Hello,

Since I’m concerned that my words weren’t understood properly, I’ll try again, and I’d be happy if you’d give your opinion.

I did not write: 1. that the impenetrability of the ball is forced upon us. 2. Likewise, I did not write that observation is unnecessary in order to recognize the ball’s impenetrability.

What I did write is: 1. The discussion of whether the ball is penetrable or not is forced upon us, simply by virtue of the fact that we are dealing with matter, just as there are many other properties that one is led to discuss a priori when dealing with matter. (Likewise, a priori we know what the implications of each possibility would be.) The decision as to which possibility is actually correct is indeed known only through observation. 2. My main claim was that causal relations after the observation are necessary, and are not a hypothesis, because from the observation we learned the fact (which had already been discussed a priori) that the ball is not penetrable, and from that the result that occurred already follows necessarily. And so too with the other cases of cause-and-effect events on the physical plane: observation is indeed needed in order to know them, but after the observation they are logically necessary, since the observation established the properties of the materials we are discussing. And after the observation this is no longer a hypothesis that one can deny or imagine the cause without its effects. There are, however, cases such as on the psychophysical plane where even after observation the causal relations remain in the realm of hypothesis, and they are not necessary.

To sum up in one sentence: in your understanding, are causal relations on the physical plane, after observation, logically necessary (as entailed by their properties), or are they still only a hypothesis that one can deny and imagine the cause-event without its effects?

I’d appreciate your response.

I didn’t understand a word. In particular, I don’t know what “logically necessary after observation” means.

—After we have an observation, do tangible things have to behave according to logic?
—If the property of impenetrability is something that can be observed or inferred in some way,
then logically, what is supposed to happen in an encounter between two balls?

If we reached some conclusion in whatever way, then that is our conclusion. That is of course a tautology. So what?

I did not write: 1. that the impenetrability of the ball is forced upon us. 2. Likewise, I did not write that observation is unnecessary in order to recognize the ball’s impenetrability.
Since I’m really struggling to find an answer to my argument in your short replies, I’m raising the main points in detail, and I’d appreciate it if you’d respond to each point, even just with correct / incorrect.

1. David Hume writes that a causal relation between two events cannot be observed, nor is there any necessity to it; therefore it is only a hypothesis that can always be denied, and one can imagine the cause-event without the effect.

2. Any discussion of matter requires, a priori, referring to its various properties, such as shape, mass, penetrability, and more, and for every possibility we choose among the possibilities there is a fixed and specific behavior.

3. Deciding what the actual properties of any material are is done by means of observation.

4. Therefore, the very discussion of whether billiard balls are penetrable or not follows from the very fact that they are matter, although the actual decision that they are not penetrable becomes known from observation.

5. After recognizing that the ball is not penetrable, it follows logically and necessarily that from the event in which ball A moves toward ball B, which is at rest, some change in one of the balls must result; that is, the cause-event (the movement of non-penetrable ball A toward ball B) entails some change—in other words, some effect—and one cannot imagine the cause without its effects.

6. It follows that the causal relation in the above case is not a hypothesis that one can deny, but something entailed by the properties of matter (even if recognizing those properties requires observation).

David Hume argued that we have no empirical or logical basis at all for attributing a cause-and-effect relation, only temporal contiguity and inductive generalization.

Kant answered this claim by saying that the relation of cause is one of our a priori forms of cognition of reality.

(I’m aware this presentation is not precise, but it’s enough so that we understand what I’m talking about.)

The claim is that there are cases in which a causal relation can be grounded logically.

In the example of the billiard balls, one ball is at rest and the other is moving toward it.

If the balls have the property of impenetrability (apparently Hume would have treated impenetrability as empirical),
then logically it follows that a change in reality must occur.

If no change whatsoever occurs at the moment the two balls meet, that would create a logical contradiction.

The moving ball cannot continue moving while the resting ball continues resting; that contradicts the property of impenetrability.

Therefore, the way out of the contradiction is a change in the state of one of the balls or both of them: either the moving one stops, or the resting one moves, or… (see the chapters dealing with momentum in any high-school physics book).

