The Attitude Toward Contradictions: 1. A General Picture (Column 549)
With God’s help
Disclaimer: This post was translated from Hebrew using AI (ChatGPT 5 Thinking), so there may be inaccuracies or nuances lost. If something seems unclear, please refer to the Hebrew original or contact us for clarification.
A few months ago I came across a paper by Rabbi Yehoshua Inbal that discusses the Sages’ attitude toward contradictions. One assumes a colleague does not put out something unpolished, and he has already proven himself with his fine articles. Yet in this paper I noticed several shortcomings that prompted me to write a systematic overview of how to relate to contradictions and, on that basis, to offer a critique of his paper. Although the topic has come up here more than once (see, for example, Column 302 and the entire series there), and I addressed it also in the previous column (when I discussed God’s subjection to logic), and I even devoted a separate article to it (based on a seminar I once gave many years ago in the Department of Philosophy at Ben-Gurion University), I have not yet written a column that lays out the picture in an orderly fashion. Here I will try to fill that gap and present such a picture. In the next column I will, in light of what is said here, present my critiques of Rabbi Inbal’s claims.
What is a contradiction?
An ordinary factual claim can take one of two truth values: if it matches the state of affairs in the world—its truth value is ‘true’; if not—its truth value is ‘false’. For example, the claim ‘It is light outside now’ is true now, but if I say it at night it will be false. The truth value of such claims depends on circumstances.
There are claims that are tautologies, namely whose truth value is always ‘true’, regardless of circumstances. For example, ‘Either it is light outside now or it is not’ is always true, irrespective of circumstances. More generally: “Either X or not-X” is always true, regardless of the meaning of X and regardless of the circumstances. This is the logical principle called the “Law of the Excluded Middle” (either X or ‘not-X’, since there is no third option). Such claims are called tautologies.
A contradictory claim is the negation of a tautology. It is a claim whose truth value is always ‘false’, independent of any circumstances. For example, the claim “Both X and not-X” (which is the negation of the tautology cited above). This claim is of course false regardless of the circumstances, and in logic this is called a ‘contradiction’.
Three types of contradictions
In Column 303 and in my article cited above, I noted three types of contradictions: analytic, a posteriori (observational, scientific), and synthetic-a priori (for short, synthetic). I will begin with the first two, whose distinction is accepted in the philosophical literature:
- An analytic contradiction is a contradiction that exists in every possible world one can imagine. These are the contradictions of the type I described in the previous section: ‘X and not-X’, or ‘Reuven is a bachelor who is married to a spouse’. The first example is a compound sentence, and the contradiction in it stems from the sentence’s structure. This is a formal (or “form”) contradiction, i.e., one that does not follow from the meanings of the concepts involved. The second example is a contradiction that follows from the meanings of the terms appearing in the claim (‘bachelor’ means a person who is not married). Strictly speaking, that is not a contradiction but an empty concept. ‘A married bachelor’ is a concept rather than a claim—a concept with no referent (there is no state of the world that it describes). ‘Reuven is a married bachelor’ is a claim that contains an empty concept. If one wishes to speak of a contradictory sentence, we must construct a compound sentence each of whose parts has meaning, but because there is a contradiction between its components the whole compound sentence is contradictory. For example, consider the following compound claim: ‘Reuven is a bachelor’ and ‘Reuven is married’. This is a contradictory sentence even though there is no empty expression here (although it is still true that this contradiction, unlike the previous example, is not formal; here the contradiction follows from the meanings of the concepts involved in the sentence).
In any case, both of these examples belong to the class of logical, or analytic, contradictions. I call them analytic contradictions because to discover that they are contradictions there is no need for observation or any special philosophical inquiry, but rather an analysis of the concepts involved or of the sentence’s structure/form. These contradictions are grounded in logic.
- An example of an a posteriori contradiction is the following compound sentence: ‘X is a stone with mass that is positioned one meter above the ground with no physical force acting on it other than gravity’ and ‘X does not fall to the ground’. This compound sentence is a contradiction since its two components contradict each other. Their inconsistency is not the result of logical or conceptual analysis, but of observation (the law of gravity is learned from observation). Such contradictions are grounded in observation or science.
Beyond these two accepted types, I argued in my article that there is a third type: synthetic-a priori contradictions (for short, synthetic contradictions):
- Synthetic contradictions do not follow from observational facts nor from logical analysis of concepts and sentences, but from philosophical (a priori) reasoning. For example, the pair of claims ‘Event X occurred’ and ‘Event X has no cause’. This conjunction violates the principle of causality, but as we learned from David Hume, the principle of causality itself is not learned from observation (it is an assumption of science, not its finding). Kant explained that it is a synthetic-a priori principle. Such contradictions are grounded in philosophy (see the series of columns 155 – 160 on defining philosophy; you will understand that the synthetic-a priori is essentially and distinctly the domain of philosophy, as opposed to logic and mathematics—the analytic—and science—the a posteriori).
