Is it “true” that when anyone is rewriting a “sentence” in Logical Form(LF) by deploying metalinguistic constants and variables, the ultimate output would reveal the ‘true’ meaning of a given sentence? In LF, a major concentration is devoted to describe and understand the ‘real world’. This supposed logical positivist “real” is incorporated in the logical analysis of sentences in the algorithmic chain of LF of S-Structure by deploying sentential calculus. LF mainly follows Fregean compositionality or its derivatives like Katz-Fodorian Model. The following questions may be asked:
1. What is “real” in this real world? (To answer such question, one may take a clue from Russell’s An Inquiry into Meaning and Truth: “We all start from ‘naïve realism,’ i.e., the doctrine the things are what they seem. We think that grass is green, that stones are hard and snow is cold. But physics assures us that the greenness of grass, the hardness of stones, and coldness of snow are not the greenness, hardness and coldness that we know in our own experience, but something very different. The observer, when he(sic) seems to himself (sic) to be observing a stone, is really, if physicist to be believed, observing the effects of the stone upon himself (sic).Thus science seems to be at war with itself: when it most means to be objective, it finds itself plunged into subjectivity against its will. Naïve realism leads to physics, and physics, if true, shows that naïve realism is false. Therefore naïve realism, if true, is false; therefore it is false.” (1940:15)
2. What happens in LF if anyone puts Russell’s paradox (1913) in LF? How do we incorporate Gödel’s theorem to tackle a formal system like LF? According to Goedel’s theorem (1931), no formal system is complete enough to handle all the problems within a formal paradigm. If anyone puts any Goedel’s proposition or Russell’s paradox (“One Calcuttan says that all Calcuttans are liars”) in LF of S-Structure, the total formal as well as mechanical algorithmic system to gauge the meaning may collapse.
3. Katz-Fodorian (1963) system of binary componential analysis ignores the prototypical cognition of meaning by the human being. As some cognitive scientist observed that the meaning as endorsed by human beings, could not be analyzed by the stipulated components as humans understand meaning through prototypical cognition. What should we follow in semantic analysis:technical intelligentsia’s critical discursive habit of paraphrasing or commonsense deployment of prototypes?
4. Let us switch over to another schooling and try to understand semantic problems raised by continental philosophers (under the umbrella o fso-called Post-Formalism/ Structuralism). These Post-Formalists are talking about plural meanings of non-disposable texts as well as something called‘surplus meanings’, which is not at all analyzable or quantifiable .According to them, the meaning-site is too slippery area and any futile endeavor to formalize such site will be ended in vain. Do you think that they are neglecting ‘science’ and its formalism by promoting“un-scientific” non-formalism?
Your very first sentence already betrays a confusion: Rewriting a “sentence” in Logical Form (LF) is not metalinguistic. When you simply translate a sentence about the world, i.e. a sentence in the object language, the new sentence is still in the object language. A sentence in the metalanguage is one which talks about the object language. For first-order logic, the wffs (well-formed formulas, which might be translations, regimentations, or abbreviations of ordinary English sentences) are in the object language, whereas the sentences describing the formation-rules (the "grammar" that specifies what it is to be a wff) and the transformation rules (rules of deduction) are in the metalanguage. Here are some examples;
- Object language sentence: "The cat is on the mat."
- Metalanguage sentence: ' "The cat is on the mat" contains 6 words.'
- Metalanguage (or meta-metalanguage) sentence: " ' "The cat is on the mat" contains 6 words.' is a sentence in the metalanguage.' "
- Metalanguage sentence: ' "Ocm" is a translation into the notation of first-order logic of the English sentence "The cat is on the mat". '
- Object language sentence: "Ocm"
- Object language sentence: "Socrates was an ancient Greek."
- Metalanguage sentence: ' "Socrates" has 6 letters" '
- Metalanguage sentence: ' "Socrates" refers to an ancient Greek '
- Metalanguage sentence: ' "Socrates" refers to Socrates. '
Peter Breuer
Oh, but it is.
“This sentence is not in the metalanguage” is false.
' "This sentence is not in the metalanguage” is not in the metalanguage.' is false.
But the two preceding metalanguage sentences are true. (← As is the immediately preceding metalanguage sentence.) You can't quite get the liar paradox underway here. 😐
Metalanguage: "A system of propositions about propositions." -- I don't wish to say nothing more about the stipulated meaning ascribed by Karl Pfeifer.
Debaprasad Bandyopadhyay My meaning is not stipulated by me; it is established usage. In fact it complies with your statement:
Metalanguage: "A system of propositions about propositions."
Consider:
1. The cat is on the mat.
2. Die Katze ist auf der Matte.
3. Ocm
Sentence 1 is about a cat and a mat, i.e. it is not about language.
Sentence 2 is sentence 1 rewritten in German, but it is still about a cat and a mat, not language.
Sentence 3 is sentence 1 rewritten in the notation of first-order logic, but it is still only about a cat and a mat, not about the notation of the logical language.
Sentences 1-3 are all object language sentences. However, suppose I say something like:
4. “Ocm” is a sentence of first-order logic that shows the formal structure of sentence 1.
Sentence 4 is a sentence in the metalanguage about a sentence in the object language.
Moreover the predicate “O” and the constants “c” and “m” are, respectively, abbreviations of "on", "the cat", and "the mat" according to some translation scheme stated in the metalanguage; they are not metalinguistic constants nor are they variables. However if I say “for any p, p is true iff ~p is false” then I am speaking in the metalanguage, and "p" is a metalinguistic variable which can take the object language sentence “Ocm” as a substitution instance; by common convention the above "~" is a metalinguistic constant that names the corresponding logical constant of the object language.