Chapter V. What Syllogism Is According to Definition.

CHAPTER V. What syllogism is according to definition. But a syllogism, which is composed immediately from propositions and mediately from terms, when taken universally and not in this or that matter, is a speech in which, when certain things have been posited, something other than the things which have been posited follows of necessity from the things which have been posited. It follows by this, or for this reason, that these things have been posited, namely also the premises; for in a syllogism these must be the cause of the consequence of the conclusion. For this is what is said by 'because these things are,' namely that the conclusion happens or follows on account of these things. But to follow or happen on account of these things which have been posited then occurs when it needs no term or proposition to be added from outside beyond those things which belong to the substance of syllogism in figure and mode, which are three terms and two propositions. These things are explained thus: syllogism is called speech and not speeches because, although two propositions are put in a syllogism, which are speeches and not speech, nevertheless, as they are put in the syllogism, they are not put as speeches but as speech for three causes. The first and most powerful of these is that they are united in the middle term uniting the extremes in every figure; and things which are united in a formal principle are not principally many, but rather simply one, though materially and in a certain respect many. The second cause is that the minor is put in the syllogism as restricting the major; but what restricts and narrows another does not fall with it into number, and thus again both propositions are narrowed to one. The third cause is that both premises are referred to one speech, which is the conclusion; and things which are united in one end are not simply diverse, but related to one end. Therefore syllogism is more fittingly called speech than speeches, especially because syllogism is one thing ordered to one thing; and therefore the things which compose it, by order to one another and to one thing, are one. But what is said, 'in which,' is said on account of necessary propositions, which are brought in for proving or declaring and which are not within the syllogism, but outside its substance. But what is said, 'certain things,' is said on account of the enthymeme, in which not certain speeches but rather one proposition is put, and from that it is concluded, as happens in rhetorical syllogisms. But what is said, 'having been posited,' says two things. For what is posited is what has been arranged in fitting order according to order and place; and so through the phrase 'having been posited' all useless conjunctions are excluded, because in those no proposition is well arranged in order and place. The posited also says the same as the granted, and thus it is put there on account of the dialectical syllogism, whose propositions ask for the consent of the respondent; for this reason Boethius too in the Topics, where he sets down the same definition, adds by saying 'having been posited and granted.' But 'something other than the things which have been posited' is added on account of the conclusion, which, although materially it is not simply something other than the premises, because it is composed from the major and minor extremes which are parts of the major and minor proposition, nevertheless formally it is something other than the premises, just as an effect and a thing principled are other than the cause and principle by which they are caused and principled. It is also called 'other' on account of the petition of that which is in the principle, not indeed insofar as it is a sophistical place, but insofar as 'non-cause as cause' is a sin against syllogism, as will be determined in what follows of this science in the second book. But what is said, 'to happen or follow from necessity,' is understood of the necessity of consequence and not of the necessity of the thing or of the consequent. This too, that it is said to happen from necessity, is said on account of induction and example, in which the consequence is not necessary. But what is added, 'because these things are,' which are the cause of the inference and consequence, is said on account of non-cause as cause, not insofar as it is a sophistical place, but rather insofar as non-cause as cause is a fault against syllogism, as will be determined in the second book of this science. And thus it is clear how the stated definition of syllogism defines the being of syllogism and excludes it from all other things. For it is said 'to happen on account of those things which have been premised,' so that this is the same as to need no extrinsic thing, namely no term or proposition, in order to come to be, that is, in order to appear necessary, that is, necessarily concluding. And although it does not need an extrinsic thing in order that it be a proposition or a term, nevertheless, in order that what is necessary in itself appear necessary, it sometimes needs a property of syllogism or of proposition, such as conversion in proposition and reduction in syllogism; for otherwise syllogisms of the second and third figure will not appear necessary unless they are reduced to the first figure. This, therefore, is the assignment given concerning syllogism. The introduced definition is also explained otherwise by some, and in many ways; but for the present speculation what has been said suffices. Yet this must be noticed: that the stated definition of syllogism generally suits every syllogism, and especially that which we call simple, because it has no necessity except that which is called the necessity of simple inference from figure and mode; but the other particular syllogisms have proof of the concluded thing in addition to the necessity of inference ¹.