Record speed this time… nice going.
As for dichotomy: what I meant to say is that the formal logical structure of every sentence is either identity (say, “Moses is a good person”) or contradiction (“Moses is not a good person”), and there is no third option (“Moses is at once a good person and not a good person”).
Therefore, if we want to describe the foundations of logic, we can say that its three fundamental laws are anchored in a single principle that ties them together—dichotomy.
That is basically the meaning—trivial though it may be—of the law of the excluded middle, which says that there are only two possibilities: either Moses is good or he isn’t.
Isn’t that so?

Michi, tell me?
It’s not that you charge extra for a quick response…? Because my bank situation isn’t great. Please be considerate.

Today it’s on sale.
“Moses is a good person” is not an identity statement. Identity is a tautology (like 2+3=5. And even that Kant questions), and this sentence is not tautological. To the extent that the first sentence is identity (and it isn’t), then the sentence “Moses is not a good person” is equally identity (an identity between Moses and not being good), and certainly has nothing to do with contradiction.

My examples weren’t good, and your correction may be in place (although some maintain that a tautology and an identity statement are in fact two different things. In addition, I still think that the sentence “Moses is not a good person” definitely contradicts the sentence “Moses is a good person”).
But all that is marginal.

And the main point, in my view:
Maybe you’ll agree with me that one can “formalize” the sentence:

Moses is a good person

and formulate it like this:

A is B (where A represents Moses and B represents a property)

But if even this is not a tautology in your eyes, I’ll go one step further:

A is A.

I would formulate the contradictory sentence in a “formalized” way like this:

A is not A.

And now my claim:
The principle of the excluded middle supposedly sums up the two previous possibilities and thus places them on one plane that reveals their dichotomous opposition.

Therefore the sentence:

“A is A”

stands in dichotomous opposition to the sentence:

“A is not A”.

True?

I completely lost you. How is the formalization of “Moses is good” equal to A is A? “A is A” is just a tautology. Analytic philosophers spent quite a bit of time on the nature of the sentence “the evening star is the morning star” (they once thought these were two different stars and it turned out to be the same star). But that’s a different question.

Another try, because I also don’t understand you…

The claim:

A is A (or Moses is Moses)

is a tautology.

Agree or disagree?

The claim:

A is also not A (Moses is not Moses)

is a self-contradiction.

Agree or disagree?

Completely agree

Good for us.

Don’t you identify, as I do, a dichotomous opposition between the first claim (or the structure of the claim) and the second claim (or its structure)?

If not, then bummer.

If yes, maybe you’ll agree with me that the law of the excluded middle is exactly what reflects that dichotomy (which is why I claimed it “sums up” the law of identity and the law of non-contradiction).

Then bummer

Presumably you do distinguish between the two claims… since one, as you agreed, is a tautology and the other is a self-contradiction.

Do you think they do not exclude one another?

And if they do exclude one another, do you believe there is a third possibility besides them in logic?

Or do you have some other idea for characterizing the relation between them, other than a dichotomous relation?

Of course a contradiction contradicts a tautology. I didn’t understand what you want to say with that. You tried to ground all of logic on dichotomy, which in my opinion has no basis. I don’t understand what connection there is between what you wrote here and our discussion.

If, in your words, “of course a contradiction contradicts a tautology,” then the meaning of that is that you yourself are saying that the relation or basic principle connecting contradictory sentences on the one hand and tautological sentences on the other is what I called it—dichotomy.

I don’t see how what you said here can be understood otherwise.

If you do see another way, please enlighten me.

In any case, even if this claim is trivial (and I have a feeling that’s what you think), its meaning is not trivial at all. If we manage to move forward, I’ll dare to present it to you later.

A is A is a tautology.
A is not A is a contradiction.
(A or not A is the principle of the excluded middle.)
Up to here I’m completely with you. That is the definition of the three fundamental laws of logic. From here on, I didn’t understand a word. As I understand it, nothing connects them, and certainly you cannot ground them all on one principle (otherwise there wouldn’t be three laws of logic but one).

The foundation of logic predates the 3 rules. And it concerns the very existence of the concepts of truth and falsehood. That is, the fact that there is such a thing as truth and falsehood is the foundation of logic. And that is the dichotomy, between truth and falsehood.

