Part Ten - About Application
1. This part is divided into 15 parts which deal with the application of:1. Implicit and explicit terms
2. Abstract and concrete terms
3. The first figure
4. The second figure
5. The third figure
6. The fourth figure
7. The definitions
8. The rules
9. The table
10. The evacuation of the third figure
11. Multiplication with the fourth figure
12. The mixture of principles and rules
13. The nine subjects
14. The hundred forms
15. QuestionsNow let us begin with the first part.
Chapter 1 - Applying Implicit and Explicit Terms
2. Implicit and explicit terms are applied as follows: take the terms contained in the question - for instance, let us ask whether God exists. The term "whether" in this question calls for the application of B, and B involves applying goodness and difference; and thus the artist can get help from the terms represented by B. And to get further help, he can apply other terms implicit in the question to the explicit terms of this art, such as greatness, eternity etc. Now if God exists, He does so through infinite greatness and eternity, so that without infinite greatness, eternity etc. God cannot exist. And this constitutes camera BCD. The artist can then discourse with these terms to prove or disprove God's existence following the way the three terms are combined with the principles and the rules.3. If the question contains two explicit terms - as when we ask whether God is eternal - we can refer to another term implicit in this question, namely power: now if God is eternal, He has the power to be eternal, and if He is not eternal, he does not have the power to be eternal.
4. Further, if the question contains three explicit terms - as when we ask whether it is good that God be as infinite in his greatness as in his eternity - we obtain camera BCD, where B implies goodness, difference and whether; C implies greatness, concordance and what; and D implies eternity, contrariety and "of what". Further, the definitions and the species of the rules are implied by these term, and thus the entire camera is applied to the question at hand to reach a conclusion. And examples such as the ones we just gave can also be given with regard to other questions and terms.
5. Further, if we ask whether God is actually greater by reason of his intellect than by reason of his eternity, "greater" applies to majority just as "lesser" applies to minority, given that "lesser" belongs to the genus of minority and "greater" belongs to the genus of majority.
6. And if we ask whether God is as powerful by reason of his power as he is by reason of his will, we shall refer to equality, a term which implies comparison, just like "greater" implies majority and "lesser" implies minority.
7. And if we ask whether God is just, we shall refer to virtue, because "just" belongs to the genus of virtue. And we can refer to goodness, given that it is good for God to be just. And likewise with other questions in their own ways.
Chapter 2 - Applying Abstract and Concrete Terms
8. This application is done in four ways. The first way is when the terms contained in the question have substantial abstractness and concreteness; for instance, igneity and fire, now igneity is a substantial essence and fire is a substantial concrete term.The second way is when both the abstract and the concrete terms are accidental for instance, take "quantity" and "quantum". And I mean "quantum" in the sense of a habit, and therefore an accident.
The fourth way is when the abstract is accidental and the concrete is substantial, as in "whiteness" and "something white", by "something white" I mean a body habituated with whiteness, and this body is a substance and not an accident.
All four of these methods are implicit in the terms of the question, and vice versa. and thus they should be applied to the conclusion, so that the intellect is not deceived by alteration in the middle term.
Chapter 3 - Applying the First Figure
Here the application proceeds according to what was said in the part about the first figure, by making affirmations in a circular way and interchanging the subject and the predicate: for instance "good greatness, great goodness" etc. But if the subject and predicate are not convertible, we use negation, for instance, take "greatness" and "eternity" - now there is some greatness that is not eternity, and vice versa; and some goodness is not great because some goodness is small, and likewise with the other terms in their own ways.Chapter 4 - Application of the Second Figure
10. The second figure is applied with its triangles and the ladders placed above the angles, for these ladders imply entirely general principles, entirely specific principles and subalternate principles. An entirely general principle is for instance difference, which has nothing else above it; an entirely specific principle is, for instance, the difference between this stone and that plant; a subalternate principle is, for instance, the difference between sensual and sensual etc. Further, these ladders imply the ascent and descent of the intellect, and without these ladders there is no way the intellect can ascend and descend.11. Let us also note that the terms of the second figure can be explained according to their positions in the figure, as described in part two of this book. Further, we say that the second figure can be applied to the first, as when we place difference between different kinds of goodness etc. as shown in the third figure.
Chapter 5 - Applying the Third Figure.
12. Here is how questions are applied to the third figure. Now if the subject matter of the question has to do with B, then apply C to B, and if applying C to B is not sufficient, apply D to B and so on all the way to camera BK. Take the meanings of the cameras, with affirmation and negation, so that the conditions and meanings of the letters are preserved. And if the subject matter of the question has to do with C, apply the other letters to C as we did with B. The same can be done with DE etc. And this application is infallible, and very general.Chapter 6 - Applying the Fourth Figure
13. Here is the way to apply questions to the third figure. Now if the subject matter of the question has to do with camera BCD, then apply it to this camera. And if the subject matter has to do with BCE rather than with BCD, then turn the inner circle and place E under C to form camera BCE. And take the meanings of the letters to solve the question, and the things we said about these letters apply to the others. This application is more general than that of the third figure, because the cameras contains three letters. And it is general to the degree that it contains all the cameras of the table.Chapter 7 - Applying Definitions.
