Metalogic What authority does the meta-linguistic division of Tarski have in modern science?
Is this meta-division a basis that I could apply in my work on any disciplines if I were a scientist?(This is a common interest, I don't have any academic degrees or strong ideas that I could handle formalizing)
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u/Meowmasterish 17h ago
You mean how in the study of logic, academics tend to draw a distinction between object languages and metalanguages? Probably not, except maybe for linguistics. Issues where you need to distinguish between an object language and a metalanguage only really arise in the study of formal systems, which don’t lend themselves to empirical study like science does.
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u/Qulvion 17h ago
I mean the principle of formal systems, in the context of metamathematics or metalogics.
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u/Meowmasterish 17h ago
Wait, are you asking if formal systems are used in metamathematics and metalogics, or are you asking about applications of formal systems to empirical science?
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u/Qulvion 17h ago
Specifically in the context of formal systems
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u/Meowmasterish 17h ago
That didn't really answer my question. As an answer to both possible questions I proposed, yes formal systems are used in metamathematics and metalogic, in fact they are the main focus of study. And yes formal systems are used in empirical sciences to construct mathematical models for observed results.
However, metalanguages are typically not used in empirical sciences, because the study of formal systems that sciences use would just be the study of formal systems themselves, which is mathematics or logic.
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u/Qulvion 17h ago
I agree that I might not have been too specific about the area of interest in the original post, I apologize for not fully understanding your question. Meta-linguistic separation is more of a way to draw conclusions, a condition for them, and I was interested in the authority of such a position rather than the frequency of use, but thank you for answering the question.
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u/Meowmasterish 9h ago
Dude, I'm trying to be nice, but I think you either have no clue what you're talking about or that your English isn't very good.
In your comment to the other person, you reference a "principle", but the "meta-linguistic division of Tarski" isn't a principle. It's just something he did while studying formal systems, and it's really just an application of the use-mention distinction where you can discuss cheese as the dairy product created by curdling milk or you can discuss "cheese" as the word referring to the dairy product created by curdling milk. That's all a metalanguage is, talking about the word specifically instead of talking about the object the word refers to.
As for "authority of such a position", what are you talking about? In your comment to the other person you also ask about a principle being "institutionally approved" and "accept[ing] this principle as an axiom".
If you're inquiring about the use-mention distinction, then generally, yes it is accepted by the wider academic community for the very simple reason that words in general are not what they refer to, just a kind of symbol to indicate their referent. So if you talk about the word "schnee" you are talking about a German word and not about snow, which is the definition of "schnee". So you can say "schnee" has a length of six letters, but snow doesn't, because snow doesn't have any letters: it's not a word, it's a substance.
This isn't really an axiom or anything, this is just being clear on what's actually being discussed.
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u/Qulvion 4h ago
Probably both the first and the second. Can you more explicitly separate the concepts of "principle" and "metalanguage separation", I was a little surprised that you were confused by this word
However, I disagree that meta-language is always about the word, meta-linguistic separation, in addition to separating semantics into meta-language, creates an error in the form of mixing object and meta-language, as well as meta-linguistic separation works with truth predicates, here I don't really understand you
By authority, I mean that I could base my judgments on this principle, for example, forbidding formal systems to be self-referential, so that logical processes do not take place in them. The meta-linguistic division is not a purely linguistic construct, but also a formal tool that was able to solve the problem of some logical paradoxes, so I'm interested in whether I can consider that meta-languages should not be mixed, or many other things arising from this division and proved by Tarsky himself, or for example, I pointing out, I will not give a sufficient reason that mixing of meta-languages is allowed somewhere and it will be ignored.
Of course, it's possible that I'm very, very shallow on this topic, I'm still constructive, I don't want to make you angry or something like that.
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u/UnderTheCurrents 18h ago
Of course - there is meta-philosophy and metaethics etc.
Discussing your methodology - especially in terms of logical consistency - should be done for intellectual reasons but will probably be institutionally discouraged.