Abraham Our Patriarch and His Hat: In Praise of Assuming the Conclusion
With God’s help
Tzohar – 2003
An educational application of the lessons of the book ‘Two Wagons and a Hot-Air Balloon’
The most common ‘proof’ in the yeshiva world is the proof that every Jew should wear a hat, and it goes as follows:
- It is written: ‘And Abraham went’ (‘And Abraham went’) (ibid.).
- And it is obvious that a Jew like Abraham our Patriarch did not go about without a hat.
- If so, just as Abraham our Patriarch found it proper always to go with a hat, it is clear that each of us, who walks in the ways of our aged father, must likewise go with a hat.
Q.E.D.
In this article we shall see that this proof is an impeccably valid logical proof.
Introduction
Not infrequently, young boys—usually students in yeshiva high schools—have approached me with questions that, at root, are very similar, and that in their view touch on the foundations of faith. It is commonly thought that today the youth are troubled by existential questions, and less by rationalistic ones of the sort that troubled us in the past. But this is apparently not entirely correct. Many adolescents whom I have met are troubled, to one degree or another, by the question of proofs for the existence of God, or of the grounding of faith in general. At the most general level, these are doubts that concern the concept of truth and its objectivity.
I suspect that even the common existential hesitations, which apparently arise at a later stage (when one understands that nothing has a proof in the utopian sense that the young adolescent expects), grow on the soil of the rationalistic doubt that was planted at a younger age.
This phenomenon is apparently fairly widespread. If I, as a teacher in a remote hesder yeshiva who has no direct connection with boys in yeshiva high schools, have encountered it quite a few times, then presumably the teachers and rabbis in secondary-school institutions encounter it much more often.
Many of the boys who turned to me felt that they had not received an adequate response from their educators, at least on this point. Quite a number of them felt that these were questions that were ‘forbidden to ask.’ Some of them received an answer from their teachers or rabbis, who explained to them that faith is ‘beyond reason,’ or that their questions are ‘answers’ and not questions, and that they arise from the evil inclination rather than from a genuine desire for clarification, and therefore they will never be able to arrive at a real answer.
It is clear that responses of this sort only intensify their sense of frustration. Beyond that, following such a conversation, the point of doubt may truly take root in their hearts (‘They have no answers for me’). Moreover, once there is no rational answer, there is more room for emotional-existential decisions, which are more subjective by their very nature, and through them—as we all see today—one may arrive at a wide variety of conclusions.
After this introduction, surprising though it may seem, I will argue that in my humble opinion those rabbis answered the students correctly, and in general they really are right. However, it seems to me that they did not do so in the proper and useful way. Below I will try to present a typical conversation that I conducted with such a boy (just a few days ago), and perhaps some educators will be able to derive benefit from it. Like Ramchal in his introduction to Mesillat Yesharim, I am aware that these points are simple, yet nevertheless, to the best of my sense, much benefit may come from sharpening and clarifying them.[1]
I recommend that the interested reader not despair at stages that seem banal, and continue onward. I did not skip these stages, in order to present a dialogue drawn from life.
Dialogue: On Hats and People
Rabbi, I have a question that perhaps one is not allowed to ask.
There are no such questions. Everything depends on motivation. If there is a point that truly troubles you, emotionally or intellectually, you are obligated to clarify it. Of course, if the motivation is merely provocative, that is something else. Elijah the Prophet says: How long will you keep wavering between two sides? If the Lord is God, follow Him; and if Baal is god, follow him. (‘How long will you keep hopping between two opinions? If the Lord is God, follow Him; and if Baal is god, follow him’). This is a very bold statement, and in my opinion it is not mere rhetoric. Elijah tells the prophets of Baal and the people that a person must choose his path and follow it consistently, and not sit on the fence. Rebekah, who sensed the kicks of the child in her womb near a study hall and near places of idolatry, goes to inquire of God. She receives the answer that these are two children, not one, and this seems to her a sufficient answer. Again: two people with backbone are preferable to one who wavers between two opinions. So yes, it is certainly incumbent upon you to clarify what troubles you.
What is the basis of faith?
I did not understand the question. Each person has his own basis.
Are there proofs for it?
For what?
For example, proofs for the existence of God.[2]
What about the proofs ‘from design’ or ‘from complexity’—that is, from the fact that the world is marvelously complex and planned. Does that not testify to the existence of a Creator behind it?
Yes, that is possible, and perhaps even likely, but not necessary. It is possible that the world came into being by chance. You know—the Big Bang, evolution…
If so, the question is what you mean by a ‘proof’.
An argument that will compel me in an overwhelming and necessary way to admit that there is a God.
That definition is still insufficient. I can compel you to do so by torture.
No, I mean intellectual compulsion.
Such compulsion is impossible. It can be achieved only through elements that already exist within you. How can one persuade someone to believe something he does not believe? Do you have an example of something that has a proof in this sense?
For example, the plane geometry that we study in high school. There everyone must admit that the sum of the angles in every triangle in a plane is 180 degrees. Everything is built in a precise mathematical way, and therefore the theorems of geometry are a paradigm of necessary and proven propositions.
And what if I do not accept the axioms of geometry?
Impossible. They are certainly true.
Who told you that? I will now ask you a question similar to the one you asked me, this time about the axioms of geometry: what is the basis for all of our belief in the truth of geometry’s axioms?
Perhaps you really are right. That too is not a necessary truth. It is a subjective belief of all human beings; perhaps it derives from some innate structure in their cognition…
What is your own opinion? What would you think of someone who came and told you that two parallel lines meet somewhere, or that through two points there passes more than one straight line (or perhaps not even one)? Do you really and truly think these are open questions? Try to examine your opinion honestly.
No, I could not accept that.
If so, what is the basis of your fanatical belief in the axioms of geometry?
Apparently I drew them from experience.
But no experience has ever followed parallel lines out to infinity in order to test whether they do not meet somewhere. Nor is there any experience that shows that no more than one straight line passes through two points in a plane (although the fact that one line does indeed pass through them is certainly learned from experience).
Even so, it seems self-evident.
If so, let us see what this example tells us about the concept of ‘proof’. A proof is the drawing of conclusions from axioms (basic assumptions). Whoever does not accept the axioms will not be compelled to accept the conclusion either.
Up to this point that is clear. Many people use this argument in order to undermine the truth of proofs. But my aim here is the opposite: I will use it to clarify the concept of proof, and thereby specifically strengthen it.
The power of the concept of proof stems precisely from the fact that it adds nothing to me beyond what is already present in my axioms. My certainty regarding the conclusions of proofs derives from the fact that they are nothing but an elaboration and analysis of the axioms that I already accept before the discussion begins.
Let us take a classic example of a logical proof:
- General premise: all human beings are mortal.
- Particular premise: Socrates is a human being.
- Conclusion (particular): Socrates is mortal.
If we examine this argument, we see that its conclusion was already hidden in the premises themselves. Whoever knows that all human beings are mortal already knows, implicitly, that Socrates is mortal. Proof (in the logical-mathematical sense) is nothing but a clarification of what I already know. It can never add anything to me beyond what I already know (and what is contained in the premises). That is its power, because for that very reason it is necessarily true. But that is also its weakness. By means of a valid logical proof one cannot arrive at new conclusions, beyond what is already known to us at the beginning of the process. This is what philosophers call ‘the emptiness of the analytic.’
