Tractate II. Chapters III-IV

CHAPTER III. Concerning the solution of paralogisms according to composition and division.

But from the things which have been said, it is manifest how those paralogisms also are to be solved which are according to composition and division, because if the divided speech, that is, the speech uttered dividedly, and the composed speech, that is, uttered compositely, signify one thing and another, although it is one materially, nevertheless it is formally diverse, as was determined in the prior book of this science. Therefore if the composed and false thing has been concluded, the contrary must be said, namely that the divided thing is true; and if the divided thing has been concluded as false, again the contrary must be said, namely that the composed thing is true. And that this may be manifested in examples, one must know that all speeches of this kind which are according to composition or division are such as these: do you think that by what you saw this man struck, by this he was struck? And the paralogism must be formed thus: by whatever you saw this man struck by someone or from someone, by this this man was struck; but with the eye you saw this man struck by someone; therefore with the eye this man was struck. For the major is multiple in this paralogism according to composition and division, from the fact that this determination, by which, can be composed or uttered continuously with this verb, you saw, with which it is naturally composed; and thus it is composed and false, under this sense: by what you saw someone struck by someone, that man was struck by that. For this is false. Or it can be divided from this verb, you saw, and uttered continuously with this participle struck; and thus it is divided and true, under this sense: by what instrument you saw someone struck, by that he was struck as by an instrument of striking. But another speech which is according to this formation is this: and by what he was struck, this you saw. And it is formed thus: by what someone was struck, this you saw him struck; but someone was struck by a sword or staff; therefore with a staff you saw him struck. And here there is multiplicity in the premise and in the conclusion. In the premise indeed, because this word, by which, can be composed with this verb, you saw, and is composed and false; or it can be divided from it and composed with the participle struck, and is true as before. And similarly one must speak concerning the conclusion, as is clear to anyone looking at it. For to this speech, by what he was struck, this you saw, one must add that he was struck; otherwise the multiplicity of composition and division does not occur. Hence when it is said, by what he was struck, this you saw, it is understood beneath that he was struck.

But although speeches of this kind which are according to composition and division are solved thus through the distinction of a certain multiple, nevertheless they are not truly multiple, so that they have actual multiplicity in one word which is naturally and formally one significative word. Rather they have something of doubtful questions or propositions which is according to potential multiplicity; and this is twofold according to composition. For the composed thing is not truly double, because that which is composed is divided only in potency. For if it is divided, the divided speech is not altogether formally the same as the composed speech. And the proof of this is that, as it is in a multiple word according to diverse understandings, so it is in divided and composed speech. But a word diversified according to accents is not formally the same word in the form of utterance. Indeed this is so because malum whose first syllable is long signifies an apple, and malum whose first syllable is short signifies the privation of good; uttered according to diverse accent or time and shortness, they formally are and signify one thing and another. But in writings, in which there is no utterance, the name is the same, since it is written with the same elements; and even in writings grammarians now make diverse signs denoting acute or grave accent, and consequently that the name must be pronounced with diverse utterance. But it is established that a word uttered with a diverse accent is not formally one. But what is truly multiple has meanings under one materially and formally uttered word; for this reason, since composed and divided diction is not formally one speech, it is clear that what is multiple according to composition and division is not double. And from this it is also manifest that not all sophistical refutations sin according to the double which is truly double so as to have actual multiplicity, as certain erring persons say.