This type of contradiction lies between the previous two. On the one hand, it is not purely logical (it does not follow from a merely conceptual or logical analysis of the claim), and on the other hand it does not follow only from observation or a law of nature. There is here a contradiction more substantive than the second type but less than the first.
The terminology I attached to these contradictions is rooted in Kant’s classification of all claims into three different types (on the Kantian distinctions along the analytic–synthetic axis and the a priori–a posteriori axis, see the series of columns 494 – 496): analytic-a priori, synthetic-a priori, and synthetic-a posteriori. In this terminology, a logical contradiction is analytic and therefore also a priori (it belongs to the first kind of sentences). It is grounded in conceptual or logical (or mathematical) analysis; an a posteriori contradiction (belonging to the third kind of sentences) is, of course, not analytic. It is grounded in scientific reasoning and observational facts; and a synthetic contradiction is also a priori but not analytic (it belongs to the second kind of sentences). It is grounded in philosophical reasoning.
What’s the problem with a contradiction?
When discussing a contradiction, people usually mean a contradiction of the first, analytic-logical type. What is the problem with a contradictory claim of this kind? Two problems can be pointed out (two sides of the same coin): 1) Such a contradictory claim is contentless; it says nothing. 2) One can derive from it any conclusion whatsoever. I will now elaborate a bit on these two points.
- Suppose I claim that I assert that I simultaneously hold claim X and claim ‘not-X’. Clearly, I have thereby said nothing. The situation is more complex regarding indirect contradictions. Consider Reuven, who asserts the following compound claim: ‘God is omnipotent (and therefore knows everything in advance)’ and ‘we have free will’. On its face there is no analytic-logical contradiction here. When one examines the sentence’s structure, there is no contradiction in it, and even the concepts do not appear on their face to be contradictory. They have meanings that are well distinguished from one another (one is not the negation of the other).
Now suppose, at least for the sake of discussion (in the comments to the series on free choice, 299 – 303, there was a heated debate about this), that one can show there is a (logical) contradiction between God’s omnipotence and the claim that we have free will (or free choice). On that assumption, the claim ‘we have free will’ is logically equivalent to the claim ‘God does not know everything in advance’. Therefore, we can translate Reuven’s compound assertion into the following claim: ‘God is omnipotent’ and ‘God is not omnipotent’, i.e., we have arrived at the contradictory form ‘X and not-X’. True, this required fairly involved philosophical-logical reasoning, but at its end we reached a contentless claim; that is, it turned out that Reuven has said nothing here.
- Basic logic shows that if I have a set of claims that contains a logical contradiction, one can infer from it any conclusion whatsoever. Hence, if a person believes in the Torah and in God, and within his set of beliefs he also holds those two claims (God’s omnipotence and our free will—again, assuming there is a logical contradiction between them), one can derive from his belief system any conclusion we like. In particular, one can derive that God is omnipotent, and also that God is not omnipotent. One can derive from them that the sun rose this morning and also that it did not. One can derive that the Messiah will come and that he will not come. One can also derive from them that Jesus is a supreme star, or that Muhammad is the sole prophet of the Jews. In short, such a person believes in nothing. Whatever he says he believes in, he also believes in its opposite. If our beliefs contain a contradiction, they lose their meaning. We believe in nothing—or we believe in everything.
For the same reason, within the belief system of a person that contains a logical contradiction, one cannot prove anything by way of negation (reductio). Suppose I proved that X is not true; that does not mean that for him ‘not-X’ is true. In effect, for such a person the Law of the Excluded Middle and the Law of Non-Contradiction do not hold. Logic has lost its meaning, and therefore so has everything he says. From now on he ought to be silent, as per Wittgenstein’s injunction at the end of his Tractatus.
What’s the problem with the other two types of contradictions?
Everything I have said thus far is true only for contradictions of the first, analytic-logical type. In an a posteriori contradiction, for example, it is easy to see that none of this is true. If a person thinks that no force other than gravity acts on the stone X, yet he thinks it remains suspended in the air, you will not succeed in deriving any contradiction from this. He may be factually mistaken, but there is no contentless claim here, and it cannot be said that he believes in nothing. The reason is that there is no logical equivalence between the claim ‘the stone remains suspended in the air’ and the claim ‘no force acts upon it other than gravity’. As a matter of fact, in our world these indeed always go together, but one can certainly imagine worlds in which they do not.[1] This is, of course, not the case with logical contradictions. There is no world in which a bachelor can be married (unless we change the meanings of the terms ‘bachelor’ and ‘married’; but with those meanings, no circumstances will change the truth value of such a claim). Likewise, there is no imaginable world in which one can hold ‘X and not-X’. It is meaningless in every possible world.
