Friday, August 5, 2022

12th Series of the Paradox

This chapter looks at the problem of paradoxes and the territory they cover. Paradoxes are opposed to good sense and common sense. Good sense is a unique sense bound by a demand of order to go in a particular direction. Discusses the attributes of good sense and common sense. Common sense is what allows identity and recognition. Examples from the paradoxical world of Wonderland and Alice show when she doesn't have good sense or common sense.

The sense from paradox goes in two directions simultaneously comparable to the two directions of Time in the Aion with the present moment splitting and be simultaneously subdivided into the past and the future. This sense goes "in tandem." More examples from Alice and Through the Looking Glass. An obscure Stoic example of going in tandem from Cicero's Academia section 29:
"one can always manage in tandem, slowing the horses when the slope becomes steeper, or decreasing with one hand while increasing with the other." This is Deleuze's paraphrase from The Logic of Sense. The full section 29 appears below. The word "sōrites" in the text below represents paradox. Paradox has as its object a donation of sense but the gift of sense happens with signification. Sense hovers over the surface. It inheres in the expression of propositions and subsists in states of affairs and attributes of states of affairs.

                             Cicero Academia section 29
 [91]    "What is it that the reason is capable of perceiving ? Your school says that dialectic was invented to serve as a 'distinguisher'  or judge between truth and falsehood. What truth and falsehood, and on what subject ? Will the dialectician judge what is true or false in geometry, or in literature, or in music ? But those are not the subjects with which he is acquainted. In philosophy therefore? What has the question of the size of the sun to do with him ? what means has he to enable him to judge what is the supreme good ? What then will he judge ? what form of hypothetical judgement or of inference from alternative hypotheses is valid, what proposition is ambiguous, what conclusion follows from any given premiss and what is inconsistent with it ? 

If the reason judges these and similar matters, it judges about itself ; but the promise that it held out went further, as to judge merely these matters is not enough for all the other numerous and important problems contained in philosophy. [92] But since your school sets so much store by that science,  see that it is not essentially entirely against you, when at the first stage it gaily imparts the elements of discourse, the solution of ambiguous propositions and the theory of the syllogism, but then by a process of small additions comes to the sōrites, certainly a slippery and dangerous position, and a class of syllogism that you lately declared to be erroneous. [29.] What then ? is that an error for which we are to blame ? No faculty of knowing absolute limits has been bestowed upon us by the nature of things to enable us to fix exactly how far to go in any matter ; and this is so not only in the case of a heap of wheat from which the name is derived, but in no matter whatsoever - if we are asked by gradual stages, is such and such a person a rich man or a poor man, famous or undistinguished, are yonder objects many or few, great or small, long or short, broad or narrow, we do not know at what point in the addition or subtraction to give a definite answer. [93] 

 But you say that the sōrites is erroneous. Smash the sōrites then, if you can, so that it may not get you into trouble, for it will if you don't take precautions. 'Precautions have been taken,' says he, 'for the policy of Chrysippus is, when questioned step by step whether (for example) 3 is few or many, a little before he gets to "many," to come to rest, or, as they term it, hesychazein.'    

'So far as I am concerned,' says Carneades, 'you may not only rest but even snore ; but what's the good of that ? for next comes somebody bent on rousing you from slumber and carrying on the cross-examination : "If I add 1 to the number at which you became silent, will that make many ?" - you will go forward again as far as you think fit.' Why say more ? for you admit my point, that you cannot specify in your answers either the place where 'a few' stops or that where 'many' begins ; and this class of error spreads so widely that I don't see where it may not get to. [94]

 'It doesn't touch me at all,' says he, 'for like a clever charioteer, before I get to the end, I shall pull up my horses, and all the more so if the place they are coming to is precipitous : I pull up in time as he does,' says he, 'and when captious questions are put I don't reply any more.' 

If you have a solution of the problem and won't reply, that is an arrogant way of acting, but if you haven't, you too don't perceive the matter ; if because of its obscurity, I give in, but you say that you don't go forward till you get to a point that is obscure. If so, you come to a stop at things that are clear. If you do so merely in order to be silent, you don't score anything, for what does it matter to the adversary who wants to trap you whether you are silent or speaking when he catches you in his net ? but if on the contrary you keep on answering 'few' as far as 9, let us say, without hesitating, but stop at 10, you are withholding assent even from propositions that are certain, nay, clear as daylight ; but you don't allow me to do exactly the same in the case of things that are obscure. Consequently that science of yours gives you no assistance against a sōrites, as it does not teach you either the first point or the last in the process of increasing or diminishing. [95]   What of the fact that this same science destroys at the end  the steps that came before, like Penelope unweaving her web ? is your school to blame for that or is ours ? Clearly it is a fundamental principle of dialectic that every statement (termed by them axioma, that is, a 'proposition ') is either true or false ; what then ? is this a true proposition or a false one - 

'If you say that you are lying and say it truly, you lie' ? Your school of course says that these problems are 'insoluble,' which is more vexatious than the things termed by us 'not grasped' and 'not perceived.' 

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