N.,

1. Correct.
2. In this section I didn’t understand a word, and in particular not the connection between the statements. What does “requires a priori” mean? The properties you listed are the result of experience, not a priori. Do you mean that there are several a priori options and experience selects among them? I don’t see why. Why isn’t it possible that experience tells me something I hadn’t imagined beforehand? I didn’t understand what it means that every possibility we choose has a fixed and specific behavior. “Choose” by observation? Then observation yields a certain behavior. Do you mean that the behavior is dictated by the observation even though it isn’t learned from it?
3. Correct, if I understood. Subject to my questions from the previous section.
4. Incorrect. You can also discuss whether demons are penetrable or not, and whether thoughts are penetrable or not. I don’t see why the tautology that something is penetrable or not is connected to the claim that it is matter. Is their being matter itself a result of observation?
5. If the meaning of the term “impenetrability” is that nothing passes through it, then indeed, after we reached the conclusion that the ball is not penetrable (which itself is a generalization based on observation and not direct observation, of course), then it indeed is not penetrable. What does this tautology add to us? This is not a relation between cause and effect, but between a concept and its definition.
6. Incorrect.

See my reply to N. above. This is not a relation between cause and effect but between a concept and its definition. When you reached the conclusion that the ball is not penetrable, what you said was that it cannot be penetrated. The phenomenon of non-penetration is not a result of the ball’s property of impenetrability but its definition. Once you reached the conclusion that the ball is not penetrable, you are already after the generalization (and causality too is implicit there).

I don’t understand. There are two problems: the problem of induction and the problem of causality.

1. The problem of induction objects to the inference from particular phenomena to general ones, and claims that this transition is not necessary (and in our example, the transition from observation/touch that the object is impenetrable to the definition that the object is generally impenetrable is not necessary in the way a logical inference is forced upon us). That is agreed.

2. There is also the problem of causality, which according to Hume is that since we have no way of observing causality, the assumption that there really is a causal connection between a pair of phenomena is based only on contiguity in time and place, and on an inductive generalization from the repeated appearance of the pair of phenomena. And since that is so, there is no obstacle to denying the causal diagnosis.

These two problems are not dependent on each other. Even after we accept induction as a possible method of inference (while recognizing its shortcomings), Hume still argues that identifying a causal relation is a hypothesis that one can deny, as above.
(I hope up to this point you agree; if not, I’d be glad if you’d respond to these claims.)

3. The new claim is that in the billiard-ball example, after observation/touch and recognition that they are not penetrable, together with the inductive generalization that the ball by definition is impenetrable, that is enough to force upon us a causal relation in this picture (even if we had never known the concept of causality), since non-penetrable ball A moving toward non-penetrable ball B at rest must necessarily produce a change in one of them (either a change in A’s motion or a change in B’s rest), and no other possibility exists. If so, Hume’s claim that the causal relation between the phenomena in this picture rests only on empirical observation of contiguity in time and place and on induction, and therefore can be denied, is not accurate. After observation/touch that the ball is not penetrable and an inductive generalization of this property, the change in question is already forced upon us.
Thanks in advance for the patience.

1-2. I agree, but not entirely. There is some connection between the problem of induction and causality. If there is causality, induction follows from it. If there is induction, causality does not necessarily follow from it.

3. Touch does not show you that the balls are impenetrable. The conclusion that they are impenetrable is your conclusion. Touch gives you some sensation, and that’s all. And if you try to penetrate the ball with your hand and fail, that only means that your hands right now do not pass through that particular ball. What about other hands, other balls, other times and places? I don’t know.
And from this it follows that impenetrability is already a conclusion you inferred from the observations, not the observation itself. That conclusion already contains within it the result that another ball will not pass through there, and therefore this is not a relation of cause and effect but a relation of identity.
This is logical entailment, not cause-and-effect relations on the physical plane.
In other words, you already made the causal generalization when you reached the conclusion that the balls are impenetrable, not when you inferred from that a conclusion about a future experiment. The change of direction that this “causes” is an interpretation of impenetrability, not a causal result of it. Incidentally, a change of direction is actually neither this nor that, since impenetrability can also lead to a situation in which the striking ball stops and stands still. It is not necessary that it continue with a change of direction (and indeed in a plastic collision that is what happens. You are talking about an elastic collision).