The rules are only meant to clarify how one can systematically determine whether a given sentence is true or false.

Not true. The dichotomous relation between truth and falsehood is one interpretation. Some challenge it (in many-valued logic).

1. What Peshita says is more or less in my direction (not necessarily locked in on a truth/falsehood dichotomy, but a dichotomy yes)
2. I deny that there are three laws in logic. In my opinion there are three aspects of a single principle or law.
3. Logic is an empty and a priori formal system, and its laws therefore are not like those in science, where they rely on experience and are not necessarily dependent on one another. In logic, the first law implies the existence of the second law. The law of the excluded middle is nothing but a combination of the first two laws.
4. In my opinion, what Michi himself wrote above (that there is a relation of contradiction between the law of contradiction and tautology) is actually exactly what I claimed from the outset. I don’t call it contradiction but dichotomy, but it seems to me we are talking about the same thing (Michi doesn’t recognize this, but in my opinion that is already a mistake).
5. In fact, this claim of Michi’s is exactly the same reductionist move I’m trying to make.

The foundation of truth and falsehood exists in our soul. This is not a philosophical theory but an emotion, a feeling, an intuition. Logic tries to describe the rules according to which the intellect of a “normal” person thinks something is true or false. In an abnormal person the rules are different and they will never be able to understand logic. (And therefore this existence of truth and falsehood is fundamental.)
(And this is exactly as the foundation of mathematics is in our ability to count one, two, three… and those who cannot count will never be able to understand anything in mathematics.)

And here is my suggestion for how to test whether the principle of dichotomy (the “contradiction”) stands at the basis of logic—that is, at the basis of its three laws—or not:

Take the principle away from the three laws, that is, cancel the very ability to distinguish among them, and see whether you still have anything left.

In my opinion, you’ll be left empty-handed.

Doron,
It’s rather amusing to find an argument dealing with logic that suffers from a logical fallacy. What you showed here (even if you were right) is that the assumption of dichotomy underlies the three laws of thought. It is a necessary condition for all three. But what you claimed is something else: that it is a sufficient condition. That is, that each of them can be grounded on it.
As I already mentioned to you, there are non-binary logical systems (like that of Łukasiewicz, for example) that accept the law of identity and contradiction, but not the law of the excluded middle. That itself refutes your claim, unless you want to argue that Łukasiewicz is inconsistent (he was quite a decent and respected logician. That would be a presumptuous claim).

Listen…

First of all, regarding His Holiness Łukasiewicz, I ask forgiveness from him and his believers (are you one of them?) for daring to raise the despicable possibility that his view is built on philosophically inconsistent assumptions. May my tongue cleave to my palate if I ever again scatter such hints.
Actually, it isn’t clear to me why you bring up the claim that there are non-binary systems in logic. Unless you yourself think they are valid. Surely you’re not trying to demolish my argument with a position that you yourself reject?
Second, as far as I understand what’s at stake, my basic intuition rejects the attempt to create non-binary logic (it reminds me of your justified critique of so-called quantum logic).
Since this is a complex subject, I need to study it a bit in order to express a more nuanced opinion, of course. In any case, whoever advances a philosophical claim that renders the excluded middle unnecessary has the burden of demonstrating how that works. Maybe then I’ll be convinced.
Third, I’d be happy if you’d explain a bit more where I am supposedly sliding unconsciously from an argument about necessary conditions to an argument about sufficient conditions. Is it connected to the possibility that the excluded middle is not valid? Explain.
Fourth, I’m glad to discover that you recoil from presumptuousness. Good news for your critics here on the site.

Rabbi Doron, don’t be angry. I don’t recoil from presumptuousness at all. I only claim that a presumptuous argument requires a serious justification (in order to claim that Einstein made a stupid mistake in physics, I would expect a very, very strong argument). I found no such thing in your words. On the contrary, not only do they lack justification, they are refuted.

I do indeed disagree with Łukasiewicz philosophically, but consistency is a logical matter, not a philosophical one. One can claim that every fairy has five wings and that is a consistent claim, but it isn’t true. Łukasiewicz’s doctrine is consistent (even if not true), and that is enough for me to reject your argument. If maintaining the law of identity and contradiction while denying the excluded middle is a consistent thesis (even if not true), then your claim has fallen on the logical plane. Note that well.