In effect, you are claiming that assuming the conclusion is a valid logical proof. What about Abraham and the hat? Is that a valid proof?
Absolutely yes.
What?…
Indeed, it is a valid logical proof. The fact that it assumes the conclusion raises no difficulty beyond that found in any other logical proof. As we have seen, every proof assumes the conclusion. Without assuming the conclusion, one cannot attain the certainty of proof. More than that: assuming the conclusion is the criterion for the proof’s logicality and necessity.
If so, what nevertheless seems dubious about the proof of Abraham and the hat?
Only a marginal point. Abraham our Patriarch is superfluous to the argument. He adds nothing. One could construct another argument that reaches the same conclusion, as follows:
- Every tradition-observant Jew should wear a hat.
- I am a tradition-observant Jew.
- Therefore I should wear a hat.
Abraham our Patriarch neither adds nor subtracts anything with respect to the validity of the argument. At most, it is a demagogic trick intended to increase the persuasiveness of the argument. Here, of course, it is grotesque, but in other cases (with more sophisticated tricks) it can work.
But all this does not detract in the slightest from the validity of the argument. It is a valid argument in the strict logical sense, and its structure parallels exactly the canonical example of logical arguments given above (regarding Socrates). This argument is valid exactly like plane geometry, and like any other axiomatic-logical system. The problem we feel is only that it contains a superfluous step, and that is not a truly important defect in a logical argument.
If so, assuming the conclusion is not a defect in a logical argument. As we have seen, one can say even more: this is the very definition of a logical argument. A logical argument is defined as an argument that assumes the conclusion.
Another point, which would be problematic only in modern yeshivot (in classical yeshivot this issue is irrelevant), is that we simply do not accept the general premise of the argument, namely that every Jew must wear a hat. But that too is not a defect in the argument; it is only a basis for disagreement with its conclusion. The logical validity of an argument does not depend on the truth of any of its components (neither the premises nor the conclusion).
So the logical argument about the hat is a valid argument, because its conclusion follows from its premises.
If that is so, I do not understand why we need logic at all. If we already know all the conclusions in advance, the whole process is superfluous.
That is not true. For example, there is no child in the eighth grade who does not understand on his own that two parallel lines never meet, and that only one straight line passes through two points. And yet there is no child in the eighth grade who would know, without studying geometry, that the sum of the angles in a triangle is 180. The theorem that the sum of the angles in a triangle is 180 is certainly contained within the axioms—otherwise the geometric proof would not be valid (for in that case it would not be assuming the conclusion)—but it is hidden within them. We are not always aware of what is contained within our premises, and sometimes considerable logical sophistication is needed in order to extract it from them.
If so, logic certainly helps us clarify what we know implicitly. That is not superfluous, because without logic and mathematics it is very difficult for us to do so. Our knowledge is not always sharpened and clarified for us, and we are not always aware of its implications and of what is hidden within it. But it is certainly true that logic cannot bring to our knowledge what was not already present there.
Good, so we have understood what a proof is. Let us now return to the original problem: is there a proof that will necessarily compel each of us to acknowledge the existence of God?
Indeed, after we have understood the meaning and nature of a valid logical proof, we can return and discuss the question of proofs for the existence of God.
In light of what we have learned, it is clear that such a proof can at most help someone who already believes to recognize that fact. It will help him sharpen what is already present within him, and discern the faith that has already been there. Clearly, if, theoretically, there is someone who truly does not believe (and is not merely unaware of it because it is hidden too deeply within him), we will not be able to intellectually compel him by means of a logical proof.
It should be noted that there is no deficiency here, for no proof in any field is stronger than this. Proofs for faith in God are no weaker than geometric proofs. One in whom this is already present can use them to sharpen his faith for himself, and one in whom it is not present cannot. Exactly as in geometry.
If so, I will repeat my question: is there a way to help me clarify for myself the fact that I already believe?
I think so. I emphasize that this is a way intended to help you yourself examine whether you believe, not to convince you of the existence of God. In this way you can examine your own assumptions and see whether you believe. This is not a confrontation between you and me. I will help you ask the questions that will help you examine your own beliefs. Your attitude should also follow from this. You can always tell me that you do not accept the argument and ‘win the debate.’ But the goal is to examine honestly (as in the example of geometry above) what you truly believe, not to win or lose an argument.
For example, anyone can claim that he indeed does not accept the axioms of geometry, and ‘win the debate’ over the question whether there is a proof that the sum of the angles in a triangle is 180. To such a person it is impossible to prove that geometric theorem. But if his goal is to examine what he himself believes, and not merely to win the debate, then he must examine his own beliefs. He must turn inward, and not argue and make claims such as ‘maybe not and maybe yes.’ In inward examination it is clear that each of us believes in these axioms.
Can you demonstrate such questions for me? Questions that can help me examine my own positions.
Certainly. I will use the type of proof presented by the American philosopher Richard Taylor (in his book ‘Metaphysics’), where the distinction between the two approaches to the concept of ‘proof’ that we encountered earlier will also be sharply illustrated.
A person is traveling by train to Scotland. After some time he sees on a hill outside the train a sign made of stones: ‘Welcome to Scotland.’
The classic proof (the proof from design, or from complexity) in such a case says: it is impossible that such a system—complex and purposive—came into being by chance, and therefore it is clear that someone planned and built it.
At this point the young skeptic comes and says: Who says?! Some form had to emerge from all the stones. Everywhere in the world, the forms that emerged are random, and here a form emerged that appears meaningful. But it is entirely possible that this form too arose by chance. There is always some chance that over time stones will arrange themselves into some form. In principle, all forms—meaningful and meaningless alike—are equally probable.
To this one can answer: granted, that possibility exists. But it is not probable. If both possibilities indeed exist, any rational person would bet on the possibility of deliberate formation.
At this point, someone especially bold can reply: indeed, but what is under discussion here is the question of the existence of God, which is itself a wholly improbable possibility (at least on the basis of my experience). Therefore I prefer the possibility that the world (the stone sign) came into being by chance over the improbable possibility that some incomprehensible entity created it.
Here Taylor introduces the special point of his proof. In fact, he reverses the direction of the discussion. In the terminology above, he should now ask the young skeptic whether he truly believes in this possibility, or whether he merely declares it as a theoretical possibility. One must remember that his goal is to examine his own positions, not to win the debate. Denial of plausible axioms is always an option open to the stubborn, as a way to reject counterarguments and win arguments.
But Taylor deals with this claim in a far more elegant way. He in fact accepts, for the sake of discussion, the possibility that the stone sign really did arise by chance. One cannot categorically rule out the theoretical possibility that the stones rolled around for billions of years and formed such a sign. But, he argues, one must notice that when we see such a sign, only two possibilities are open to us:
- To accept it as true, that is, as a sign arranged by some reliable agent, and begin preparing to get off the train.
- To assume that it arose by chance. In that case there is no reason at all to prepare to get off the train, and we must wait for an official announcement.
