Thanks.
As for mathematics, I understand and accept that.
As for syntax: I myself also hesitated about that. The concept of syntax refers to the “combination” of signs that carry meaning (or can carry it). Signs that cannot carry meaning are not really signs at all, but “objects.” Therefore it seems to me that whether we like it or not, we are smuggling the definition of logic back into semantics through the back door.

??

You said something here. Are you expecting some kind of answer?
I don’t think semantics comes in through the back door, and even if it does, it lies behind consciousness. Mathematics itself deals only with signs. Our understanding makes use of meaning.
True, there are theorems in logic about adequacy and completeness (between semantics and syntax), but even that is determined syntactically.

What do you need to study in order to understand the discussion here?
Doron, in your question I didn’t understand what you mean by “semantic relations,” and how they differ from logical implication. Could you explain, please? Maybe identifying that two words (sun and orb) are synonymous is a semantic relation without implication? And what is the difference between logical implication and inferential implication? Do you mean softer forms of inference (as explained here and there) that yield probability rather than certainty (analogy, etc., as explained here and there)? Could you illustrate your proposal with a standard argument like: all humans are mortal, and Socrates is a human, therefore he is mortal? What is the “semantic relation” here that makes this argument part of logic, when the whole point is that you can replace the terms (human, mortal, Socrates) with syntactic symbols.
What does it mean that every mathematical claim is a semantic relation? (For example, the claim that if x is greater than 1 then x squared is greater than x—how would you characterize that?)
What is the difference between “signs” and “objects”? What is a plain symbol like p?
Complicated.

Michi,

I don’t understand what “behind consciousness” means.

Questioner,

First of all, I have a certain intuition that I’m trying to test. It’s not that I’m one hundred percent settled on this.
Second, I didn’t ask about mathematics and didn’t claim anything about it.

This is more or less my intuition:

1. There are relations between abstract signs, and they precede any “implication.” For simplicity, think of linguistic signs, that is, words, and think for example of relations of opposition, similarity, identity, etc. between words. Is the relation between “sun” and “orb” purely syntactic? Implicational? I’m not sure. It seems to me to be a semantic relation presenting an identity in the meaning of these two signs. Does anything have to “follow” from anything else in order for there to be identity between sun and orb? It seems to me not.

2. Another relation that exists between signs is a relation of “implication.” Every implication is a relation, but not every relation is an implication.
Implication is actually found in every sentence we utter… for example in the following sentence: “Today I visited the marina in Herzliya.” This sentence has four words spread out in thought (and in writing) along the axis of time. The sentence cannot really “be realized” unless you pass from its first word (“Today”) through all the words to the last one (“in Herzliya”). I think it is justified to call this logical implication, since the full meaning of the sentence only came fully into actuality at the end.

3. An inferential relation is simply the relation between a reason/premise and a conclusion. Every inferential relation is implicational, but not every implication is an inferential relation. The sentence above (“Today I visited the marina in Herzliya”) is not an inference, even though it is implicational.

4. In summary: I get the impression that a description of logic—at least the kind that stands behind natural language—without even a trace of semantics is an incomplete description.

Hope this little experiment of mine is understandable..

Thanks for the explanation, Doron 🙂
A question about point 1:
If I understood correctly, you’re saying that semantic relations are conclusions from analytic analyses of individual concepts (and such an analysis certainly requires semantics)? Or do you also call “regular” logical arguments (Socrates etc.) semantic relations, even though the argument is valid under any substitution?
And are you using the term “logic” here not in the sense of the formal discipline developed here and there, but in the sense of “the structure of our thinking when we discover certain truths”? Right?

By the way, regarding mathematics, you agreed that the definition “semantic relations” includes it (and that made me realize that apparently I don’t understand what you mean by the term semantic relation).

Logic deals with investigating and discovering the laws that lead us to think that a certain sentence is true and another is false.

Remember that you can put those laws into a mechanical computer. No soul needed.

So first of all, regarding the analysis of individual concepts, the answer is yes.

As for “regular” logical arguments: ostensibly, you’re right. The power of logic lies in its formality, that is, in its being empty of content, and therefore interchangeable variables can be substituted into it. So apparently here one should not speak of “semantics” but of syntax and nothing more.
But there is one point here that bothers me a bit: at least when we are talking about linguistic signs (words) that make up arguments, we are talking about meanings by virtue of logical functions that are not distinctly syntactic. At least that is how it seems to me at first glance. I mean subject, predicate, etc.

Take again the sentence “Today I visited the marina in Herzliya.” What is the set of elements of this sentence? The answer, of course, is the set of words that compose it (4 words in this case). And what is the lawfulness that constitutes the relations between those elements? The answer would be a “standard” syntactic analysis: “Today” (adverbial of time), “I visited” (subject + predicate), “at the marina in Herzliya” (adverbial of place).

But now try comparing the lawfulness underlying this sentence with a non-linguistic set whose elements are not signs but “objects.” Take, for example, 4 physical things (say a stick, a stone, a telephone, and an iron) and try to analyze the relations among them in terms of description, subject, predicate, etc…. It seems to me that you will immediately feel that something is off here.

The question is why that is so. After all, ostensibly we could have expected that the lawfulness constituting the connections between linguistic elements would not differ from the lawfulness constituting the connections between non-linguistic elements (physical objects). For if everything is only syntax, then everything is formal and empty of content (semantics)…

My initial answer is that the logical functions that appear in language (subject, predicate, etc.) are not distinctly formal functions. At the very least, they are not formal in the way we usually understand “formal.”

As for my use of the term “logic”… perhaps you are right and I am changing the term somewhat. But even if so, I don’t see a problem with that. If the philosophical definition of logic seems incomplete to me and I’m trying to reopen it in order to “expand” it, then I don’t think that’s problematic.

Sorry for the clumsy style. The visit to the marina today has completely drained me of whatever scraps of IQ had somehow still survived in me.

(For me this style is clear, meaning it’s easy for me to put my finger on what I understood, what is being asked, what is being claimed, and so on. And even if there is a question one can think about—and not just a proposed idea—that at least from my perspective makes it much easier to understand.)

As for language, there are syntax trees and grammars in order to formalize well-formed structures in natural languages too, and that is indeed logic in every sense of the term (not that I have clear knowledge about the terminology, but it seems that way to me. People study it as formal languages, and that’s the only place from which I know a little “linguistics”).
But connections that stem only from semantics—it’s not clear to me how one could formalize them (all symbols are symbols in the same way, and every semantics is semantic in its own way..). The syntactic role (subject, predicate, etc.) is the symbol here, and the semantics is the specificity within the specificity—that is, visited (and not walked, drove, danced, slept). Studying the well-formed structures of occurrences of syntactic elements and how one derives one structure from another is completely logic, and I don’t see even a trace of semantics in it. Presumably they choose the derivation rules in accordance with the semantic model they are trying to capture syntactically (adequacy and completeness, as mentioned above), but beyond that semantics is not formalized. In any case, I have no idea, and it seems you’ve already clarified enough for me.