NOT identify the causal properties of the entities.

Valid induction is not a matter of reducing theories to an identity, but of FINDING the identity between the entity and it's characteristics and/or actions -- in REALITY.

How do you know when you've found it? When can you say that a set of rational, explanatory, apparently tautological propositions matches the chain of identities you are trying to grasp?

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In order to understand the particular things one deals with in one's life, it is necessary to apprehend the relationships between things.

Sometimes, but not always.

If some of your generalizations lead to A and other generalizations lead to NOT-A, it is to your benefit that you resolve the apparent contradiction.

If it is the SAME generalization, then you have a problem. If they are two different generalizations, you may or may not have commonalities.

No, [all phenomena] are not [explained by logically prior generalizations]. They are explained AND validated by reference to reality ... only.

How can you do that without showing how the nature of the thing causes the action?

You say "Look. This is what the thing is. Look at what it does. Observe that what it is accounts for what it does." No prior generalizations necessary.

If further investigation tells you that a certain causal inference is wrong, you did NOT identify the causal properties of the entities.
Obviously, but there is a correct way of establishing something as a cause and if you validate the cause that way, you can be absolutely certain.

How do you know when you've found it? When can you say that a set of rational, explanatory, apparently tautological propositions matches the chain of identities you are trying to grasp?

No, when a set of rational, explanatory observations reveals properties that are the same properties you are trying to grasp.

Here's an example.

You observe that all calico cats seem to be females. Genetic analysis reveals that the gene for calico coloring resides on the X chromosome and is recessive-- i.e., TWO copies of the gene must be present for the color to express itself.

Only females have two X chromosomes.

Therefore, the thing which makes the cat calico (having the calico gene on two X chromosomes) is the SAME thing that make the cat female (having two X chromosomes). "All calico cats are female" reduces to an identity.

Therefore, it is certain that all calico cats are female.

You get to that conclusion by studying cats -- NOT by playing around with generalizations and other propositions.

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Tom: In order to understand the particular things one deals with in one's life, it is necessary to apprehend the relationships between things.

Betsy: Sometimes, but not always.

No, always.

You cannot even form concepts without relating things.

Since undetected contradictions compound errors in judgement and decision, it is crucial that you check for contradictions. Yes, you need to get as much of it right the first time as possible. Yes, you need to be sufficiently comfortable with your models in order to act. But you shouldn't be carelessly comfortable with your models.

Betsy: No, [all phenomena] are not [explained by logically prior generalizations]. They are explained AND validated by reference to reality ... only.

Tom: How can you do that without showing how the nature of the thing causes the action?

Betsy: You say "Look. This is what the thing is. Look at what it does. Observe that what it is accounts for what it does." No prior generalizations necessary.

You cannot understand the explanation for calico phenotype without the generalization that genes for calico are inherited.

Tom: How do you know when you've found it?  When can you say that a set of rational, explanatory, apparently tautological propositions matches the chain of identities you are trying to grasp?

Betsy: No, when a set of rational, explanatory observations reveals properties that are the same properties you are trying to grasp.

How do you know whether you've grasped the properties you are trying to grasp?

You can't say "when you can reduce the phenomena to a set of identities" because the notion of "chain of identities" brings up the question of whether you've recognized the chain of identities. Knowledge is much more than justified correspondence. Yes, proof presupposes knowledge, but you need something similar to proof in order for the result to be knowledge.

On a less contentious note, here's what we've mapped out so far regarding the process of induction:

1) You abstract something from the content of your observations, subsume your observations under that concept, and then form a hypothesis (preferably several).

2) If you find that your hypothesis withstands experimentation and demonstrates predictive power, then you're ready to start hunting for the cause.

3) After investigating matters further, you may find evidence that the phenomena you were studying was an instantiation of some subtler, wider phenomena. At that point, you can attempt a causal explanation. It's still only probable at this point, but you're closer to induction than hypothesis alone.

4) If you have enough evidence to settle upon one explanation out of many alternatives, then you can be even more certain.

5) If being correct within the context of your knowledge is sufficient for induction, then you're done. But if we need more...

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[...]

How do you know whether you've grasped the properties you are trying to grasp?