Theoretically, there is also a third possibility:
- To assume that the sign arose by chance, and nevertheless prepare to get off the train.
This possibility is, of course, theoretical only. Whoever assumes that the sign arose by chance cannot infer anything from it. In such a situation it would be sheer foolishness to begin packing one’s belongings. That person has no indication whatever that he is indeed at the gateway to Scotland.
One should notice that there is no claim here against the probability of the assumption that the sign arose by chance. We are prepared to accept that claim. But it is clear that whoever assumes this will have to act consistently with his assumptions. That is, the claim is the reverse: if he starts packing his belongings, that is a sign that he assumes that the sign did not arise by chance but by intention.
The analogue, according to Taylor, is our senses. Let us take, as an example, the sense of sight. Our visual system is astonishingly complex. It depends on the precision of many parameters, which depend on one another. Here too two possibilities arise:
- To assume that this system was created intentionally, and therefore it enables us to know the world in a way that corresponds to reality itself.
- To assume that the system arose randomly, in a chance process. In that case it is clear that we have no basis at all to assume that sight in any way reflects reality. Why assume that such an unlikely coincidence occurred?
Yet the fact is that all human beings assume that the visual system does indeed correctly reflect the world itself. In the terms of the earlier example, they are preparing to get off the train. But if so, that itself testifies that they believe that the visual system (or the stone sign) did not arise by chance.
One should notice that the claim here is not that the complexity of the visual system testifies to a planner or creator, and that it is unlikely that it arose by chance. In principle, it may have arisen by chance. The focus of the argument is that we have no way to know this. If someone does in fact assume a random origin for the visual system—and that is a legitimate position in this discussion—he has no justification for continuing to place trust in this system.
From another angle: in principle, random formation may preserve a correspondence between the picture in our cognition and the world itself, but for that we would need to know that such a correspondence did in fact come about. Here we have no indication other than what our eyes tell us. But that itself is what is under doubt here. If Elijah the Prophet were to come and say that our eyes do indeed reflect reality, there would be no problem. But he has never told us this. We assume it as self-evident. If so, we have discovered that a hidden faith lies within us: that there is an agent that created this system in correspondence with the world itself. This parallels exactly the train passenger in Taylor’s example.[3]
[The reader would do well to pause here for a moment and make sure that he fully understands the focus of the argument. Many who heard this from me later revealed several fundamental misunderstandings of this argument. It is certainly not equivalent to the argument from complexity or from design (which is based on the assumption that something complex does not arise by chance). This is a subtle and confusing point.]
In this argument we proved nothing to someone who does not believe. We only helped a person whose faith was implicit ask himself the questions that would direct him. He should ask himself (and not create a situation in which we ask him): Do you trust your visual system? And what about the other sensory systems? And what about the logical-intellectual axioms (two parallel lines do not meet…)?
At this point the skeptic can answer that he indeed does not trust them. In such a situation he has indeed won the debate (of course, I do not mean that he has proved that there is no God, only that it has not been proved to him that there is one). In such a case nothing has indeed been proved. This reflects the fact that one cannot prove the existence of God to someone who truly does not believe in Him. But if, in inward reflection, he is honest with himself, he will find within his soul the simple intuition that anyone who denies the evidence of the senses and the accepted axioms requires hospitalization (physical or psychiatric).
It is important to understand here an essential point that characterizes skeptics as such. Usually every person trusts his senses and the prevailing rational axioms. The skeptic too is usually no different from the rest of humanity in this respect. The skeptical condition is created when he tries to give himself an account of the grounds for this trust.
And indeed, we have no distinct rational grounds for it. How do we know that the senses really reflect the world correctly? How do we know that our logical basic assumptions correspond to reality as such? In modern philosophy oceans of ink have been spilled, without any success, in order to answer these fundamental questions (see an extensive survey in Hugo Bergman’s book ‘Introduction to the Theory of Knowledge,’ chapter 9; and compare the introduction to his book ‘Thinkers of the Age’). The sophistication of Taylor’s approach is that he does not look for an answer to these questions at all. He assumes this trust and seeks the assumptions that lie implicitly at its base. He turns inward, not outward.
As stated, this argument does not answer these unresolved questions. I do not think there is any rational answer to them. But one thing does emerge clearly from this argument: if we do in fact place trust (whether justified or unjustified) in these systems, then we are believers, in some sense.
If so, this argument cannot prove to anyone that there is a God. It can only help him discover this faith that is already present in his heart. To the best of my understanding, this faith is present in the heart of every person, and therefore an honest examination ought to yield the proper fruits. Our task is to bring about an honest and genuine examination (and at all costs to prevent the situation of a debate between us and the skeptical youth, in which the question is who will win).
Summary: Back to the Introduction
Here we return to the answers of the educators I described above. It turns out that their answers are indeed correct. Usually the youth does possess faith, but he forces himself to cast doubt upon it, because he has no logical grounding for it. The youth (like many adults in our time) is convinced that in order to be rational he must follow intellectual proofs and abandon subjective ‘gut feelings,’ even though, as stated, these exist in him too, like in everyone else.
These educators are also correct in their claim that he indeed cannot find what he is looking for. Also in the claim that his questions are ‘answers,’ at least in a certain sense. More than that: it really is ‘forbidden to ask’ these questions. As we have seen, this is not a religious prohibition but a logical one. They have no ‘answer’ (in the naïve sense of that term) on the logical plane, and neither does any other question—including questions in mathematics. This distinction we must explain very clearly to our skeptical interlocutor.
As we have seen, to do so one must redirect his attention to the fact that he does not fully understand the term ‘logical grounding.’ In the usual terms, the natural self-evidence that each person possesses is the highest logical grounding possible. Geometry too is based on that same feeling of certainty (‘evidence,’ in Cartesian terminology). Faith in God can be grounded no less than the propositions of geometry (of course, for one who already implicitly believes in it).
Here too there is no impediment to assuming the conclusion. Is it only in geometry that one may do so? The ‘gut feelings’ that accompany him are precisely what ground his trust in geometry. Does he cast real doubt on that too? Apparently these are not gut feelings, but intuitions that correspond to reality. They are tools for cognition and understanding of reality. This is intellectual intuition, not subjective emotion. This correspondence itself, between intuition and the world, constitutes the ‘proof’ of the existence of a coordinating agent. We can use the very existence of the mechanism of proof itself as a proof.
This demonstrates the importance and significance of the reversal in discussions of this type: turning from the direction of a ‘compelling’ proof on the basis of axioms (in the terminology of my book: ‘philosophical proof’) to the direction of an inner clarification of beliefs already hidden in the axioms (in my book: ‘theological proof’). We do not compel anyone; we merely help him understand himself. We are not advancing our own interest, but helping him in his own aims, to understand what he himself believes.
Tried and tested.
[1] The points presented here are one of the focal points of the argument in my book ‘Two Wagons and a Hot-Air Balloon,’ except that there this skeleton is burdened with a rather ‘heavy’ framework, and it is less accessible to one who is interested only in this point. Several educators told me that these types of arguments helped them greatly with educational problems, and therefore I found it appropriate to write this article.
