The Question of Knowledge and Choice 2 (Column 301)

Let us return to the foolish analogy.

If the fool has a logical contradiction that is not really a logical contradiction, but only one in his own mind, does that mean that if we fail to solve it for him according to his own illogic, then we are somehow lacking?!

It is similar to saying that God is not omnipotent because He cannot create a shell of purple size.

I don't think you addressed that.

I did address it and answered it. I'll answer again: that fool indeed has no way of holding both beliefs.

I think there is a typo in the last formalization. The necessity marker appears on A, but from what you wrote it seems it should appear on B.

And I will elaborate on the rabbi's point.
Yes, the fool cannot believe both that the Holy One, blessed be He, is omnipotent and that there is such a concept as a purple shell.
Now let us think about the analogue: either the Holy One, blessed be He, is not omnipotent, or there is no such concept as “free choice”; therefore you must choose which belief we are supposed to retract.
Michi has already addressed the first possibility, namely the option of denying free choice (determinism). So what remains now (the fourth option) is only to discuss the attribute of “omnipotence” of the Creator of the world.
There is another option, namely that the fool claims that the question itself is simply incorrect, that in truth there is no contradiction between the two things; but insofar as there is a contradiction, he cannot grasp both extremes. In the last post Michi addressed this point and showed that there really is a contradiction between them.

You wrote: “If I hold two contradictory beliefs, then I simply do not believe either of them (I only say both of them, paying lip service). Our beliefs are subject to the constraints of our logic and our thought, and if they depart from those, then they have no meaning for me.”
I seem to recall that you wrote somewhere that one must distinguish between a logical contradiction within the very same concept itself, like saying of a triangle that it is round—which has no meaning at all—and a logical contradiction between two things, each of which is intelligible and true on its own, while only their combination creates the contradiction. If so, I seem to recall that there you wanted to say [perhaps in Two Carts?] that regarding foreknowledge and free choice, since each concept is intelligible in itself, with respect to their combination one can say that we have no conception of God and His essence and do not know how the two are integrated in Him; but that does not prevent our minds from accepting each premise on its own as true.

Søren Kierkegaard claimed that the philosopher thinks he is investigating the world, while in truth he is investigating concepts. A metaphor he used is of a man who sees a sign saying “Shoes repaired here,” and when he enters the shop he discovers that the sign itself is what is for sale.

Dear Shagal.

The better option for the fool, if he has a little sense left, is to conclude that he is a fool, and therefore the problem exists only in his own mind; and the fact that he cannot solve it is no reason for drawing conclusions, because reality is stronger than the limitation in his mind.

As for the purple shell, it seems you did not grasp my intention. I meant to suggest yet another limitation of God—after all, He cannot create a shell with a purple length and a yellow width with touches of liter.

And the analogue is this: every conceptualization you have is not reality but a concept. If you change the concepts and call length a color and color a length, the results will be precise. But so long as you have not changed the concepts, then you are speaking unclearly, and you should not expect people to understand you. And if they did not understand you and therefore did not stop the shell you wanted, you have no basis for drawing conclusions about the recipient of your clumsy request; rather, the deficiency and the problem lie in your request.

For our purposes, God does not solve problems that are not really problems, but rather mental disturbances.!
He can certainly bring you to the state of “If I knew Him, I would be Him,” and then perhaps you would grasp that you asked for nothing at all, because asking for a shell of purple length means asking for nothing!

Shagal, that really is a better idea.
I understood your intention.
By the same token, you can say that the “omnipotence” of the Creator of the world is a concept that perhaps I should revise.
And that is precisely Michi's last option.

You wrote: “At first glance, this experiment proves that such a position is impossible. If a person has free choice (that is, the world is not deterministic), then there is no way to assume that the information exists in advance (that there is such a prophet). That assumption leads us into contradiction.”
I disagree. Indeed, the assumption that the information exists in advance leads us to a contradiction, but Maimonides’ claim is not that the information exists in advance [in a way that it can be ‘calculated’ somehow, that is, that the choice is a product of something in the present], but rather that it exists in the future after his choice, and whoever has the power to sail into the future can know it in advance. In the case of the paradox, a person will never be able to choose something other than what God foresaw, because what he chooses “in practice” is what He saw. How that would work does not interest me [why the person would be compelled to comply with it], but there is no contradiction here.
All in all, you simply do not accept that such a notion as seeing future events in the present is possible. But if we accept the strange assumption that God is above time, there is no contradiction at all between that and a person’s actual choice.

Shagal.

If the fool does not understand how a vehicle moves, and for some reason in his feverish mind he sees a logical contradiction in the very movement of the vehicle (see the paradox of the tortoise and Achilles),

he has two options: (a) conclude that the vehicle does not move; (b) that the vehicle does indeed move, and he is the one who suffers from defective understanding.

The analogue is that we have two options: (a) the One who created our meager minds and the whole universe does not “move”… that is, His power is limited. (b) He does indeed “move,” that is, His power is unlimited, and we are the limited ones.

Let each person infer what is more plausible of the possibilities. Even if the fool concludes that the vehicle does not move, of course we will continue riding in the vehicle to our desired destination.

Tam.

I did not understand the rejection of the film theory. After all, the claim that the Holy One, blessed be He, knows what will happen is equivalent to the claim that He is not subject to time (in a non-deterministic world), and therefore the claim is not that God knows—today—what I will do—tomorrow—but that God stands at the “end of time” and knows what I chose.

How many free choices per day does a person choose on average?
Are some people’s choices freer than others?

I don’t see here a response to the central proposal that there is no contradiction between knowledge and choice. You raised an approach that formalizes the answer logically, and it was indeed refuted, rightly so. But there is still no rejection here of the answer itself. These are the key sentences:
“When the Holy One, blessed be He, knows in advance that I will do X, then I do not truly have the possibility of doing something else. Therefore it is hard to relate to this as an act done by my free choice. Of course I could have done Y, and then God too would have known that I would do Y, and all of this is entirely possible. But on the assumption that God already now knows that I will do X, I have no possibility of doing Y tomorrow. This is information (that is true), and not merely the truth-value of a proposition.”
The statement that there is no possibility is skipping a step. If God knows that I will do X, then necessarily in the end it will come out that I do X, but that does not contradict the fact that I had the possibility of doing Y. So in fact there is no rejection here of the answer at all, only a repetition of the same assertion. Even with the prior information, there is still no reason whatsoever that affects my choice other than the choice itself—and the absence of an external cause is precisely the definition of free choice.

