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Updated: May 21, 2025
This is the way that weird geometry proceeds: it sets before beginners certain strange assumptions, and insists on their granting the existence of inconceivable things, such as points having no parts, lines without breadth, and so on, builds on these rotten foundations a superstructure equally rotten, and pretends to go on to a demonstration which is true, though it starts from premisses which are false.
It is likewise the first chapter of the book, and it sums up the whole of the building. "But certainly these conclusions forestalling the premisses are very strange; this recapitulation, placed at the very beginning of the work, when it ought, in fact, to be placed at the end, in the apse!
In Petitio Principii, the premisses are not even verbally sufficient for the conclusion, since one premiss is either clearly the same as the conclusion, or actually proved from it, or not susceptible of any other proof. Men commonly fall into it, through believing that the premiss was verified, though they have forgotten how.
He accepted willingly, and even enthusiastically, the household conclusions on religion and politics, but they were not properly his, for he accepted them merely as conclusions and without the premisses, and it was often even a little annoying to hear him express some free opinion on religious questions in a way which showed that it was not a growth but something picked up.
The two senses of the word "correlation" must be carefully distinguished; it would be a downright paralogism to adopt one of them in the premisses of the reasoning, and the other in the conclusion.
And they tell us, that the sole ground which a syllogism affords for assenting to the conclusion, is that the supposition of its being false, combined with the supposition that the premisses are true, would lead to a contradiction in terms.
The advantages of this order of proceeding in the present instance will manifest themselves as we advance, in a manner superseding the necessity of any further justification or explanation. Of Induction, therefore, we shall say no more at present, than that it at least is, without doubt, a process of real inference. The conclusion in an induction embraces more than is contained in the premisses.
Thus by "erroneous" is meant, according to Viva, a proposition which is not immediately opposed to a revealed proposition, but only to a theological conclusion drawn from premisses which are de fide; "savouring of heresy," when a proposition is opposed to a theological conclusion not evidently drawn from premisses which are de fide, but most probably and according to the common mode of theologising, and so with the rest.
Professor Ward, in Naturalism and Agnosticism, says: "From the strict premisses of Positivism we can never prove the existence of other minds or find a place for such conceptions as cause and substance; for into these premisses the existence of our own mind and its self-activity have not entered.
The frequent errors in processes such as Conversion and Opposition, which are in appearance, though not in reality, inferences from premisses, may for convenience be here referred to.
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