Thanks for the reference.

I read the article, and it seems to me that its central insight (from the methodological angle) is your distinction between factual statements, which have a truth-value, and modal statements (in this case obligations and responsibility), which do not have a truth-value.
Did I understand correctly?

Assuming so, I also understood something else: in your view, the sharp principle of binarity applies only to factual statements, since only for them do judgments of identity or contradiction apply.
True/false.

And here’s my question:
I’m interested in the relations between modal statements and factual statements. Beyond the fact that the two kinds of statements represent two different kinds of ontology, it seems to me that there is a kind of principled priority (logical…?) to modal statements.

For example, the statement:

“It is raining” (= a factual statement with a truth-value)

is conditioned by the modal statement:

“It is possible that it will rain” (or something along those lines).

After all, if there were no logical possibility of rain falling, then the statement expressing the actual state of affairs (rain actually falling) would be meaningless.

Agree/disagree?

If I’m right, then it turns out that the principle of sharp binarity is “restrained” (or maybe even subject to) a non-binary principle that is not contradiction but only reflects tension.

Your view?

I don’t know where you saw all that in the article. I don’t recall any discussion there of possibility statements (modal statements, in your terminology). I deal there with explanations for a certain halakhic law (liability to pay damages), and argue that the explanations don’t have to exclude one another. But not because there is no contradiction; rather because they can combine with one another. The claim “the explanation for law A is only X” contradicts the claim “the explanation for law A is only Y.” But the claim “the explanation for law A is X” does not contradict the claim that the explanation is Y. So there is no obstacle to combining the two explanations and saying that the explanation for law A is (X and Y) or (X or Y).
All this is unrelated to logical binarity. If some statement is true, its opposite is false, and vice versa. Accepting some claim as both true and false simultaneously is just empty nonsense. There is no qualification to that meaning of logical binarity. The problem is that many people identify binarity where there is none, and about that I’ve written more than once. Here this is one example.

1. You did address modal statements in the article (or at least modality in logic):
You weren’t discussing someone who actually paid, but a possible reality, namely what is “correct” or “proper” to do.
2. In your reply to me above, you didn’t address my question: at bottom it wasn’t about the distinction itself between factual statements and modal statements (a distinction I believe you accept), but about the relation between them and the connection of all this to binarity.
3. Your remark that self-contradictory statements are empty nonsense seems right to me. But it doesn’t really seem connected to my question.
4. You made another remark (and in my opinion a justified one): sometimes people confuse contradiction and tension. They claim, rightly, that one can “contain” opposing positions (between which there is tension), but since they call them “contradictions,” they come away with the mistaken insight that contradictions can be “contained.” In your view (and mine), that really is just empty nonsense.
5. But as much as I agree with that remark of yours, it also doesn’t really relate to my question.
6. I illustrated my question with statements about rain. Do you agree that the claim “It is raining” is conditioned by the modal claim “It can rain”?
7. The reasoning: if the latter claim has no meaning, it follows that the former claim can’t have meaning either.
8. By the way, statements of the type “God can create a square triangle” don’t belong to either of the two groups I referred to above. These are statements that are not factual claims, but also not modal statements. They are simply contradictory and therefore meaningless.

1. That’s not modality in your sense. But let’s set that dispute aside.
2. I answered that in my view this has no connection to logical binarity or qualifications on it.
6–7. Correct. If the possibility of rain is self-contradictory, then there’s no possibility of speaking about the fact that it is raining. So what?
8. Correct.
So where’s the dispute?