We’re repeating ourselves.

There really is an element of repetition in what we’re saying, but that stems mainly from your short and vague formulations, which I have trouble understanding. Also, you argue against things I didn’t say, and that leads me to go back and restate my words precisely. (For example, I too wrote, like you, that induction does not force causality, and that causality presupposes induction, but let’s leave that aside.) If you don’t want to clarify your words, that’s your right; I for my part won’t refrain from responding as long as I feel my words haven’t been properly understood.

1. You wrote: “Touch does not show you that the balls are impenetrable. The conclusion that they are impenetrable is your conclusion etc., and from this it follows that impenetrability is already a conclusion you inferred from the observations and not the observation itself.”

That is exactly what I wrote above: the extension from a ‘feeling of impenetrability’ to a general definition of ‘impenetrability’ rests on induction from observation/touch, not on observation.

2. You wrote: “Impenetrability is already a conclusion you inferred from the observations, not the observation itself. That conclusion already contains within it the result that another ball will not pass through there, and therefore this is not a relation of cause and effect but a relation of identity. This is logical entailment, not cause-and-effect relations on the physical plane.”

I don’t understand. I never claimed that the impenetrability between the balls is the result. I wrote explicitly that impenetrability is an induction from sensation/observation, and yes, in exactly the same way this property will manifest itself in the encounter between the balls. That is indeed logical identity and not a result.

3. You wrote: “A change of direction is actually neither this nor that, since impenetrability can also lead to a situation in which the striking ball stops and stands still. It is not necessary that it continue with a change of direction (and indeed in a plastic collision that is what happens. You are talking about an elastic collision).”

Again, lack of precision: I was talking about a change in momentum, not a change in direction. I wrote that in the collision of ball A with ball B, assuming they are impenetrable, a change in momentum must necessarily occur in one of them (even if the first one stops—that is, a plastic collision—a change in the momentum of the first has occurred). There is indeed a possibility that the change in momentum will be expressed as a change in direction, but the main point is that the assumption (the inductive one!) that the balls are impenetrable necessarily leads to the result of a change in the momentum of one of them.

Up to here these are mostly fine points, but below is the main thing I can’t understand:

4. You wrote: “The change of direction that this ‘causes’ is an interpretation of impenetrability and not a causal result of it.”

That is a sentence I really don’t understand. A change in direction (= in momentum; see 3) is an interpretation of impenetrability?? And not its causal result?? I don’t understand the meaning of that sentence. Clearly, the change in momentum in one of the balls, even according to David Hume, is a result (!) of a collision between impenetrable balls: from the event of ball A moving toward ball B at rest, a result is caused—a change in the momentum of one of them. That is not an interpretation of impenetrability. One ball’s not passing through the other—that is an interpretation of impenetrability. By contrast, a change in the momentum of one of the balls is already a necessary result of impenetrability, not an interpretation of it.

And this is where my claim comes in: the result (the only result here) of ‘change in momentum’ (which, as I understand it, Hume too sees as a ‘result’) is a result necessitated by the property of impenetrability (which is known from inductive generalization), and it is not merely a hypothesis that rests on contiguity in time and place and induction of repeated phenomena, as David Hume claims.

Again, I think something important and basic is being clarified here, and I’d be glad if you would clarify these points.

I want to return and sharpen N.’s point.
I think there is a very important discussion here.
1. I am willing to accept (for the sake of the discussion) that impenetrability as a general property of every ball is Hume’s problem of induction.
But the impenetrability of a particular object, these balls lying before me, I can observe their impenetrability.
(I can try to put one ball inside another ball.)
So in a particular case I can observe causality itself: the impenetrability of these particular balls entails a change in the state of at least one of them when one moves toward the other.
(Even stopping is a change.)
2. Hume’s problem of causality is the problem of the source of the very concept of causality, even at the particular level; the problem of generalizing a causal law for every similar object is the problem of induction.