In other words, there is no principled problem in imagining a world where the laws of nature are different—for example, where there is no law of gravity. In such a world, a stone with mass would remain suspended in the air even if only gravity acted upon it. That does not constitute a contradiction. In our world this, of course, does not happen, but that is a contingent fact, i.e., a mere happenstance. The world could have been created otherwise, with different laws of nature. By contrast, the fact that ‘X and not-X’ is impossible is necessary (and not contingent). It does not depend on circumstances, laws of nature, or this or that world. A world in which this logical law does not hold cannot be created. Hence, if there really is a logical contradiction between God’s omnipotence and the existence of free will in us, then this should be true in every possible world one can imagine. This contradiction is not tied to such-and-such facts in our world but to the meanings of the concepts themselves.
What about synthetic contradictions? Here the situation is more complex. These are contradictions grounded in philosophy rather than observation. That is, they are a priori principles, yet not logic or pure conceptual analysis. Could there be, in another world, a case where an event occurs without a cause? Seemingly yes. True, our principle of causality is not drawn from observation but from philosophy, and therefore it would seem it should not depend on which world we live in. But that is not precise. I have explained more than once that synthetic-a priori claims (like the principle of causality) are also based on observation, only of another sort. It is an observation by the mind’s eye of ideas, or a non-sensory observation of our world. If it is an observation of ideas, there may be room to say that it should be true in every world (and even that is not certain), but if it is an observation of our world—even if not sensory—then it is certainly possible that in another world the results of such an observation would be different.
Thus, for the latter two types of contradictions one cannot say that whoever articulates them has said nothing. The sentence has meaning, and the only question is whether (in the world under discussion) it is true or not. There may be worlds in which such claims are true—unlike what we saw regarding logical contradictions.
Conflict vs. contradiction
To complete the picture, I will add another category that looks like a contradiction, but on closer inspection is clearly not a contradiction but a conflict. I will use my well-known chocolate example. Reuven says it is worthwhile to eat chocolate because it is tasty. Shimon argues against him that it is not worthwhile because it is unhealthy. There is no contradiction between these two claims, and one could even say this is not really a dispute. Clearly both are right: the chocolate is both tasty and unhealthy. True, at the practical level (whether it is worthwhile to eat it) there is opposition, but we will call this a conflict and not a contradiction. A person who holds both claims is not in contradiction; however, at the end of the day he must decide whether health considerations outweigh pleasure, or vice versa. There is no theoretical problem here, hence this is not a contradiction. It is a dilemma entirely on the practical plane, and therefore there is at most a conflict.
This is the case as well with value dilemmas. When there is a clash between a religious value and a moral value, or between two moral values, it is a situation of conflict and not contradiction. Take as an example Sartre’s student’s dilemma in Nazi-occupied Paris. He hesitated whether to remain and assist his sick, elderly mother, or to flee abroad and join the Free French forces to fight the Nazis. This is not a case of contradiction but of practical conflict, since there is no contradiction between the value of assisting an elderly mother and the value of fighting evil. On the contrary, any reasonable person holds both, and this poses no problem for him. In that particular case, a situation arose where those two values clashed and created a conflict: the person cannot realize both and must decide which to fulfill. The same applies to clashes between two halakhic values such as saving life versus Shabbat, or a positive commandment versus a prohibition (see, for example, the questions here), and likewise to clashes between halakhic values and moral values (see in detail in Column 541). All these are conflicts, but certainly not contradictions.
And what about God being above reason and logic?
Many claim that this entire discussion is irrelevant when we deal with matters of faith, especially those that pertain to God. Faith and God are above our intellect and understanding (remember, God is omnipotent), and therefore above the laws of logic. According to them, there is no impediment to believing contradictory claims about God, and our faith is not bound by the laws of logic. In my article cited above I explained that this is true only for the latter two types of contradictions, but not for logical contradictions.
The main reason is that a believer’s claims are claims about himself, not about God. When I say ‘I believe in God’ or ‘I believe that God is good’, and the like, these are claims that describe what is in my mind and in my belief system. If I, as a human being, am subject to the laws of logic, then I cannot hold such claims—if only because they say nothing (see above). Returning to the example of foreknowledge and free will: some wish to argue that since God is omnipotent there is no impediment to holding both beliefs regarding Him. But this position is absurd. First, the claim that I have free will is certainly a claim about me, not about Him. But even the claim that He knows in advance what I will choose describes what I believe (about Him). If, for me, those beliefs are logically contradictory, then holding both is tantamount to saying “I believe that God knows everything in advance and also does not know everything in advance.” Even if God is omnipotent and of immense might, that does nothing to pour meaning into my beliefs. I believe in nothing, and from my beliefs one can derive any conclusion whatsoever. God may be able to do everything, but I cannot believe that. Nor can one say about God that He can create a shell that pierces every wall and also a wall that stops every shell. If you do not want to say that God cannot create both of those together, you can phrase it this way: I cannot believe that God can do both of those things together. That is already a claim about you, not about Him. But bottom line, my beliefs cannot contain logical contradictions. This has nothing whatsoever to do with God’s abilities.
