Part Seven - Multiplying with Figure Four
1. We will deal with this figure in five ways. First, we will show how to produce multiple reasons for one and the same conclusion; second, a way to find many middle terms to reach conclusions through syllogisms. Third, we will deal with the major and minor premise. Fourth, a way to detect fallacies. Fifth, a way to learn other sciences more quickly and accurately by applying this science. Now let us begin with the first mode.
Chapter 1 - Producing multiple reasons.
2. Column BCD of the table showed by example how twenty reasons can apply to the same conclusion in answer to the question: "Is the world eternal?". Likewise, we can multiply this figure's cameras beginning with BCD, BCE, all the way to camera BCK and each camera yields twenty reasons. Second, we continue multiplying cameras through BDE, BDF, etc. where each camera also yields twenty reasons. Third, we continue multiplying successive cameras as we treat camera CDE like we treated BCD in the previous multiplications. And DEF is treated as was CDE, and so on with the others in their way, ending with camera HIK as we artificially revolve the circles again and again until the eighty-four columns of the table are formed. This feature of figure four was mentioned in part 5 about the table. Here, multiplication brings each principle into multiple combinations with the others and each principle takes on the habits of the others with proper and appropriated passions. Further, in the fourth multiplication, figure four contains figure three: for instance, camera BCD contains cameras BC and CD of figure three, and likewise camera CDE contains cameras CD and DE of figure three, and so with the others.
Chapter 2 - Finding the Logical Middle Term.
3. In camera BCD and in other cameras, C stands in the middle circle between B and D and as C joins B to D due to certain positions, habits and situations that occur between subjects and predicates, this art always uses the middle circle to investigate the middle term. Now as "animal" stands as a middle term of measure and conjunction between "substance" and "man" when we conclude that man is a substance, likewise the letter in the middle circle must stand between the letter in the upper circle and the letter in the lower circle, in arguing as follows: all C is B, but all D is C, therefore all D is B. And as certain conjectures and passions necessarily lead to conclude that an animal is a substance and man is an animal, so should the artist of this art conjecture the things signified by BCD, namely the subalternate principles where B says or means goodness, difference and whether; C signifies greatness, concordance and what; and D signifies duration, contrariety and of what. And the things said or signified by the letters include the definitions of the principles and the species of the rules used by the artist to conjecture about any issue by matching the middle term with the letters above and below it.
And here the intellect builds science with universal affirmation and universal negation, particular affirmation and particular negation,
possibility and impossibility.
4. The intellect acquires the habit of using these five modes as follows, by saying: "All C is B, and all D is C," which is proved as we recognize, for instance, that greatness is good on account of goodness and goodness is great on account of greatness; and goodness has great correlatives signified by the second species of C and greatness has good correlatives signified by goodness and the second species of C. And likewise with greatness and duration with their respective conditions.
5. Saying that all C is B and all D is C involves universal affirmation and negation as well as particular affirmation and negation because B implies difference and D implies contrariety.
First we say: "All animals are substance. But all men are animals, therefore all men are substance."
Second: "No animal is a stone. But all men are animals, therefore no man is a stone."
Third: "All animals are substance. But some men are animals, therefore some men are substance." In other words: all C is B but some of D is C, therefore some of D is B. This is because contrariety implied by D cannot be concordance implied by C, nor can great evil be great good for if it could, an object would be intrinsically opposed to itself, which is impossible and against the correlatives in the second species of rule C.
Fourth, we say: "No animal is a stone. But some men are animals, therefore some men are not stones." In other words: "No C is B, but some D is C therefore some D is not B." This reasoning is patterned on the third syllogism which concludes with a particular affirmation.
6. The four ways of making syllogisms we described first indicate instances of necessary reasons to the intellect, as when it negates that all C is B, since created goodness cannot be created greatness because difference posits that each principle exists per se, but also posits that it is possible for goodness to be habituated with greatness; and when the intellect affirms that not all B is D and not all D is C, it can tell what is possible or impossible. Then it sees how to demonstrations are made with the first species of rule G and directed combinations with the second species of rule G: this is indicated by all the cameras containing G in the third figure.
