The Attitude Toward Contradictions: 1. A General Picture (Column 549)
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 Sabbath, 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 medieval authorities (for example, Maimonides 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 legal aspects’
In the world of lomdus (analytic Talmudic analysis), since R. Chaim of Brisk it has been common to use a logical structure called ‘two legal aspects’ (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 legal aspects”.
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 medieval authorities 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.
Discussion
Maimonides’ wording there is not clear. The Raavad already comments on him that one should not raise a difficulty without giving an answer. He assumed that Maimonides did not answer it. But many understood that Maimonides does in fact offer an explanation. The statement that His knowledge is not like our knowledge is unclear. Does knowledge in our sense not exist in His case? If so, then his claim is that the Holy One, blessed be He, has no knowledge.
In any case, even if Maimonides means to adopt both sides, that is either because in his view the contradiction there is a priori and not analytic (and with that I disagree), or because he is mistaken.
How do you understand Guide of the Perplexed I:72?
Is this a contradiction (God is pure and separate; God governs and watches over), and what does one do with the contradiction (perhaps live as the defeated do?). This is his language:
And the Blessed Name is not a force in the body of the world, but separate from all the parts of the world; and His governance, exalted be He, and His providence are connected to the world as a whole by a connection whose true nature is hidden from us, and human capacities fall short of knowing it. For demonstration establishes His separation, exalted be He, from the world and His freedom from it, and demonstration establishes the existence of the act of His governance and providence in every one of its parts, even the smallest and least subtle. Praised be He whose perfection has defeated us!
In the previous comment, the word “How” was omitted from the beginning.
An excellent example of something that is not really a contradiction. At most this is a synthetic contradiction, and in my opinion just “two laws” (which is not a contradiction at all).
Here is one explanation of the example (there may be others): He is pure and separate from the world, and is not part of its physics. But He has influence on the world in ways that are not clear to us (because this is not physics).
I would remind you that Maimonides himself insists that the Holy One, blessed be He, is subject to the laws of logic (He cannot create a square whose diagonal is shorter than its side).
I didn’t come now to argue (because typing is still hard for me due to the accursed rheumatism), only to ask.
It may be that elsewhere you elaborated, but here you were too brief. Seemingly there is also a contradiction (or conflict, or whatever name and title it may have) that you did not address, and I mean simultaneity. Let us consider conspiring witnesses. One set of witnesses testifies that it saw a certain event at a certain time, and another set testifies, “You were with us.” Since a person cannot be in two places at the same time, if we believe the latter set it is clear that the first set is lying (and let us leave aside for now the Gemara’s question, “Why do you see fit to rely on these rather than those?” etc.). In other contexts, an alibi claim (the defendant was not at the scene at the time of the crime) is accepted as the strongest defense claim, based on similar logic.
But (and here I am entering a minefield, since I am not a physicist), quantum mechanics tells us that a particle can be in two different places at the same time (at least statistically, and this is not the place to elaborate) and that 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 wrote that despite this, these anomalies disappear on large scales. But I still do not understand what importance scale has. The very possibility of the anomaly is the (logical) problem. 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 manipulation was performed on a particle at place X, and a reaction was observed in a particle Y that was thousands of kilometers away from it, as though the manipulation had been performed on it itself and at the same time. He tried to explain to me how this could be, and I admit I did not really understand.)
If so, if a particle can be “above time” and “know” where it will be when I apply observation or some other manipulation to it, perhaps the same applies to the Holy One, blessed be He, who can know in advance what I will do even though I have free choice? (At least statistically.) So what if the Holy One, blessed be He, belongs to a larger scale? (Perhaps this is what is meant when people say that the Holy One, blessed be He, is “above time.”)
I have more questions, but it is hard for me to type. Little by little…
I did not understand why the question of simultaneity is connected to contradictions. What you are describing is the EPR experiment (Einstein-Podolsky-Rosen), which, surprisingly enough, has indeed been measured in practice (this year they received the Nobel Prize in Physics for it). It deals with instantaneous effects at a distance, not with contradictions. There the focus is relativity theory, not only quantum theory. Some connect this also to questions of time travel, but in my opinion there is no connection at all. I clarified this in posts here on the site.