I have often explained that what confuses us here is the common term ‘laws of logic’. This term creates the mistaken impression that we are dealing with a system of laws, like the ‘laws of nature’ or the ‘laws of the state’. But that analogy is utterly wrong. The laws of the state or the laws of nature are laws that someone legislated. They could have been otherwise (one can imagine a world in which the laws of nature or of the state are different from those in our world). But no one legislated the laws of logic. They could not have been otherwise. To say they could have been otherwise would require us to be able to imagine a world in which the laws of logic are different. But we have no way to imagine such a world, because anything outside the laws of logic is meaningless—at least for us. The laws of logic are forced upon us and upon our thinking, unlike the laws of the state or even the laws of nature (which are forced upon us, but not upon our thinking).
Hence there is no need to assume that God is not subject to the laws of logic. The term ‘subjection’ in this context does not operate like subjection to the laws of nature or of the state. There, someone can fail to be subject to them, and therefore one can speak of subjection in its ordinary sense. But there is no subjection to the laws of logic. To operate outside the laws of logic is not difficult—it is undefined. There is nothing outside the laws of logic (at least in our thought—and after all, our discussions can concern only the contents of our thought). Put differently: God’s omnipotence means that whatever is possible and imaginable is not beyond Him. But the fact that He cannot do what is impossible does not impair His omnipotence, simply because there is no such “thing,” and therefore there is nothing to discuss whether God can do it. The sentence ‘God cannot make a round triangle’ does not express a lack in His abilities, since it contains an empty concept. It is neither a true nor a false sentence. It is a string of words that is not a sentence and has no meaning. In short: once you explain to me what a round triangle is, I will be happy to discuss whether God can make such a thing or not.
‘Unity of opposites’
As noted, one cannot believe such claims because they are contentless, and this is a logical consideration. Therefore, sources that address this do not carry weight; they neither help nor harm. Sources that say the opposite simply say nothing. Yet because of the alleged radicality of this assertion, I will just note that it already appears among the early authorities (for example, the Rambam and the Rashba, cited in Column 303, among others). A comprehensive survey on this matter can be found in Yisrael Netanel Rubin’s book, What God Cannot Do.
This implies that the term ‘unity of opposites’ (a term taken from the title of Nicolaus Cusanus’s book), which for some reason in recent generations was imported from Christian thought into Judaism (mainly by Hasidism and Rabbi Kook),[2] is simply nonsense. It is usually employed to ‘handle’ logical contradictions, and when one declares them to be a unity of opposites, there is a sense that something profound has been said that solved the problem. But it is merely a fig leaf for nonsense. Thus, for example, regarding the problem of foreknowledge and free will, some are wont to toss off the statement that this is a unity of opposites. This claim is neither true nor false; it is simply a contentless string of words. It is certainly not to be seen as a resolution of a logical contradiction.
I will only note that sometimes such a statement is used for contradictions of the latter two types, not for a logical contradiction, and then of course it has some sense.[3] But when it comes to such contradictions, there is no need to resort to this pompous term, since one can simply show that there is no logical contradiction, and that’s that. When I say that God could have created a world in which the principle of causality does not exist, that is a very clear claim, and there is no need to invoke a vague term like ‘unity of opposites’ for it. It is not for nothing that Rudolf Otto wrote in the preface to the English edition of his well-known book, The Holy, that “the unity of opposites is the refuge of the lazy.” One who is too lazy to think and to undertake a systematic logical analysis of the issue prefers to broadcast into the air that this is a ‘unity of opposites’. Thus he signals to everyone that he has very profound thought, and this frees him from the intellectual effort required to resolve the contradiction.[4]
‘Two dinim’
In the world of lomdus (analytic Talmudic analysis), since R. Chaim of Brisk it has been common to use a logical structure called ‘two dinim’ (among the professionals: Tzvei Dinim). Rather than speak abstractly, let us take an example. In the halakhic law of evidence there is the principle of ‘migo’. A person advances a claim X in court, but he could also have claimed Y and been believed. If a suspicion arises that he is lying, we rely on migo—namely, we presume he is telling the truth—because if he wished to lie he could have told a better lie and been believed. In addition, later authorities showed that in different places ‘migo’ receives a different meaning: the power of a claim. It is not a logical principle (“why would I lie”), but a legal principle that says that one who could have claimed Y receives the power to claim X as well. An analysis of various sugyot indicates that, simply put, migo assumes both meanings together. It has a rational-evidentiary aspect and a formal-legal aspect. This is one example of “two dinim”.
There are many additional examples of this kind of analysis in the world of lomdus (including cases where the logical structure is slightly different from this example). For instance, the presumption formed after three occurrences (such as an ox that gores three times and becomes mu’ad) can be understood as the ox’s habituation into becoming a gorier, or as evidence that it is by nature a gorier. One can also say that this presumption can be understood in both ways together (three times both serve as an indication of its nature, and—even if its nature were otherwise—it would habituate into goring after three times).
