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FORE:Turning from sense to reason, Carneades attacks the syllogistic process on grounds already specified in connexion150 with the earlier Sceptics; and also on the plea that to prove the possibility of syllogism is itself to syllogise, and thus involves either a petitio principii or a regress ad infinitum.235 Such a method is, of course, suicidal, for it disproves the possibility of the alleged disproof, a consideration which the Stoics did not fail to urge, and which the later Sceptics could only meet by extending the rule of suspense to their own arguments against argument.236 Nevertheless the sceptical analysis detected some difficulties in the ordinary theory of logic, which have been revived in modern times, and have not yet received any satisfactory solution. Sextus Empiricus, probably copying an earlier authority, it may be Carneades himself, observes that, as the major premise of every syllogism virtually contains the minor, it is either superfluous, or assumes the proposition to be proved. Thus we argue that Socrates is an animal because he is a man, and all men are animals. But if we do not know this latter proposition to be true in the case of Socrates, we cannot be sure that it is true in any case; while if we know it to be true in his case, we do not need to begin by stating it in general terms. And he also attempts to show the impossibility of a valid induction by the consideration, since so often urged, that to generalise from a limited number of instances to a whole class is unsafe, for some of the unknown instances may be contradictory, while the infinite, or at least indefinite multiplicity of individuals precludes the possibility of their exhaustive enumeration.237Another principle in planing machines which deserves notice is the manner of driving carriages or platens; this is usually performed by means of spur wheels and a rack. A rack movement is smooth enough, and effective enough so far as a mechanical connection between the driving gearing and a platen, but there is a difficulty met with from the torsion and elasticity of cross-shafts and a train of reducing gearing. In all other machines for metal cutting, it has been a studied object to have the supports for both the tools and the material as rigid as possible; but in the common type of planing machines, such as have rack and pinion movement, there is a controversion of this principle, inasmuch as a train of wheels and several cross-shafts constitute a very effective spring between the driving power and the point of cutting, a matter that is easily proved by planing across the teeth of a rack, or the threads of a screw, on a machine arranged with spur wheels and the ordinary reducing gearing. It is true the inertia of a platen is interposed and in a measure overcomes this elasticity, but in no degree that amounts to a remedy.

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