Topic: PARACONSISTENCY
A QUESTION TO THE DEFLATIONISTS
As always, I shall try to be as concise as possible. (1) below is a classic principle of Logic:
(1) T(S) iff F(~S)
Still, given that in classic logic (2) is valid:
(2) if F(B) then T(A)
By (1) and (2), and by substituting ~S for B and S for A in (2), it is not obvious that (3) is blocked:
(3) if ~S then S
Thus, a sentence like (4) should make sense in a human language:
(4)#If Marilyn Monroe did not pass out then she passed out.
But (4) is nonsensical in English or in other natural language. There are several manners to fix (4) in a natural language like English:
(5)
a. If it is false that Marilyn Monroe did not pass out then it is true that she passed out.
b. If it is false that Marilyn Monroe did not pass out then she passed out.
And there are other ways not to fix it:
(6) #If Marilyn Monroe did not pass out then it is true that she passed out.
(7) below is the main deflationist claim:
(7) Adding it is true that to a sentence S adds nothing to its content.
(7) can explain why there is no difference of status between (5a) and (b), and why (6) cannot be an option to (4).
On the other hand, given that (8) below is not valid:
(8) if T(B) then F(A)
One should not expect (9) to be ok:
(9) If it is that true Marilyn Monroe did not pass out then it is false that she passed out.
But (9) is sensible in a natural language like English. Of course, in such case one might argue that, unlike in an artificial language, English if... so constructions might be interpreted as if and only if statements in some cases like (10), in the context of a mother talking to her daughter:
(10) If you break another vase in the house, you will have no ice cream tonight.
Where the daughter does not expect to be punished in the event that no vase is broken in the house. But (4), (9) and (10) are precisely the kind of evidences used to argue that natural languages are not semantically closed, i.e., they do not abide by (1) in all instances.
But if one dispenses with (1) in the case of natural language semantics, how can one maintain (7) or explain the cases where the sensical/ non-sensical status is not altered by the addition of it is true that ...?
Before advancing any proposal of my own, I would like to hear your thoughts on this matter.
Posted by Tony Marmo
at 03:14 GMT
Updated: Thursday, 4 November 2004 09:57 GMT