You probably didn’t understand my claim against you. What I said was that you are arguing here that if we remove the assumption of dichotomy (which you still haven’t explained what it is), the three laws of thought collapse. And to that I said that even if you were right (and you aren’t), that still does not mean that they can all be grounded on the principle of dichotomy (which I don’t know what it is).
I’ll put it formally. You claim that the three propositions A, B, and C can be grounded on a principle X. Meaning that all three are really different faces of one proposition (we don’t need all three; it is enough to establish X and that’s it). But your “proof” (which itself is incorrect; see Łukasiewicz) was that if we reject X, those three propositions collapse. But logically, that argument (even if it were correct) only says that X is a necessary condition for all three, whereas you claimed it is sufficient. That you did not prove, even if your proof had been correct. Beyond that, the proof is also incorrect in itself.

In short, three problems with your claim:
1. You did not explain what the principle of dichotomy is.
2. Your proof is not correct (when one removes X, it is not true that the three laws collapse).
3. Even if that proof were correct, it would prove that dichotomy is a necessary condition for the three laws, not a sufficient condition as you wanted to show.
Other than these minor matters, everything is excellent. 🙂

1. The principle of dichotomy means the existence of 2 elements standing in sharp and decisive opposition. If you want to indulge in quibbles and “precisions” beyond that you may do so, but I take no responsibility for it. For this philosophical discussion my definition is enough.

2. Regarding the holiness of Łukasiewicz: I trusted my nose earlier because I smelled that you oppose non-binary logics “philosophically,” and so I will once again remain loyal to that same organ. My nose tells me that if we investigate the reason you oppose Łukasiewicz and the like, we will discover that you think this: even if his model is consistent, it does not fit with his own underlying philosophical assumptions. There is a sharp analytic scent in the Łukasiewiczian air, and I think you smell it too.

Given that this is the case (please correct me if it’s not), then this holiness is, after all, not consistent with the philosophical assumption at its foundation (the analytics obsessively chase consistency and in the final reckoning always remain without it).

3. Necessary condition and sufficient condition: well, I’m not sure I understand what you want from me. Maybe you attribute to me the following position: the necessary condition is dichotomy and the sufficient condition is the three laws of thought. Given that this is what I’m arguing (according to you), I might perhaps—if I defeat the saint—be able to show that the laws of thought would collapse without dichotomy, but I would not be able to claim that they can be “grounded” on that necessary condition.

If this is your claim, then:

First, contrary to your words, I described the three laws of thought not as “propositions” but as “aspects” of a single principle. Maybe you’ll say that now I’m the one quibbling, and maybe that’s even true… but it’s important to me to secure my forward defensive line before I approach the thickening of the main wall of defense.

Second (here I have now reached the wall of defense), it may be that I don’t understand what “reduction” is, but this is how I define it: the ability to translate one system into its more basic foundations and thereby both reduce it and preserve the original relations between its elements.

If my definition is reasonable, one can show that dichotomy (now you also know what it is..) characterizes not only the necessary foundational condition but also the laws of thought that it carries on its back (the sufficient conditions).
There is no such thing as “identity” in a world in which no other possibilities are possible, standing in dichotomous opposition to it. Consequently there is also no such thing as “contradiction” if there is no positive substrate (“identity”) that precedes it and that it can contradict. See Parmenides.
Thus dichotomy rules everything, the upper and the lower, the necessary and the sufficient. As the waters cover the sea.

By the way, your analogy between Łukasiewicz’s method and a fairy with 5 wings seems mistaken to me. Even if no such creature exists in our world, there are possible worlds in which it could exist. On the other hand, Łukasiewiczianism, if I am right and it is based on a contradiction between itself and the philosophical assumption at its basis, would hold in no possible world. It follows that Łukasiewiczianism is not only not true but is also logically impossible.

Doron, it’s hard for me to discuss things like this. You are dealing in the field of logic and, pardon me, you do not have the tools and skill to do so. You do not formulate your claims properly and do not define the concepts. When logicians seek to ground one claim on another claim or claims, they do so in a precise and unambiguous way. Otherwise one cannot really discuss. You did not define what dichotomy is. You did not show how the three laws of thought rest on it (that is, how they can be derived from a single principle you called dichotomy), and until you do that there is no point in the discussion.