Also regarding Newcomb’s paradox—I do not see there any rejection of the deterministic approach. Suppose the prophet knows how to calculate exactly the causal chain that will lead the person to the choice; he also knows in advance all the calculations the person will make in his head. Therefore, if the person chooses both boxes, the prophet will know the chain that led him there, and will make sure to leave the opaque box empty.

If I understand correctly the definition here of “information” (as opposed to the logical truth-value of truth), then the game is rigged from the outset.
Information is something that does not allow choosing contrary to it, and therefore of course no matter how you twist the discussion you will end up with the conclusion that knowledge contradicts choice—because that is how the concepts were defined in advance.

My personal inclination is to ask why knowledge must be defined this way.
We define information this way because we conceive of the world of time as linear, and it is impossible that after the event of choice there should be a change in the information.
But in a non-linear conception of time, knowledge and choice ought to be defined differently.
(I think this is a point that comes up a lot in the comments, simply in different wording.)

It is somewhat reminiscent of the debates about free choice in general, where the term “choice” is very vague—and the different intuitive conception people have of what that concept is sometimes generates the positions from the outset.

I join Eliezer’s remarks and want to add my own formulation:

In terms of Newcomb’s paradox, it is correct to say that in practice it will never happen that the chooser chooses differently from what the prophet foresaw. But it must be emphasized that this is not because the chooser was compelled to do so because of the information possessed by the prophet. On the contrary, the information possessed by the prophet is the result of the chooser’s *free* choice.
So why is it that the chooser really will not choose differently from what the prophet foresaw? I really do not know, but that does not matter. The main point is that there is no contradiction at all in assuming that the choice is free even though it was foreseen.

I think the problem lies in the connection between possible worlds and the concept of freedom. Freedom can exist even without there being possible worlds in which I chose differently and yet the prophecy in them was the same prophecy as in our world. For there to be freedom it is enough that there are possible worlds in which I chose differently and there was in them a different prophecy from the one in our world.

In other words:

It is true that there is no possible world in which the prophet foresees X and I choose Y. But that still does not mean that if the prophet foresees X I am compelled to choose X.
By the same token, there is also no possible world in which I choose Y and you, looking back afterward, know X. And that still does not mean that if you know X I was compelled to choose X.

Indeed. All the formulas got scrambled in the transfer to the site, but I left them as they were because it came out clear except for that formula, which I corrected. The formula numbers also disappeared and turned into asterisks.

Indeed (at the end of Two Carts). I’ll get to that in the next post.

Eliezer,
Not נכון. In the first post I explained that foreknowledge is not relevant here. I am willing to accept that the Holy One, blessed be He, may have foreknowledge, and the problem is how after that I still choose freely.

Phil, that is exactly what Judith Ronen argues. I disagree. If in no possible world can it occur otherwise, that is what is called here necessity. But I will address your question in the next post (because there I intend to raise a few doubts).

That changes nothing for our purposes. Even if our business is with concepts (and I do not agree with that), we still use them to describe our beliefs.

He can stand wherever He wants. The information exists today. The indication of that is that He can convey it to a person who is here today.

Why is that important?
There are people who are subject to weaker constraints in given circumstances (for example, people who are less prone to violence).

I addressed that in the interpretation of alternative worlds.

As for Newcomb, what will you say about the transparent box?

I don’t know what to say. In my view, information is a well-defined concept, and indeed it includes within it the impossibility of changing it. So what? That is exactly the claim. Do you want to play with the definitions in order to reach a different conclusion?

In the transparent box there is a causal influence of the prophet on the chooser, so of course he cannot predict his action. Therefore it neither adds nor detracts from our discussion.

And regarding alternative worlds—I do not see how that changes the answer: in the end, the question is whether the chooser chooses מתוך absolute freedom or whether his choice is influenced by an external factor. Since the direction of causality is from the choice to the knowledge (backward in time), and not from the knowledge to the choice (forward in time), the choice is the source of both and therefore it is free. So indeed there is necessity between them, just not in the direction you mean.
Unlike Newcomb’s prophet, who according to the deterministic interpretation predicts the choice by means of the circumstances that led to it, God’s knowledge is “supernatural,” and it is caused by the future.

It is important in order to know that you have some idea what you are talking about. To know that you are talking about things in reality and not about things in imagination alone.

1. You did not define what free choice is, and how one identifies when such a free choice has occurred.
2. Can the person himself, who made a free choice, know that this indeed happened, and can it be that he is mistaken and it did not happen?
3. Constraints. Who knows, and how, that there is a state without constraint? By feeling?
4. When you think or write in Hebrew, do you feel constrained to Hebrew? (Seemingly there is no feeling of constraint. It is simply what flows.) Does that mean that the choice of the language of writing is free?

1. Why does it not matter if we are dealing with concepts? After all, concepts are only meant to help us understand what we can manage to understand in a more user-friendly way, and nothing more.

2. Why do you disagree that we are dealing with concepts? After all, logic is not everything. It is important, yes, but there are other components too, no less important.

3. Regarding the implication for our beliefs.
If we managed to describe our beliefs in concepts, tafadal (excellent in Uzbek). And if not, why is the conclusion compelled?
Take the example of the vehicle: if I, a small person, manage to understand how it works according to my limited conceptual world, excellent; and if not, it will still continue to travel!
It would not be wise if, on the basis of my limited understanding of how the vehicle works, I were to conclude that the vehicle does not travel and that this is only an optimistic mistake. I can say that, of course, but it would be a mere statement.

If He conveys the information, that will be a factor influencing the choice, and in His role as lord of time He will know in advance what that information will cause the person to do.
At most, the meaning of this is that He cannot necessarily tell the person what will happen, since that telling changes reality and therefore changes the knowledge and therefore changes the telling itself—but there is no defect in the knowledge.
What needs definition here is time. For if He can move between points in time, then necessarily He knows what was and what will be and can make use of that information; and if He cannot move between points in time, then He has no way whatsoever of knowing what will be.

I claim as you do, only adding something else to complete the argument: “By the same token, there is also no possible world in which I choose Y and you, looking back afterward, know X. And that still does not mean that if you know X I was compelled to choose X.” The reason the knowledge does not compel the choice is that the opposite direction is the correct one—the choice compels the knowledge backward in time (as I also wrote below).

Thank you. You mentioned Taylor, and I had already wondered why you are not a fatalist like him. The distinction between logical truth and information opened my eyes.