1. I’m not at all sure there’s actually a dispute between us here. At least for now…
In any case, I’m talking about two different senses of the concept of binarity: with respect to factual claims and with respect to modal statements.
2. I didn’t understand. In your view, is there no connection between a modal statement and a factual claim? I think there is an implication here—even if in a weak sense—from the first to the second.
3. What do you think?
4. If there is such an implication (or at least if it exists as a necessary though not sufficient condition), then it follows that the binarity implicit in the world of modal statements (a binarity of tension and, in my opinion, also of paradox) in some sense gives rise to the binarity of the laws of identity and contradiction.
5. In sum: in my view the two different senses of binarity bear a logical relation to one another (and I believe also a metaphysical-ontological one, but let’s leave that aside for now…)

You’ve lost me. There are no different senses of binarity. There is no difference between modal statements and others. There is no truth and falsehood simultaneously, neither here nor there. I already wrote that I agree there is a connection between possibility and actual existence.

First sense: claims that can be contradicted.
Second sense: claims that have meaning but no truth-value, and therefore cannot be contradicted (for example, “It is forbidden to smoke”).
What’s wrong with that?

Besides, in my brazenness I’m not satisfied with your agreement that there is a connection between possibility and actual existence. I claimed there is a relation of implication, even if in a weak sense.
Agree or not?

These are not two senses of binarity but the distinction between claims and what does not claim anything at all—a distinction as old as Aristotle, old with age and still looking fine.
The implication relation also seems trivial to me, at least if we mean it in the material sense (that it cannot be that the antecedent is true and the consequent false). In that sense it is clear that existence entails possibility (and not vice versa). Put differently: possibility is a necessary but not sufficient condition for existence, and existence is a sufficient but not necessary condition for possibility (these are, of course, two logically equivalent claims).

1. Indeed, you corrected my terminology accurately. There aren’t two kinds of claims here.
2. But that technical point (important as it is) neither adds nor subtracts from the substantive point I raised: in both cases we are dealing with utterances or statements that express the principle of binarity in different ways. In the one case, binarity (= doubleness, duality) is based on contradictory opposition; in the second, the opposition is not contradictory.
3. If in the past you argued—and it seems to me that you did—that logic (in the sense of claims that have a truth-value and therefore can be contradicted) stands on the first floor, then now you agree with me that there is a sense in which logic itself stems from a more basic ground floor. You even claim that positing such a ground floor and the principle of implication from it is a trivial assumption. You’re right.
4. This level is expressed in modal statements.
5. You can of course argue that the modal ground floor is still part of “logic.” If you choose to do that, I’m not sure I’ll object to that conclusion.
6. But in any case it is clear that adopting such a strategy would indeed restrain the binary principle in its sharp sense of either true or false, by subordinating it to a much softer principle of binarity.
7. I’m sure you understand perfectly well what I’m driving at. If the “logic” on the ground floor is not so sharp, that opens the first door to introducing a transcendent ontology into the human being, one that has a paradoxical character.

I understand perfectly well what you’re driving at, and there isn’t the slightest connection between the trivial claims that came up here and your desired destination.

If we ignore my desired destination for a moment—ontology—you still haven’t denied that you accept the existence of a logical ground floor “that lies entirely in the modal spheres.”
Do you accept that or not?

Doron, I have a hard time with you. Who doesn’t accept trivial statements like that? What does it have to do with our topic?

1. My heart goes out to you for the terrible suffering you’re enduring because of me. Perhaps you can console yourself with the thought that the suffering I cause myself is far greater?
2. Trivial statements: in my opinion, good philosophy often deals with what seems trivial to one person but is hidden from the eyes of others in certain contexts. You yourself often make claims that seem trivial to you (for example, about the meaninglessness of contradictory claims) that others were not aware of, or at least were not aware of in the context you raised.
3. My claim about the modal principle at the basis of factual statements is an example of a “trivial” but useful statement. At least I hope so.
4. This statement is also well connected to our topic in the following ways:
5. Certainty: it explains better why certainty cannot be attained in philosophy. Logical certainty can exist only in the absence of possible worlds in which certain claims receive a different truth-value. If we rule out such worlds in advance, we are left with “factual statements” having a single truth-value, that is, certain claims (and of course also empty of content).
6. The existence of a modal ground floor at the basis of propositional logic—which sits on the first floor—allows claims to escape the demand for certainty. There is surely much to elaborate and qualify here, but this is not the place.
7. The intuitive faculty in the human being: one who believes, like you (and surely like me), in the existence of an intuitive faculty may be glad to discover that intuitive cognition has a parallel in human language (and thought): just as our intuitions operate directly on their object, so too modal utterances do so (of course in a somewhat different way, since their “content” is embedded within them, unlike the content of intuitions).
8. Very soon my book, “I Was the Brain Behind Yuval HaMevulbal,” will be published, and there I will present all these points at length and in detail.

