Is symbolic logic just a non scientific way when it comes to interpret human natural language?

Question

Let me ask you a thing it is about implication: when I say, if I go to London, I will talk to Paul, I mean an implication, or S=>P. Well, implication means it is necessary that S belongs to P, example: if it is a duke, it is a bird. Now, talking to Paul is not a necessary event or relation that follows my trip to London, it is the infamous "future contingent". Which means: S => ( P v ~ P ). Which means: S => ( P => P ). Or: S & P => P. So, if I go to London and talk to Paul, than I talk to Paul. Am I right? Well, someone may say that I should interpret the relationship of implication here as a promise because I must understand it in its context. My question: translating human's natural language to symbolic logic means understanding the context of the speech, or its language game, so it is an interpretation. But is interpretation a scientific operation? Isn't it a kind of art or a language game? I could translate "if I go to London, then I talk to Paul" even as a biconditional, S <=> P, and justify I did it because the context of the speech. So is it an art or a science? Does it worth to indeed study it when it comes to natural human language?

Answer 1

You can analyse a statement such as 'if I go to London then I will talk to Paul' in one of two separate ways. You can analyse it as a sentence without considering the context. In that case it is superficially similar to 'if x is less than seven, then x is less than ten', but clearly the similarity is misleading. To be sure that you are representing the natural meaning, you must analyse the sentence in its proper context, taking account of the character of the person who uttered it, the circumstances, idiom, nuances such as sarcasm, irony and so on. So, clearly, yes, you can use symbolic logic to summarise the intention of human language, but you cannot do it mechanistically simply by analysing the structure of sentences.

Answer 2

I mean an implication, or S=>P. Well, implication means it is necessary that S belongs to P

For an implication S → P, Aristotle says, "P belongs to all S" (not "S belongs to P" as you put it). By this he meant that P is the predicate which applies to any S. Thus, in "all dogs are mammals", or D → M, being a mammal is a quality which belongs to every dog.

if I go to London, I will talk to Paul (..) talking to Paul is not a necessary event or relation that follows my trip to London, it is the infamous "future contingent". Which means: S => ( P v ~ P ).

We will say "if I go to London, I will talk to Paul" whenever we believe that it will be true that we will talk to Paul if it is true that we go to London. We don't know that this conditional is true since it is a future event, but we will assert it if we believe that this is what is going to happen or what we mean to happen.

S → (P ∨ ¬P) is necessarily true but does not fit what the speaker means in this case.

S => ( P v ~ P ). Which means: S => ( P => P ).

No. S → (P ∨ ¬P) is just true because P ∨ ¬P is true in every logical case, so whatever S may be, P ∨ ¬P is true, so if S is true, P ∨ ¬P is true, so S → (P ∨ ¬P) is true.

S => ( P => P ). Or: S & P => P. So, if I go to London and talk to Paul, than I talk to Paul.

S → (P → P) is indeed equivalent to (S ∧ P) → P, and both are obviously true.

But (S ∧ P) → P does not translate "If I go to London, I will talk to Paul".

I should interpret the relationship of implication here as a promise.

No you shouldn't. An implication has nothing to do with a promise.

My question: translating human's natural language to symbolic logic means understanding the context of the speech, or its language game, so it is an interpretation. But is interpretation a scientific operation?

Humans do understand each other. Scientists can only do good science if they understand each other. So, our ability to correctly interpret what other people say cannot be doubted. Many people make a lot of mistake, but we can do it correctly.

Isn't it a kind of art or a language game?

Analogies are invariably counterproductive to logical reasoning. There is an analogy between language and games but there is exactly the same analogy with mathematics and with science itself, namely that in every case we do what we please as long as we follow the rules.

I could translate "if I go to London, then I talk to Paul" even as a biconditional, S <=> P, and justify I did it because the context of the speech.

No, "if I go to London, then I talk to Paul" is a conditional and can only be translated as an implication. Context is irrelevant here because there is no margin for interpretation.

EDIT - If you translate what has been said, namely, "If I go to London, I will talk to Paul", then it is a conditional so the translation can only be an implication S → P, but if you translate not only "If I go to London, then I will talk to Paul" but also the implicit "If I don't go, of course I won't talk to him", then, yes, it is a biconditional and the translation will be a double implication S ⇔ P.

So is it an art or a science?

It is certainly an art, but it could be a science, although this would require serious work. I guess this is what people behind systems like ChatGPT are trying to do. Whether they succeed, I don't know but I am very sceptical.

One fun possibility is that AI technology came to evolve to reproduce human logic by chance, as it were. This seems exceedingly unlikely but not absolutely unconceivable.

Does it worth to indeed study it when it comes to natural human language?

It depends. Making a scientific investigation of natural language to be able to interpret what people say is definitely an objective that academia should pursue. However, to do that, you would need to understand logic and the academic expertise on the subject is close to zero. So, first, you would have to understand how logic really works. Very many bright people have worked on the subject for 2,500 years already, without success. So, you would have to be both young and bright. And this would require all your time and energy. Worth it? You tell me.

Answer 3

In Chomsky's Theory of Universal Grammar, it is stated that the human comprehension of natural languages is similar to each other. The main problem is this: since people initially understand the concept of time in language later, they perceive language as present tense. This is more convenient as art, because it can be detrimental to the human perception of natural language.

Answer 4

You ask:

Translating human's natural language to symbolic logic means understanding the context of the speech, or its language game, so it is an interpretation. But is interpretation a scientific operation? Isn't it a kind of art or a language game?

So, you've touched on a very important topic since the linguistic turn. The question of meaning and translation between languages and grammars was a topic visited by both Wittgenstein and Quine, the latter in his thesis indeterminancy of translation. From WP:

The classic statement of this thesis can be found in his 1960 book Word and Object, which gathered together and refined much of Quine's previous work on subjects other than formal logic and set theory.1 The indeterminacy of translation is also discussed at length in his Ontological Relativity.2 Crispin Wright suggests that this "has been among the most widely discussed and controversial theses in modern analytical philosophy".3 This view is endorsed by Putnam, who states that it is "the most fascinating and the most discussed philosophical argument since Kant's Transcendental Deduction of the Categories".4

So, obviously, anyone who gives you a quick yes or no or has a simple system doesn't quite grasp this rather complex topic. What can be said is this. That philosophical logic in its modern form, that of mathematical logic, is one of at least three important types of formal semantics that express some aspect of the meaning that inheres to natural language.

So it is definitely an art, and not a science. To translate from natural language to a syntactical formalism means picking the right one for the job, because there is no formalism that can substitute for an entire natural language. Starting with Frege in the 19th century, formal systems began being proposed to cover math and logic, and have since been brought together under mathematical logic. Noam Chomsky rocked the philosophical world and introduced his universal grammar in the 50's. Richard Monatague proposed a grammar to try to combine linguistic and mathematical logical formalisms, and today, computer scientists are trying to use the various grammars that have been developed to achieve natural language understanding using NLP. One of the key problems is trying to understand how natural language ontologies (SEP) actually function so that they can be simulated.

So, absolutely, when translating from natural languages to formal systems like those of logic, math, and language, one has to rely on intuition and research and experimentation. It's still very much an active area of research in philosophy, mathematics, logic, linguistics, and computer science. One can think of the development of these formalisms and the practice of translation very much a language-game in the Wittgensteinian sense.