One can see in such moves as well a unity of opposites. A lomdus analysis of the sugya of migo will begin with presenting the rational possibility, then raise an alternative (formal-legal) possibility, and finally conclude with a synthesis—a unity of opposites—i.e., the assertion that both possibilities are correct. There is no problem calling such a move a ‘unity of opposites’, but it adds nothing. We would have understood everything just as well without it, and after it is said, nothing deeper has been added. There is no breach of logic here and no bridging of a contradiction. There simply is no contradiction. Therefore, I would not call this move a ‘unity of opposites’, or at least I would avoid using that term for it. I think the tendency to see such syntheses as a unity of opposites is the result of the lomdus methodology and its manner of presentation. Because we began by setting out two opposing possibilities, asked which is correct (brought proofs for this and for that, and perhaps showed disputes among Rishonim on the question), we accustom ourselves to relate to them as two opposites—even though there is no real contradiction between them. Hence, when at the end we synthesize them, it is perceived as a union of opposites. But in truth, there is no opposition or contradiction here at all, and therefore the unification is not a unification of opposites. It is more akin to a conflict than to a contradiction, though simply speaking it is not even a conflict (since practically one need not choose between the possibilities or decide which is stronger).
Here I conclude the presentation of the logical and methodological background. In the next column I will move on to a critique of Rabbi Yehoshua Inbal’s paper.
[1] The discussion of possible worlds we can imagine is rooted in the modal account of necessity and contradiction (see Column 301). According to this account, ‘necessary’ means ‘true in every possible world’, and ‘contradictory’ means ‘false in every possible world’.
[2] See, for example, Rabbi Meir Monitz’s article, “The Logical Basis for the Unity of Opposites in Rabbi Kook’s Thought” (and also his book, here).
[3] See, for example, Benny Ish-Shalom’s book, Rabbi Kook Between Rationalism and Mysticism, where in two places (you can find them in the index) he ‘explains’ an apparently contradictory idea of Rabbi Kook as a unity of opposites. He even supports this with Łukasiewicz’s three-valued logic, like many others, but this is simply a mistake. No one can bridge contradictions logically. Łukasiewicz’s logic is merely a formal system that describes a possible three-valued logic, but it itself is discussed and employed within ordinary binary logic. To see in it a basis for a philosophy that includes deviations from logic is a misunderstanding.
[4] Regarding Monitz’s article (note 2 above), I have written more than once that there is no logical basis for nonsense. And if his intention is to speak of contradictions of the latter two types, then there is no need for a logical basis, since the problem is not in the logical domain. One must simply analyze the issue and show that there is no contradiction, rather than declare that there is a unity of opposites.
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But Maimonides, as I believe from the laws of repentance, says that man's choice and the Creator's knowledge both exist even though we are unable to understand it. So is this a mistake?
The language of the Rambam there is unclear. The Rabbi already comments on him not to raise a problem without giving an excuse. He assumed that the Rambam would not make an excuse. But many understood that the Rambam did offer an explanation. The statement that his knowledge is not like our knowledge is unclear. Does knowledge in our sense not exist with him? If so, then his claim is that the Almighty does not have knowledge.
In any case, even if the Rambam intends to adopt both sides, it is either because in his opinion the contradiction there is a priori and not analytic (and I disagree with this), or he is mistaken.
Do you understand the teacher, confused A.B.?
Is this a contradiction (God is pure and distinct, God leads and oversees), and what do we do with the contradiction (perhaps we live as if we have been defeated?). This is his language:
And God, the Blessed, is not a power in the body of the world, but separate from all parts of the world; and His leadership will be exalted and His providence is connected to the world as a whole, a connection that has lost its purpose, and human powers fall short of His knowledge; for the miracle will stand on His separation, exalting Him from the world and His purification from it, and the miracle will stand on the reality of the act of His leadership and supervision in every part of its parts, even the smallest; Praise be to Him Who has conquered its entirety!
An excellent example of something that is not really a contradiction. It is at most a synthetic contradiction, and in my opinion just a ‘two laws’ (which is not a contradiction at all).
Here is an example explanation (there may be more): It is clean and distinct from the world, and is not part of its physics. But it has an effect on the world in ways that are not clear to us (because this is not physics).
I mention that the Maimonides himself insists that the Almighty is subject to the laws of logic (cannot create a square whose diagonal is shorter than its side).
thanks
In the previous response, the word "how" was omitted from the beginning.
I didn't come here to argue (because typing is still difficult for me because of my damned rheumatism), just to ask.
