The right way, then, is either to divide apparent proofs and refutations as above, or else to refer them all to ignorance of what 'refutation' is, and make that our starting-point: for it is possible to analyse all the aforesaid modes of fallacy into breaches of the definition of a refutation.In the first place, we may see if they are inconclusive: for the conclusion ought to result from the premisses laid down, so as to compel us necessarily to state it and not merely to seem to compel us.Next we should also take the definition bit by bit, and try the fallacy thereby.For of the fallacies that consist in language, some depend upon a double meaning, e.g.ambiguity of words and of phrases, and the fallacy of like verbal forms (for we habitually speak of everything as though it were a particular substance)-while fallacies of combination and division and accent arise because the phrase in question or the term as altered is not the same as was intended.Even this, however, should be the same, just as the thing signified should be as well, if a refutation or proof is to be effected; e.g.if the point concerns a doublet, then you should draw the conclusion of a 'doublet', not of a 'cloak'.For the former conclusion also would be true, but it has not been proved; we need a further question to show that 'doublet' means the same thing, in order to satisfy any one who asks why you think your point proved.

Fallacies that depend on Accident are clear cases of ignoratio elenchi when once 'proof' has been defined.For the same definition ought to hold good of 'refutation' too, except that a mention of 'the contradictory' is here added: for a refutation is a proof of the contradictory.If, then, there is no proof as regards an accident of anything, there is no refutation.For supposing, when Aand B are, C must necessarily be, and C is white, there is no necessity for it to be white on account of the syllogism.So, if the triangle has its angles equal to two right-angles, and it happens to be a figure, or the simplest element or starting point, it is not because it is a figure or a starting point or simplest element that it has this character.For the demonstration proves the point about it not qua figure or qua simplest element, but qua triangle.Likewise also in other cases.If, then, refutation is a proof, an argument which argued per accidens could not be a refutation.It is, however, just in this that the experts and men of science generally suffer refutation at the hand of the unscientific: for the latter meet the scientists with reasonings constituted per accidens; and the scientists for lack of the power to draw distinctions either say 'Yes'

to their questions, or else people suppose them to have said 'Yes', although they have not.

Those that depend upon whether something is said in a certain respect only or said absolutely, are clear cases of ignoratio elenchi because the affirmation and the denial are not concerned with the same point.For of 'white in a certain respect' the negation is 'not white in a certain respect', while of 'white absolutely' it is 'not white, absolutely'.If, then, a man treats the admission that a thing is 'white in a certain respect' as though it were said to be white absolutely, he does not effect a refutation, but merely appears to do so owing to ignorance of what refutation is.

The clearest cases of all, however, are those that were previously described' as depending upon the definition of a 'refutation': and this is also why they were called by that name.For the appearance of a refutation is produced because of the omission in the definition, and if we divide fallacies in the above manner, we ought to set 'Defective definition' as a common mark upon them all.