Schrödinger’s cat is a different phenomenon, superposition. There, seemingly, there is a contradiction, 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 is not connected to relativity. But there too some claim that this refutes accepted logic, and I have already explained in several places that this is a mistake. After all, the discussion within quantum theory itself is conducted on the basis of accepted logic (mathematics is also based on proofs by contradiction). Even after quantum theory, we do not hold both a claim and its negation simultaneously. Moreover, if quantum theory gives up the law of contradiction or the law of excluded middle, then one can infer from it any conclusion one likes, and in fact it says nothing at all.
Therefore it is clear that there is no contradiction here. Our picture, as though the cat is either alive or dead, is based on an incorrect understanding of what a cat is. A cat is a wave function, and the cat familiar to us (either alive or dead) is a specific realization of it. What is in superposition is not the cat (that is, the creature you see as a cat) but its wave function (of course one may call that “the cat,” but then the cat is neither alive nor dead nor both, since dead and alive are properties of a cat as it is familiar to us, not of wave functions).
And with this the mistake of many who hold the view called “quantum logic” becomes clear, as though changing logic provides an explanation for the oddities of quantum theory. That is nonsense, of course. Logic has not changed in any way בעקבות quantum theory (since logic, by its very nature, is not open to observational refutation or confirmation. It is their precondition. Science does not underlie logic; logic underlies it). And even if there were such a change, it would explain nothing; it would only empty the whole theory of content. On this matter, it is worth seeing posts 50 and 318.
Thank you
I estimate there is a high chance that this comment of mine too will come to nothing, since we argued about this in the past without much fruit. Maybe at least the readers will enjoy it (or suffer).
I’ll begin with a question: logically speaking, do you distinguish between talk about God’s attributes and actions and God Himself (“His essence,” in your religious jargon)?
I ask because it is clear to me that talk about His attributes and His actions is necessarily subject to logic: one cannot attribute to God 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 whether you believe this—you will still have to give an account of His logical status as such. So what, then, is the logical difference between the first description and the second? I suspect you will answer that there is no difference… but perhaps I’ll be surprised…
The question is not well defined. What does it mean to exist even without His attributes and actions? Does it mean He could act differently?
In any case, it is not relevant. Any claim I utter is subject to logic. It does not matter what it is about.
Your assumption is that logic is entirely formal, and therefore the concepts and the propositions concerning them are entirely “indifferent” to the meaning (content) of the objects it deals with. Therefore, on your view, we could never say of anything that it is a thing and its opposite at the same time.
The direction I am trying to take is different. I begin from the ontological proof and claim that there is one unique concept only (which I will tentatively formulate as “a being that is absolutely necessary”) in which not only can this not be avoided, but in fact we necessarily do it. We all actually do it, except that not all of us are aware of it (you, for example). I interpret this concept as one whose sole strict meaning is possible only if we assume it has a paradoxical truth value: that same absolutely necessary being to which the concept points exists, and therefore necessarily does not exist, and vice versa. That is, there is precisely a necessary link here between the concept and its content. I previously gave you the example of space, which expresses exactly the same paradoxical status. Therefore there is no contradiction here and there cannot be one. There is a paradox.
You will of course argue against me that what I say is nonsense and that I do not understand that in our speech we are bound by logic. I will answer that we really are bound by it, except that you interpret that binding incorrectly (and here I would refer you to Wittgenstein’s conclusion at the end of the Tractatus, and to what I think is right and wrong in that conclusion).
In my opinion, your main way of undermining my position should be to try to show me that, contrary to what I say, the concept “an absolutely necessary being” cannot be “excepted” from logic.
I almost forgot the most important thing: I estimate, with 93.87% probability, that your response will be that you did not understand a thing 😉
With one small correction: in my estimation, you too did not understand a thing about this. Simply because there is nothing to understand. If you claim X and also not-X together, our conversation ends here.
A lovely post. What caught me was an incidental point, a quotation:
“In another formulation I would say that God’s omnipotence means that anything possible and conceivable is not beyond Him. But the fact that He cannot do something impossible does not detract from His omnipotence.” It seems to me that this is the most beautiful definition-answer to the idiotic question, “Can God create a stone He cannot lift?” Well done.
