Questions on the Posterior Analytics

By Walter Burleigh

Translated by John Longeway

From the edition of Mary C. Sommers

            "Every teaching and every learning etc." Concerning this book, let us ask first whether a logician, acting as a logician alone, can make a demonstration from first principles proper to a subject. Then, whether there are any demonstrative syllogisms. And in the third place, it being supposed that a demonstration can be produced from first principles proper to a subject, and that there are demonstrative syllogisms, let it be asked whether there can be scientific knowledge about them.

[Question 1: Whether a logician, acting as a logician alone,

can make a demonstration from proper first principles.]

            1.1. [First Principal Argument] Concerning the first question, it seems that a mere logician cannot produce a demonstration from first principles proper to a subject, since a definition is the middle term in demonstration. A mere logician does not define since, if he were to, a mere logician would consider a reality in respect of what-it-is. The consequent is false, since this is a consideration appropriate to the metaphysician. The inference is clear, since a definition indicates the quiddity of a reality. Therefore, if the logician does define, he considers a reality in respect of what-it-is. The consequent is false, therefore a mere logician does not define. If this is so, then he does not produce demonstration from first principles proper to a subject.

            1.2. Moreover, if a mere logician defined something, since it is appropriate for the metaphysician to define the same thing, I ask then, whether the same definition is given by the metaphysician and the logician. If the same, I argue against this: They show different passions of the reality defined by them, therefore they use different middle terms, and the definition is the middle term, therefore they use different definitions. The inference is clear, since different effects have different immediate causes. Therefore there is not the same definition.

            1.3. If one is different from the other, I ask then about that in which one definition differs from another. Either it is something made by the intellect, or is placed in the intellect beforehand. Certainly the first is not to be doubted, nor the second, since <if it is false> then those two definitions differ in something that does not depend on the soul, and since the definition is primarily (primo) of the same definitum, it follows that the definitum differs from itself in something that does not depend on the soul, since whatever is in the definition is in the definitum.

            1.4. Moreover, if the definitions differ in something that does not depend on the soul, since the definitions are primarily of the same definitum, it follows that one and the same thing differs quidditatively from itself.

            1.5. Moreover, if these definitions differ in some reality outside the soul, let A be that reality in which one definition differs from the other. But whatever is in the definition is in the definitum, therefore A is in the definitum. And in the same way, whatever is in the definitum is in the definition, therefore A is in both definitions. If this is so, then one definition does not differ from the other in A.

            1.6. It is replied to this that the mere logician cannot make a demonstration from first principles proper to a subject, since he does not have a definition proper to the subject. For a mere logician can define nothing, indeed, he takes his definition from the metaphysician.

            1.7. Against this: Metaphysics presupposes logic. Hence the logician does not take his middle term from the metaphysician, since logic is a prior science that is in the logician. Therefore he has his own first principles, and so he does not take the definition from the metaphysician. In the same way, since it is presupposed by the metaphysician, logic does not depend on metaphysics, for a prior science does not depend on one that is posterior. If this is so, then neither do the principles of logic depend on metaphysics.

            1.8. Moreover, it seems that the mere logician does not take the definition from the metaphysician, since metaphysics does not define the reality that the logician considers, since the metaphysician does not define any reality except what falls under his own consideration. But a reality that the logician considers does not fall under the consideration of the metaphysician, since the logician considers a being that is true (ente vero). But the Philosopher in Metaphysics VI excludes a being that is true from his consideration. Therefore metaphysics does not consider a being that is true. If this is so, then it does not define the reality that the logician considers, therefore the logician does not take his middle term from the metaphysician.

            1.9. Moreover, logic is one science and distinct from the other sciences, therefore it has distinct principles proper to its subject matter. If this is so, then the mere logician can make a demonstration from first principles proper to his subject.

            1.10. Further, if the mere logician does not define, then demonstrative science does not belong to the mere logician. The consequent is false. The inference is obvious, for if demonstrative science can belong to him, he can make a demonstration; but if he makes a demonstration, it is necessary for him to define, since a definition would be the middle term; therefore he will be a metaphysician, and consequently, will not be a mere logician.

            1.11. Therefore a different view is maintained, that the mere logician can make a demonstration from first principles proper to his subject, and it is held that the mere logician can define a reality that he considers, and the metaphysician cannot define that reality, for he excludes a being that is true from his consideration.