14. The method of this art requires that the artist define the terms contained in the question, be they implicit or explicit. For instance, if we ask whether God is infinite. Then the respondent must define God and infinity as follows. God is a being so perfect that He needs nothing outside Himself. And infinity is a being which must have its own infinite correlatives without which it cannot exist at all. Further, if we say that goodness is a being by reason of which good can do good, we can likewise say that greatness is a being by reason of which great beings can do great things, and likewise with the other principles in their way.15. Further, a term contained in a question can be defined in several ways, by going through the species of the rules. Thus, by the first species of rule C, man is a rational animal. By the second species, man is an animal who has his own correlatives, namely the homifier, the homifiable and homifying, just as fire has its own innate ingnifier, ignifiable and ignifying. By the third species, man is an animal who operates with mechanical tools, for instance he practices arts like writing, horseback riding etc. By the fourth species of this rule, man is the animal who has ownership of, and dominance over irrational animals and plants. By the first species of rule D, man's sensitivity ranks first in nobility among sentient beings. By the second species, man is a being made of a soul and a body. By the third species, man is a being to whom irrational animals, plants etc. are subjected. By the first species of rule E, man is a substance by reason of his humanity. By the second species, man was created to serve God with the help of the vegetal and animal worlds. By rule F, man is a being with quantity, continuous throughout the elementative, vegetative, sensitive, imaginative and rational powers of which he consists. And these five powers, due to their difference, are discrete parts of man. By rule G, man is the being whose proper function is to produce man, and he is a being who can laugh, write, ride on horseback and so forth. By rule H, man is a being who exists in time as he understands, reads and so forth. By rule I, man is a being who tills vineyards and who prays to God in church. By the rule of modality, man is a being who has ways of mechanizing his work and of generating another man. By the rule of instrumentality, man is a substance that generates another man through the help of a woman, and he is a being who makes nails with a hammer, and so forth. And this provides a doctrine which enables one to make diversified definitions of one and the same thing, to make it known through true definitions in a way in which it was not known before. And so the artist must define things in such a way as to keep the definitions intact.
Chapter 8 - Applying the Rules
16. When inquiring into an uncertain subject, the artist must apply the question to the sequence of the rules; now just as a crystal placed on a red surface takes on its red color, or when placed on a green surface, it takes on the green color, and likewise with other colors, similarly, when an unknown term is combined with the rules and their species in sequence, the unknown term is colored and clarified by the species of the rules in which it is placed subjectively and objectively; and thus through the species of the rules, the intellect gets to know what it did not previously know. And as in the preceding chapter we gave an example of how man is defined by the rules, now for further clarification we want to give an example of how to combine nature with the sequence of rules.17. With the first species of rule C we say that nature is an essence sustained in its natural concreteness and moved by the natural motion in which it also reposes. With the second species of rule C it is an essence that has natural correlatives, namely the naturizer, the naturizable and naturizing without which it cannot exist. By the third species, nature is active and passive in the subjects in which it exists with its act of naturizing. By the fourth species nature has action, passion and an act in the subjects in which it exists through the natural agent, its natural form, matter and end, and its natural instruments.
18. By the first species of rule D, nature is a primordial essence. By the second species it is made of its correlatives that ascend to the essence, and its concreteness is derived from them through descent and contraction. By the third species of the same rule, nature belongs to the subjects in which it exists as they naturally make use of it.
19. By the first species of rule E, nature exists because it is a being comprised of its constituent correlatives. By the second species, nature exists to enable other beings to exist and act naturally.
20. By rule F, nature is an essence that has continuous and indivisible quantity, and its concretes make up its discrete quantity.
21. By rule G, it has its own actions and passions, as does the nature of fire in the act of heating. It has appropriated actions and passions, as in hot water that has in itself the heater, the heatable and heating. And here the intellect sees where nature comes from.
22. By rule H, the intellect recognizes that nature exists in time both continuously and successively; continuously by reason of its continuous quantity, and successively by reason of its discrete quantities through which nature exists in time.
23. By rule I, nature is in its locus, just as content is in its container, or a doer in the doable; and it is sustained and moved in the subjects in which it exists.
24. By the rule of modality, nature has modes for mixing, generating, corrupting and so forth.
25. By the rule of instrumentality, nature exists with its instruments, as does substance with its accidents, or a mechanic with his tools, and so forth.
26. When nature is thus combined with the species of the rules in sequence, it becomes known to the intellect, because the species signify what nature is in existence and action. And as we dealt with nature, so we can also deal with other abstract or concrete things according to their properties. But we cannot say the same about the miraculous as we did about nature, for when the intellect discourses on the miraculous with the sequence of rules, it can find out about it by considering its opposite, given that the miraculous enters into the species of the rules in a way contrary to the way in which nature enters into them. And here the intellect sees how an opposite can be known through its counterpart by applying the rules.