I referred in my remarks to post 302, and there this issue is applied to the stone question as well. And likewise in other places on the site (you can search).
Thank you.
As usual, I invite anyone who agrees with Michi, with me, or with neither of us, to express his opinion. A reasoned one, of course.
Although I’m creating a chain of frustration here (I once caused Doron to become frustrated), I’ll enter the discussion nonetheless.
“ I interpret this concept as one whose sole strict meaning is possible only if we assume it has a paradoxical truth value: that same absolutely necessary being to which the concept points exists, and therefore necessarily does not exist, and vice versa.”
You did not explain why it must sustain this contradiction; as things stand, what you wrote is simply unclear (you defined that a certain concept must sustain a contradiction; you did not explain on what basis you reached that conclusion about the concept, or how this differs from any ordinary concept).
By the way, I didn’t read the post; I was responding purely 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 like it: Newtonian space exists if and only if it is infinite, abstract (non-material), and homogeneous. Given that it is all this, it does not have even a single positive property—meaning it does not exist. And conversely: given that it “does not exist,” it fulfills all the logical conditions for the existence of Newtonian space; that is, it does exist.
This is, of course, an analogy that has didactic value in my eyes, in order to support my claim. Elsewhere I added another layer and claimed that it is not only an analogy… but there is no point getting into that. If the analogy helps make my position intelligible, that is enough for me.
Yishai, you also asked what distinguishes this concept from others. 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 that strong sense). A kind of primary transcendental principle without which there is no logic. As I said, one can make use of the Tractatus to illuminate my claim even better (I can’t believe I’m turning to Wittgenstein, my sworn enemy, for assistance… as if I were Zehava Galon turning to Simcha Rothman asking for help…).
Your Newtonian space is basically—God…
Indeed, decades ago I read somewhere that according to the kabbalists God is the existent nothingness, or something like that. My knowledge of Kabbalah is meager to nonexistent, so I did not look into it. But if you are right, and if the kabbalists are right (well, they’re the rabbis from the well-known Hasidic story…), then at least with respect to God the law of the excluded middle is indeed excluded…
I am writing all this in a half-Purim atmosphere (apart from the accursed rheumatic pains of typing), but who knows, maybe it’s not entirely Purim-ish…
My dear Mordechai, neither Purim nor half-Purim. I devoted my entire book (Let Childhood Last Forever – Philosophical Studies in Space and Time) to making precisely this thesis intelligible: that God and space are one and the same. I myself am acquainted, albeit superficially, with this kabbalistic-Hasidic thesis, and I have no doubt that the intuition behind it (as also behind the Buddhist concept of emptiness—shunyata) is one and the same thing. This certainly also bears on logic and on the question of contradictions that Michi is dealing with here.
Why, if it has no positive property, does it not exist?
If I understand correctly the uniqueness of the concept, one can basically make an analogy to a proof that rests on the fact that everything has a cause. In the end one has to arrive at something that has no cause and creates the whole chain, so at some point one has to stop. Is the analogy correct in your opinion?
The questions are meant to get me to a point where I really understand what you mean and what you are actually claiming.
I haven’t yet read the post, so I didn’t understand why you assume there is a contradiction. From a superficial glance it is clear to me that what Rabbi Michi says is the truth and more. It is the basis of discussion and understanding in everything.
But in any case, I think one could use the expression “truth function” by analogy with the wave function, for what you are proposing here…
Nav
Again you are addressing me…?
If so, my answer is that I am not assuming a contradiction but a paradox.
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 like numbers, values, ideas, you name it. Note that this entity must also serve as the Archimedean point for everything that exists.
As for the analogy to the cosmological proof, it seems to me that it is indeed a good one.
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 other than gravity.’ As it happens, in our world these do indeed always come together, but one can certainly imagine worlds in which this is not so.”
I am not knowledgeable in physics, and I would be glad for a very brief explanation of how one can imagine 1) a world in which the law of gravity exists, 2) this law alone, without any additional force, acts on the stone, 3) and the stone remains in the air.
As an aside, I will write that only recently I began listening to your lectures and reading your articles, and I wish to write you a heartfelt thank you (or perhaps an intellectual thank you?..)