3. Not every concept can apply to every concept.
You wrote: “You can also discuss whether demons are penetrable or not, and whether thoughts are penetrable or not.”
According to you, can a good character trait be square?
Impenetrability is a definition connected to place; a concept that is non-local, like a thought, cannot be defined by a local concept.
Just as an object with shape must have a definite shape (it cannot be both round and square at the same time),
so too an object that is in a place and has spatial dimensions must be defined with respect to its impenetrability.

Y.,
As I wrote, the change in momentum is a logical result (not a physical one) of impenetrability. What does it mean that the ball is not penetrable? That it is impossible to pass through it. And from this it follows that the object that collides with it cannot continue forward and therefore must choose another path, meaning change momentum. Therefore the change in momentum is an interpretation of impenetrability, not a causal result of it. A necessary logical derivative is not a causal result.
More generally, I would say that if B follows logically from A, that means it is contained in its concept. Therefore when you know that A obtains, it is clear from logical analysis that B obtains. But as I explained in my book Science of Freedom, the causal relation includes, in addition to the logical connection, also a physical relation (causing). A relation that is purely logical cannot be a causal relation. The effect is not a logical derivative of the cause.
And from this it follows that the causal relation cannot be obtained from observation, nor from logical derivation, and therefore it is a result of our thinking. That is Hume’s claim. Except that in his view this is a convenient fiction, and in my view it is a synthetic a priori insight.

Yaakov,
First, you have to limit your conclusion not only to the object you observed but also to the specific case you observed. That is, you cannot infer impenetrability of an object, but at most its impenetrability in a certain case.
Second, you are actually assuming causality implicitly. After all, how did you reach the conclusion that the ball is impenetrable? Because something collided with it and changed momentum. And of course you assume that a change in momentum is caused (causally?) by impenetrability. From that you inferred that there is impenetrability. And then again you infer from the impenetrability that there will be a change in momentum.

I think we’ve exhausted this. I don’t know how to explain it any better.

1. You write: “The change in momentum is an interpretation of impenetrability and not its causal result. A necessary logical derivative is not a causal result.”

That means that according to you, in the billiard-ball example there is no causal relation at all, but only a logical derivative. That is a very strange claim, considering that David Hume chose precisely the example of billiard balls in order to illustrate the problem of causality (which means that he does see the change in momentum as a causal result, only that in his view this causal diagnosis rests on contiguity in time and place and is not necessary—a claim that neither of us accepts).

2. As for the substance of the matter, in my understanding there is really no disagreement between us. You too acknowledge that the change in momentum is logically necessary, only you refuse to call that a cause-and-effect relation and insist on calling it an ‘interpretation of the ball’s impenetrability / its logical derivative.’ Whereas I call that too a cause-and-effect relation, with one difference: unlike causal relations elsewhere, which are not necessary but rest on contiguity in time and place alongside repetition, there are places such as the billiard-ball example where the result is necessary, as you too agree.
(It’s a shame this took so long; it’s the result of overusing the term tautology. To say ‘impenetrable balls will not pass through each other’—that’s a tautology. But ‘an encounter between impenetrable balls causes a change in their momentum’—that is not a tautology.)

Still, since this is not merely a semantic dispute (as it seems at first glance), I’ll dwell on this point and its important implications.

The question we now need is: what may be called a causal relation? (And from here it’s a short step to claim that there are ‘causal relations’ that are forced upon us, even if not all of them are.)