You may have gone too far elsewhere, but here you went too short. There is also apparently a contradiction (or conflict, or whatever you call it) that you didn't address, and I mean contemporaneity. Let's look at conspiring witnesses. One group of witnesses testifies that they saw a certain event at a certain time, and another group testifies that "you were with us." Since a person cannot be in two places at the same time, if you believe the latter group, it is clear that the former group is lying (and let's now consider the question of where the witness came from, etc.). In other contexts, the alibi claim (the accused was not at the scene at the time of the crime) is accepted as the strongest defense, based on similar logic.
But, (and here I enter a minefield since I am not a physicist), quantum mechanics tells us that a particle can be simultaneously in two different places (at least statistically and quantitatively) and its final location is determined at the time of measurement, and Schrödinger's cat can be alive and dead at the same time. In various places you have written that nevertheless, these anomalies cancel out on large scales. But I still haven't understood what importance the scale has. The very possibility of the anomaly is the problem (logically). How can a particle be in two places at the same time?
(By the way, from my physicist friend Prof. Kirsch I heard about an experiment in which a particle was manipulated at location X and a reaction was observed in particle Y that was thousands of kilometers away from it, as if the manipulation had been applied to it at the exact same time. He tried to explain to me how this is possible, and I admit that I didn't really understand it.)
So, if a particle can be “above time” and ”know” where it will be when I observe or otherwise manipulate it, maybe the same is true for God who can know in advance what I will do even though I have free choice? (At least statistically). So what if God belongs to a larger scale? (Maybe that's what they mean when they say that God is “above time”).
I have more questions, but I'm having a hard time typing. Kamaa Kamaa
I didn't understand why the question of simultaneity is related to contradictions. What you are describing is the EPR experiment (Einstein Podolsky Rosen), which surprisingly was actually measured (this year they received the Nobel Prize in Physics for it). It talks about immediate effects at a distance and not about contradictions. The focus there is the theory of relativity and not just quantum mechanics. Some also link this to questions of going back in time, but in my opinion there is no connection. I explained this in the columns here on the site.
Schrödinger's cat is a different phenomenon, superposition. There is supposedly a contradiction there, since the same particle or cat can be in two different (and therefore contradictory) states at the same time. This is rooted only in quantum theory and not related to relativity. But there are also those who claim that this is a contradiction to conventional logic, and I have already explained how much I have argued that this is a mistake. After all, the discussion of quantum theory itself is based on conventional logic (mathematics is also based on proof by negation). Even after quantum theory, we do not hold the proposition and the converse at the same time. Furthermore, if quantum theory abandons the law of contradiction or the avoided third, then we can draw any conclusion we want from it, and in fact it says nothing.
Therefore, there is clearly no contradiction here. Our image as if the cat is either alive or dead is based on an incorrect view of what a cat is. A cat is a wave function, and the cat that we know (either alive or dead) is a specific realization of it. The one in the superposition is not the cat (i.e. the creature you see as a cat) but its wave function (we can of course call it ‘the cat’, but then the cat is neither alive nor dead, and neither dead nor alive are properties of a cat as we know it, and not of wave functions).
And this explains the error of many who hold to the method called "quantum logic", as if the change in logic constitutes an explanation for the peculiarities of quantum theory. This is nonsense, of course. Logic has not changed in any way following quantum theory (since logic, by its very nature, is not subject to observational refutation or confirmation. It is a condition for them. Science does not underlie logic, but rather it underlies it). And even if there were such a change, it would not explain anything but would only empty this entire theory of its content. On this matter, it is worth seeing columns 50 and 318.
I estimate that this response of mine will also be a source of controversy, as we have argued about this in the past without any real fruit. Perhaps at least the readers will enjoy (or suffer).
I will begin with a question: Do you logically distinguish between talking about God's attributes and actions and God himself (his "essence" in your slang)?
I ask because it is clear to me that talking about his attributes and actions is necessarily subject to logic: God cannot be attributed the ability to create "unmarried bachelors" or "round triangles".
But if, say, you believe that God himself exists even without his actions and attributes - I don't know if you believe that - you will still have to account for his logical status as such. What then is the logical difference between the first description and the second? I suspect you'll tell me there's no difference, but I might be surprised.
The question is not well defined. What does it mean to exist without its properties and actions? Can it act differently?
In any case, it is irrelevant. Every claim I make is subject to logic. It does not matter what it is based on.
Your assumption is that logic is completely formal and that concepts and claims about them are therefore completely “indifferent” to the meaning (content) of the objects it deals with. Therefore, according to you, we can never say about something that it is both a thing and its opposite at the same time.
The direction I am trying to take is different. I start from the ontological proof and claim that there is one and only one concept (which I will tentatively formulate as ”an entity that is absolutely necessary”) in which not only is it impossible to do so but in which we actually do so necessarily. We all do so in practice, but not all of us are aware of it (you, for example). I interpret this concept as one whose only serious meaning is possible only if we assume that it has a paradoxical truth value: that absolutely necessary entity that the concept points to exists and therefore necessarily does not exist, and vice versa. In other words, there is actually a necessary connection between the concept and its content. I gave you the example of space in the past, which expresses exactly the same paradoxical status. Therefore, there is no contradiction here and there cannot be. There is a paradox here.