In this connection, by the way, I will quote a nice saying that I heard several times from the Chabad mashpia Rabbi Yoel Kahan of blessed memory:
There is the familiar Talmudic expression about the students of the yeshiva of Pumbedita: “they can pass an elephant through the eye of a needle.” And one expositor explained it as follows: one can imagine a pin whose eye is enormous, the size of an elephant, so that the elephant could pass through it. One can also imagine an ordinary needle’s eye, but an elephant with such a narrow shape that it could pass through the needle’s eye. But an elephant that is an ordinary elephant entering an ordinary needle’s eye—one cannot even imagine that.
This is not expertise in physics but in using the imagination. Try it and enjoy. It is a world in which even if a force acts, it does not move the object.
Doron,
For some reason I can’t reply directly to your comment, so I’ll reply here.
The fact that I don’t have an example at the moment is not an inherent deficiency in the thing’s existence; explain to me why something does not exist if it has no positive property. This sounds more like something that cannot be found than something that does not exist.
Yishai
If you have no answer to the challenge I posed to you, perhaps there is a problem with your position…
No?
As a student of yours and of Rabbi Inbal and his study hall, I think I can explain each side to the other. In my opinion, you are using two different languages, and that is the main reason for the argument (besides a substantive disagreement that indeed exists, but is not the main problem).
I will begin by saying that in light of Rabbi Inbal’s article I was somewhat surprised by the logical shallowness, and in general by the article’s lack of systematicity. It is evident that it did not go through serious editing, which perhaps indicates Rabbi Inbal’s own lack of clarity regarding what he wants to say. In my opinion, his internal problem also stems from a linguistic failure.
Your post says one thing: what Rabbi Inbal calls a contradiction is not a contradiction at all. One cannot but agree with that. A contradiction is a statement of the type “X is not X,” and no one thinks that Hazal said such things. Rabbi Inbal means something that you would call complexity—that is, Hazal’s way of containing complexities and clashing concepts together. But Rabbi Inbal calls these logical contradictions, as though there were even anything to say about innovations in logic (not everything is Wittgenstein’s logic [what does Wittgenstein have to do with this?]).
This is a fairly common phenomenon, even among intelligent people: they identify logic with dichotomous thinking. Very often people say “logic” and mean common sense, or scientific method, and the like. And yes, this leads people to express themselves in outrageous terms. For example, Rabbi Yitzhak Shilat, who is an intelligent and profound man, once wrote (in a criticism of you, if I remember correctly) that we as Jews believe that it is not always the case that X = X. What he means is that X is not defined unambiguously and has several facets and dimensions. He sees in X = X an analytical and dichotomous spirit that is certain it can understand everything, and even with mathematical symbols. Yirmiyahu Yovel, in his introduction to the Critique of Pure Reason, writes that according to Kant the subject is not equal to itself, using logical terminology and the notation X = X. That sounds absurd, but once you understand their language, everything changes.
As to the matter itself, Rabbi Inbal speaks of duality, complexity, and ambivalence. The opposite of these is dichotomousness, square thinking, or analytical thinking. Rabbi Inbal identifies the latter with rigid logical “laws” that limit thought in delicate and profound matters, and therefore he writes that in the logic of Hazal (as opposed to Wittgenstein) the law of contradiction does not exist. If Inbal were aware of the meaning of his words, he would not say them, for if there is no law of contradiction, then he is right and not right, and he is also a banana and Thursday.
What remains is the question whether this is unique to Hazal. I do not know how crucial this part is for Inbal, but if it is, then that is the disagreement between you, and it indeed exists outside the issue of language.
Notes:
1. My comment belongs under the next post, and was sent here by mistake.
2. I now see that you already raise the possibility that Inbal means contradictions that are not really contradictions, except that you leave it in doubt because of his vague formulations. It is important to me to emphasize that even if Inbal’s wording were unambiguous, and he explicitly declared that Hazal also recognized genuinely logical contradictions that violate the law of contradiction—he would still be mistaken, and he would not understand his own intention. He is speaking about the unity of opposites in the soft sense, what you called conflict or synthetic contradiction and the like.
But Maimonides, if I remember correctly, in Hilkhot Teshuvah says that both human choice and the Creator’s knowledge exist, even though we have no ability to understand this. So is that a mistake?