Not true. The chooser can decide contrary to his interest. Therefore even if the box is full, he can decide not to take the other one, or yes to take it.

If necessity is defined according to the interpretation of possible worlds, then the term “necessary” is defined through examination of all possible worlds. Therefore you cannot say that although in all worlds it is so, still it is not necessary. That is the meaning of necessity. You cannot dance at two weddings: define necessity through worlds and then split hairs and say that although something exists in all worlds, it is still not necessary.

That is of course not a defect in knowledge, but there is still a limitation here. Therefore I asked: what did you gain from all this?

I don’t think he is a fatalist. He only tried to define what fatalism is.

You are introducing here reverse causality in time. I wrote that I do not accept this, and that Judith Ronen indeed argues in its favor. If you accept such a thing, then of course one can say anything.

God can inform a person what he will choose in the future, and by this the Creator has exercised His ability to deprive the person of freedom of choice; and God can keep the information to Himself and leave the person his freedom of choice. What is the problem with that?

Regards,, Gal Quentin, nicknamed Shatzal [Two Sides to Reality] 🙂

Exactly so. That is what I am arguing. But both to know and to leave freedom of choice apparently do not fit together.

Ariel, I will try to clarify Rabbi Michi’s claim further:
You are indeed correct that logical determination is not physical/causal determination. Foreknowledge determines the future event, but it is not *the cause* of its existence. The physical cause must be sought separately, and theoretically it is even possible that the event has no cause at all, but rather appeared “something from nothing” spontaneously. There is no contradiction between “being fixed and necessary in advance” and “occurring without a cause.” Therefore foreknowledge does not necessarily entail determinism in the physical sense.
The trouble is that the idea of *free* choice does not mean only “acting without an external physical cause,” but also “acting without being predetermined.” If there are two doors before me, one of which is locked, it cannot be said that I am free to choose which one to enter. And for this purpose it makes no difference whether the first door is locked with a physical lock or with a lock of logical necessity.

To Rabbi M. D. A. — greetings,

So long as only God, who is/already is in the future, knows what the person chose, the person’s freedom of choice is not negated. Only “informing the chooser” would prevent his choice.

Regards, Gal Quentin

There is no deficiency here. The claim is that what He says influences reality, and therefore a statement that changes the outcome cannot logically be true—like the question whether the Holy One, blessed be He, can say something true that is false.
With a lack of knowledge, reality has control over the Holy One, blessed be He; but here He can do everything and say everything, provided only that the statement itself does not bring about a result that contradicts it.
Perhaps that is why prophecies are obscure, and perhaps that is why a good prophecy is not revoked while an evil prophecy can indeed be revoked—because naturally people try to change a bad prophecy, and therefore there are more cases in which the prophecy itself changes reality.

I did not notice that Shatzal’s comment relates to this thread. I do not think I am saying anything different from him.

I argue that even the absence of knowledge is not a deficiency. Not knowing nonexistent information is not a deficiency. Beyond the fact that I do not agree with the very claim that His knowledge does not compel the choice, in my view this solution (that He does not know) is more called for. See the next post.

I do not understand how that bears on our discussion. If the box is transparent, there are two possibilities:
1. The prophet will understand that the person will choose the box if it contains money and will not choose it if it does not contain money, and will simply declare that in this case he cannot prophesy.
2. The prophet will know that the person will not choose the box even if it contains money, and in that case will agree to prophesy.
Where is the problem?

So again we enter the same claim of mine, that time does not matter: for the purpose of determining necessity, what difference does it make whether I chose before the information exists or after the information exists?
What matters is the cause of the action, and it is—free.

And what about determination afterward? What is the difference?

The question is whether there is a good reason not to accept this. I have a good reason to accept it, in order not to “force” myself to diminish God’s powers (every diminution of His powers is in fact strained, and this, for example, was clear to Maimonides). The fact that it contradicts physics of course does not bother me at all, because God Himself is not part of the physical system.

I understand.
The combination of the assumptions of foreknowledge together with human free choice in effect entails that the Master of the Universe does not truly have freedom to do as He wishes. He is bound to the future as determined by people’s choices. This is also what emerges from science-fiction stories dealing with time travel. The hero becomes deterministic and loses his creative freedom.

The example that comes to mind—spoiler alert—is The Anubis Gates by Tim Powers (there is also a story by Stanisław Lem in which the hero gets trapped in a time loop repeating 31 days, but that is no small challenge). In the story, the hero travels back in time from the 21st century to the 19th and, after a series of adventures, finds himself playing the role of the fictional poet William Ashbless, whom he studied in his doctoral dissertation. After we finish the book, the question arises: who actually composed Ashbless’s poem “The Twelve Hours”? It was not the hero who traveled back in time, because he merely scribbled the poem he had studied in his dissertation in the future. Nor was it the poet, because the poet is really the doctoral student who traveled back in time only to find himself playing the poet in the past. The conclusion is that the poem was created by the universe (which is of course Tim Powers himself).

The moment we say that the Holy One, blessed be He, knows the future and at the same time we human beings have free choice, the meaning is that the Master of the Universe has no free choice. He is obligated to do what He will do so that the future will occur. In effect, the Holy One, blessed be He, ceases to be the first link in the chain determining what happens. There is a prior link that determines for God what He will do and how He will do it in order for the future to occur. In this way, God ceases to be the God of the causal proof. He is merely another factor in the natural world.

Newcomb’s paradox (and I thank the rabbi for returning to it, because on previous occasions I couldn’t follow it) is, according to this, a special case of Kenneth Arrow’s dictator theorem, according to which it is impossible to produce a consistent ordering of preferences together with independence from the preference system of the participating individuals. If the Holy One, blessed be He, knows the future—that is, the consistent ordering of preferences—then either we have no free choice (God is the dictator) or God has no choice (man is the dictator). There is no other possibility. The other possibility is that God really does not know the future. There is no consistent system of preferences, and the final outcome depends on the different systems of preferences of the participating parties, human beings and God alike.

By the way, I will note that the fact that we are creatures of the Holy One, blessed be He, does not mean that we have no freedom of choice vis-à-vis Him. I once read a quote from Amos Oz who told how at one breakfast one of the characters in a story he was writing appeared to him and announced that she had decided to get divorced. Amos Oz tried to argue with her and tell her that this did not fit the plot he had planned, but she insisted. In the end the character got divorced and Amos Oz had to change the plot (the quote is on Nir Stern’s website, A Living Person).