You can't say "when you can reduce the phenomena to a set of identities" because the notion of "chain of identities" brings up the question of whether you've recognized the chain of identities.  Knowledge is much more than justified correspondence.  Yes, proof presupposes knowledge, but you need something similar to proof in order for the result to be knowledge.

[...]

I have been trying, unsuccessfully, to nail your floating abstractions to sense perception. I have been trying, unsuccessfully, to get you to acknowledge the role of REALITY and real entities and their real properties.

Perhaps the reason I have failed is that you DON'T "know whether you've grasped the properties you are trying to grasp." I can explain a lot of things, but not that. That gets the discussion into the kind of pathology I am not equipped to deal with.

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I have been trying, unsuccessfully, to nail your floating abstractions to sense perception. I have been trying, unsuccessfully, to get you to acknowledge the role of REALITY and real entities and their real properties.
Where exactly do you think I've denied the validity of the senses? Where exactly do you think I've denied the role of reality?

I have no difficulty accepting that my senses and the evidence at my disposal indicates that a doorknob shock is caused by charge separation.

But the notion that a set of explanatory propositions about charge separation is sufficient as the product of induction neglects the contextual nature of knowledge and the broader natural laws at work.

Perhaps the reason I have failed is that you DON'T "know whether you've grasped the properties you are trying to grasp." I can explain a lot of things, but not that. That gets the discussion into the kind of pathology I am not equipped to deal with.

So anyone who even mentions the problem of induction suffers from a pathology?

This is not how to fight Hume (and he does need to be fought).

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But the notion that a set of explanatory propositions about charge separation is sufficient as the product of induction neglects the contextual nature of knowledge and the broader natural laws at work.

I read this three times and I cannot make it sensible. Can you explain what you mean in some simple words? Also, though I personally would have no difficulty in your using "charge separation" as an example, it might be useful for others if you replaced it with a more commonplace example.

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Sorry, but I just noticed this from several days ago.

We seem to be talking passed each other.

There is often more than one set of rational, explanatory, apparently tautological propositions possible given the same set of facts. At that point, you should regard those sets as tentative--as probable but not certain.

But even if you settle on one set of propositions, you still still face the problem of bridging the gap between abduction and induction. At what point should you regard the set of propositions as a recognition of the chain of identities? Should you just add the qualifier "within the context of my knowledge" and leave it at that? If so, how do you reconcile your view with the necessity of proof? If not, how do you reconcile your view with the contextual nature of knowledge?

Before I even attempt to make any sense out of this, do you or do you not agree with what I expressed in my words that you quoted? I am asking you outright whether you acknowledge that granted a causal chain that has occured in physical reality, is there or is there not a unique set of causal explanations that truly explain the behavior?

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Before I even attempt to make any sense out of this, do you or do you not agree with what I expressed in my words that you quoted? I am asking you outright whether you acknowledge that granted a causal chain that has occured in physical reality, is there or is there not a unique set of causal explanations that truly explain the behavior?
There is only one mental relationship among cognitive products which accurately, precisely, and completely matches the causal relationship you are trying to grasp.

If you have multiple theories which reduce to tautologies, either only one of them is true or none of them is true. Recognize that you're still in the abductive phase and gather more knowledge.

If you only have one theory whose propositions reduce to tautologies, stop testing them as mere hypotheses, bind them to their respective metaphysical contexts, and move on because you're done.

Tom: But the notion that a set of explanatory propositions about charge separation is sufficient as the product of induction neglects the contextual nature of knowledge and the broader natural laws at work.

Stephen: I read this three times and I cannot make it sensible.

In the case of getting zapped by a doorknob, you'd look toward a relationship between feet-shuffling, free electrons, identities about charged bodies, and the broader natural laws of orbital shells.

Once you find that relationship, you can reduce it to an identity by means of some theory. However, you would never regard your theory as contextless or complete, only correct within certain metaphysical ranges, some of which may be unknown to you.

it might be useful for others if you replaced it with a more commonplace example.

In the case of boiling water, you'd look toward a relationship between water molecules, molecular kinetic energy, the resulting vapor pressure, and atmospheric pressure.

Once you find that relationship, you can reduce it to an identity by means of a theory of molecular behavior. However, you would never regard your theory as contextless or complete, only correct within certain metaphysical ranges, some of which may be unknown to you.

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