Therefore it is clear how, by right solution, one responding must divide according to utterance and the distinction of utterance. For it is not the same to see a struck man with the eyes and to say that one saw with struck eyes. But this solution is adaptable to all such paralogisms, as is also clear in the speech which belongs to a certain sophist Euthydemus, which is this: let it be asked, do you think that you, being in Sicily, saw ships now coexisting in Piraeus? But Piraeus is a harbor of ships in Greece, which is contemplated by one existing on the shore of the sea opposite in Sicily. And the paralogism is formed thus: whoever, being in Sicily, sees ships now coexisting in Piraeus is outside Sicily; but you, being in Sicily, see ships now coexisting in Piraeus; therefore you, existing in Sicily, are outside Sicily. This conclusion is false. And the minor of this paralogism is multiple from composition and division, because in it there is one determinable and two determinations; and that determinable can be determined through an antecedent or consequent determination. And this determinable is being: if it is determined through this determination, in Sicily, thus it is composed and true, under this sense: you, being in Sicily, see ships now coexisting in Piraeus. Or the determinable being can be said to be divided from the same determination with this determination, in Piraeus; and thus it is divided and false, because thus this determination, in Sicily, is bent back to what I call ships coexisting, under this sense: you see in Piraeus, in Sicily, or you, being in Piraeus, see ships coexisting in Sicily. This is contrary to what was posited, because it was posited that you, being in Sicily, see ships coexisting in Piraeus. But I say that this speech is more composed than divided when the posterior determination is referred to the participle being, because the posterior determination has the nature of a determination more than the prior one does, although it is posited later; although both of those determinations in the speech of Euthydemus precede the determinable according to word, nevertheless according to understanding the posterior determination follows it as naturally joined to it.

Similarly this must be distinguished if it is said in the formation of a syllogism: whoever, being in Sicily, sees ships now coexisting in Piraeus is outside Sicily; but in the opposite way it is true and false. For if the participle being is composed with this determination, in Sicily, then it is false and composed under this sense: whoever, being in Sicily, sees ships coexisting in Piraeus, is; and it is divided and true, because thus this determination, in Sicily, is bent back to this determinable which I call ships coexisting, and the sense is: whoever, being in Piraeus, sees ships now coexisting in Sicily is outside Sicily; for this is true. But others have said that those speeches are double from this, that the adverb now can be composed with this participle coexisting, or with this verb sees. But in such things no great force must be placed, because it is posited only for an example of the adaptation of right solution to the paralogism of composition and division.

It is the same in this speech, if it is asked thus: do you think that a good shoemaker is bad? And when someone says yes, let him infer: but whoever is bad is not good; a good shoemaker is bad; therefore he is not good; therefore a good thing is not good. But it is clear that the major of this paralogism is multiple from the fact that the determinable shoemaker can be composed with the determination of the following adjective which is bad, and thus it is composed and false under this sense: whoever is a bad shoemaker is not good; and thus it is false, because someone good is sometimes a bad shoemaker and is not simply good. Or the same determinable can be divided from that adjective and composed with the adjective good; and thus it is true, because whoever is a bad good shoemaker is not good.

Another reason to be solved similarly and like that one is this: do you think that those things whose sciences are good are good disciplines, that is, are good to be learned? And it must be formed thus: those things whose sciences are good are good disciplines, and conversely. But the science of evil is good. For Boethius says that knowledge of evil cannot be lacking to the good, because evil is not avoided unless it is known. Therefore the discipline of evil is good, that is, that evil should be learned; and this is false, because Aristotle says in book XI of first philosophy that it is better not to learn or know certain evils through discipline. Hence when it is asked, do you think that those things whose sciences are good are good disciplines? and with the respondent granting yes, let the opponent infer: but the discipline of evil is a good science, and let him conclude: therefore the discipline of evil is good. And let the opponent proceed further to the contrary thus: but the discipline of evil is also evil; wherefore, that is, because, the discipline of evil is evil, and the discipline of evil is not good. And against this, proceeding again, let the opponent say: but the disciplines of evils are good, because the sciences of evils are good. And this can also be the solution, that it be said that the disciplines of evils are good, and not that an evil discipline is good. So that this may be better understood, let it be said that the major of the posited paralogism is said to be multiple from the fact that what I call discipline can be constructed, that is, composed with this adjective good which follows it; and then this whole, good disciplines, falls in the predicate, and thus it is composed and false under this sense: those things whose sciences are good are good disciplines. For this is false, because evils whose sciences are good are not good disciplines. Or this very thing, disciplines, can be divided from the following adjective; and then this very thing which I call disciplines falls on the part of the subject, and what I call good falls on the part of the predicate; and this proposition is divided and true under this sense: those things whose sciences are good, their disciplines are good. And in this sense it cannot be concluded that the discipline of evil is good; rather, of evils there is a good discipline, namely contemplative discipline, because discipline is equivocal to contemplative discipline, which is through demonstration and is called in Greek epiphormi, and to practical discipline, which is operative training in morals and is called in Greek edia; and this generates difficulty in that speech.