Maybe I’m about to mix together the plane of free choice with the subject under discussion, or drift into the fourth possibility. But perhaps the solution to the difficulty is that the Holy One, blessed be He, knows what a given creature will choose according to its nature (that is, He knows that according to all the natural and sociological data, my character type for example, I will choose to belong to the stream of the Shas people), while at the same time He gives me the possibility (free choice) to go beyond my nature and choose another path.

With God’s help, 12 Iyar 5780

To Ratzai — greetings,

It may be that the explanation you propose is what the Raavad says about knowledge of the future “in the manner of the astrologers,” who foresee the future in accordance with the character toward which a person tends according to the time of his birth—a forecast that does not provide absolute certainty, since the person’s choice has the power to overcome his natural inclination.

Regards, Shatzam Chanakal

Shatzal
That is what I was aiming at, only in a more radical form.
For the Holy One, blessed be He, knows the structure of my psyche best. He knows not only to what parents and environment I was born, but also what my sensitivities are, my character traits, my moral qualities, my intelligence quotient, and so on—in such a way that on the basis of that knowledge He can foresee not only whether I will choose good or evil, but also what I will choose to eat tomorrow morning.
In such a way, in my view, free choice can exist as a matter of a complete overcoming of nature (such as conversion or repentance from the most terrible places and the gravest sins). Admittedly, the question of the ordinary person’s simple free choice remains here in question, but it can be said that anyone in principle can make this sort of “leap.”

With God’s help, 27th of the Omer 5780

To Ratzai — greetings,

A drastic leap in choice is a relatively rare thing, but everyone has, in Rabbi Eliyahu Dessler’s formulation (in “Kuntres HaBechirah” in Michtav MeEliyahu), a “point of choice,” a certain range within which there is a likelihood of change this way or that. And the more one succeeds in choosing the better option, the more the “point of choice” rises in level.

If we take breakfast as an example: there is a person who cannot do without sugar in his tea, and his range of choice is between two and three teaspoons. He worked on himself and got used to two teaspoons in his tea—his “point of choice” rises, and his good inclination begins to suggest to him that he make do with one teaspoon of sugar. He succeeded in that too and got accustomed to one teaspoon of sugar—his “point of choice” rises, and he begins to think: perhaps it is possible without sugar at all.

And that is in fact how the counting of the Omer is built. After the “drastic leap” that occurred in the Exodus from Egypt, in going out from the forty-nine gates of impurity to become “the people of the Lord,” there then begins the gradual process of refinement and improvement, step by step, through the forty-nine days of the counting of the Omer, until the “point of choice” rises to the level where one can receive the Torah.

Regards, Shatz

The problem is that the prophet is supposed to see the future. So let him fill the box and tell us what will happen. A declaration that he cannot does not solve anything, except for admitting that there is no such prophet who can see everything that will happen in the future. Then God cannot either.

The question is whether this contradicts physics (in which case of course there is no problem) or logic (in which case there is a problem). The arguments here concern logic. It seems to me that the discussion has been clarified. I will return to it in the next post (and there I plan to present reservations, some of which are connected to what was said here).

Indeed, that is the fourth possibility. See the next post.

Not exactly. The concept is indeed well-defined, but not for the conditions of the question.

Notice that by your very definition we are dealing with something that cannot be changed: namely a present existence and a future change.
The definition itself assumes the linearity of time. But when the question deals with something that is not linear in time, that definition is not suitable.

Therefore I think that defining things in advance in a way that does not fit the question is like shooting the arrow and drawing the target afterward.

Ratz"i, Shatzal, and may the next post come upon us for good.
I do not understand.

1. If God implanted in me a nature such that I see a million dollars or ten shekels, and I have no human ability to choose the ten shekels, then there is no basis to punish me for that either, because He implanted this nature in me (this seems deterministic). After all, if He had implanted in me the nature of Hillel the Elder or of Jacob our father, then I would have acted differently (necessarily, by virtue of the different causes).

2. In the final analysis, if my nature compels me one hundred percent to act according to it, the fact that I say I have a choice does not count as choice. For example, to jump into fire when one is offered a happy life may indeed count as an option without natural impediment, but in practice no one will punish the rational chooser who chose life.

3. According to the above explanation, can a person really change his nature? For if so, it turns out that the Holy One, blessed be He, did not foresee what he does in this exceptional case; and if He did foresee it, apparently it is part of his nature.

Ratz"i called it a kind of leap, and I did not understand: is this leap unknown to the Holy One, blessed be He? If so, what have we gained?!

4. The explanation I propose: the principle of probability.

It is common knowledge, for example, the airplane parable of the fool in this locale, and Rabbi Chaim’s parable about a drunk in the yeshiva world.

When there is one explanatory option, as against several options each of which requires its own separate explanation in order to reach one result, then the more plausible one is the single option; and one who introduces a novelty bears the burden of proof (as the Chazon Ish said).

And therefore I do not understand why all of you prefer to arrive at several explanations that lead to one result. Is not one explanation preferable, with all the questions disappearing?

That is: if I see two parts in a vehicle, and I understand how each works on its own, but I cannot understand how the two connect, while the vehicle still moves even though I do not understand it, and the vehicle expert tells me that there is an explanation for how they work together, except that I cannot understand it unless I study auto mechanics for some 30 years—shall I conclude that because I do not understand, the expert is wrong?!

The options you offer lead to the conclusion that there is some limitation in the Holy One’s ability, and for this you posit several assumptions. Is it not simpler to assume that we have a mental disturbance that prevents us from understanding the additional step?! (“If I knew Him, I would be Him…”)

As I said, a shell of purple size, or a round triangle of liter length, is indeed not included in the Holy One’s power—but the reason is that these are simply not matters of ability at all, but mere gibberish. He can do anything that is a request and not gibberish, and in our case our request contains some gibberish, because the concept of ability is not reality but a concept in our minds.

Omnipotent is an intelligible thing, choice is an intelligible thing, the winning combination is not intelligible—okay, so what?! Therefore shall we assume He is limited?! Why not assume that the limitation is in us?!..

If the human mind cannot explain Zeno’s paradox of the tortoise and Achilles, or the dichotomy paradox,
shall we therefore stop moving?!
No!! We continue—and as every person who cannot explain the paradox does, apparently our mind is limited. What is so difficult about that?!