[2] Since my purpose here is only demonstration, I will not distinguish between the philosophical God and the religious God. Parenthetically, I refer the reader to note 25 in my book, where I discuss the connection between the two questions. There is such a connection, but this is not the place.
[3] Several reservations can be raised about this proof, and this is not the place to discuss them all. Here I wish only to demonstrate the method. In fact, to the best of my understanding, the proof is valid. It was tested in a lecture before third-year philosophy students at Tel Aviv University and was found to be faultless. For fuller detail, expansion, and much broader generalization, see my book ‘Two Wagons and a Hot-Air Balloon’ in general, and especially notes 21 and 25.
Discussion
Yahli Shafi
I am sorry for the rabbi’s confusion between axioms and logical inferences. The examples include an axiomatic assumption, and therefore no logical inferences are required beyond it. The basic example of a logical inference is enough: if A equals B and B equals C, then A equals C, to demonstrate an inference that contains no axiomatic assumption.
And to Eitan: if you do not accept all the axioms of plane geometry, you can accept a geometry of curved spaces in which some of the axioms do not hold. This geometry was developed by mathematicians many years ago and was used by Einstein in describing the forces operating in the universe (which is a curved space).
5 months ago
Michi
Hello Yahli.
Now you really have managed to confuse me (because it seems to me that there is no confusion at all in what I wrote, though perhaps that itself is my confusion). So I would be glad if you would clarify more fully the source of your sorrow (= what causes you distress), and perhaps I can ease it for you somehow. It is hard to see someone immersed in sorrow and remain inactive.
On the other hand, it seems to me that there is conceptual confusion in what you wrote. You need to distinguish between the following argument, which is a logical inference:
Premise A: A=B
Premise B: B=C
Conclusion: A=C
and a claim (not an argument) that is not an inference in any sense: if A=B and B=C, then A=C.
Here there are no premises and no conclusion, only a logical implication of the consequent (the “then”) from the antecedent (the “if”).
The first argument derives a conclusion from two premises, and in this case it is a valid argument. By contrast, the claim derives nothing from anything (since it is a claim and not an argument), though it is a tautology (its truth value is always “true”).
In short, there is no inference that is not based on premises. An inference, by definition, is the derivation of a conclusion from premises. So in my great poverty I have not understood what you said.
Two conceptual ambiguities arose for me upon reading your words, and perhaps my lack of understanding is rooted in them:
A. You use the term “heqesh” [syllogism/inference]. Do you mean an inference (= argument) or a claim? I assume you mean an inference, but then I do not see how one can speak of an inference without premises.
Descartes tried to do such a trick with his cogito, and Anselm in the ontological proof. But it is generally accepted that there is no inference without premises.
B. Or perhaps I did not understand the meaning of the expression “axiomatic assumption” that you used. Alternatively, perhaps you could explain to me what a “non-axiomatic assumption” is?
5 months ago
Michi
And perhaps one more note, this time not about logic but about physics. Non-Euclidean geometries are not used to describe forces operating in the universe, but to describe the behavior of the world without forces. Curved geometry is a substitute for the force of gravity. Still, one should know that for the mathematicians the assumptions of these geometries were arbitrary or hypothetical (you assume them and check what follows), whereas for physicists these are factual claims. Geometry deals with “if X then Y” (and does not care whether X or Y are true), while physics deals with X and Y themselves. Here we have returned to my previous response to your remarks.
5 months ago
Yahli Shafi
Thank you for the response.
Regarding physics: non-Euclidean geometries are used to investigate the laws governing curved spaces, but in physics, in Einstein’s general theory of relativity, they describe the effect of objects on curved spaces and the effect of curved spaces on the behavior of objects. The basic force, the left-hand side of the equation, is the force an object exerts on space and determines the degree of its curvature.
Regarding logic: a logical inference is not necessarily an inference from premises; it can also be an inference from facts. The fact that A=B and B=C gives rise to the conclusion. True, this is the same result we would get if we assumed the existence of the data that led us to the conclusion, but the rabbi’s discussion depends on facts. The sign for Scotland in the discussion is a fact and not an assumption; otherwise Taylor’s argument loses some of its force (in mathematics we assume that certain premises are facts—axiomatic rather than theoretical assumptions). We arrive at the conclusion regarding the sum of the angles of a triangle in a plane because parallel lines do not meet, not if they do not meet. The problem is the question of what a fact is. The rabbi’s proposed technique of relying on our senses leads to mistaken conclusions. Thus, for example, it is a fact that there is relative motion between the earth and the sun, but what appears before our eyes led the sages of the world and the sages of Judaism for hundreds and thousands of years to think that the sun and the moon move around the earth—a conclusion that is only partly correct, regarding the moon alone, and even there it is the motion of both bodies, in both cases around the common center of gravity and not one around the other.
And one more point. The conclusion from the Scotland sign or from finding a watch in the desert (in another well-known example) is a conclusion dependent on time and place. A person walking in the desert today knows and recognizes that the watch is the result of (human) design, but Abraham our father would have seen in it a divine miracle. Thus everything not known or understood in its time is attributed to God, and He will always exist, because enlarging the sphere of the known merely opens up further unknowns that we had not previously recognized.
5 months ago
Michi
On the physics issue we disagree, but there is no point in conducting that here.
On the logic issue I did not understand what you wrote. Premises and facts are one and the same in my view. There are premises based on observation (and you implicitly assume that it reflects reality), and there are premises from other sources. In the logical sense they have the same status: an intuition on which the inference to the conclusion is based.
Of course the sign about Scotland is a fact. Where was it said otherwise?
When you assume that some premise is a fact, why is this not an assumption like any other? I did not understand this distinction.
The conclusion regarding the sum of the angles is based on an assumption about parallel lines in a plane (that they do not meet). How do you know they do not meet? Because you assume it. On what basis? It is an assumption like any other, and it does not matter how convinced you are that it is correct. Others are convinced that facts they observe are correct to exactly the same degree. I do not see any principled difference.
If you do not rely on the senses, you can throw out everything you know about the world from A to Z. Nothing remains. This does not mean that the senses cannot deceive. Of course they can. Where did I say otherwise? But why does the possibility of error lead you, in your view, to abandon trust in the senses? Do you have another source of information?
As for your claim about conclusions that depend on time and place, I disagree. I explained this in my book “God Plays Dice.” 1. There is no “God of the gaps” problem here (because this is an essential gap, not a temporary one). 2. Even regarding the watch, the conclusion is that a person made it and that it did not arise by itself. Exactly the same with the world: the conclusion is that there was someone who created it and that it did not arise by itself. There is no difference at all (regarding the influence of our experience, according to which watches are created by people, see the last appendix of the book “God Plays Dice”). See all this also in the third notebook on the site.
5 months ago
Yahli Shafi
And again, thank you for the response.
The difference between premises and facts is, in my humble opinion, that facts are a subset of premises—those that can be refuted (something similar to the principle of falsification). Other premises cannot be refuted because they are theoretical in nature. The matter of sense perception is not relevant here.
You sent me to the last appendix in your book, and I went back to read it. It seems to me that it actually proves my claim about conclusions that depend on time and place. The fact that at a certain time we do not possess evidence by way of “relating the unfamiliar to the familiar” cannot lead to a conclusion that has no support at all, but only to an admission of ignorance. Clearly, relating the unfamiliar to the familiar depends on what is familiar, and that is a question of place and time.
