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The proposition, Every poet is a man of genius, is confessedly æquipollent with “No one who is not a man of genius is a poet,” and in this the petitio principii, as regards A B, is no longer implied, but express, as in an ordinary syllogism of the first figure.
It is needless to remark that this whole argument, whatever may be said of the former one, is a pure fallacy, and a petitio principii throughout. The Cartesian form of it is the most glaringly fallacious, and indeed exposes itself; for by that reasoning we might prove the existence of a fiery dragon or any other phantom of the brain. But even King's more concealed sophism is equally absurd.
Still, with the same 'petitio principii' that the Reformed religion and the dogmas of the Contra-Remonstrants were one and the same thing, he assured the Assembly that the authority of the magistrates would be sustained by him so long as it did not lead to the subversion of religion. Clearly the time for argument had passed.
Here you see, instead of a Proof or Reason, there is only a petitio principii. For, in plain words, his sense is this, "Two things are as impossible as one another: because they are both equally impossible." But he takes those two things to be granted as impossible; which he ought to have proved such, before he had proceeded to prove them equally impossible.
This is perhaps to the advantage of both natural science and religion: to the advantage of religion because it can with difficulty co-exist with the universal dominance of the mathematical way of looking at things; to the advantage of natural science because, in giving up the one-sidedness of the purely quantitative outlook, it does not give up its “foundations,” its “right to exist,” but only a petitio principii and a prejudice that compelled it to exploit nature rather than to explain it, and to prescribe its ways rather than to seek them out.
This reasoning I conceive to be entirely fallacious, as indeed Dr. Brown, in his treatise on Cause and Effect, has shown with great acuteness and justness of thought. We have before remarked, that almost every fallacy may be referred to different genera by different modes of filling up the suppressed steps; and this particular one may, at our option, be brought under petitio principii.
Is it not, then, a petitio principii to say, that the fact ought to be disbelieved because the induction opposed to it is complete? How can we have a right to declare the induction complete, while facts, supported by credible evidence, present themselves in opposition to it?
With this response, somewhat more tart than agreeable, the nobles were obliged to content themselves, and they accordingly took their leave. It must be confessed that they had been disposed to slide rather cavalierly over a good deal of ground towards the great object which they had in view. Certainly the petitio principii was a main feature of their logic.
But if it be answered, "Aye! but we must not interpret St. Paul as we may and should interpret any other honest and intelligent writer or speaker," then, I say, this is the very petitio principii of which I complain. Still less do the words of our Lord apply against my view.
To speak of an uncoördinated diversity to which order is superadded is therefore to commit a veritable petitio principii; for in imagining the uncoördinated we really posit an order, or rather two. This long analysis was necessary to show how the real can pass from tension to extension and from freedom to mechanical necessity by way of inversion.
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