Likewise also in the case of those that assume the original point，andthose of false cause，and all that treat a number of questions as one:
for in all of them the deception lies in the smallness of thedifference：for our failure to be quite exact in our definition of”premiss” and of ”proof” is due to the aforesaid reason.
Since we know on how many points apparent syllogisms depend，we knowalso on how many sophistical syllogisms and refutations may depend.Bya sophistical refutation and syllogism I mean not only a syllogismor refutation which appears to be valid but is not，but also onewhich，though it is valid，only appears to be appropriate to the thingin question.These are those which fail to refute and prove peopleto be ignorant according to the nature of the thing in question，whichwas the function of the art of examination.Now the art of examiningis a branch of dialectic：and this may prove a false conclusionbecause of the ignorance of the answerer.Sophistic refutations on theother hand，even though they prove the contradictory of his thesis，donot make clear whether he is ignorant：for sophists entangle thescientist as well with these arguments.
That we know them by the same line of inquiry is clear：for the sameconsiderations which make it appear to an audience that the pointsrequired for the proof were asked in the questions and that theconclusion was proved，would make the answerer think so as well，sothat false proof will occur through all or some of these means：forwhat a man has not been asked but thinks he has granted，he would alsogrant if he were asked.Of course，in some cases the moment we add themissing question，we also show up its falsity，e.g.in fallaciesthat depend on language and on solecism.If then，fallacious proofs ofthe contradictory of a thesis depend on their appearing to refute,it is clear that the considerations on which both proofs of falseconclusions and an apparent refutation depend must be the same innumber.Now an apparent refutation depends upon the elementsinvolved in a genuine one：for the failure of one or other of thesemust make the refutation merely apparent，e.g.that which depends onthe failure of the conclusion to follow from the argument (theargument ad impossible) and that which treats two questions as one andso depends upon a flaw in the premiss，and that which depends on thesubstitution of an accident for an essential attribute，and—a branchof the last—that which depends upon the consequent：more over，theconclusion may follow not in fact but only verbally：then，insteadof proving the contradictory universally and in the same respect andrelation and manner，the fallacy may be dependent on some limit ofextent or on one or other of these qualifications：moreover，thereis the assumption of the original point to be proved，in violationof the clause ”without reckoning in the original point”.Thus weshould have the number of considerations on which the fallaciousproofs depend：for they could not depend on more，but all willdepend on the points aforesaid.
A sophistical refutation is a refutation not absolutely butrelatively to some one：and so is a proof，in the same way.For unlessthat which depends upon ambiguity assumes that the ambiguous termhas a single meaning，and that which depends on like verbal formsassumes that substance is the only category，and the rest in thesame way，there will be neither refutations nor proofs，eitherabsolutely or relatively to the answerer：whereas if they do assumethese things，they will stand，relatively to the answerer; butabsolutely they will not stand：for they have not secured astatement that does have a single meaning，but only one that appearsto have，and that only from this particular man.
The number of considerations on which depend the refutations ofthose who are refuted，we ought not to try to grasp without aknowledge of everything that is.This，however，is not the province ofany special study：for possibly the sciences are infinite in number,so that obviously demonstrations may be infinite too.Nowrefutations may be true as well as false：for whenever it ispossible to demonstrate something，it is also possible to refute theman who maintains the contradictory of the truth; e.g.if a man hasstated that the diagonal is commensurate with the side of thesquare，one might refute him by demonstrating that it isincommensurate.Accordingly，to exhaust all possible refutations weshall have to have scientific knowledge of everything：for somerefutations depend upon the principles that rule in geometry and theconclusions that follow from these，others upon those that rule inmedicine，and others upon those of the other sciences.For thematter of that，the false refutations likewise belong to the number ofthe infinite：for according to every art there is false proof，e.g.
according to geometry there is false geometrical proof，andaccording to medicine there is false medical proof.By ”according tothe art”，I mean ”according to the principles of it”.Clearly，then,it is not of all refutations，but only of those that depend upondialectic that we need to grasp the common—place rules：for thesestand in a common relation to every art and faculty.And as regardsthe refutation that is according to one or other of the particularsciences it is the task of that particular scientist to examinewhether it is merely apparent without being real，and，if it bereal，what is the reason for it：whereas it is the business ofdialecticians so to examine the refutation that proceeds from thecommon first principles that fall under no particular special study.