P.S. It seems to me that the rabbi did not answer this, but only answered that in the fool’s mind the things do not work out, and they certainly constitute a contradiction. But I did not understand: if things do not work out for the fool, does that mean that for the fool the vehicle does not move?!
No! There is the plausible option that he is simply a fool, and the limitation lies in his mind. Therefore, what he understands—tafadal; and what he does not—well, it is a pity, but he should not draw foolish conclusions. And if he does, then he has proved to us that he is indeed a complete fool.

Tam.

Tam,
You are mixing apples and oranges.
There is a “contradiction” between concepts, and there is “lack of understanding”:
The concept “God’s omnipotence,” in its broad sense, contradicts the concept “choice.” There is no lack of understanding here.
As for the tortoise and Achilles, this is one concept that we do not understand; the essence of the concept is not defined for us and is not clear.
Every “end” you define includes, by virtue of being an end, infinitely many parts, and it is not understood how an end is possible. But here there are no concepts that contradict one another.
Reflect on this and you will understand.
(For the same reason I disagree with Michi regarding the Rivash’s answer: all of the Creator’s foreknowledge is not defined for us, and therefore the objection “the information exists in the world, therefore I cannot change my choice” is irrelevant.)

The Holy One, blessed be He, does not have knowledge in the human sense, but He has another kind of knowledge, and similarly to a human being, this knowledge provides Him with information about the future, yet it does not contradict our choice.
We do not understand His knowledge, and therefore we do not understand how it does not contradict future choice.
This is Maimonides’ intention.
[You assumed that if He has knowledge like that of a human being, meaning the information, then this necessarily creates a contradiction from our perspective. But one can say that there is a third kind of knowledge, God’s knowledge, which we do not understand, and yet it provides Him with information regarding our choice and yet does not contradict our choice.

Something of which we have no apprehension (God’s knowledge) does not allow us to count it as in contradiction with our choice, because we do not understand God’s knowledge, even though we know that it gives Him knowledge regarding the future.
It seems to me that this is a kind of combination of two of the views you presented at the beginning: “1. The concept ‘knowledge’ as it appears with respect to Him is not understood by us, and therefore it cannot ground a difficulty with respect to our freedom of will. 2. Some will go further and say that the Holy One, blessed be He, is above logic, and therefore they are not troubled at all by logical contradictions in our concepts regarding Him.”

Why is this claim invalid?

It is valid, only it is not a claim. I am asking whether He has information or not. That is all. Yes-no question.

He has no information (in the sense we know), but He knows.
How can this be? I do not know.
{But the picture Maimonides describes in The Guide of the Perplexed (Part I, chapters 50–60 inclusive) describes how impossible it is to understand God, and how the less a person understands, the closer he is to the truth (ch. 59).
The person who attributes concepts to the Holy One, blessed be He, and says that God is wise does not understand God at all, but only says “God” and generally thinks of something else that does not correspond to the true concept. For example, chapter 60—
The parable for this is of a man who heard the name “elephant,” and knew that it was a living creature, and sought to know its form and true reality. And the mistaken one—or the one who misleads—said to him: it is a living being with one leg and three wings, dwelling in the depths of the sea; its body is transparent, and it has a broad face like that of a human being in shape and form, and it speaks like a human being, and at times it flies in the air and at times swims like a fish.
I do not say that this person depicted the elephant contrary to what it is, nor that he does not apprehend the elephant well, but I say that this thing he imagined for himself with this description is a false invention.}

It thus follows that He exists—not in existence; thus He lives—not in life; can—not in ability; and knows—not in knowledge.

Does that not solve the problem? Sorry for the length.

Here we have passed, as was clear to me from the outset, into the realms of nonsense. I have nothing to say about something that is not a claim and that you yourself do not understand what you are saying. So why do you want me to respond?

There are two different issues here: there is the deterministic prophet, who knows the choice by means of its causes—he analyzes the chooser’s brain and all the external influences and knows exactly what he will choose. Such a prophet cannot cope with a case of a transparent box. By contrast, there is the non-deterministic prophet, who knows the choice simply because he can look into the future.
Neither prophet will be able to cope with the transparent box, because there is an influence of their knowledge of the future on the person’s choice, and therefore it is impossible. Likewise, if God’s knowledge influences the chooser causally, then of course he will not choose freely. But so long as there is no causal chain leading from the knowledge to the choice, the choice will be free.
I am not sure you read everything I wrote earlier. I am afraid the discussion here is getting a bit lost because of the lack of continuity, and there are several points I wrote that remained unanswered.

Dear Shagal.

Please explain to me: is a square circle a contradiction between concepts?

After all, a circle is a clear concept, and a square is a clear concept. Does this show a deficiency in the ability of the Master of the Universe?!

For our purposes: the concept of “cannot” is an intelligible concept, but it is not ability—it is a concept!
That is, “cannot” is not ability, and therefore the question whether God can be unable is not a logical contradiction that shows a deficiency in His power, but an unintelligible request, as in the parable of the square circle, where His inability to make it involves no deficiency in the Holy One’s ability. Like the shell with purple length, and like the fact that He cannot produce ma'aye'abachtzaliyahatme.

As for the dichotomy paradox, the tortoise and Achilles:
So long as the infinite is a necessary reality, then if you do not understand it, that does not mean it does not exist; and this is proof that the deficiency is in our meager minds, not in our God!

Consider this and forget it..
Regards, Tam.

I understand the claim:
He has no information (in the sense that we understand the concept of information), but He knows, and therefore there is no contradiction _
This is a claim (you wrote that it is not a claim).
I do not understand how He knows without information (in the sense we know), but that is how it is supposed to be—we cannot understand God, as Maimonides explains in the Guide of the Perplexed.
“It thus follows that He exists—not in existence; thus He lives—not in life; can—not in ability; and knows—not in knowledge” (Part I, ch. 57).

It is clear to me that this is Maimonides’ intention in the Mishneh Torah, and not as you try to attribute to him (according to you, he said something truly foolish: that we do not know how the information reaches Him; and as you wrote, clearly that does not begin to answer).

Pinchas.

The rabbi wrote at the beginning of his remarks: “In this post I will discuss the third possibility, which is the trickiest of them all. I will already say in advance that I tend not to accept it, but a shadow of doubt always accompanies me with regard to the arguments against it.”

And if his intention is the third possibility, namely something like your claim: that we little ones cannot understand Him, and all the patterns in our minds that create logical contradictions for us exist only in our small minds,

then the rabbi too is accompanied by a shadow of doubt on this matter, except that he expects people to say things in their proper terms, and perhaps that is what he means by the nonsense in your remarks.
From his perspective, quoting Maimonides without understanding the meaning amounts to chatter that cannot be responded to.