The obvious but unwarranted need to explain what is unknown with mere hand-waving explanations is harmful, because then there is no further need to search for other explanations, ones that meet the standards we demand of explanations. The word God is as good an explanation as saying “I do not know,” but around this ignorance there has grown a strange system of relationships between human beings and that ignorance, to which we gave the name God. This system is called religion. There is no criticism or endorsement here of such systems, certainly not of the one closest to my heart.
5 months ago
Michi
Hello Yahli.
Facts can be refuted exactly like any other assumption. The confirmation and refutation of facts are based on observations, and you have to assume that observation is a decisive criterion. That itself is an assumption that cannot be refuted. Moreover, it is not true that every fact can be refuted. Furthermore, even if we place complete trust in our observations, the claim “there are a million worms in the soil of Haifa” is a factual claim. Now go observe and refute it. The identification of fact with observational falsifiability is a positivist mistake. Therefore I repeat my claim that all assumptions of whatever kind are based on theories that are not observationally falsifiable.
In the appendix to my book, I spoke only about relating the familiar and the unfamiliar. I did not discuss there the question that Dawkins calls “the ultimate explanation,” that is, whether there is a gap that science cannot bridge. As I wrote to you, I explained that in the book (and also in the third notebook here). I completely agree with your claim about the God of the gaps, and I have written this more than once. And yet, as I explained here, this is not a gap that is supposed to be closed scientifically. In this case, God’s existence is not merely the result of intellectual laziness.
What you say seems to me like someone who sees footprints in the sand and says that apparently someone passed here, and you would tell him that he is calling his ignorance “someone.” That is a mistake. He is only determining that someone passed here, and the name of that someone is not really important, nor is further knowledge about him (apart from the fact that he exists and passed here). Now you can try to investigate what that someone is like, but that is only because you reached the conclusion that he exists—that is, that there was someone there. The claim of existence is not a substitute for scientific research; on the contrary, it provides the basis for research.
The same is true regarding the world and its laws. The physico-theological argument claims that their complexity and their special structure indicate that there was someone/something that created them (this is a gap that science cannot bridge, because science operates only within the framework of the laws, while the fundamental question is about the laws themselves. After you have finished all scientific research and arrived at the unified field laws, you then ask who created them. That is not a matter for scientific research). Whether you call him God or Moshele is not really important, and I make no further claim about that. If you wish, go up to the Torah and change His name. The same applies to factual information about Him. Whether He is black or brown, male or female, good or bad—I have no idea, and I have made no claim about that. We have no knowledge of who He is or what His nature is, but it is not true that we are trying to cover over this ignorance by giving it a name. That is nonsense. We have established the existence of something, and indeed we do not know much about it (apart from the fact that it created the world). Now one can begin an investigation in order to clarify its nature and gather the relevant information, just like the footprints in the sand. That is all the cosmological and physico-theological arguments claim, and they claim it well.
The details known about Him (in my view with very limited confidence) are the result of tradition. It gives us details, but trust in them is based on the belief that there was contact with Him at Mount Sinai. You may accept that or not, but you are mistaken when you say that people give a name to ignorance and then derive information from it. That is simply not true. Those details are not the result of ignorance, and no one accepts them because of ignorance. They accept them because they think the tradition is reliable. As I said, even if you disagree, in their view this is certainly the situation from their perspective. Therefore your claim/criticism about covering over ignorance—a very common claim in atheist circles—is simply incorrect.
5 months ago
Yahli Shafi
If I may, one more response.
The parable of the footprints in the sand is, in my view, a good example for my claim regarding the lesson. A common answer to footprints in the sand is aliens (see the Nazca Lines), a hypothesis that receives confirmation from similar phenomena elsewhere on the surface of the earth. The number of believers in this theory is astonishing, and many of its adherents also testify to physical experiences with aliens (not to mention the traffic jams of flying saucers above their heads). These two answers—aliens or God—differ from the bare knowledge that someone indeed passed through the sand and from the attempt “to track him down.” From the moment answers such as God or aliens are given, ignorance has ended in answers that do not permit genuine research, because the properties attributed to these answers are not investigable, almost by definition. They are begging the question by those who believed in these answers long before they saw footprints in the sand (as a parable for the universe). These are nothing but a solution to the basic fear of ignorance, meant to calm the soul of one whose soul is disturbed by the existence of ignorance, or which harm the authority of those who know everything (see your discussion of cults on the site). These are answers that cannot be refuted, and therein lies both their strength and their weakness.
I came across this site by chance while looking for answers to a question entirely unrelated to the topic. From this article I went on to read the entire site. I would like to strengthen your hands in this work. Very few are the places, amid the jumble of information and abuse, where I have encountered such a level of discussion and writing.
5 months ago
Michi
Hello Yahli.
I disagree. Again this returns to the same distinction between questions based on an accidental gap and those based on an essential gap. An accidental gap is closed by scientific research, present or future. But an essential gap (one for which it is clear that science will not be able to provide an answer, such as the origin of the fundamental laws of science) is a question that requires a different kind of answer, and there is no research alternative here. I explained this in detail in the second and third notebooks.
If I have reached the conclusion that there is no answer and can be no answer to the meaning of the footprints—then indeed I will accept an answer of aliens (without saying anything about the nature of the alien, apart from the fact that there is such a thing that left the footprints in the sand; let us call it an alien). That is a logical and compelling conclusion, far more so than the conclusion that no one left those footprints. After all, that is the only alternative. One must understand that an essential gap is not open to research, and therefore a theological answer does not prevent such research.
This is no more begging the question than any other logical argument. The argument is very simple: there is a phenomenon and it has a cause. It has no cause in terms of scientific explanations, therefore it must have another cause. Let us call that cause God. That is all. A completely sensible and logical argument, and not at all begging the question (at least no more than any other logical argument).
Thank you for the compliments. They are a pleasure to me.
5 months ago
Yahli Shafi
I am not standing by my own words and am adding another response. The boundary between an accidental gap and an essential gap is a question of time and place. What was once defined as an essential gap became over time an accidental one. The inhabitants of the New World saw Cortés’s men descending from their large ships as sons of the gods (it took them a little time to realize that at most they were messengers of Lucifer, and mortal like themselves). General relativity closed a gap that shortly before had been considered essential (it seems to me that Planck himself warned Einstein that there was an essential gap here and warned him that there was no point in trying to close it. And if I remember correctly, it was Kelvin who at the end of the 19th century claimed that all the secrets of physics had already been solved and only a few small gaps remained). No one knows what we will understand when a theory is developed that unifies the great theories in physics (perhaps we will receive an answer that brings us closer to the origin of the laws of nature), when we crack the secret of dark energy, or when we understand the operation of the brain.
I would be grateful if you could direct me to where on the internet one can find the notebooks in which you explained these matters in detail.
5 months ago
Michi
Again I disagree.