            1.12. Against this view: If a mere logician defines, then he considers the reality in respect of what-it-is. The consequent is false. The inference is clear, since definition indicates what a reality is.

            1.13. Moreover, according to the Philosopher, the metaphysician and the logician labor over the same thing; therefore the metaphysician does not exclude those things from his consideration which are settled by the logician. If this is so, then there will be several definitions of the same reality, and so the principle difficulty still remains.

            1.14. Moreover, it seems that the Philosopher does not exclude a being that is true from his consideration, for in Metaphysics IV he considers a being that is true, for he considers there the first principle, “of every affirmation or negation etc.,” and investigates the conditions under which it is so. Consequently, he decides about a being that is true there, and so he does not exclude a being that is true from his consideration.

            1.15. And therefore, a different view is maintained, that the mere logician can define the reality he considers. The metaphysician considers the same reality the logician does, since according to the Philosopher they labor over the same, but the metaphysician does not define that reality, for it does not pertain to metaphysics to consider the individual quiddities of individual beings, but this rather belongs to the special sciences. Hence the metaphysician does not define that reality, but considers that reality insofar as it is. And this is the consideration of the metaphysician, for the metaphysician does not define these special beings, but considers these beings insofar as they are beings.

            1.16. Against this view: This absurdity follows from this answer, that the consideration of the metaphysician is the most imperfect consideration, even though it is the most perfect of all the ways of considering. The assumption is clear, for the most imperfect consideration of something is of it insofar as it is a being, since the most imperfect cognition of something is cognizing it insofar as it is, for unless one cognizes about the thing that it is a being, he would have no cognition of it at all. Therefore the most imperfect cognition of something is cognizing that it is a being. If this is so, then the most imperfect consideration is of something insofar as it is a being.

            1.17. Therefore, another position is held, that a mere logician can make a demonstration from principles proper to the subject, and that a mere logician defines the reality he considers, and similarly, the metaphysician can define that same reality, but different definitions will be given by the metaphysician and the logician, for the metaphysician defines the reality in its essence, and the logician defines the reality he considers under some second intention, and so the definitions of the two are different.

            1.18. Against this position: If each one is a true definition of the reality, then through each definition it can be suitably responded to a question made using “quid” <i.e., a question why it is so (propter quid est) or what it is (quid est)>. The consequent is false, for each question has but one way of being settled.

            1.19. Moreover, if one reality has several definitions, then if one man should answer through one definition to a question made using “quid,” and another through another definition to the same question made using “quid”, then each would answer well. And consequently, one could answer one question made using “quid,” well with several different answers, which is absurd, since one certain definite question seeks one certain definite answer. And consequently one cannot respond to one question using different answers at one and the same time without absurdity.

            1.20. Moreover, if one reality had two different definitions, then one definition would differ from the other. Take that in which one differs from the other, and let it be A. A is not caused by the intellect, that is certain, but is rather presupposed in the intellect. Therefore A is something belonging to the reality itself signified by the definition. But the same reality is signified by the definition and the defined. If, then, one reality had two definitions, since one reality is signified through the definition and the defined, and vice versa <that is, through the defined and the other definition>, therefore the same reality will be signified through one definition and the other definition. But A is something belonging to the reality itself signified through one definition; therefore it will be something belonging to the reality itself signified by the other definition, for the reality signified by the one definition and the other is the same. If this is so, then one definition does not differ from the other in A.

            1.21. Again, let B be the defined, and let C be one definition and D the other definition. Let A be that through which C differs from D. Then, since A is something belonging to the reality signified by C, I argue thus: Whatever is in C is in B, since whatever is in the definition is in the defined, for the reality signified by the one and the other is the same. But if whatever is in C is in B, and A is in C, then A is in B. And what is more, whatever is in B is in D, since whatever is in the defined is in the definition; and more, therefore A is in D. But if A is in D and A is in C, then C does not differ from D through A.

            1.22. Moreover, if there are several definitions, there will be several things defined, since a definition is the same as its primary definitum.

            1.23. Moreover, it seems that the metaphysician would not define a reality that the logician considers, according to the argument previously made, since the metaphysician does not define a reality that falls under his consideration. But a reality that the logician considers does not fall under his consideration, since the logician considers a being that is true, and the Philosopher excludes a being that is true from his consideration; therefore the metaphysician does not define the reality the logician considers.