You will of course argue against me that my words are nonsense and I do not understand that in our speech we are bound by logic. I will answer you that we are indeed bound by it, but that you are misinterpreting this bondage (and here I will refer you to Wittgenstein's conclusion at the end of the tractate and what I think is right and what is wrong in this conclusion).
In my opinion, your main way of undermining my position should be to try to show me that, contrary to my words, the concept of an "absolutely necessary being" cannot be "excluded" from logic.
I almost forgot the most important thing: I estimate at 93.87% that your response will be that you did not understand anything 😉
With one small correction: I estimate that you didn't understand anything from this either. Simply because there's nothing to understand. If you claim both X and not X at the same time, this is where our conversation ends.
Thank you.
As usual, I invite those who agree with Mikhi, with me or not, to express their opinion. Reasoned, of course.
Although I am creating a chain of frustration here (I once made Doron frustrated), I will nevertheless enter the discussion.
” This concept is interpreted by me as one whose only serious meaning is possible only if we assume that it has a paradoxical truth value: that absolutely necessary entity that the concept points to exists and therefore necessarily does not exist, and vice versa”
You did not explain why it must satisfy this contradiction, at the moment it is simply not clear what you wrote (you defined that a certain concept must satisfy a contradiction, you did not explain on what basis you came to this conclusion regarding the concept and that it is different from any ordinary concept).
By the way, I didn't read the column, I was just responding to what you wrote.
I did not claim that this is a contradiction, I claimed that it is a paradox. And a paradox, at least this paradox, has two opposing truth values at the same time.
In the past, I illustrated this at length using the concept of Newtonian space, or something similar to it: Newtonian space exists if and only if it is infinite, abstract (immaterial), and homogeneous. Given that it is all of these, it does not have a single positive property, meaning it does not exist. And God forbid: Given that it “does not exist” it fulfills all the logical conditions for the existence of Newtonian space, meaning it does exist.
This is of course an analogy that has didactic value in my opinion to support my claim. Elsewhere I added a layer and claimed that it is not just an analogy… but there is no point in going into it. If the analogy is useful in explaining my position, then fine.
Yishai, you also asked what distinguishes this concept from other concepts. My answer: A correct and consistent interpretation of this concept shows that its meaning is that it is a necessary and absolute condition for the very existence and validity of other concepts (which are not necessary in the same strong sense). A kind of primary transcendental principle without which there is no logic. As mentioned, one can use the treatise to illuminate my claim even better (not to believe that I am turning to the hated Wittgenstein for help… as if I were Zehava Galon turning to Simcha Rothman for help…).
Why if it doesn't have a positive attribute then it doesn't exist?
If I understand the uniqueness of the concept correctly, it is actually possible to make an analogy to a proof that relies on the fact that everything has a cause. In the end, you have to reach something that has no cause that will create the entire chain, and therefore at some point you have to stop. Do you think the analogy is correct?
The questions are intended to get me to a point where I really understand what you mean and what you are really claiming.
Your Newtonian space is actually – God…
Indeed, decades ago I read somewhere that according to the Kabbalists, God is the non-existent or something like that. My knowledge of Kabbalah is minimal to non-existent, so I didn't delve into it. But if you are right, and if the Kabbalists are right (well, they are the rabbis from the well-known Hasidic story…) then at least with regard to God the third law that is avoided is really avoided…
I am writing all this in a semi-Purim atmosphere (except for the damned rheumatic typing pains), but who knows, maybe it's not entirely Purim…
Dear Mordechai, neither Purim nor half of it. I dedicated my entire book (“There Will Always Be Childhood– Philosophical Studies in Space and Time”) to explaining precisely this thesis that God and space are one. I myself am familiar, albeit superficially, with this Kabbalistic-Chassidic thesis and I have no doubt that the intuition behind it (as well as behind the Buddhist concept of emptiness – Shunyata) is the same thing. This certainly also reflects on the logic and the question of contradictions that I am dealing with here.
Yishai please give me an example of an entity – other than space (=God) that exists and has no properties at all. Including of course abstract entities such as numbers, values, ideas, etc. Note that this entity should also serve as the Archimedean point for everything that exists.
Regarding the analogy to the cosmological proof, I think it is indeed successful
Doron,
For some reason I can't respond directly to your comment so I'll respond here.
The fact that I don't have an example right now is not a fundamental disadvantage in the existence of the thing, explain to me why something doesn't exist if it doesn't have a positive attribute. That sounds more like something that can't be invented, than something that doesn't exist.
I haven't read the column yet, so I don't understand why you assume there is a contradiction. From a cursory review, it's clear to me that what Rabbi Michi says is the truth and beyond. It's the basis of discussion and understanding in everything.
But still, I think we can use the expression "truth function" borrowed from the wave function, for what you're proposing here.