I am talking about an essential gap that does not depend on time and place. I explained this in my book “God Plays Dice,” and more sharply in the third notebook here on the site. The gap I am talking about is not what physics today does not know how to explain. That is indeed a temporary and local gap, and the God that emerges from it is what is called “the God of the gaps.” But I am talking about the fundamental system of laws that we will discover when we finish all scientific research—that which lies at the foundation of everything (the unified field). It will surely be complex and special, since its products are such (like living creatures). Now I ask who created it. By definition there is no scientific answer to that and there will not be one, since we are speaking of the most fundamental system. Alternatively, if you find another, more fundamental system, I will ask the same question about it. This is a gap that lies outside science and not within it, and therefore I regard it as an essential rather than an accidental gap.
The only way to overcome it is solely if you prove that all our laws of nature are a branch of mathematics. That is, there are no laws of nature and no facts, but only definitions and their derivatives. That is, at the foundation of our physics there are no facts but only definitions and analysis of them. But that is of course absurd.
Two more comments:
1. Of course someone may come and show that I was mistaken here, and that there is another option besides definitions or an essential gap. But that seems impossible, and not merely because our knowledge is lacking and partial. And if that is what atheism is built on, then our situation is quite good.
2. Everything we infer about the world (beyond the direct data of our senses) is the result of this sort of reasoning. There is a gravitational force because I see phenomena that it explains. But perhaps this is only partial knowledge and in fact there is no such force? Why assume a “force of the gaps”? We use the knowledge we have to the best of our ability. One should be humble and understand that perhaps we are mistaken, but the assumption that we are mistaken is certainly no more reasonable than the assumption that we are not. A rational person relies on the knowledge he has, while at the same time knowing that he may turn out to be mistaken. But to give up what I know because perhaps in the future it will turn out to be false—it sounds to me bizarre and irrational. To the best of my understanding, the physico-theological argument is very strong, and the claims that perhaps in the future it will turn out that we were wrong become “the monster (spaghetti) of the gaps,” that is, a proof of atheism on the basis of gaps. No less absurd than the God of the gaps.
5 months ago
Hello, Michi.
You wrote: “But I am talking about the fundamental system of laws, which we will discover when we finish all scientific research.
That which lies at the foundation of everything (the unified field).
It will surely be complex and special, since its products are such (like living creatures).
Now I ask: who created it?
To this, by definition, there is no scientific answer and there will not be one, since we are speaking of the most fundamental system.
Alternatively, if you find another, more fundamental system, I will ask the same question about it.
This is a gap that lies outside science and not within it, and therefore I regard it as an essential rather than an accidental gap.
The only way to overcome it is solely if you prove that all our laws of nature are a branch of mathematics.
That is, there are no laws of nature and no facts, but only definitions and their derivatives.
That is, at the foundation of our physics there are no facts but only definitions and analysis of them. But that is of course absurd.”
A) If I understood correctly, the need to fill an essential gap is based on the understanding that the laws of nature are perceived by us as existing in themselves,
and not that they are “only definitions and their analysis” (which you called absurd).
My question, then, is: why does the question “who created the definitions and the analysis?” not itself require “filling a gap”?
Do you mean that every question and answer is made of definitions and analyses, and that they cannot speak about what lies above them?
B) What is absurd about saying that everything is definitions?
And although this is not a proof, of course, it seems to me that this is precisely the method of “emanation from the spiritual to the physical,”
meaning that the “physical” facts are “drawn down” (by a mysterious mechanism) from “pure concepts,”
and not only that, but even these “concepts” are themselves “drawn down” or “emanated” from “something even higher” of which we have no apprehension (God)?
Hello.
Facts are not drawn from concepts. A concept is not a cause because it does not exist. A cause has to be something—that is, an existent being. What is not a being and does not exist cannot be the cause of anything.
Laws require a lawgiver. Therefore we are speaking of a chain that must end in an entity and not in a law or a definition. The last entity in the chain, if one does not wish to fall into infinite regress, is an entity of a kind unfamiliar to us from experience, one for which no prior cause is required. See the second and third notebooks.
Could you explain what you call “an existent being” and “an entity” and “something,” and what is called “non-existent”?
Until today I thought that only what is absent “does not exist,” and everything that is not absent exists.
Trees and stones, plants and animals and other objects, sound, sight, and smell, taste and other sensations,
love and fear and other emotions, ideas and notions and other intellectual things—
all these I call “existing” because they are not absent, and only what is absent “does not exist.”
And yet I distinguish between them according to the way in which they “are given to me” (in Kant’s language), that is, by what tools I apprehend them.
What I am aware of through the five bodily senses is a “being” of one kind, and what is apprehended by my emotions is a “being” of another kind,
and what I apprehend with my intellect is a “being” of a third kind, and “I” am a fourth kind.
In addition, it seems to me that there is a hierarchy among these “types,” meaning that they are not all “existent” or “present” on the same level:
what is apprehended by the bodily senses is, for a human being, in a certain sense more “existent” (in the sense of “present”) than what is apprehended by feeling,
and what is understood only by the power of the intellect is less “present” (or more “abstract”) than emotions.
If you agree up to this point, I will ask you logically: what would you say regarding the type of existence (unfamiliar from our experience) of God?
For if you say that He is of an even more “elevated,” “abstract” type—say, even less “present”—than all the other types,
how is He a cause of the universe? For surely, if the type of definitions, which is more “present,” cannot be a cause,
then an even more “abstract” type all the more so?
In my opinion there are no different levels of existence. Something either exists or does not exist. Contrary to what some philosophers say, I also think that a necessary existent does not exist more than a contingent existent (a non-necessary one). Both exist fully.
Therefore I do not accept your divisions between levels of existence. All of these are beings that exist in the same sense. They have different properties (for example, some of them have no mass and do not occupy a defined place in space). But as I wrote in the first notebook, existence is a claim about the essence of a thing, whereas properties belong to its form (or: its accidents).
Therefore my claim stands that only beings can be causes of events or things. Which beings? In principle, any being of any kind. But what is not a being cannot be the cause of anything.
You wrote: “In my opinion, there are no different levels of existence. Something either exists or does not exist. …
Therefore I do not accept your divisions between levels of existence. All of these are beings that exist in the same sense.”
If I understood you correctly, it follows that “thoughts” and “concepts” too are an existent being.
What, then, did you mean when you wrote: “A concept is not a cause because it does not exist”?
You are identifying a thought with a concept, and that is not so. A concept such as a democratic state does not exist (except perhaps in the Platonic world of ideas). When one thinks about it, something happens in the brain, and that is a physical event that can be the cause of something.
In my opinion one can define “thought” without needing brain science.
Would you say that a soul, after it has left the body, does not think?
Apparently thought is a “tool” in which the concepts “are given” (or, more neutrally, “are found”).
In other words: thought is the part of the self by which I grasp/receive concepts.
The very presence of the concept in my thought is its existence, since it is not absent from me—it is indeed given to me.
That is, the principle by which I determine what exists and what does not is “being-given-to-me”; what is given to me exists, and what is not— is absent and does not exist.
Of course, “being-given” can happen in several ways; testimony about the thing also “gives” it to me,
though on a lesser level (its certainty is less for me than what is given to me through my own sight).
With your permission, I would like to clarify this issue before returning to the question about the type of existence of God.
What do you think?