            1.24. Another <the second> principal argument: A logician is a common artificer, therefore he must use common terms, and consequently, he cannot make a demonstration from first principles proper to a subject, since every demonstration made from first principles proper to a subject is a demonstration restricted to a single thing, and is a demonstration made in terms related to a species (specialis); and such a demonstration does not belong to the logician, since he is a common artificer, and consequently, the logician cannot make a demonstration from first principles proper to a subject.

            1.25. Moreover, another <the third> principal argument: If a mere logician could make a demonstration from principles proper to a subject, then a mere logician could have demonstrative science. The consequent is false, for a mere logician considers the way of coming to know scientifically (de modo sciendi) and the way to scientific knowledge (via ad scientiam); but a way of coming to know scientifically differs from scientific knowledge.

            1.26. On the other hand, logic is a science distinct from other sciences, therefore it has distinct first principles proper to its subject. Consequently, a mere logician can made a demonstration from first principles.

            1.27. Moreover, a mere logician has a passion, subject and definition proper to his art, and these principles suffice for demonstration. Therefore a mere logician can make a demonstration from first principles proper to an art. That the logician has a proper definition is clear, since otherwise one must grant that the logician takes the definition from the metaphysician. The consequent is false, since the metaphysician presupposes logic, and since the metaphysician does not define that which the logician considers, since he excludes that from his consideration, for the metaphysician excludes a being that is true from his consideration.

            1.28 <2.22>. In response to the first question it must be held that a mere logician can make a demonstration from proper principles, since logic is a distinct science from other sciences, therefore it has principles distinct from other principles. If so, then a mere logician has proper principles that suffice for demonstration. So, then, a mere logician can make a demonstration from proper principles.

            1.29 <2.23>. Through this, in response to the arguments:

            In response to the first <principal> argument, [1.1] when it is argued that “if a logician can make a demonstration from proper principles, then a logician’s job is to define,” one must reply by granting the conclusion, that a logician can define that reality which he considers. And it is replied that if a metaphysician’s job is to define that reality, then there will be definition given by the metaphysician other than that given by the logician, and what is defined will be other; [1.2-3] for the metaphysician defines that reality in respect of what-it-is, but the logician defines it under some second intention. Through this point it is replied to the arguments to the contrary.

            1.30 <2.24>. When it is argued, “If it is the job of a mere logician to define a reality, then it is his job to consider the reality in respect of what-it-is,” [1.1] it is replied denying this inference. For consideration in respect of what-it-is is more general than defining. Therefore this consequence is not valid, “It is the job of a mere logician to define, therefore it is his job to consider a reality in respect of what-it-is.”

            1.31 <2.25>. In response to the other argument, when it is argued, “if one reality has two definitions, if they are both true definitions, then one can answer well using either one to a question made using “quid” [1.18]; one replies to this by granting the conclusion. And then, when it is argued that “a single question seeks a single answer,” this is granted, though this still stands, that it is the logician’s job to answer it using one definition and one answer, while the metaphysician’s job is to answer it using another definition and another answer. Hence it is not the job of the mere logician to answer that question except through one definite answer, and the metaphysician using another definite answer. Hence the same question must be settled by the one in one way, but it might very well be settled in different ways by different people. Nor is it absurd that one definite question should be settled by several answers. For instance, if it were asked, “Who is running?”, one might do well to answer, “Socrates runs.” In the same way, if someone else said “the philosopher runs,” he would have answered well to this. Hence it is not absurd that one question seeking a certain answer should be settled by several answers from different people, as long as each gives a certain definite answer.

            1.32 <2.26>. In response to the other argument to the contrary, when it is argued, “If there are several definitions of any reality, there will be several things defined,” [1.19] it is granted, for as there are several definitions, so there are several things defined, since just as the definition given by the metaphysician is other than that given by the logician, so is the defined another, since the reality under the form under which it is considered by the metaphysician is other than the reality taken under the form under which it is considered by the logician. Hence the metaphysician defines and considers the reality in connection with what it is, and the logician considered and defines the reality under some second intention. And so just as the definitions are different, so the things defined are different.