Nav
Are you addressing me again?
If so, my answer is that I am not assuming a contradiction but a paradox.
Yishai
If you don't have a response to the challenge I set for you, maybe there's a problem with your position…
Isn't that right?
A lovely column. I was caught by a point, by the way, quote:
“In other words, God's omnipotence means that everything that is possible and imaginable is not impossible for Him. But the fact that He cannot do something impossible does not affect His omnipotence” as it seems to me that this is the most beautiful definition-answer to the idiotic question “Can God create a stone that He cannot lift”. Good luck.
I referred in my remarks to column 302, and there this matter is also applied to the question of the stone. And so on in other places on the site (you can search).
Hello Rabbi Michi,
In your words you wrote: “There is no logical equivalence between the claim ‘the stone remains standing in the air’ and the claim ‘no force acts on it except gravity’. Incidentally, in our world these do indeed always come together, but it is certainly possible to imagine worlds in which this is not the case”.
I am not versed in physics and would be happy to give a brief explanation of how it is possible to imagine 1) a world in which the law of gravity exists 2) this law alone, without the participation of any additional force, acts on the stone 3) the stone remains in the air.
In the margins, I will write that I only recently started listening to your lessons and reading your articles, and I would like to write you a heartfelt (or intellectual?..) thank you.
In this context, by the way, I will quote a nice saying that I heard several times from the influential Rabbi Yoel Cohen, the late Rabbi:
There is a well-known Gemara expression about the students of the Pomdita Yeshiva: “Ma’aylin Phila in Kofa Damchata.” And the one who explained it explained: You can imagine a pin with a huge needle the size of an elephant, so that the elephant can pass through it. You can also imagine a regular needle, but an elephant with such a narrow body that it can pass through the needle. But an elephant that is a regular elephant that fits inside a regular needle – you can’t even imagine
This is not an expertise in physics but in the use of imagination. Try it and enjoy. This is a world where even if a force acts, it does not move the object.
As a student of yours and of Rabbi Inbal and his school, I think I can explain both sides to each other. In my opinion, you are using two languages, and this is the main reason for the argument (apart from a fundamental disagreement that does exist but is not the main problem).
I will start by saying that in light of Rabbi Inbal's article, I was a little surprised by the superficiality of logic, and in general by the lack of systematicity of the article. It is clear that it has not undergone serious editing, which perhaps indicates Rabbi Inbal's own lack of clarity regarding what he wants to say. His internal problem also stems, in my opinion, from a language error.
Your column says one thing: what Rabbi Inbal calls a contradiction is not a contradiction at all. It is impossible not to agree with this. A contradiction is a statement of the type “X is not X”, and no one thinks that the sages said such things. Rabbi Inbal means something you would call *complexity*, meaning the way of the sages to contain complexities and conflicting concepts together. But Rabbi Inbal calls it logical contradictions, as if there is anything to talk about innovations in logic (not everything is Wittgensteinian logic [what's the connection with Wittgenstein?]).
This is a fairly common phenomenon, even among intelligent people, that they identify logic with dichotomous thinking. Often they say “logic” and mean common sense, or scientific method, and the like. And yes, it leads people to express themselves in outrageous terms. For example, Rabbi Yitzhak Shilat, who is an intelligent and profound man, once wrote (in criticism of you, I think) that as Jews we always believe that X=X. He means to say that X is not unambiguously defined and has several facets and dimensions. He sees in X=X an analytical and dichotomous spirit that is certain that everything can be understood and even more with mathematical symbols. Jeremiah Yuval in his introduction to the Critique of Pure Reason writes that according to Decant the subject is not equal to itself, using logical terminology and the notation X=X. This sounds delusional, but when you understand their language everything changes.
In essence, Rabbi Inbal speaks of duality, complexity and ambivalence. The opposite of these is dichotomism, quadratic or analytical thinking. Rabbi Inbal identifies the latter with rigid logical “rules” that limit thinking on subtle and profound subjects, and therefore he writes that in the logic of Chazal (in the era of Wittgenstein) the law of contradiction does not exist. If Inbal were aware of the meaning of his words, he would not have said them, since if the law of contradiction does not exist, then he is right and unjust, and he is also a banana and a Thursday.
What remains is the question of whether this is unique to the sages. I don't know how fundamental this part is to Inbal, but if so, this is the debate between you and it does exist outside of language.
Notes:
1. My response is appropriate for the next column, and was mistakenly sent here.
2. I understand that you already raise the possibility that Inbal means contradictions that are not real contradictions, but you leave this in doubt because of his vague formulations. It is important for me to emphasize that even if Inbal's formulation were unambiguous, and he explicitly stated that the sages also recognized real logical contradictions that contradict the law of contradiction – then he is wrong, and he does not understand his own intention. He is talking about the unity of opposites in the soft sense, what you called conflict or synthetic contradiction, and the like.