Your Honor, have you decided to string me along? Are we like the people of Sodom? Have we become like peanut butter?
You discuss a certain subject with me at length from a philosophical point of view, and suddenly you decide that I have no tools and skills, so you flee to the logical and technical plane? Have you forgotten all your efforts to distinguish philosophy from the sciences? Has your critique of Dawkins evaporated from your memory, namely that he suffers from a philosophical misunderstanding of the scientific field (in which even by your own account he is knowledgeable and skilled)? You repeatedly address an educated but non-“professional” audience in your explanations on the assumption—not even stated outright—that not only can you explain fundamental matters in philosophical language, but also that that audience will understand… and suddenly now it does not understand and cannot understand… in your opinion…

It reminds me of the story about the fish that wanted to improve its swimming and invited a physicist to teach it the principles of mechanics (a “professional” field), because it had heard that understanding its laws would enable it to maximize its performance in the water. When the physicist bent over the water to explain Newton’s three laws to the fish, he slipped and fell on top of it. Since he did not know how to swim, he grabbed the fish until he drowned together with it (in this fable fish can drown). The fish’s friends were very pained by its death, but were comforted by the fact that it had mastered the science of mechanics even better than the physicist, since unlike him it knew how to swim…

As for our matter:

The concept of dichotomy is common in intellectual and even journalistic discourse. The attempt to elevate it to new heights is irrelevant to this discussion. I could also have used the term “opposition” (which in my view is less successful), but then perhaps you would have told me that I didn’t define what opposition is…

As for many-valued logics that reject the principle of the excluded middle: my philosophical claim (and I suspect yours too, though perhaps you’ll deny it) is that they make an effort to reject this principle—that is, to reject the exclusivity of dichotomy—while making use of it itself. To me they seem inconsistent, and certainly that is problematic from a fundamental philosophical standpoint (and maybe also from a “logical” standpoint).

As for sufficient condition (I am ignoring the matter of the necessary condition, since the answer to that is bound up with my previous section), my explanation of what “identity” is (that it depends on the concept of contradiction) and what “contradiction” is (which in turn depends on the concept of identity) seems to me more or less suitable for high-school level. Since I do not suspect you of suffering from excessive high-schoolness, I stand gaping, as a fish would stand before a physicist, before your answer.

Other than that, as stated, everything is perfectly fine 🙂

My Honor has not decided to exclude you. You are discussing the subject in a very amateurish way and do not enable me to discuss it with you. Sorry if you don’t even see the problem. That only means the lack of skill is even more serious than I described (again, I am truly not trying to string you along or put you down. I am writing entirely matter-of-factly. I really cannot discuss it in this way. I suggest you turn to any logician, and I promise you that you will get the same answer).

In the field of logic I am indeed an amateur, except that as stated, here the discussion is a bit different and quite simple.
Let the reader judge for himself.

If you can write me half a sentence on why you object to Łukasiewicz (or to many-valued logics in general), I’d appreciate it. Since you declared that your objection to him is not logical but “philosophical,” there is even a chance I’ll understand something of what you say.

Łukasiewicz argues that regarding future propositions, one cannot say that they are true or not true. We do not know about them. Therefore, there the law of the excluded middle does not exist (but the law of contradiction and identity do).
I do not agree, because the fact that we do not know does not prevent us from saying that the proposition is either true or not. I discussed this at length in the book on time logic in the Talmud (the fourth in the Talmudic Logic series).
But regarding the matter itself, one sees from his doctrine that it is possible to argue consistently (even if incorrectly) that the law of the excluded middle is not true and still remain with the law of contradiction and the law of identity.

Okay, and what do you say to the claim that Łukasiewicz is inconsistent because he makes use of the excluded middle in order to reject that very principle?

First, I do not see such a use. Second, even if there is one, that would at most negate the use of his theory in the future (because his claim is about the future).

I didn’t understand.

After all, his idea can be summed up in the claim that:

The law of the excluded middle is not valid.

But that very claim itself pretends to be 100% true, that is, it is built on the assumption that claims of this kind are either completely true or false, with no middle way.

