„[...| Stupid, said Geryon’s brother
and left him.
Geryon had no doubt stupid was correct. But when justice is done
the world drops away.“ (p. 24)
I am going to demonstrate the logical form of Appendix C to the „Fragments of Stesichoros“ which precede Anne Carson’s Autobiography of Red. Why would someone want to analyse literature for it’s logical form? First, I am very fond of logic and literature. Second, I have never tried to mix them. But third, and this is the only point that actually seeks to provide this project with a scientific value, I am doing this in preparation for a claim about the text, namely the claim that the seesaw between logic / form and content / language use is itself a very central subject – in the text, and for Geryon.
Appendix C to the Fragments of Stesichoros consist of written fiction by Anne Carson and differs insofar from Appendixes A and B, which contain excerpts from several authors of Greek mythology. This third addendum consists of twenty-one consecutively numbered sentences. In the terminology of logic, all of them but the first one are material implications (those correspond to grammatical conditionals, or ‚if‘-clauses). The first sentence, however, is a disjunction (Either.. or..) of a proposition and its negation, and so are all the consequents of the following implications! The antecedent of the implications is each time one of the disjuncts of the former sentence’s consequent. In formal notation, then, the outlook is the following:
I. (1.) ....... A v !A ........ „A or not A“ (simplified!)
II. (2.-21.) .. A -> (B v !B) . „If A then B or not B.“ (simplified!)
III. (x(II.+1)) B* -> (C v !C). „If B then C or not C.“ (simplified!)
, whereas (Definitions:)
A -> B . is the sentential connective of the material implication (If A then B);
A v B .. is the sentential connective of the disjunction (A or B);
! A .... is the sign for negation (Not A);
A, B, C, [...] Z are simple propositional sentences (like „Stesichoros was a blind man“).
Now a disjunction (like 1.) claims that one of the propositions it takes is true. More precisely, it claims that at least one is, but this is exactly the simplification I marked above (see II., III.). I think it is possible for our purposes to simplify in this way, because all the disjunctions we are facing in (I. - III.) are of the kind that one of the disjuncts is the negation of the other disjunct. This is a special case, because it is a logical contradiction to claim that both propositions are true. In other terms, it is impossible for a proposition to be true while its negation is true. In logic, this is shown with a truth table, where each result shows F (for false):
A || A ^ !A
-------------
T || T F F
F || F F T
(Def.: A ^ B is the sentential connective of the conjunction (A and B).)
(In the case where A is true the conjunction of A and !A is false.)
(In the case where A is false the conjunction of A and !A is false.)
What this means, then, is that the first sentence does not make a claim about anything! It simply asks, says that A („Stesichoros was a blind man“) is true, or that it is not true, and that both cannot be true. Since all following sentences are logical conditionals, with the If-clause being filled with a proposition, which comes from this kind of disjunction, none of the antecedences are ever claimed. And this means, that also the consequences, whose truth in a conditional fully depends on the truth of the respective antecedents, are no claims. What we learn is, that, in Appendix C, not a single simple proposition is actually claimed to be true!
If you have followed this so far you must be thinking: what is all this discussion of logical form good for when there are no claims? This, however, is exactly the notion this Appendix C in my view is there for to provoke. The reader is provoked to ask „What is the use of such a beautifully engineered thought, when eventually it does not refer back to the world and make claims about it?“ This question, however, is one which the world of Autobiography of Red and its characters keep asking our tragic hero Geryon.
Maybe I will post another entry discussing the resulting dialogue in Autobiography of Red.
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I had the right idea here, but committed many mistakes, being new to the worlds of formal logic. Most importantly, the fact that the consequences of the disjunctive form A v !A (unsimplified: contrapositive form A v !A ^ !(A^!A) ) are necessarily always true does not demand that the implications' antecedences are never claimed, but that their negation can not be found logically. B > C <=> !B v C: If C is always right, the implication will never help with qualifying the truth value of B. And, this was my point here, because C in these cases is, as put in my original post, always A v !A, which is always true, even if we knew the truth value of either A or B, this specific form of implication would not ever help with determining the respective truth value of the other sentence. The disjunctive, truist form of the consequence obliterates any purpose of (unquantified, unmodified) implication in a logical sense.
ReplyDeleteOf course, the real use of narrating those implications is to be found in possibilities, not in gained knowledge about the world. Postmodernists readings would probably like to claim that this proved how useless logic was for creative purposes. The obvious reply is to be found in modal logic, diamond logic, the logic of worlds within reach of previous statements: logic that formulates sentences like "It may be the case that there exists at least one x which is postmodernist and stupid."