Binary

Thanks for the reference.

I read the article and it seems that the central insight in it (from the methodological aspect) is your distinction between factual sentences that have a truth value and modal sentences (in this case, duties and responsibilities) that do not have a truth value.
Did I understand correctly?

Assuming that I did, I also understood something else: in your opinion, the principle of sharp binary applies only to factual sentences, since only for them do judgments of identity or contradiction hold.
True/false.

And my question:
I am interested in the relationship between modal sentences and factual sentences. Apart from the fact that the two types of sentences represent two different types of ontology, it seems to me that there is a principled (logical..?) precedence for modal sentences.

For example, the sentence:

“It is raining” (=a statement of fact with a truth value)

Conditioned by the modal sentence:

“There is a possibility that it will rain” (or something like that).

After all, if there were no logical possibility of rain falling anyway, the sentence expressing the current state of affairs (the actual rain falling) would be meaningless.

Agree/disagree?

If I am right, then it follows that the principle of single binary is “restrained” (or perhaps even subordinated to) a non-binary principle that is not a contradiction but merely reflects tension.

What do you think?

I don't know where you saw all this in the article. I don't remember there being a reference to possibility sentences (modal sentences, in your language). I'm dealing with explanations for a certain halakhic law (obligation to pay damages), and I'm arguing that the explanations don't have to be mutually exclusive. But not because there is no contradiction, but because they can be joined together. 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. Therefore, there is no reason to combine the two explanations and say that the explanation for law A is (X and also Y) or (X or Y).
All of this has to do with logical binary. If any sentence is true, its opposite is false, and vice versa. Accepting any claim as true and false at the same time is a bit of a blunder. There is no restraint on this meaning of logical binary. The problem is that many people identify a binary where there is none, and I have written about this more than once. Here is one example.

1. You did address modal sentences (or at least modality in logic) in the article:
You did not discuss who actually paid, but rather a possible reality, i.e. what is “right” or “proper” to do.
2. In your answer to me above, you did not address my question: In essence, this was not about the distinction between factual sentences and modal sentences (a distinction I believe you accept) but about the relationship between them and the relationship of all this to binary.
3. Your comment that self-contradictory sentences are egg rolls is correct in my opinion. But it seems to me that it is not really related to my question.
4. Another comment (and justified in my opinion): Sometimes people confuse contradiction and tension. They claim, and rightly so, that it is possible to “contain” Opposing positions (that are in tension), but since they are what they call “contradictions” the mistaken insight is created in their heads as if contradictions can be “contained”. In your opinion (and in my opinion) these are really egg rolls.
5. But as much as I agree with this comment of yours, it is also not really related to my question.
6. I demonstrated my question with sentences about rainfall. Do you agree that the claim that ”rains” is conditional on the modal claim “it can rain”?
7. The reasoning: If the latter claim has no meaning, it follows that the former claim also has no meaning.
8. For example, sentences of the type “God can create a round triangle” They do not belong at all to either of the two groups I referred to above. These are sentences that are not factual statements but are not modal sentences either. They are simply contradictory and therefore meaningless.

1. This is not modality in your sense. But let's leave this debate.
2. I answered that in my opinion it has nothing to do with logical binary and its reservations.
6-7. Right. If the possibility of rain falling is contradictory then there is no possibility of talking about the fact that it is raining. So what?
8. Right.
So where is the debate?

1. I'm not at all sure that there is an argument between us here. For now…
In any case, I'm talking about two different solutions to the concept of binary: in relation to factual claims and in relation to modal sentences.
2. I didn't understand. In your opinion, there is no connection between a modal sentence and a factual claim? I think that there is a consequence here - even if in a weak sense - from the first to the second.
3. What do you think?
4. If there is such a consequence (or at least if it exists as a necessary but not sufficient condition), then it follows that the binary implicit in the world of modal sentences (a binary of tension and, in my opinion, also of paradox) in some sense results from the binary of the laws of identity and contradiction.
5. In conclusion: In my opinion, the two different solutions of binary have a logical relationship between them (and I believe also a metaphysical-ontological one, but let's leave that for now…)

I lost you. There are no compromises to binary. There is no difference between modal sentences and others. There is no truth and falsehood at the same time, neither this nor that. I have already written that I agree that there is a connection between possibility and actual existence.

First meaning: Claims that can be refuted.
Second meaning: Claims that make sense but have no truth value and therefore cannot be refuted (e.g. “Smoking is not allowed”).
What is wrong with this?

Besides, I am not content with your agreement that there is a connection between possibility and actual existence. I argued for a connection of emanation, even if in a weak sense.
Agree or disagree?

These are not two solutions to binary but a distinction between claims to what does not claim anything that is as old as Aristotle's, a great old age and a beautiful complexion.
The connection of derivation also seems trivial to me, at least if we are talking about the material sense (that it is not possible for the premiss to be true and the conclusion to be false). In this sense, it is clear that existence entails feasibility (and not vice versa). In other words: feasibility is a necessary but not sufficient condition for existence, and existence is a sufficient but not necessary condition for feasibility (these are two logically equivalent claims, of course).

