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babou
babou
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Applied to formal metalanguage, this means that even though we can have a specialized language B to express precisely some aspects of English, it is only used as a scaffolding to actually express ourselvesour thinking more precisely in English, as we would do (with less precision) if we simply used English reflexively. So even the use of metalanguage ends up in reflexive use of the language, at least where natural language is concerned.

This is precisely what is done when defining the syntax of BNF in BNF. (BNF is just a specific notation for context-free syntax).

Further remarks

I cannot explain this text much more, as he does not seem to me that the author justifies all his assertions in the available text fragment. And furthermore, I do not always agree with them, short of more developed arguments.

To begin with the OP's question, I would definitely consider that a reflexive statement is a meta-linguitics statement about the language (here English) expressed in the language itself. The language is then its own metalanguage. If a language B has and expressive power that goes beyond the expressive power of a language A, while fully covering it, then one may expect that B would permit more general statements, or simply more statements about A than the reflexive use of A for itself. But that is somewhat a trivial remark.

The point of view of the author seems however to be that reflexive statements in English can cover more ground than the use of a formal language, since, for lack of a constraining formalization, it will be adaptable to a wider range of concepts and situation. This may well be true, at the expense of precision, univocality of expressions, and possibly accuracy of reasonning and avoidance of paradoxes.

Hence, it may indeed be undesirable to identify metalinguistic statements and reflexive statement as they do not serve the same purposes. Except maybe when the metalanguage is itself another natural language, hence having pretty much the same properties as English used reflexively. Still, it seems that the paragraph in red states that this identification necessarily occurs when using a formal metalanguage.

I disagree with the last sentence of the first paragraph (which should have a question mark added). My view is that there is substance (semantics) and names (syntax) used to physically denote that substance. Whatever we do is syntactic. If I write "Socrates has eight letters", I am certainly using the word Socrates, but I am using it as substance, not as a name for another substance. And one never accesses substance directly, but only through a name, if only to always proceed consistently. But, the author says it is unreasonable. He may have reasons to think that, but I do not see that he is giving them. Furthermore, we remarked that using English reflexively, or German as a metalanguage for English, is about the same. Using German as metalanguage, would he oppose considering "'sesquipedalian'" as a name for an English word. I do not know. But that is what it is in formal metalanguages (programming languages for example). Would that say something about a possible difference between formal and natural languages, rather than about the concept of reflexivity.

Regarding the sentence in red. I do agree with it on a first level. Usual discourse on English, even when based on a formal metalanguage, will make use of English itself (let's forget other languages), and will hence fall back on reflexive use of English. But, as I said, the formal metalanguage is still there as a scaffolding, possibly not very visible. And this scaffolding does structure discourse so that it will not wander beyond the limits set by the formal metalanguage. Hence there is not much that is changed by reflexive use of English, whathever "its richness, complexity and alleged inconsistencies". At best, you can get analogies and support for personnal intuition, but without really changing the end result. English is used reflexively in a formal sense, but it has little consequence ... unless the discourse starts bearing on the adequacy of the metalanguage. But this is yet another game, as English is then used as a metalanguage for the formal metalanguage.

I would rather not comment the rest of the text, which encompasses too many things, And I do not understand the reason for preferring to talk "in terms of use and mention" rather than substance and name as I did. I made up this terminology to avoid the more formal syntax and semantics. My opinion is that the philosophers'view (according to the author) is a lot more limitative because it is absolute rather than relative. Recall that higher up I wrote «"'sesquipedalian'"» so has to have a name for the notation of the name of a concept. This allows recursive use of the concept of naming, while use and mention do not allow it, if I am not mistaken in my understanding of their intended meaning.

If you reached this line without skipping, you won a coffee next time we meet.

PS I thought "sesquipedalian" qualified a bicycle with a broken pedal. I was apparently wrong.

Applied to formal metalanguage, this means that even though we can have a specialized language B to express precisely some aspects of English, it is only used as a scaffolding to actually express ourselves more precisely in English, as we would do (with less precision) if we simply used English reflexively. So even the use of metalanguage ends up in reflexive use of the language, at least where natural language is concerned.

This is precisely what is done when defining the syntax of BNF in BNF. (BNF is just a specific notation for context-free syntax).

Applied to formal metalanguage, this means that even though we can have a specialized language B to express precisely some aspects of English, it is only used as a scaffolding to actually express our thinking more precisely in English, as we would do (with less precision) if we simply used English reflexively. So even the use of metalanguage ends up in reflexive use of the language, at least where natural language is concerned.

This is precisely what is done when defining the syntax of BNF in BNF. (BNF is just a specific notation for context-free syntax).

Further remarks

I cannot explain this text much more, as he does not seem to me that the author justifies all his assertions in the available text fragment. And furthermore, I do not always agree with them, short of more developed arguments.

To begin with the OP's question, I would definitely consider that a reflexive statement is a meta-linguitics statement about the language (here English) expressed in the language itself. The language is then its own metalanguage. If a language B has and expressive power that goes beyond the expressive power of a language A, while fully covering it, then one may expect that B would permit more general statements, or simply more statements about A than the reflexive use of A for itself. But that is somewhat a trivial remark.