The explanation of why certainty cannot be attained in philosophy is so simple that I don’t understand what all this adds for us. There’s no need to escape certainty when there was never any initial thought that there would be certainty.
You write that certainty is conditioned on there not being possible worlds in which the truth-value is different. That is nothing but the modal sense of certainty (necessary = true in all possible worlds), the old familiar one.
But I await the book with eager anticipation. 🙂

1. “Initial thought”: are you serious? You send me off into the wilds of the internet to look for a translation of your yeshivish Aramaic, and then you complain that I’m making your life difficult? Shame on you.
2. As for certainty: lucky you that you’ve already arrived at the insight that certainty is a wild goose chase. Unlike you, there are great and important philosophers who assume, mistakenly, that certainty can indeed be reached (sometimes their assumption is implicit, perhaps even hidden from their own eyes). So it may be important to attack the error from another direction. I tried to do that from within a broader context; maybe I even succeeded, I don’t know.
3. I’m glad that my definition of certainty accords with the formal and accepted definition. I don’t see how that weakens my claim.
4. You didn’t address the matter of intuitions and their structural similarity to modal utterances.
5. To remind you: the subject of the question and the claim I raised from the start was binarity. I argued then, and still argue now, that there are two kinds of binarity for statements: contradictory binarity, expressed in factual claims, and binarity of opposition, expressed in modal utterances.
6. My attempt was to explain systematically, to the best of my modest abilities of course, the relations between the two kinds and to consider their philosophical and methodological implications.
7. My central claim was that there is a relation of implication (perhaps weak) between the two types. In the end, you agreed with me, except that you attached to your agreement the derogatory word “triviality.” I’m afraid that if we continue down this road, you’ll agree with me also about the ontological structure of the world and about its paradoxical character, only adding the reservation that it’s “trivial.”
8. I’m beginning to worry about your well-being over this matter.

No need to worry. For now I’m doing fine.
I didn’t agree to two kinds of binarity, and certainly not to an implication between them. I agreed to two kinds of statements. Indeed, triviality is not a criticism, only a remark about the importance of the discussion and its necessity.

1. I think you’re mistaken—you didn’t agree to two kinds of “claims.” After all, you yourself corrected me (rightly) that one kind is claims and the other is not (your distinction was “between claims and what does not claim anything at all”).
2. Isn’t it a shame that even where you are right and I am wrong, you waste an opportunity to rejoice and exult?
3. Binarity means duality or doubleness. If you agreed to two kinds of “claims,” you are really talking about the same doubleness I’m talking about. Everything else is hair-splitting (I wanted to phrase that in juicy Aramaic, but nobody bothered to teach me the language).
4. You most certainly did agree to a relation of implication:
“The implication relation also seems trivial to me, at least if we mean it in the material sense (that it cannot be that the antecedent is true and the consequent false). In that sense it is clear that existence entails possibility (and not vice versa).”
4. Now we can hairsplit about the nature of this implication.

1. These are two kinds of statements. But what you called modal versus factual are two kinds of claims.
4. The implication is of one claim from another claim, not of one kind of binarity from another kind of binarity (unless I haven’t understood what binarity we’ve been discussing for an entire thread).
Well, it seems to me this isn’t really progressing. Let’s part once again as friends. 🙂

Be well.