1. You did correct me in terms of terminology. There are not two kinds of claims here.
2. But the technical (important) matter does not add to or detract from the essential point I raised: in both cases, we are dealing with statements or sentences that express the principle of binary in different ways. In the first case, binary (=duplication, secondness) relies on a contradictory opposition, in the second case the opposition is not contradictory.
3. If you claimed in the past, and I think you did, that logic (in the sense of claims that have a truth value and are therefore contradictible) stands on the first floor, then now you agree with me that there is a sense in which logic itself derives from a more basic ground floor. You even claim that the assumption of the existence of such a ground floor, as well as the principle of deriving from it, is a trivial assumption. You are right.
4. This floor is expressed in modal statements.
5. You can of course argue that the modal ground floor is still part of the ”logic”. If you choose to do so, I am not sure I would object to this conclusion.
6. But in any case, it is clear that adopting such a strategy would certainly restrain the binary principle in its sharp meaning of either true or false, by subordinating it to a much softer binary principle
7. I am sure you understand very well what I am trying to achieve. If the ”logic” on the ground floor is not so sharp, then a first opening opens for the introduction of a transcendent ontology for man, one that has a paradoxical character

I understand perfectly well where you are going, and there is no connection between the trivial claims raised here and your desired outcome.

If we ignore for a moment the realm of objects, ontology, you still haven't denied that you accept the existence of a logical ground floor ‘which is entirely in the modal spheres.
Accept or not?

Doron, I have a hard time with you. Who doesn't accept trivial statements like this? What do they have to do with our case?

1. My heart goes out to you for the severe torment you are going through with your gender. Perhaps you will take comfort in the thought that the torment I am causing myself is much greater?
2. Trivial statements: In my opinion, good philosophy often deals with what is perceived as trivial in someone's eyes, 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 your inferior would not have been aware of, or at least would not have been aware of in the context you raised.
3. My claim about the modal principle at the basis of the laws of fact is an example of a “trivial” but effective statement. At least that's what I hope.
4. This statement is also closely related to our concerns in the following ways:
5. Certainty: It better explains why certainty cannot be achieved in philosophy: logical certainty can only exist 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 “fact claims” with 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 base of propositional logic - located on the first floor - allows claims to escape the requirement for certainty. There is certainly much to expand and qualify what has been said here, but this is not the place.
7. The intuitive faculty in man: Those who believe, like you (and certainly like me), in the existence of an intuitive faculty may be pleased to discover that intuitive cognition has a parallel in human language (and thinking): just as our intuitions act directly on our minds, so do modal statements (of course, in a slightly different way, since their “content” is embedded within them, unlike the content of intuitions).
8. My book “I Was the Brain Behind Confused Yuval” will be published very soon, and there I will present all these points in detail and in detail.

The explanation of why certainty cannot be achieved in philosophy is so simple that I don't understand what all this adds to us. One should not evade certainty when there is no way that there could be certainty.
You write that certainty is conditional on the fact that there cannot be worlds in which the truth value is different. This is nothing but the good old modal meaning of certainty (necessary = true in all possible worlds).
But I will eagerly await the book. 🙂

1. “Hey Amina”: Are you serious? You send me to the wilderness of the Internet to look for a translation into your stilted Aramaic and you still complain that I make your life difficult? Shame on you.
2. Regarding certainty: I am glad that you have already come to the insight that certainty is like a flower. On the other hand, there are great and important philosophers who mistakenly assume that certainty can indeed be achieved (sometimes their assumption is hidden, perhaps even unnoticed by them). Therefore, it may be important to attack the fallacy from another direction (I tried to do this from a broader context, and perhaps I succeeded in doing so, I don't know).
3. I am glad that my definition of certainty is consistent with the formal and accepted definition. I don't understand how this weakens my argument.
4. You did not address the issue of intuitions and their structural analogy to modal statements.
5. To remind you: The subject of the question and argument I raised from the beginning was binary. I argued then and still argue now that there are two kinds of binary for the genitives: a contradictory binary expressed in factual claims and a binary of opposition expressed in modal statements.
6. My attempt was to systematically explain, to the best of my modest abilities, of course, the relations between the two kinds, as well as to examine their philosophical and methodological implications.
7. My central argument was for a (perhaps weak) causal connection between the two kinds. You agreed with me, in the end, only that you attached to your agreement the derogatory word "triviality." I fear that if we continue on this path, you will also agree with me about the ontological structure of the world and its paradoxical nature, and will only qualify this by saying that it is "trivial."
8. I'm starting to worry about your well-being in this matter.

Don't worry. For now, I'm fine.
I didn't agree to two types of binaries, and certainly not without a derivation between them. I agreed to two types of claims. Indeed, triviality is not a criticism, but only a comment on the importance and necessity of the discussion.

1. I think you are wrong - you did not agree with two types of “claims”. After all, you yourself corrected me (and rightly so) that one type is a claim and the other is not (your distinction was “between claims and what does not claim anything”).
2. Don't you feel bad that even where you are right and I am wrong, you waste an opportunity to rejoice and joke?
3. Binary means duality or duality. If you agreed with two types of “claims” you are actually talking about the same duality that I am talking about. Everything else is gibberish (I wanted to formulate this in juicy Aramaic but no one bothered to teach me the language).
4. You also agreed with the connection of derivation:
“The connection of derivation also seems trivial to me, at least if we are talking about the material sense (that it is not possible that the premiss is true and the conclusion is false). In this sense, it is clear that existence entails possibility (and not vice versa). ”
4. Now we can wonder about the nature of this emanation

1. These are two types of sentences. But what you called modal vs. factual are two types of claims.
4. The derivation is of a claim from a claim and not of a type of binary from another type of binary (unless I didn't understand what the binary is that we've been dealing with for a whole thread).
Well, I don't think this is really progress. We'll part as friends again. 🙂

Sha Bracha