In my understanding, the concept of causality comes to describe a certain relation between two events. That is, if our observation of events can bring to our awareness only the occurrence of an event or a sequence of events, and no more, causality adds that there is also a causal connection between the events, meaning that event B was caused by event A, and without event A, event B would not have come about. Up to here, I think everyone agrees.
In the picture of the billiard balls, observation (together with induction) yields: event A, ‘billiard ball 1, non-penetrable, moves toward billiard ball 2, non-penetrable and at rest.’ Event B, ‘a change in momentum of one of the balls.’ In my understanding these are two separate events, and no observation manages to ‘see’ the causal relation in them, and therefore identifying this relation is an addition by us, the observers. The remaining question is: on what is the assumption based that there is a causal relation between the events? That is, how do we know that event A caused event B, and that without event A, event B would not have happened? And here the split appears: Hume says the diagnosis rests on contiguity in time and place and on repetition of the phenomena; I say that the event of ‘change in momentum’ is a necessary result of the event of the ‘encounter between impenetrable balls.’ (Whereas you say that although it is necessary, it is not a causal relation at all.)

You may ask why I decided to call this a causal relation. Because in my understanding every pair of events that direct observation does not connect, but for other reasons we want / are able to determine that without event A there would not be event B, should be called a causal relation. I cannot understand why the fact that the result is a logical derivative of the cause deprives them of the status of a causal relation, and it seems to me that the burden of explaining this lies on you.

I maintain that even if there are pairs of events whose causal relation is a hypothesis, as Hume says, there are pairs whose causal relation is necessary, and this is a logical opening to understand the concept of causality even if, hypothetically, causal thinking had not been built into cognition.

You explained your position very well, so the discussion can continue.
1) You write: “You have to limit your conclusion not only to the object you observed but also to the specific case you observed. That is, you cannot infer impenetrability of an object, but at most its impenetrability in a certain case.” According to what you’re saying, is the problem of induction the problem of the stability of objects?
(Maybe objects do not preserve their properties.)
2) You write: “After all, how did you reach the conclusion that the ball is impenetrable?”
Answer: from the fact that I wasn’t able to place them in the same spot.
Even without a change in momentum, I tried to insert one ball into another while both were at rest, and I didn’t succeed (unfortunately).
3) I await your response regarding your statement:
“You can also discuss whether demons are penetrable or not, and whether thoughts are penetrable or not.”
Do you stand behind that?

Y.,
It may be only semantics, and still I stick to my point. If B follows logically from A, then A is not the cause of B. Causality is not a logical relation. For precisely this reason (?) I do not accept your claim that the change in momentum is a result and not an analytic derivation from the meaning of the concept of impenetrability.
I’ll put it this way: when one ball hits another ball and cannot pass through it, that means it will not pass through it. Up to here, tautology. But its not passing through it means that its momentum will change. Again, tautology (for momentum preservation would mean that it continues into it and passes through it).
Of course, if you define causality in your way, you can conclude that a causal relation can be derived by logical tools from observation. But that too is again tautology.
So here, I’ve added the term tautology three more times (four, including this one). What can I do—these really are tautologies.
It seems to me we’ve exhausted it, unless there is a new claim.

Yaakov,
See the explanation I gave here to Y. That I was unable to force it in is a change in momentum. It’s simply a verbal translation. Momentum being preserved means that the ball continues at the same speed and enters the place of the impenetrable ball. If it does not do so, the momentum changes. A purely logical relation. I really don’t understand what is so complicated about this.
3. According to your method—definitely yes. The definition of impenetrability that you propose (which is not logically connected to change in momentum) could also apply to the salty taste of watermelon. But I don’t think I’ll continue discussing this here, because this discussion is going nowhere. We have clarified our positions, and let the chooser choose.

For the sake of good order, I’m posting a summary of the discussion.

One of David Hume’s central claims is that a causal relation between events is not something necessary, since causality itself cannot be directly observed, and our ability to infer a causal relation is based on contiguity in time and place between the two events, and on the fact that those same two events occur one after the other again and again, which allows us by induction to infer that there is indeed a causal relation between the two observed events.
Hume illustrates his claim by means of an example: let us take a billiard table on which two billiard balls are at rest, and we give ball A a push so that it is now moving on a collision course with ball B. Hume claims that there is no way to know what will happen to the balls when ball A collides with ball B, and only observation of the two events—(1) the event of the collision, (2) the event of the change in momentum that will happen to the balls or to one of the balls—which reveals contiguity in place and time between them, together with the repetition of this pair of phenomena, leads us by induction to the determination that there is indeed a causal relation between these two events.