Similarly it is in this speech: do you think it is true to say now that you have been made? And when one says and responds yes, let him infer: therefore you have been made now. And the paralogism can be formed thus: concerning whatever it is true to say that it has now been made, it itself has been made now; but now it is true to say that you have been made; therefore you have been made now. Or the divided and the composed signify another thing; and this is the solution, because the minor proposition of the paralogism signifies one thing when uttered dividedly and signifies another thing when uttered compositely. For it is true to say now that you have been made, but it is not true to say that you have now been made. For this determination, now, can be composed with the present verb which is to say, and thus the proposition is composed and true; and with the following phrase, that you have now been made, and in this way it is divided and false, as is plain for anyone to see. For it is true to say now that you have been made, but it is not true to say that you have been made now.

A similar mode is in this speech: do you think that as you are able and the things which you are able to do, so also you will do these very things? And when the respondent says yes, let the opponent proceed to the contrary: but while not playing the cithara, you have the power of playing the cithara; therefore you will play the cithara while not playing the cithara. The paralogism can be formed thus: whatever things you are able to do and as you are able to do them, so also you will do them; but while not playing the cithara you are able to play the cithara; therefore while not playing the cithara you will play the cithara. Or the question shows the solution: and you do not have power of this sort, namely that while not playing the cithara, that is, while you do not play the cithara, you play the cithara; rather you have the power to do afterward what you did not do before this. For the minor of the paralogism is multiple from the fact that what I say, not playing the cithara, can be uttered continuously with what I say, you have the power of playing the cithara; and thus it is composed and false, under this sense: you are able to play the cithara while not playing the cithara, that is, while you do not play the cithara; and this is false while you imply that you are able to do opposites at once. Or the same phrase can be uttered discontinuously with the same; and thus it is divided and true, under this sense: you who are not now playing the cithara are able to play the cithara.

But certain erring persons solve this last paralogism also otherwise, saying that the first proposition of the paralogism was not given universally, namely this: the things which you are able to do and as you are able, you will do. For it was not given thus, that you will do in every way in which you are able, but indefinitely, as you are able, you will do; therefore, not doing, you will do, although not doing you are able to do. Hence they do not say that it happens through consequence, if he granted that as you are able to do, someone not playing the cithara is able to play the cithara; for the ability to do was not given entirely or universally when it was given as being able. And they say that it is not the same thing to do as you are able indefinitely and entirely to do as you are able universally.

But it is manifest that this is not the right solution. For of all sophistical speeches which are false because of the same thing, that is, because of the same defect, there is one and the same solution. Therefore if this is the solution, it will fit all apparent paralogisms according to composition and division. But this solution cannot be adapted to other paralogisms which have the same cause of falsity and are according to the same fallacy; therefore it is manifest that it is not the right solution, because it does not fit all similar paralogisms of this fallacy, nor does it entirely or universally fit speeches asked according to composition and division. And therefore this solution is to the man questioning or opposing, for impeding him, and is not for solving the speeches.

CHAPTER IV. Concerning the solution of those paralogisms which are according to accent.