Chapter Nine - Applying the Table
27. Applying the table consists in applying the terms of the questions to the table. For instance, if the terms of the question have to do with the first column, namely BCD, the question must be applied to the first column; as when we ask whether it would be a great and good thing for the world to exist from eternity; or whether there is an eternal act. Now, given that goodness is a reason for good to do good, and that greatness is a reason for this act to be great, and that duration makes this act last from eternity and in eternity, there must be some infinite act.28. Further, if the terms of the question have to do with the second column, namely BCE, as when we ask why greatness of goodness of power exists, we reply that it exists through the correlatives of goodness, greatness and power, and so with the other columns in their way.
29. Moreover, each column can be applied to the other columns, for instance, the second column is applicable to the first and the third columns because it has BC in common with both, and the other columns are also interconnected in this way. And here the intellect realizes that all the columns can be applied to one identical conclusion, and thus it understands that it has reached a high level of generality through this highly general application.
30. Further, if we ask whether the world is eternal, then the second camera of the first column, or BCTB, applies to the camera above it and to those below, all the way to camera TBCD. And this is because "eternity" is an explicit term of the question.
31. And now if we ask whether the world's power is infinite, the answer is obtained by applying column BCD in the same way as when we dealt with the question about the world's eternity. And the answer is negative, for just as there would be major inconvenience if the world existed from eternity, so would there be major inconvenience if the world had infinite power.
32. Further, if we ask whether one angel produces another angel, the answer is obtained by applying BCD because between the essence of an angel, a man or a rose there is a great difference. Now the human body exists within the general matter of the elements, and for this reason one man can produce or engender another man, and one rose can produce another rose, but this is not the case with angels, for an angel has not the wherewithal to produce another angel, as it is not derived from one identical general angelic matter, but each angel is ultimately primordial. These examples we gave with the table can be applied to many other things in their way.
33. Applying the table requires that the species and rules of the cameras be preserved, and that the things they signify with regard to the issue at hand and its conclusion be applied through affirmation and negation, by distinguishing what is convenient from what is inconvenient, as shown in the above examples.
Chapter Ten - Applying the Evacuation of the Third Figure
34. The evacuation of the third figure is done as follows: apply the explicit terms of the question to the evacuation of the third figure, and to the camera most relevant to these terms. If we ask whether it is a great good that goodness and greatness have substantial correlatives and whether these correlatives are in good and great concordance, the question applies to camera BC and is solved with the help of what we said about this camera in part 6 chapter 1. And likewise with other questions, following the way their terms can enter into a camera, by making affirmative and negative statements and distinguishing between what is convenient and what is inconvenient.35. Further, a general question can be applied to a particular one and conversely, for instance if we ask whether goodness has great innate correlatives. This question is applied to the following one, namely whether the goodness of Socrates or of this rose has great innate correlatives. Then the questions are applied to camera BC, where the answer is found, already signified by the things said in that chapter.
36. Further, if we ask: "what do the correlatives of greatness consist of, and what do the correlatives of Socrates consist of?" These questions are applied to camera CD and the general question is applied to the particular question, and then the solution can be found, as it is clarified and signified by what we already said about the camera, and likewise with the other cameras. We will give an example of this in part eleven which deals with questions.
Chapter Eleven - Applying the Multiplication of the Fourth Figure
37. We said in part seven that the multiplication of the fourth figure is done in five ways, namely, by finding the middle term, by proving the major and minor premises, by exposing fallacies, and by following the doctrine whereby other arts can be learned easily. If the artist wants to multiply many reasons for the same conclusion, he can apply the method we used in multiplying reasons with the fourth figure, because this is a universal method that regulates and clarifies particular methods, for the particular is reflected in the universal and conversely. Now this should suffice because the matter has already been made clear enough.Chapter Twelve - Applying the Mixture of Principles and Rules
38. This chapter is divided into two parts: the first deals with explicit principles, and the second deals with implicit ones which we apply to the explicit principles and to the loci of the rules of this art. These implicit principles are called the hundred forms, and we include them to provide more material through the art for the human intellect in seeking out many conclusions. However, we do not intend to say much about these forms, to avoid prolixity. But the things we do say about them enable the artist to proceed by combining each form with the entire sequence of rules, using the same process we followed in combining the explicit principles with the rules. Now let us begin with the first part on applying the hundred forms.39. If the question contains explicit terms of this art, as when we ask whether there is a good, great and eternal being, then we refer to the chapters on goodness, greatness and eternity and see how goodness and the other principles combine with the sequence of principles and rules. Then, a conclusion is reached, by making affirmative and negative statements in keeping with the nature of the principles, so that the principles and rules are not violated. And then the intellect finds out the truth about the subject of its investigation, clarified by this discourse. And examples like the ones we gave with goodness, greatness and eternity can likewise be made with the other principles. Now this is sufficient for the first part, for the sake of brevity. (Translator's note: the second part begins farther below in chapter 14.)
Chapter Thirteen - Applying the Nine Subjects
We already dealt with the nine subjects, and thus, if there is a question about God, apply it to the first subject and follow its discourse about God so that the affirmative or negative conclusion agrees with the text. If there is a question about angels, apply it to the second subject with its discourse on angels and solve the question in a way that agrees with the text. The same applies to the other subjects each in its way.