            1.33 <2.27>. In response to the other argument to the contrary, when it is argued, “either one definition is wholly the same as the other, or it is other,” [1.20] it is to be replied that the one definition is other than the other. And when it is asked through what one differs from the other, it should be replied that they differ through forms and real considerations that do not depend on the soul, hence the reality under the formal form <that is, form belonging to a thing formally, not concomitantly> under which the definition is given by the metaphysician, differs from this same reality taken under the formal form under which falls the definition given by the logician.

            1.34 <2.28>. And when it is argued: “that real thing through which one definition differs from another, let it be B. Since then whatever is in the definition is in the defined, and B is in the definition, therefore B is in the defined. And more, whatever is in the defined is in the definition, therefore B is in both definitions, therefore one definition does not differ from the other in B.” [1.21] It is replied to this that this proposition is false,, “whatever real thing is in the definition is in the defined,” if a distinction is made through a real form (pro ratione reali), since there is some real form not depending on the soul in the definition, which is not also in the defined. Now if it is understood thus, that a distinction is made through a real being, as distinguished from a real form and a real consideration, under this concept it can be granted that this is true, “whatever real thing is in the definition is also in the defined.” But if it be taken under B, through which one definition differs from the other, then the minor will be false, since it was said that one definition differs from another only by a formal form.

            1.35 <2.29>. In another way, it must be replied by granting this, “whatever real thing is in the definition is in the defined,” and then, when it is argued “B is in the definition, therefore it is in the defined,” the conclusion is granted. And then, when it is argued, “whatever is in the defined is in the definition, therefore B is in both definitions,” the conclusion is granted, that B is in both definitions, for B is in one definition as a formal form taking the reality signified through that definition, and it is in the other definition as a concomitant form. Hence it is not absurd that some two things should be distinguished through something that is in one formally and in the other concomitantly. Indeed, it is necessary, since otherwise a reality signified by a definition would in no way be other than the reality signified by the defined.

            1.36 <2.30>. In response to the other argument to the contrary, [1.22] it is granted that the same reality is signified by one definition and by the other, taken under a different consideration and under a different real form not depending on the soul, and under another formal form, and this formal form suffices for this distinction.

            1.37 <2.31>. In response to the other argument to the contrary, when it is argued, “The metaphysician excludes a being that is true from his consideration, concerning which the logician decides, therefore it is not the job of the metaphysician to define a being that is true,” [1.23] it must be replied that the metaphysician does not have the job of defining a being that is true under that form under which a being that is true is excluded from his consideration. Hence he does not exclude a being that is true under every form received under his consideration, since in the fourth book of the Metaphysics the Philosopher decides about the first principle, which is a being that is true. In the same way, according to the Philosopher the logician and metaphysician labor over the same thing, but the metaphysician excludes a being that is true from his consideration under that form under which the logician considers a being that is true, and under that form the metaphysician does not define a being that is true. For it was said earlier that even if the logician and metaphysician have the job of defining the same reality, this is still under different forms and under different formal considerations.

            1.38 <2.32>. It must be replied to the other <second> principal argument, when it is argued “the mere logician is a common artificer, therefore it is his job to use common terms,” [1.24] it is replied by granting the conclusion. Hence the logician in this book uses a demonstrative syllogism, which is common and applicable to every demonstration and every demonstrative syllogism. And when it is argued further, “Every demonstration made from proper principles is a demonstration restricted to a single thing,” the conclusion is granted. And when it is argued further, “Every demonstration restricted to a single thing is in terms related to the species,” it must be held that these terms are related to the species, since they belong in species, and principally to logic, and in this way it is granted that the logician uses terms relating to a species.

            1.39 <2.33>. Nor does this consequence hold, “the demonstration is restricted to a single thing, therefore the terms are singular,” for a syllogism so restricted can be in common terms, for instance, if it were argued thus: “Every being is a being or a non-being, some reality is a being, therefore some reality is a being or a non-being.” this syllogism is restricted to a single thing, and still it is in the most common terms.

            1.40 <2.34>. In response to the last <principal argument>, when it is argued, “A mere logician can make a demonstration from proper principles, therefore a mere logician can have demonstrative science,” [1.25] this conclusion is granted.

            1.41 <2.35>. In response to the proof, “A logician considers the way of coming to scientific knowing and the way to scientific knowledge, therefore he does not have scientific knowledge,” one replies by denying this consequence, since there is scientific knowledge of the way of coming to scientific knowing.