A defense of the description theory of quotation

Transcript

1. A defense of the description theory of quotation Yoriyuki Yamagata June 16, 2019
2. The description theory of quotation Examples “Alice swooned” is a sentence According to the description theory, “Alice swooned” is a description of the sequence of alphabets Alice swooned .
3. Davidson’s attack to the description theory 1 Impure quotation 2 Mixed case of use and mention 3 Quantification over quoted variables 4 Picture-like property of quotation 5 Possibility of infinite alphabets
4. Naming relation Definition Name(d, n) ⇐⇒ n is a name of d Remark If d has a unique name n, write n = Name(d) Examples Name(Anapurana, Anapurana ) quotation = Name(quotation)
5. Impure quotation Examples Quine says that quotation ‘. . . has a certain anomalous feature’. Interpretation Quine says that Name(quotation) :: has a certain anomalous feature
6. Mixed case of use and mention Examples Dhaulagiri is adjacent of Anapuruna, the mountain whose conquest Maurice Herzog described in his book of the same name. Interpretation Dhaulagiri is adjacent of Anapuruna ∧Maurice Herzog described Anapuruna in his book x ∧ ∃n.(Name(Anapuruna, n) ∧ Name(x, n)))
7. Quantification over a quoted variable I Examples This is not a valid inference 1 “Alice swooned” is a sentence 2 ∃x. “x swooned” is a sentence The description theory predicts this behavior, because x inside quotation is a mere character, not a variable.
8. Quantification over a quoted variable II Examples According to the description theory, this is a valid inference 1 “Alice swooned” is a sentence 2 ∃x. x :: “swooned” is a sentence 3 ∃x, y. x :: y is a sentence Davidson commented “quotation marks play no vital role in the spelling theory; and also that this theory is not a theory of how quotation works in natural language.” However, these two examples illustrate that the description theory predicts an important behavior of quantification and quotation: Quotation blocks the scope of quantification.
9. Quantification over a quoted variable III The second example has a natural counterpart of mixed quotation Examples 1 “Alice swooned” is a sentence 2 Alice “swooned” is a sentence 3 There is something which it “swooned” is a sentence or better, Examples 1 Quine says that “quotation has a certain anomalous feature” 2 Quine says that quotation “...has a certain anomalous feature” 3 There is something which Quine says that it “...has a certain anomalous feature”
10. Picture-like property of quotation I Examples Davidson consider the following transformation 1 “Alice” is a word 2 ‘A’ :: ‘l’ :: ‘i’ :: ‘c’ :: ‘e’ is a word 3 eeh :: el :: ai :: si :: ee is a word 4 ee ::r si ::r ai ::r el ::r eeh is a word By this transformation, Davidson argues that the description theory does not capture picture-like property of quotation. However, our goal is to create a semantic theory of quotation, not a mere syntactic paraphrase. Therefore, as long as the semantic value of a quoted expression retains its structure of the quoted expression, the theory is justified.
11. Picture-like property of quotation II Examples Davidson consider the following transformation 1 “Alice” 2 ‘A’ :: ‘l’ :: ‘i’ :: ‘c’ :: ‘e’ 3 eeh :: el :: ai :: si :: ee 4 ee ::r si ::r ai ::r el ::r eeh All of them denote the sequence of alphabets Alice which is exactly the same object as a quoted word “Alice”. Therefore, from the semantic viewpoint, the description theory preserves picture-like property of quotation.
12. Possibility of infinite alphabets I Examples “♥” means “love” We can use any kind of a symbol inside of quotation. Therefore, the description theory may need infinite number of alphabets to interpret quotation. This would be against Davidson’s thesis that the language must have finite number of primitives.
13. Possibility of infinite alphabets II We seems to have two options. 1 Argue that there are only finite number of symbols, by the limitation of human cognitive capacity 2 Deny thesis that the language must have finite number of primitives I am inclined to the second option. The essential property of natural language is that it is infinitely extensible. This is not against learnability, because in any point of time, the language is finite.
14. Conclusion We introduce naming relation Name(d, n) and using this, interpret impure quotation and mixed case of use and mention. Further, we argue that Davidson’s criticism to the description theory based on quantification and picture-like property of quotation is groundless. Finally, we discuss possibility of infinite number of alphabets. We inclined to accept this possibility, based on infinite extensibility of a natural language.