Here I want to sharpen an important point. The term ‘causal relation,’ in its simple sense, comes to describe a special relation between two separate events, according to which event A caused event B—that is, if not for event A, event B would not have occurred. And every such diagnosis (made in the way Hume described) between two events is called a causal relation. (Later we will see that according to M. Abraham, the concept of causal relation is defined differently.)

Immanuel Kant further sharpened this point and explained that causality is a priori knowledge, and is one of the forms of human cognition, similar to the other a priori concepts.

What one can apparently remark against Hume’s words is that in the billiard-ball example (and in many additional cases) one can ground the relation between the two events logically, and the causal relation between them is not merely a hypothesis but is forced upon us.
Let us begin by taking the two billiard balls and trying to force them into each other. This is impossible, and that leads us to the conclusion that the balls are not penetrable. (The question whether the balls are penetrable is a question that should be entertained even before experience decides whether they are penetrable or not, since the balls are matter which by definition occupies space; therefore the question naturally arises whether one can pass through them, i.e. occupy their place.)
By means of induction, or by virtue of the accepted claim that objects preserve their properties (the problem of the stability of objects), one may infer that in the future as well, the balls will not pass through each other.
Now let us return to consider the experiment Hume presents in light of these points. When there is an event in which ball A moves toward ball B, which is at rest, Hume claims that one cannot observe the results of this event, and even after observing the results, attributing the result to the cause is only a hypothesis.
Here one can comment on his words: since we have already seen that the balls are not penetrable (through observation / the sense of touch), then necessarily, in event A where ball A moves toward ball B at rest, one cannot conceive of ball A continuing its motion through ball B, and therefore some change in momentum of one of the balls must occur (ball A stops and B begins to move, or A continues moving and B remains at rest, or both move, or both rest).
This change in momentum, which is the event of the effect from event A (the movement of ball A), is forced upon us by the prior examination showing that the balls are not penetrable. It therefore turns out that in this picture, attributing the effect to the cause is not a hypothesis that can be denied, as Hume says, but an attribution forced upon us.
M. Abraham argues against this that the concept of a causal relation does not exist here, because a causal relation exists only when there is no possibility of perceiving the connection between the two events. But wherever one can recognize in the properties of the object in question its implications (as here, where the balls do not pass through each other and thereby block momentum from continuing through), this is a relation between a concept and its definition, not between cause and effect. In other words, any case in which the effect necessarily follows from the cause cannot be called causality.
That is, M. Abraham also agrees that the event of the effect (a change in momentum in at least one of the balls) is necessitated by the cause-event (the movement of non-penetrable ball A toward non-penetrable ball B), only in his view one cannot call the relation between the two events a relation of cause and effect (in your words: “If B follows logically from A, then A is not the cause of B. Causality is not a logical relation. Precisely for this reason (?) I do not accept your claim that the change in momentum is a result and not an analytic derivation from the meaning of the concept of impenetrability”).

Although this seems like a merely semantic difference, and what difference does it make what we call the same sequence of events, this point is nevertheless of great importance. For if we accept that such a relation may also be called a causal relation (except that it is not a hypothesis but necessary), that changes our entire worldview regarding causality, and places it (in certain cases) on the same level as all the other items of knowledge forced upon us.
The main claims I have against your approach are: 1. Your definition of the concept ‘causality’ is very novel, and it seems to me that most would agree with the definition that ‘any two separate events that appear one after the other, and from event A event B follows (that is, if not for event A, event B would not have come about), then the relation between them is a causal relation.’
2. According to you, in the picture of the billiard balls no causal relation exists at all, so it is very puzzling how David Hume (and many others after him) chose דווקא this very example to illustrate the problem of causality.

That is the summary regarding causality.

As an aside, I think there is room for a separate discussion about an important and fundamental point (even more than ‘causality’) that arises from these remarks, and it deserves its own discussion (perhaps elsewhere). I am speaking about the issue of attributing one concept to another.

In the course of the discussion I wrote: “The discussion of whether billiard balls are penetrable or not follows from the very fact that they are matter, although the actual decision that they are not penetrable is known from observation.”