But speeches according to accent, when only by voice, are not many unless they are uttered with metrical pronunciation; for with meter they are uttered as lengthened or shortened, and with aspiration and without aspiration, and sometimes two words are uttered under one accident, and sometimes one under two accidents, and then frequently paralogisms are made according to accent. Nor are they made even in those speeches which are written, unless, as was said, signs for accent are made over syllables and words, as was customary to be done in ancient times. Nor are they made even in those speeches which are spoken by voice with prose utterance, except if a few are made, as here: just men ought, that is, it is fitting, to weigh, with the middle syllable shortened, that is, to ponder and esteem more; one ought not to hang just men, with the middle syllable lengthened, that is, suspend them in concealment or on a gibbet. To be hung, with the middle syllable lengthened, is to suffer; but to weigh, with the middle syllable shortened, is not to suffer but to receive honor. But how such speeches must be solved is indeed plain: through the distinction of what is to hang or weigh. For it does not signify the same thing when pendere is pronounced in the middle syllable gravely, that is, lengthened, and acutely, that is, shortened; and thus diversity of signification accepted under one materially identical word is the cause of fallacy and falsity, and when it has been distinguished and adapted, it belongs to the opponent to solve the paralogisms by right solution.

But note that this doubleness does not seem to some persons to exist, because a word which is uttered with diverse accents is not one, and thus several things are not gathered under one something, which is required in multiples. And therefore certain persons have said that in potential multiplicity the unity of diction or speech is that which is in the mind, of which that which is in the voice is the sign, and of that, that which is in writing is the sign; and therefore they say that the one under which the many are accepted is nothing except the unity of speech which is in the mind, or, if it is speech in voice or in writing, it is in it only according as it is referred to the mind. But this is proved to be nothing from this, that accent does not belong to speech insofar as it is in the mind. But the one of multiplicity, in which many things are gathered as in one, must be such a one as is referred to many things and contains those things in itself; and this can in no way be mental speech, nor also the speech which is in writing, for the same reason. And therefore one must hold what was said in the prior book of this science, namely that the unity in which many things are gathered, which make multiplicity, is material unity, which consists in the gift of elements and syllables, and is the unity of words and speeches into which several things are gathered, and not formal unity, which is in the mode of utterance. And therefore it is called potential multiplicity, because such material unity can be referred to diverse forms of utterance as it is referred to diverse senses.

But whether doubleness is a certain multiplicity, so that doubleness is a species of multiplicity and multiplicity is the genus of doubleness, is vain and frivolous to dispute, because genera and species and the mode of genera and species are diversified according to the diversity of the things in which they are. For they are argued and constituted in one way in universal wholes, and in another way in integral wholes, and further in those things in one way in discrete things, another in continuous things, and another in powers. For in substances, according to the account of the universal whole, they are coeval in the genus and go out from it through opposed differences. But in integral wholes they are not coeval, because in them the genus is led out and constituted from parts, as multiplicity from doubleness, tripleness, fourfoldness, and so with the others; and in this way a genus is not constituted in substances, and therefore they are not coeval in that either. Rather, the multiplicity which is greater is prior, and that which is lesser is posterior, and they do not begin equally from the genus in predication. And in almost the same way it is in continuous things, because body is quantity more than surface is, and surface more than line, because it receives the predication of quantity through more accounts of quantity, that is, divisible in length, divisible in breadth, and divisible in depth, because, as Aristotle says, it is always divisible, that is, to infinity. And it is almost similar in figures in which one is generated from another, as the quadrangle from the triangle, and the pentagon from the quadrangle, and so with other polygonal figures. And similarly in powers, because in those, according to Aristotle in the book On the Soul¹, and in book XVI On Animals, the sensitive is produced from the vegetative, and is in it as a triangle in a quadrangle; and from the sensitive the rational is produced, and is in it. Hence it is frivolous and vain to dispute about such things, because this belongs to a greater inquiry than the intention of the present business.

Therefore it must be known that doubleness is a species of multiplicity, and multiplicity is the genus; and they are such genera and species as the continuous or discrete has species and genera, in which one species is produced and generated from another, as is proved both in the first and in the second book of the Arithmetic of Pythagoras; but the genus is produced from the species and is participated equally by them.

But if someone says that potential multiplicity is not multiplicity, because what is only in potency is not, this has no force for the present intention, because the middle between the simply one and the simply many is multiple; and for the being of multitude it is sufficient that it be one in some way and many in some way. For this reason material unity and potential multitude or plurality are sufficient in it. Therefore let these things have been said concerning potential multiplicity, which is in composition and division and accent.