Why do you think so? 🙂
I don’t see why you couldn’t discuss his claim too within a three-valued logic. But beyond that, I already said that regarding the present, he too accepts standard logic.

As for your first claim, that there is no problem at all discussing the matter within three-valued logic—that seems to me complete nonsense.

How can one even classify the above claim (“The law of the excluded middle is not valid”) as a factual claim about the world? By three-valued standards we would have to judge it in non-binary terms (that is, it does not enter at all into the “superficial” category of true/false).

Does that mean that Łukasiewicz and the like do not really believe what they say..?

I really do not see any complicated technical or professional matter here.

Doron, you insist on dealing with things for which you do not have the tools.
First, this really is not a complicated topic. When I spoke of complexity, I was referring to your first question (the attempt to ground the laws of thought on one principle). Second, there is no problem at all in saying that the claim is true, but the term truth itself is discussed within a three-valued framework. When one says that the discussion is within a three-valued framework, that does not mean that one does not believe the claim one is making. That is simply a misunderstanding. It means that if you prove that the claim is not true, you still have not proved that it is false; perhaps it has a third truth value (for example: undetermined, paradoxical, and the like). It is like saying that the claim that a triangle has a total of 317 degrees seems to you like nonsense. There are geometrical systems in which that is the case. So too in logical systems in which the law of the excluded middle does not hold.
In short, with all due respect, even in this relatively simple problem you do not have the tools to deal with it.

Michi,

I insist on dealing with a subject that in no way seems to me professional-technical. Maybe I am mistaken in that distinction, but that’s what I think, and so I am compelled by that thought. You can keep showering me with compliments about my lack of understanding and lack of proper tools, but I think you’re bursting through an open door.

As I understand it, non-professionally and non-technically, your last answer makes use of something similar to what you called a “shadow concept.” You turn truth into such a shadow concept, and then you insert it into a three-valued framework (and then indeed there is no problem, because we are no longer speaking about truth but about “truth”).

As for the matter itself: if Łukasiewicz’s view, expressed in the proposition

“The law of the excluded middle is not valid”

itself has the logical status of “undetermined” (your own words), then the meaning of that proposition is also not fixed… and therefore one who holds this position is actually holding a different position (since it is not fixed, it changes…). Heaven forbid.

In any case, the good news for you is that you can always go back to scolding me for my ignorance, presumptuousness, and foolishness, and you can always tell me that I do not understand the concept “not” and the concept “fixed” (or even the concept “concept”).
There is no end to wonders.

So here I will allow myself once again to make use of the option of scolding you for lack of skill and close the discussion. I see no point in conducting it. It seems to me similar to someone arguing with me about relativity theory and then protesting my claim that he does not have the knowledge or skill to conduct the argument. Logic too is a profession (though, at least elementary logic, is an easier field than physics. I too have no formal education in it, but I have studied it quite a bit).

Your scolding has been recorded and filed in my notebook.
To close the discussion I summoned the spirit of Łukasiewicz for our benefit, so that it might express its opinion on the matter. Besides warmly recommending that I hire a personal logician who could explain to me what I really mean every time I dare open my mouth, he took the trouble to interpret his philosophical position for me. “I espouse such-and-such,” he emphasized, “but since the truth value of what I espouse is ‘undetermined,’ at the moment I no longer espouse it.”
We parted on good terms.

Happy holiday, sir,

After our debate about the allegedly problematic philosophical aspect of many-valued logics, in my opinion, I took the trouble to do some homework on the matter.

To my astonishment, I discovered that there are professional logicians who hold more or less the position I defended in the debate.

Suszko goes even further and argues that the idea of many-valued logic (more than two values) is “madness.”

This teaches you that the question of the consistency of those logics—I emphasize that we are talking about consistency from the standpoint of the philosophical assumption in the background, not the internal consistency of the system itself—is an open question. Contrary to what you said.

Thus, in my opinion, a basic methodological problem in the background of your claim is also exposed: you argued that mortals like me (lacking technical knowledge and skill) are not capable of conducting a philosophical debate on the subject.
And yet here we see that a worm of Jacob like me succeeded, without any “professional” knowledge and skill, in arriving at the same insights as someone who does have such knowledge. From your point of view, it seems to me you would have a very hard time explaining my ability (in fact all of our ability) to do that. From my point of view, by contrast, the explanation is easy and simple—common sense.