But it seems to me that your remarks imply that our intentions are similar, and about that the rabbi wrote that he has an inclination to accept them.

By the way, if the rabbi has an option in the blog toolbox to explain the paradox to us, then it is certainly preferable to use it and not go off into the realms of probability.
But if he has no such tools, then what is more plausible is simplicity; and for that, one must examine what the rabbi has to offer in the next post, and examine which of the options is more plausible in the simple sense.
Or alternatively, in which option do we diminish the ability of the Giver of our toolbox in order to explain the matters according to the limited toolbox He gave us? And in which option do we throw up our hands and say: okay, we are missing tools in the toolbox. It seems that the side saying we are missing tools is more plausible.

Correction.

And about that the rabbi wrote that a shadow of doubt accompanies him with regard to the arguments against it.

(Stepping carefully, because a thick pillar of cloud is going before me in everything concerning free choice, and I can’t find my nose or my mustache.)

A. Judith Ronen’s argument—
1. If I understand her argument correctly, it works just fine even if B=A. Is that indeed so?
2. If I understand correctly the interpretation involving possible worlds (which seems like the only interpretation here), then all the sting disappears. You excised the sting in the post (“To understand the problematic point”), but afterward you added that it is rather confusing. I am confused by not understanding what confusion remains.
In this world it is known that A, but it is not necessary that A (because there exists or may exist another world in which not-A).
In this world God knows that I will do A, and therefore I necessarily “choose” to do A, but it is not necessary (because there exists or may exist another world in which God knows that I will not do A, and there I necessarily “choose” not to do A).
What is gained here? In this world I am compelled to do A, so what difference does it make that there is another world in which I am compelled דווקא not to do A (and there God knows that I will not do A)? According to this, obviously there is not even a trace of a problem, even if A=B.

B. From the extreme brevity here I could not understand how one can both assume free choice, also disagree with Łukasiewicz, and also reject the argument of logical determinism. I have not read The Science of Freedom; is there a fuller explanation there? Perhaps in the fourth volume of Talmudic Logic?

Thank you, Tam.
I definitely think that is the direction, and I am not quoting Maimonides merely to clarify that he understood this was a sensible claim—that He knows, but not by knowledge, and that this is indeed how one ought to attribute matters to God, in my opinion.
And I tried accordingly to formulate an answer to Michi’s question, “Does He have information or not?” in light of the fact that we do not understand the Holy One, blessed be He. A short and sharp answer.
And it can be formulated thus: He has no information (in the sense that we understand the concept of information), but He knows.
Tam, do you agree?

Michi, in any case, at least it is clear that Maimonides did not mean what you attributed to him, as I wrote above.
And I will conclude with a quotation from Leibowitz: “The ultimate recognition is to recognize the one attribute that there is God, and that He is God, and every additional word about Him only detracts.” It detracts because beyond that we do not understand.

Cardigno.
I also did not understand the ant argument against Łukasiewicz. After all, he spoke about what has not yet happened, which is in the category of the unknown, and with respect to which the words truth or falsehood are not applicable. By contrast, the ants exist right now, and truth or falsehood are the only options available for defining the correctness of the number. In this case, ignorance certainly does not change the correctness of the number.

As for A, whose being known compels me to choose it, that is of course our assumption based on the toolbox given to us for examining what knowledge is. But if we are missing an additional tool for examining the concept of His knowledge, then it is possible that our conclusion is mistaken.

Pinchas.
The question is what seems more plausible to us beyond the toolbox at our disposal, and not what others think, so long as they have not addressed the question of probability, but rather the logical toolbox available to them, wise though they may be.

As to the substance of the argument, I definitely agree.
In my opinion, the definition “He has no information in what we define as information” is not the most accurate, just as it is not correct to say that He lacks the ability to create a table of black height. The concept “cannot” is not a concept of ability, not even אצלנו, and likewise ignorance is not an ability but an inability; and the whole concept of inability is merely a limitation of those who are able. Therefore, with the Master of all abilities and powers, there is no concept of inability or ignorance, just as there is no such concept for Him as a square circle. Therefore the proper definition is: “He has all the information; we just need to define information correctly.” He simply does not understand what we want from Him.

If, for example, you say that He has no information in drach'achiyatchamam, that would indeed be true, but it would be more accurate to say: He has all the information, you just have to define correctly what you want.

Have a wonderful rest of the day, Pinchas. Just a recommendation: instead of Leibowitz, I would recommend that you quote Hazal, who preceded him both in years and in wisdom.

You began with Maimonides, and I will end with Maimonides.
In The Guide of the Perplexed (I:15, II:10), on the verse (Genesis 28:12): “And behold, the angels of God ascending and descending on it,” concerning the ladder set up on the earth with its top reaching heaven—the divine wisdom ascending upward to the top of the ladder has a great entrance into political wisdom descending downward at its foot.
And if in one part of these two the branches are so many that human survey cannot encompass them, all the more so in both together, being intertwined and interlocked, “The heavens for height and the earth for depth.”

We see only the tip of the iceberg!

Tam, you again mixed several things together, and here I will conclude the discussion (I will; you can go on babbling until “infinity”), because you are repeating the same claims I already answered, and the discussion is becoming circular, with no exit and no destination.
You proved from the fact that there are things we do not understand that even between concepts there can be “contradictions” that are only in our eyes and in truth are not contradictions.
To that I replied that the proof is incorrect and irrelevant, because there is a “contradiction between concepts” and there is a “concept” that is not understood.
A contradiction between concepts means—they do not stand together.
Something that is not understood means that we did not succeed in grasping it with our minds.
But it does not contradict anything. Therefore we can still hold it.
Now you return and say, “It is indeed proof.” To that I say: there is no point in returning to discuss this. You have added nothing new here; you are simply saying “It is indeed proof.” That is not how one conducts a discussion.
Additionally, you added something else about the square circle. I do not understand Chinese, please: a circle, by its very definition, is not square.
I have exhausted the matter, as stated.
Good evening.

P.S.
One more general piece of advice: the condescending style in your wording does not contribute to the discussion, and apparently prevents you yourself from noticing what is the main argument and what is a side argument, what is the question and what is the answer—and in the language of our sages, “asks pertinently and answers according to the law.” I do not know whether the condescension is what causes you not to understand the argument, or whether there is some other reason why you are not responding to the arguments themselves.