The point of view of the author seems however to be that reflexive statements in English can cover more ground than the use of a formal language, since, for lack of a constraining formalization, it will be adaptable to a wider range of concepts and situation. This may well be true, at the expense of precision, univocality of expressions, and possibly accuracy of reasonning and avoidance of paradoxes.

Hence, it may indeed be undesirable to identify metalinguistic statements and reflexive statement as they do not serve the same purposes. Except maybe when the metalanguage is itself another natural language, hence having pretty much the same properties as English used reflexively. Still, it seems that the paragraph in red states that this identification necessarily occurs when using a formal metalanguage.

I disagree with the last sentence of the first paragraph (which should have a question mark added). My view is that there is substance (semantics) and names (syntax) used to physically denote that substance. Whatever we do is syntactic. If I write "Socrates has eight letters", I am certainly using the word Socrates, but I am using it as substance, not as a name for another substance. And one never accesses substance directly, but only through a name, if only to always proceed consistently. But, the author says it is unreasonable. He may have reasons to think that, but I do not see that he is giving them. Furthermore, we remarked that using English reflexively, or German as a metalanguage for English, is about the same. Using German as metalanguage, would he oppose considering "'sesquipedalian'" as a name for an English word. I do not know. But that is what it is in formal metalanguages (programming languages for example). Would that say something about a possible difference between formal and natural languages, rather than about the concept of reflexivity.

Regarding the sentence in red. I do agree with it on a first level. Usual discourse on English, even when based on a formal metalanguage, will make use of English itself (let's forget other languages), and will hence fall back on reflexive use of English. But, as I said, the formal metalanguage is still there as a scaffolding, possibly not very visible. And this scaffolding does structure discourse so that it will not wander beyond the limits set by the formal metalanguage. Hence there is not much that is changed by reflexive use of English, whathever "its richness, complexity and alleged inconsistencies". At best, you can get analogies and support for personnal intuition, but without really changing the end result. English is used reflexively in a formal sense, but it has little consequence ... unless the discourse starts bearing on the adequacy of the metalanguage. But this is yet another game, as English is then used as a metalanguage for the formal metalanguage.

I would rather not comment the rest of the text, which encompasses too many things, And I do not understand the reason for preferring to talk "in terms of use and mention" rather than substance and name as I did. I made up this terminology to avoid the more formal syntax and semantics. My opinion is that the philosophers'view (according to the author) is a lot more limitative because it is absolute rather than relative. Recall that higher up I wrote «"'sesquipedalian'"» so has to have a name for the notation of the name of a concept. This allows recursive use of the concept of naming, while use and mention do not allow it, if I am not mistaken in my understanding of their intended meaning.

If you reached this line without skipping, you won a coffee next time we meet.

PS I thought "sesquipedalian" qualified a bicycle with a broken pedal. I was apparently wrong.

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babou
babou
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A reflexive use of a language A is the use of the language A to talk about itself, for example to analyze its own structure.

Instead, one can use another language B to talk about A. Then B is a metalanguage for A.

For example, if you define a mathematical formalism, say BNF, to express the syntax of languages, then BNF can be used (to some extent) to define the syntax of English, analyze it, talk about it, and do a variety of things. BNF is then a metalanguage for English, or more precisely for the syntax of English.

But you could also use English to describe the syntax of English, as many grammarians did in the past. Then it is a reflexive use of English to describe its own syntax.

An interesting note, not considered in the text you copied, is that a meta language like BNF can be used to define its own syntax. Then, it is a reflexive use of the metalanguage.

What the part in red says is that, even when we do mathematics, we conduct the discussions in English, or whatever language we happen to speak (some people believe there is only one). This is only partly true as computer scientists and mathematicians are developping systems that can conduct mathematical work in a purely formal way. But we tend not to do that when exchanging between human beings, and rather use natural language.

Applied to formal metalanguage, this means that even though we can have a specialized language B to express precisely some aspects of English, it is only used as a scaffolding to actually express ourselves more precisely in English, as we would do (with less precision) if we simply used English reflexively. So even the use of metalanguage ends up in reflexive use of the language, at least where natural language is concerned.

This said, you can talk perfectly well about English in German or other natural languages. In this case, German becomes a metalanguage for English. And native German speakers do not have to resort to English to say whatever they have to say, thus contradicting in a way the statement in red. Nevertheless, this remark does not really weaken the argument of the author, since we use metalanguages for mathematical precision. German as a metalanguage is probably not much more precise than English used reflexively. The author is really using the word "English" to mean natural language (his responsibility). By the way, this was a reflexive use of English, as I was discussing the meaning of an English word in a sentence, and the current sentence is a reflexive sentence talking about itself.

A problem is that metalanguages need also to be understood and precisely defined. So we could build a further metalanguage for the purpose, ... But this would not end. So at some point we cannot escape using reflection.

This is precisely what is done when defining the syntax of BNF in BNF. (BNF is just a specific notation for context-free syntax).