Who mentioned brain science here? You keep confusing concepts, and I keep trying to correct you, apparently to no avail.
A thought is not a tool, not at all, but the object of a mental activity.
Thinking is a mental activity (within which thoughts are produced).
The intellect is the tool that performs the thinking and contains the thoughts.
A concept is an abstract object that does not really exist in the ordinary sense (except perhaps in the world of ideas).
When one thinks this concept, one performs a mental activity, and that is an occurrence in the world.
I do not know what happens to a soul after it leaves the body.
What is unclear here?
Sorry if I’m being a bit annoying, but I’m trying to understand.
What is the difference between “the object of a mental activity” and “an abstract object”?
Apparently the object is the very thing that is the object?
For example, suppose that right now I am thinking the following thought: “A democratic state is a good form of government.” My intellect is engaged in the activity of thinking. It thinks. What does it think? The thought in quotation marks above. This is a thought that is inside it. Therefore that thought is the object of a mental act. It is what is being thought. An abstract object is a kind of being. The thought “A democratic state is a good form of government” is not an abstract object but the object of a mental act. Therefore this thought cannot be the cause of something. How can such a thought (I mean the content itself, not the event of the intellect thinking it) cause something? Can the idea of the color red be the cause of something, that is, act in the world? Likewise, the above thought cannot cause something.
By contrast, God (not the concept “God,” but the abstract object that this concept describes) can cause things and do things. But the concept God cannot.
Now I understand:
1. The object of the mental act (call it a “thought” or “concept” or “idea”) is in the intellect (that is, inside me and not outside me).
It does not “exist in itself” (which is the ordinary meaning of existing).
It is only a description of an object that is an entity “existing in itself” (outside me).
2. Only what exists in itself can be a cause of other things, but what is only in the intellect cannot.
(After I understood 1, 2 became as simple as pie, but it helped me understand 1.)
If this is so, then you do admit that there are nevertheless two levels of existence:
1. Existence at the level of thought (presence in the intellect alone)
2. Existence at the ordinary level (outside me).
I do not understand what “existence at the level of thought” means. I am willing to accept the existence of an idea, but that is not in thought; it is in the world of ideas.
The thought is not in the intellect, but is done by the intellect. The intellect thinks, and the thought is the content of the thinking. It is not a thing that is in the intellect, nor a thing at all.
Sorry again, but I am perplexed:
In an earlier message you wrote: “My intellect is engaged in the activity of thinking. It thinks.
What does it think? The thought in quotation marks above. This is a thought that is inside it.”
From this I understood that the thought is “a thing that is in the intellect.”
But in the latest message you wrote: “It is not a thing that is in the intellect, nor a thing at all.”
How am I supposed to make sense of this?
A thought “is” in the intellect in a borrowed sense. It is not a being. It is the content of the act of thinking. The color red is perhaps an abstract spiritual being (an idea), but a thought about the color red is not an idea. Here the thought about the color is simply the content of the act of thinking.
I have now thought of the following analogy: is the speed of a car a being? It is a property of the car, or of an event that the car performs (which is carried out by the car). Of the motion of the car one may say that it is an event (which still has some sort of existence in the world; it occurs in the world), but the speed is only a description or property of the event (= the motion).
The relations between the analogy and the thing illustrated:
the car = the intellect
the motion = thinking (an event/occurrence that takes place in the intellect)
the speed = the thought about the color red (the content of the thinking)
the idea of motion = the idea of the color red (the abstract being one is thinking about)
Thank you very much for your response and answers.
You explained very clearly that a thought “is” present in a borrowed sense.
Accordingly, it seems to me that you would agree that it is correct to say that a thought is not absent.
If so, why is it not correct to say that between “absence” and “being in the ordinary sense” (present in the world—outside me),
there is an intermediate level, which is neither absence (as above) nor ordinary being, but rather “presence” in another sense (a borrowed one)?
Similarly, when speaking about the car’s motion, you wrote:
“Of the motion of the car one may say that it is an event (which still has *some sort of existence* in the world; it occurs in the world).”
Do the words “some sort of existence” not mean a different kind of existence (perhaps a “weaker” one)?
The question is: relevant to what? The motion of the car can cause something because it is an event that takes place (but does not “exist”) in the world. But a concept or a thought cannot bring about anything.
This sounds like philosophy, which I like. Honorable rabbi, if I may: a thought can cause phenomena that identify with it. For example, if a person thinks about an attack, he will become anxious; if a person thinks about food, he will feel hunger. It arouses something in the brain and then creates reactions in the body. About Joseph the righteous it is said that he did not sin because he saw the image of his father before his eyes. We are commanded to walk with tzitzit so as to see them as a reminder of the commandments and not transgress them.
Thought is an inner seeing pictured in the brain, or seeing with the eyes influences thought.
So I am not asking anything, only contributing a familiar perspective and awaiting your response.
Researchers discovered that thinking about certain things activates certain areas in the brain, and thinking about other things activates other areas in the brain.
So we agree that there are at least two kinds of existence, namely: A. existence in the world, B. existence in the intellect,
and only one of them has the power to act and bring things about (so long as I do not yet know what you will say about Mosheh’s remarks above).
Now, with your permission, I would like to understand regarding what you wrote above (in the car analogy):
the speed = the thought about the color red (the content of the thinking)
the idea of motion = the idea of the color red (the abstract being one is thinking about)
This “abstract being”—is its existence of type A or of type B?
(If I understood you correctly up to this point, it seems to me that the answer will be that the “content of the thinking” is of type B, and the “abstract being” of type A.)
So that I can understand better,
could you map the two parts of the analogy (the above one—of the car) onto a thought other than a thought about colors?
Maybe a thought about something more concrete. For some reason the color is confusing me…
Forgive me, but it is hard for me to continue this discussion.
I would appreciate it if you could add an explanation for me.
Regarding Taylor’s argument, I think there is a possibility that our senses were not created by a designer, nor randomly either, but rather by natural selection (the theory of evolution), and therefore they see reality correctly.
2. Even if they were formed randomly, the achievements of science show that we understand reality.
Thank you very much.
I explained both of those things in the fourth notebook.
Thank you.
Hello Rabbi,
You wrote in the summary:
“Here too we have no obstacle to begging the question. Is it only in geometry that one may do so? The ‘gut feelings’ that accompany him are what ground his trust in geometry. Does he cast real doubt even on that? Apparently these are not gut feelings, but feelings that correspond to reality. These are tools for cognition and understanding of reality. This is an intellectual intuition, not a subjective emotion. This very correspondence, between intuition and the world, constitutes the ‘proof’ of the existence of a coordinating factor. We can use the very existence of the proof mechanism itself as proof.”
1) I did not fully understand your conclusion about the proof of a coordinating factor. What is the connection to the rest of the article? I understood you to mean that there are axioms that cannot be proven and yet we rely on them. If so, I would have understood it had you said that, like the assumptions of geometry, other assumptions that we are supposedly certain about can also be relied upon, and some of them are also connected to faith. But I did not understand how the proof of a coordinating factor entered here. How is it connected at all to unproven intuition? How does it follow from the course of the article?