If God’s knowledge entails that there is only one future,
and free choice entails that there is more than one future,
then the contradiction arises immediately.

The question is how human beings can know what God knows or does not know.
The answer to that too is simple: they cannot know.
From this it follows that this whole discussion hangs in midair.

Yet another impudent attempt by human beings to reconstruct the psychology of God, which in their insolence they decided He has.

But what does it matter. The main thing is the casuistry. For not study is the main thing, but casuistry.

I am of course talking about a non-deterministic prophet. As I wrote, he has no causal influence on the chooser (not in the sense that it determines his steps), for he can do something that is not to his advantage. True, the chooser takes into account what the prophet places before him. So what? Why shouldn’t the prophet look at the future and see what he will do? I do not agree with this distinction. True, in the next post I will raise some doubts I have, and some of them go in directions I saw in what you wrote. I think we should stop here, because I have lost the context (there are hundreds of questions here simultaneously in several different threads all the time). It is hard to keep one’s head above water with all of them.
I am also not sure I read everything—there is a flood here and it is hard for me to keep track. Sorry.

That is not what I wrote about Maimonides, and I will explain my understanding of his words in the next post. I suggest we stop here. This is not going anywhere.

I lost track of you, and I am also flooded here. It is hard for me to get into it any further. In the next post I will present some doubts I have (as I also wrote here), and some of them probably hit what you wrote here.

Not directly related to the post, but it arose from it—

Several of us were sitting and discussing the above question. The conversation rolled on into a dispute about the chapter “Precedent in Halakhic Ruling” in the book, and then we realized that we do not know how to define clearly what distinguishes the Orthodox approach from the Conservative and Reform ones.

Do you have a post in which you discuss the differences?
One in which you define the lines that demarcate each approach, giving rules of thumb for where to place proposals/conceptions/etc.?

There is no sharp difference between Orthodox and Conservatives. Reform do not issue halakhic rulings because they have no halakhah. And how is this connected to this post?

Shagal.

Apparently I did not penetrate the depth of your view.

And heaven forbid, I did not mean to be condescending. If my words came out sounding condescending, I ask your forgiveness.

Gentlemen, everyone keeps dealing with resolving the contradiction, and no one is talking about the basic injustice of forcing free will upon us without our having freely chosen it in the first place. We are simply stuck with free will, whether we like it or not. If God had asked me first, it is not at all clear to me that I would have wanted to have free will. What is the gain? Reward for choosing the good? Very nice, but in practice, every day sin crouches at the door, and no matter how much I try I cannot manage to shut the door in its face. On a rough average, most of us got the short end of the stick precisely because of this coercion. But the problem is doubly compounded. Even if God were to give me right now the choice whether to get rid of free will, I would not be able to do it. For if I gave it up, every evil deed I do in the future would be a sin by definition—not a sin at the moment of the deed itself (for at the moment of the deed I would no longer have free will), but a sin of now, of the moment in which I freely gave up free will itself. I constantly have the feeling that God has put me in a Catch-22: I sin because I have free will, and if I give it up, that itself is a very great sin!!! So God gave us free will without asking us, and now sees us as responsible for our deeds, and we have to abide by an agreement we never signed. The angels and the stars and the spheres, by contrast, won the cosmic lottery, and this is explicit in Maimonides, Hilchot Yesodei HaTorah: “And all these forms are alive and recognize the Creator, and know Him with a very great knowledge. Each and every form according to its level, not according to its size … And all the stars and spheres, all of them possess soul, knowledge, and intellect. And they live and endure and know Him Who spoke and the world came to be. Each and every one according to its size and according to its level praises and glorifies its Maker like the angels. And just as they recognize the Holy One, blessed be He, so they recognize themselves and recognize the angels above them.” Whoever is not in this exalted group has a wholly justified complaint against Heaven. As for myself, I feel positively cheated. For the average person has a not insignificant chance of going to hell, and did anyone ask me whether I even wanted to participate in a game with negative expected value ???

1. According to the Or HaChaim’s view, that He decided not to know, our knowledge of the Creator’s knowledge is necessary and not contingent. If so, there is no possibility that He does not know, just as He cannot create a stone He cannot lift, or a square triangle.

2. According to Rabbi Hasdai’s view, that the Creator’s knowledge is only of actions—how can it be that our thoughts do not affect actions?!?!

Already at the beginning there was someone who knew what God knows. And here too there seem to be his followers.

To say that God knows by some other knowledge is indeed not a claim, but in my opinion it is a statement that undercuts the very question, because we attribute to God a property of time and say that He “knew beforehand what I was about to choose”—so where is the choice?
And to this comes the explanation and says—there is no beforehand and no afterward; this whole concept is void. One may indeed assume that God knows everything by virtue of His authority as God… but one cannot attach His knowledge to times. This is not an explanation; it is a refutation of the question.
Another thing I still have not understood: how is certain knowledge connected to lack of choice? To say that I did not choose something means that someone else chose for me or caused me to choose, and I am only a puppet on strings.
But certain knowledge does not contradict the fact that I caused the choice for myself independently of that one who knew. For example, if whenever I had two options to choose between, say a red object or a green one, every time I chose the red one (let us say this happened a million times, so there is no doubt what I will choose the next time)—but I did not notice this strange tendency in myself; rather, each time I deliberated anew and finally decided to choose the red one. Yet someone observing from the side identified this point in me and knew in advance that this is what I was about to choose. Did his certain knowledge contradict the fact that in the end I chose the particular object?

Yosef—1. You are mixing things up [like everyone]. The question is not “how the information of the future reached God,” to which your answer is valid, but how the information of the future exists. Think carefully about Newcomb’s paradox [with the addition of the transparent boxes]; it clarifies the contradiction perfectly.

2. Certainly no one chose for me. But if it was clear that I love red—then I did not really “choose.” Meaning: it is impossible to punish me for an act I will certainly do, even if I was not “forced” to do it, if someone sins and has no possibility of overcoming it, then even if he sinned willingly, by force of circumstances it is not a sin for which he should be punished [from the standpoint of punishment, not deterrence].

I recommend Raymond Smullyan’s dialogue that deals exactly with this: Is God a Taoist? It appears in his book The Tao Is Silent. True, I do not agree with his approach, but it is certainly amusing.

1. Why necessary? For example, I think He does not know.
2. That is his claim, that our relation to actions is passive (epiphenomenal). I agree that this is a problematic position.