I noticed that although the subject of our debate might be perceived as “dry,” it had many followers. But to my sorrow, the number of participants in it (aside from Your Honor and myself and a brief appearance by Peshita) was zero. I’m sure many among the followers are at least as wise as I am (though certainly not as wise as His Excellency 🙂 and could share their insights with us. In light of that, and from completely selfish motives, I urge them to express an opinion.

Happy New Year

https://plato.stanford.edu/entries/truth-values/suszko-thesis.html

Amusing. For all those who are not versed in logic, good luck reading the attached entry. And to my friend Doron, sorry, but your misunderstanding continues here as well. This is not about logical consistency.
Happy New Year to all of us

Indeed, it is not about “logical” consistency. I emphasized that well in my last response too, so I do not understand the meaning of your remark.

Suszko’s philosophical claim is simple—many-valued logic can be reduced to two-valued logic. From this it follows that the idea that many-valued logic is consistent is itself an inconsistent idea (it itself relies on dichotomous two-valued thinking).
All the rest is details. Very important details no doubt, but still only details.

They say in Einstein’s name that only a fool thinks that if he does the same action twice the result will change. When Michi is in the mood to answer, he answers every snot-nosed nobody, and when Michi isn’t in the mood to answer, he doesn’t answer even those with a nose as parched and dry as yours. If the spirit of the Polish Suszko had contacted you directly, then presumably it would have advised you what that same Pole who was in Canada for medical treatment wrote to me in an online poker game in the Google Translate English chat: relief. That’s my opinion about the thread.
Fortunate are you that Michi has merited to look down on you. And if you’re that desperate for this virtual discussion to continue, then maybe I really will read it thoroughly. But I liked the attitude, brother. If anything, instead of a specific answer to the question you asked, I’d be interested in a column explaining what it is that causes Michi to shut down discussions in general.

Many thanks for the refined and matter-of-fact language.

4 points:

1. Suszko’s philosophical position (that many-valued logics can be reduced to classical logic) contradicts Michi’s words, yes or no? And if not, a justification please.
2. When Michi attributes to the position advocating many-valued logics a status of “undetermined” or “paradoxical,” the burden of explanation is on him to say what he means. I do not advocate a position to which such a problematic status is attributed, so it is not on me to clarify my intention.
3. Michi often expresses opinions on matters in which he himself admits he is not an expert (psychology, sociology, political science, and even certain areas of philosophy). Even when I disagree with his analyses in those fields, I almost always view positively the very attempt to distill philosophical principles out of non-philosophical disciplines. That is regarding his claim that absence of expertise/professionalism disqualifies the very justification for expressing an opinion on the matter.
4. In the next comment I will attach a few quotations + links to the words of a figure whom I actually appreciate very much, saying things that on the face of it seem completely opposite to what Michi is saying. In essence: the exclusivity of classical logic and the nonsensical status of every attempt to depart from that logic.

1. “Below I will try to show that Weil’s questions, as well as those of my students on the topic of conditions, are based on the same mistake, whose root lies in a misunderstanding of the halakhic concept of ‘taking effect.’ We will, with God’s help, see that all these statements are subject to the law of contradiction and fit very well with it, as well as with all classical logic. Before I do so, I would like to clarify another point about the impossibility and the lack of philosophical legitimacy in fleeing from classical logic (ordinary reasoning).”

מהי ‘חלות’: לימוד, לוגיקה ודבקות

2. ttps://mikyab.net/%D7%A9%D7%95%D7%AA/%d7%9c%d7%95%d7%92%d7%99%d7%a7%d7%94-%d7%9e%d7%95%d7%9b%d7%a8%d7%97%d7%aa

And see the last sentence of the writer in the thread.

More on the possibility—in fact the philosophical necessity—of reducing many-valued logic to two-valued logic:

“The resort to Łukasiewicz’s theory as an explanation for phenomena of logical absurdity is very common, and it is important to clarify that this explains nothing. In Łukasiewicz there is a formal description of a logical system with three truth values, but there is no explanation there of the reasoning behind such ‘thinking.’ There is no doubt that the understanding of Łukasiewicz’s logical system is itself carried out (in the metalanguage) in terms of conventional (two-valued) logic.”