2) Is this “coordinating factor” not refuted according to Kant’s view? Namely, that the world simply appears according to my categories, and therefore of course it is an exact appearance of my basic assumptions? And according to your synthetic approach as well—if I have the ability to identify “basic assumptions” with the eyes of the intellect, why do I need a coordinating factor?
Indeed, this contradicts Kant’s conception. I discussed this at length in my book “Truth and Stability,” where I showed that there is no possibility of trusting intuitions without assuming a coordinating factor. Something like this is also found in notes 21 and 25 in “Two Carts.”
See also the fourth notebook on my site (mainly in the second part).
Hello, and thank you for dealing with uplifting topics amid the dreary reality surrounding us.
Regarding Kant, a comment and a question:
A. Even according to his view, the fact that we impose categories on reality as it is in itself and are able to function in this situation without collisions and in correspondence with it is a miracle, and I think he mentions this.
B. The question: regarding what is said in the article, from Kant’s perspective his categories are indeed things in which we all believe as part of our perception of reality. They are a priori; we have no proof of their correctness, and some of them even lead to contradiction if we try to impose them on reality as it is in itself. Therefore his solution is that they have no validity when imposed on reality as it is in itself, but they are valid for living by them within the framework of the phenomenal world. Consequently he would answer your argument: indeed I believe in them, and indeed I live by them, but I am aware of my limitation and smallness, and it would be presumptuous to project them as correct also onto reality as it is in itself, and therefore onto the issue of the existence of God. And this without falling into self-deception. The truth is that with respect to place, time, change, and therefore causality in practice, he is also correct according to the view of Judaism. I would qualify this by saying that I do not identify with his view except for points of compatibility with Judaism, but I am very curious about your response.
A. I’m not familiar with that.
B. In my opinion there is no contradiction at all in applying them to reality. Incidentally, some of them are probably not correct (modern physics teaches that space and time are not fixed as he thought).
I have explained here several times already that in my opinion Kant does not mean to say that we have limitations in our perception of reality, but rather that this is how we perceive it. There is no perception of something detached from tools of perception. Search the site.
There is no such thing as “the view of Judaism.” There is a correct view and an incorrect one. I discussed this at length in the second book of my trilogy.
Does not every statement about the world (axiom, logical proof, etc.) implicitly assume the basic assumption that the world exists at all (for without a world there is no axiom)? If so, then every axiom is built on the axiom that a world exists at all?
Not exactly, but why is that important?
I didn’t understand.
Why, if we say that the sign off Scotland is there by chance, does that mean we have no reason to prepare for departure when we see it?
Could there not be a situation in which it was both made by chance and also happened by chance to be near Scotland?
The same applies to the senses: could there not be a reality in which they both came about on their own and also testify to reality?
Why, if I claim that this happened by chance, does that also mean I cannot rely on it?
I can claim two things:
1. It came about by chance in a process of gradual formation over time.
2. It really does testify to reality, from experience we see that it really works that way.
I explained this. It is certainly possible, but you have no way of knowing that this is the case. How will you know that the sign was indeed formed at the gates of Scotland? If you have an independent source that says so, then fine, and then you can propose explanations such as evolutionary formation. But from the sign itself you cannot know that. The same applies to the senses. You have no source other than the senses to testify that they are indeed reliable. Everything you perceive comes from the senses.
Eitan
Hello Rabbi.
Regarding the article (fascinating, by the way) “In Praise of Begging the Question,” which also appears in Appendix A, “What Is a Proof,” in the book “God Plays Dice,” the rabbi repeats the claim that axioms can always be challenged. The rabbi writes: “What will happen if I do not accept the basic assumptions of geometry?”
A. I wanted to understand better how one can fail to accept these axioms. Aren’t they scientifically proven? Is it really logically possible to claim that parallel lines will meet at some point?
And is the rabbi בעצם, implicitly (or not so implicitly), trying to say between the lines that just as it is rather ridiculous and unreasonable to say that parallel lines might one day meet, so too it is ridiculous to claim that there is no Creator of the world? (By virtue of the comparison the rabbi draws between the two examples.)
B. Where does the faith dimension come in here? I understood that a proof is begging the question. Is faith believing in the thing begged, in the axiom? Can one argue about this and cause people to believe in an axiom?
Thank you very much, and Shabbat shalom.
Eitan.
6 months ago
Michi
Hello Eitan.
A. Axioms are never scientifically proven, if only because there is no such thing as scientific proof. There is scientific confirmation. The axioms seem self-evident to us, but we have no proof for them, for if we did they would not be axioms. Logically, it is possible to claim that parallels meet, and this is in fact claimed in non-Euclidean geometry. But that describes a space different from the space familiar to us. In flat space, one cannot say that.
As for faith, I do not necessarily mean a quantitative comparison. What I meant to say is that there are beliefs we accept because they seem reasonable to us, without any proof. Like axioms. Not all of them are necessarily at the same level of force. There are assumptions for which I have no proof and that seem correct to me at the 80% level, and others that seem correct to me at 60%. The comparison between faith and the axioms of geometry is not about the level of certainty, but only about the lack of necessity for proof. In terms of certainty, the axioms of geometry personally seem stronger to me.
B. Faith is our capacity to identify axioms and know that they are true without proof. One can argue about this, and even persuade or be persuaded, and the tool for doing so is rhetoric, not logic. I wrote about this in my book “Truth and Stability.”
6 months ago
Eitan
“Axioms are never scientifically proven, if only because there is no such thing as scientific proof. There is scientific confirmation. The axioms seem self-evident to us, but we have no proof for them, for if we did they would not be axioms. Logically, it is possible to claim that parallels meet, and this is in fact claimed in non-Euclidean geometry. But that describes a space different from the space familiar to us. In flat space, one cannot say that.” This is how the rabbi answered me (I didn’t see it here, so I’m quoting it).
Sorry if I’m repeating the question, but I still don’t sufficiently understand what the rabbi means. What does it mean that there is no such thing as scientific proof and there is scientific confirmation? Why does the rabbi distinguish between proof and axiom, claiming that if the axiom were proven it would not be an axiom? It would seem the opposite: it is an axiom because it is beyond dispute and proven, no?
If in flat space it cannot be said, does that mean it is proven?
I’d be glad to get an example of an axiom in geometry that can be logically challenged. (And if we challenge it—then all its derivatives, such as parallel lines, 180 degrees in a triangle, etc., also won’t be true, or at least won’t necessarily be true.)
Does the rabbi have other examples (not geometry) of things that seem to us completely proven and totally clear, but one can challenge the foundations on which they rest?
The rabbi gave the example that all human beings are mortal, Socrates is a human being, and the conclusion is that Socrates is mortal. Can one really challenge the fact that human beings are mortal?
Thank you very much.!
6 months ago
Michi
Do you have a proof that only one straight line passes through two points? It is self-evident, but not proven. Don’t you see the difference between self-evident and proven?
Here is the example: several straight lines pass through two points. There are completely consistent geometries that do not assume this.
Additional examples: the principle of causality (that everything has a cause). That all human beings are mortal. Why can’t one challenge that? It seems correct, but here it is far from being as certain as the axiom in geometry. Elijah the prophet, for example, ascended to heaven and did not die. And so did Enoch.
6 months ago