That is the point: He cannot know in advance, because you may choose otherwise. You are covertly assuming determinism. You are speaking about the film theory discussed in the post.

Nur.
1. That is exactly what I am saying: I do not know how the information about the future exists, if only because it is impossible to know.
Rabbi Michi said that this is not a claim and therefore he does not answer it, and I want to say that it does not intend to be a claim. Rather, the one who objects, “Where is the choice?” is assuming that knowledge means knowing before the act was done, and to that I say that this is an unfounded assumption when we attribute knowledge to God.
To this he answered that if so, this is not knowledge and the one speaking of knowledge has said nothing.
But one can say: let us not call this knowledge, let us call it “mango.” It does not matter. The idea is that nothing is hidden from God; how this happens I have no idea, and I do not think one needs to explain it.

2. The second paragraph depends on the first, because if the knowledge does not contradict the choice (for I do not know what that knowledge is), one can still assume that I am the one who chose and that nothing was clear about it in advance.

1. There is another side. But the side that He does know is the necessary side. What we know about God is necessary, because it is impossible to imagine a world in which it does not exist. More precisely: from where does the information about God’s knowledge come? From the certainty that it follows from His perfection, and that is something necessary.

1. “Information about the future” is a paradox, even if you call it mango, if that is what you mean by it.
Accordingly, do you believe that God can create a triangle lacking sides [because we have no understanding of it]???
I agree with you that if there were a clear tradition about the knowledge, I would believe as you do; but from reason alone it seems like a paradox.
2. Correct. Pharaoh’s case, where God hardened his heart, was an exceptional case, and even that is disputed. But that is not the issue under discussion.

What happens if we replace the two participants in Newcomb’s paradox with two computers: an all-knowing computer and a computer with a function that tries to obtain the highest possible sum? If I am not mistaken, the paradox will remain as it is. And since no one imagines that a computer has free choice—there must necessarily be another solution to the paradox.
I once wrote to you in the Q&A with my proposal, and you disagreed with me. I did not really understand why, because you used terms from mathematics that I barely know the meaning of. But even if you do not agree with the solution I proposed, my question about the choosing-computer still stands, and another solution must be found. Here is the link:
https://mikyab.net/%D7%A9%D7%95%D7%AA/%d7%a9%d7%90%d7%9C%D7%95%D7%AA-%d7%A2%D7%9C-%D7%9E%D7%93%D7%A2%D7%99-%D7%94%D7%97%D7%95%D7%A4%D7%A9

That is regarding determinism.
The rabbi was speaking about the contradiction between knowledge and choice.

You are needlessly assuming that a deterministic device can know everything that will happen in the future. But there is no such device, because the future is not computable. I am speaking about seeing the future, not calculating what will happen in it. Therefore this is a property that God has, or one who receives information from Him. So it is preferable to formulate the question in terms of a human (or divine) prophet and a choosing computer.
But a computer is a deterministic creature, and it will do exactly what its programmer tells it to do (via the software). Therefore there is no problem at all. I too can be such a prophet: I will read the software and know exactly what it will do. I will also know what it will do if I fill the box and if I do not fill it. I will know this through calculation, not through seeing the future. So again the question collapses. And if the programmer allows himself to intervene in the computer’s operation, we have returned to a human chooser rather than a mechanical one.
Therefore, in my opinion, this question can be presented only about two non-deterministic beings.

Newcomb is not a paradox at all, but rather a jumble of various examples from different planes.

Such a prophet—its status of existence is unclear. After all, he could have predicted what he was going to predict and spared all the trouble of putting money in the box and simply given the greedy person the money immediately without tormenting him. The fact that he is required to torment him casts doubt on the accuracy of his predictive ability.

The existence of such a prophet would mean that the halting problem can be decided. Which it cannot.

It is not described what happens if the miserable fellow, out of frustration, decides to toss a quantum coin.

How any conclusions can be derived from such a confused story full of contradictions and ambiguities is not clear to me at all.

I did not understand why the question does not exist when the chooser is a computer. The logic of a human being in a deterministic world and the logic of a computer program ought to be identical. Just as the prophet can read the software, he can (theoretically, not practically) calculate the decision that will be reached in the brain of a person-without-free-choice, because the laws of physics are deterministic, as you often explain.
The software was indeed written in advance, but its execution depends on what the prophet places in the boxes: the software will decide to take both boxes, and then it will understand that this will cause(?) the prophet to leave the closed box empty, so it will change its decision and prefer to take only the closed box; then it will understand that in such a situation it is more worthwhile to take both, and so on. The logic of the software ought to be identical to human logic, and therefore it ought to run into the same dead-end of an infinite loop that a deterministic human being would run into.

The side that He has no knowledge is because knowledge does not derive from His perfection [because it does not exist],
and the side that He does is because it does derive from His perfection, and His perfection is of course necessary.

You answered yourself. In a deterministic person that is indeed the same thing. But in a non-deterministic person there is no software that determines what he will do, and therefore there is no way to read him and know what he will do. One must observe the future (if that is possible).
The software was written in advance, but I can feed input into it and know what will come out. I will check what will come out if I put in a million or if I leave it empty, and then I will know everything that will happen.

I think there is a serious flaw in Newcomb’s paradox:
There is no situation in which, if I choose box A, it will contain $1,000,000, and if I choose both it will be empty!!!!!
If the boxes are transparent, certainly there is no such situation.

The prophet can know, but there is no such reality!

Correct.
The confusion and contradiction in the presentation of the problem can be sharpened still further.
One could have made a paradox about a case in which the prophet who predicted the future revealed his prophecy to the miserable fellow. And the miserable fellow can do the opposite of the prophecy. Then it turns out that the prophet is the miserable one. And so is the one who wrote it as a paradox.

All sorts of miserable people get dragged into problems of this kind, trying with all their might to deny reality according to common sense in order to justify various impulses.

Whatever P does not say, Q twists straight;
Q causes P to come out rather idiotic.
For if P is right—it turns out she lied;
and if she lies—it’s truth she supplied!

Such an elegant paradox emerged,
simply because of P, the invented procedure.
If you assume that P is true—you got entangled;
in the trap I set—you were snared!

So how shall we escape so tangled a distress?
No need for me to tell you; guess it yourself.
A necessary conclusion: in this world,
a legendary creature like P does not exist at all.

http://www.new.tzura.co.il/t/art/10920