Your response to that was: “One can discuss whether thoughts or demons are penetrable or not, and not only matter.”

And in response to that Yaakov wrote to you: “According to you, can a good character trait be square? Impenetrability is a definition connected to place; a concept that is non-local, like thought, cannot be defined by a local concept.
Just as an object with shape must have a definite shape (it cannot be both round and square at the same time), so too an object that is in a place and has spatial dimensions must be defined with respect to impenetrability.”

Your response to that was: “The definition of impenetrability that you propose (which is not logically connected to change in momentum) could also apply to the salty taste of watermelon.”

1. First, look at the thread above: the claim that “one can discuss whether thoughts or demons are penetrable” was written by you in response to the claim that “the discussion of whether billiard balls are penetrable or not follows from their being matter,” and without any connection to the definition of the concept of impenetrability. That is, in your understanding one can attribute the concept of penetrability to the concept of a demon or a thought (in the sense of passing through the place where it is found).

2. On the substance of the matter, Yaakov did not claim that the definition of impenetrability is unrelated to change in momentum; on the contrary, the definition of impenetrability forces a change in momentum. Only in his understanding this relation (of a collision of impenetrable balls that leads to a change in the momentum of one of them) is a relation of cause and effect, as above.

3. In addition, I saw on the site that you do not see a problem in attributing positive attributes to God.

All three of these points show that according to your approach there is no obstacle to attributing any concept to any concept, and this is far from reason. Not every concept can be attributed to every concept. For example, one cannot attribute the concept of ‘intellect’ to the concept of the ‘inanimate,’ or the concept of ‘sweet’ to the concept of ‘square,’ since no such attribution has any meaning. This leads us to the claim that every concept has a certain range of concepts that can be attributed to it, in some meaningful way, and there are other concepts that cannot be attributed to it by virtue of their very concept. It is hard to know whether there is a rule that determines which concepts can be attributed to which concepts, but by considering the full and precise definition of each concept one can determine whether the proposed attribution between two concepts is possible or impossible.
If you agree to this, then there is no possibility of attributing the concept of penetrability to a demon or a thought, since these do not occupy space and there is no meaning at all to passing through them.
In addition, attributing attributes to God already assumes that we have some conception of His essence (just as we do not attribute wisdom or might to an inanimate object, because such concepts can be attributed only to things to which such attribution is relevant), and it seems to me that everyone agrees that we have no ability to posit God as a defined entity to which one may attribute concepts of description such as these.

According to your claim, a thing’s being a triangle is the “cause” of its angles summing to 180, and it is also the cause of its having corners (three corners to my hat). And likewise, my being married is the cause of my having a wife. A strange and unconventional definition, but I see no point in arguing about semantics.
In any case, this semantic discussion does not have the slightest importance. The entailment you are talking about is necessary and logical. Therefore, according to my approach it is not a causal entailment, and according to your approach it is also a causal entailment. Fine. So we both agree that there are entailments that follow logically from observations; we only disagree about whether these are entailments that can be called causal (semantics). The question is whether the regular entailments—those that both of us attribute a causal character to and define as causal entailments—are indeed logically derived from the observation. Both of our answers to that are no. So in fact the disagreement remains only in terminology, while in content we completely agree. If so, what importance is there to the discussion of what to call the necessary entailments? We both agree that the necessary ones are necessary, and that regarding those that are not necessary, Hume is right: they cannot be derived from the observations and are our assumption (or fiction, in his view).
[By the way, Hume did not claim only that this is not necessary, but that it has no basis and therefore there is no reason to assume it is true (Russell’s teapot).]

1. So according to you, David Hume was mistaken in the example of the billiard balls, since no causal relation exists there?

2. What is your position regarding the attribution of one concept to another? Can every concept be attributed to every concept, or are there limitations as above?

1. If he brought that example in that sense, then indeed he was mistaken. Is there some “do not deviate” command regarding him, and I didn’t know it?
2. There are limitations, of course, and I never claimed otherwise. But I’m not going back to that nonsense here.