Vincenzo LATRONICO: An a-priori derivation for the weak Spencer Anthony conjecture (excerpts)

An a-priori derivation for the weak Spencer Anthony conjecture (excerpts)

by Vincenzo Latronico
21 October 2011

[…]

4.2       On the other hand, the conventional idea about induction/interpretation/investigation is pretty much this: you have a finite set of random known elements (clues, inductive base) and an infinite structured set of unknown elements (story). The latter’s structure is what allows you to figure out the infinite set in all of its details, motives, characters, based only on a small part of it.

       4.2.1       Clues hence induce an ultrafilter on the story, or a Kleene star if the story is defined as necessarily expressible in words.

4.3       According to this idea, you proceed by narrowing down possible stories. You have a single clue (say, a shovel), and pretty much any story could be built around it. Add other clues and the amount of possible stories will radically diminish (a shovel, a parachute, a hard-drinking lion tamer). There is an inverse correspondence between the elements in the set of clues and the possible stories, converging asymptotically to 1 when the clues tend to infinite (when, that is, the set of clues is identical to the single, true story itself). Of course, you will never reach this point: but you can aspire to it.

        4.4       This corresponds pretty much to the way Leibniz saw the logics of knowledge. Leibniz considered every entity, object and event, or collection thereof, to be characterized by infinite attributes; “identifying it”, pinning it down, meant knowing enough of those infinite characteristics so as to be able to infer the rest. In Leibniz’s theory, complete identification was possible only to God’s mind. Everyone else had to guess and hope she was right.

*******

5       Of course, this idea of induction is wrong.

5.1       If you define a story as a combination of clues, this implies that there are more stories than clues – since the set of stories is the powerset of the set of clues (or a subset thereof closed under some relevant operation). The clues are all given (but perhaps unknown as of yet, or inaccessible), the stories are not.

       5.1.1       But the clues are not given.

5.2       Clues, in fact, seem to generate each other. You judge whether X is a clue based on the clues you already have. You only see the lion tamer as relevant to your investigation because those on the shovel could very well have been his fingerprints; you would have never thought of him before, and in fact you were looking elsewhere.

5.3       This implies that, the more clues you have, the more clues you could possibly have: otherwise, the linear decrease in possible clues corresponding to the growth of actual clues would, in a finite number of steps, bring a halt to the process of investigation, since there would be no possible clues left. This would amount to saying that nothing can be known. We cannot accept this.

5.4       It follows from 5.2 and 5.3 that the set of clues to any given story is at least infinite countable, since it grows linearly with the iterations of an operation – the discovery of a clue – that can be iterated indefinitely. This can be conjoined with a version of the weak rationality principle (WRP), that states that the set of knowable entities to any subject S is always countable.

5.5       It follows from 5.4 and WRP that every knowable thing is a clue.

       5.5.1       There is a strategy to reject 5.5: and that is stating it in hypothetical form. We have started from the assumption (2.3, 2.7) that clues exists. This axiom could very well be considered a mere hypothesis: we would then have proven that, if anything is a clue, everything is.

*******

6       Q.E.D. As claimed in 1.2, it is hence possible to provide an a-priori derivation of the weak version of the Spencer Anthony conjecture (wSAC).

6.1       I was reaching the bus stop to Oxford Circus when the lady came to me. She seemed in a hurry and aloof, as if talking to herself. “There’s something you dropped”, she seemed to gesture as she whizzed past, but I didn’t know if it was true or not. A week has passed, and still I don’t.

Vincenzo Latronico is a writer based in Milan. His novels are published in Italy by Bompiani; his art criticism has appeared on frieze, Kaleidoscope and Rolling Stone.