7. Second, the intellect finds means to contract the principles, by taking an entirely general principle and contracting it to a principle that is neither entirely general nor entirely specific. Difference, for instance, as a supremely, or entirely general principle, is contracted to the differences between sensual things, which are neither entirely general nor entirely specific. And when it is contracted to the ultimately or entirely specific differences like those of a given animal, a given plant or a given stone, where the individual is constituted both substantially and accidentally of its own quantity, quality, etc. and the individual is placed in its own species etc., those intermediary differences are middle terms between entirely general and entirely specific principles. And we can say the same about goodness, etc. as about difference: now goodness is a supremely general principle and when it is contracted to greatness, etc. then it is neither supremely general nor supremely specific; but when great goodness is contracted to a given concrete being constituted of this great goodness, in its form, its matter and in its quantity, its quality etc. and when this being is placed in its own species, in which it becomes individuated, then the great goodness which is neither supremely general nor supremely special is a middle term standing between abstract and concrete things, and participating in the nature of both extremes. This naturally allows the artist to find the middle term that naturally stands between the major premise and the minor premise. And through this middle term, demonstrations proceed from primordial, true and necessary principles not subject to any exceptions.
8. Third, the middle term is found under its own letter and in its own circle, namely under F which stands for the middle term and in the middle circle: for instance as we put F under B and above C, considering that F has goodness and difference from B and also greatness and concordance from C; and thus F stands between B and C, on account of which C transits through a middle term to B, as when we say: "All F is B, but all C is F, therefore all C is B," but only with regard to the genus of medium. And what we said about camera BFC also applies to camera CFD and to camera DFE, etc. The things said here about the middle term provide the artist with very general subject matter for finding many middle terms. And this is clearly shown by the definitions of the principles and the species of the rules.
Chapter 3 - The Modes of Proof
9. Proof is a general entity divided into three species, namely demonstration by cause, by equality and by effect. Let us now give an example with the following syllogism: "All animals are substance, but all men are animals, therefore all men are substance." First we will prove the major premise, then the minor one. And let us begin with a demonstration by cause: an animal is constituted of differences between various sensual things, because it is elemented, vegetated and endowed with senses and imagination, whence it follows that it is a substance because it is composed of substantial parts, and as substance stands above and the animal below, so this animal is caused by higher causes, namely its constituting form and matter and its parts are below because they are caused by form and matter which are general principles. And thus we truly conclude, according to the causes, that animals are substance.
10. The same is proved as follows with a demonstration by equality: general form and general matter are equally primordial causes, as the first species of rule D shows, and as an animal is cause by its own form and its own matter sequentially combined with the elementative power, the vegetative power, etc. which are equally principles of this animal, it then follows that an animal is a substance constituted of its own form and matter which equally descend from equal and supremely general principles, namely prime form and prime matter. And this is shown by the second species of rule D, the first species of rule E and by rule B.
Third, let us demonstrate the same by effect: an animal exists, and because it exists, so do its causes, namely its constituting form and matter without which it cannot be what it is. And since form and matter constitute substance, it truly follows that this animal is a substance.
11. Now let us prove the minor premise with the same three species, beginning with proof by cause. As an embryo is constituted of the elementative, vegetative etc. in the womb where it is outlined to grow into the shape of human limbs, and when the rational soul, which is a substance, is introduced into the embryo, it then constitutes a human being from itself and its lower parts. And thus, the animal that is the embryo, is transmuted into a human by the human species in which it is placed with all its coessential parts. And so it follows that the soul is the cause on account of which man is an animate substance. And the first species of rule C clearly shows this.
12. The proof by equality goes as follows: the rational soul has equal coessential parts, namely intellect, memory and will, as does the embryo which is equally constituted of the elementative, vegetative etc. And as its principles are substantial and equal, man is entirely, equally and substantially comprised of these principles when the rational soul is joined to the human body. And thus, rules B C D E clearly show that man is an animal.
13. The proof by effect is as follows: Socrates exists because he is an animal, without which he cannot exist. The minor has been proved with the three said species of proof, and of these, the ones that yield the most powerful conclusions are the proofs by cause and by equality; proofs by effect are not as potent because causes have preponderance over effects.
14. Further, just as we gave an example of proofs that man is a substance where we used "animal" as the middle term, we can likewise speak of irrational animals, plants and stones. And thus the intellect builds science by proving the major and minor premise with this art which disposes the intellect to find every conclusion, and this is evident from what we have said.
Chapter 4 - Detecting Fallacies
15. The general source of all fallacies lies in the diversion of the middle term. And because F signifies the middle term, F in the middle circle is an instrument used to detect and recognize fallacies by forming cameras as F is placed successively under the letters in the upper circle and above the letters in the lower circle. For instance, place F below B and above C and look at how BC relate to F in fallacies and vice versa, and then place D under F etc. in turn, and you will detect the deviation in the middle term. Now we will give examples of this, and first let us deal with fallacies in the word and then with fallacies in the subject matter.
About Fallacies in the Word
Article I - False Conclusions due to Equivocation or Ambiguity
16. Equivocation is the diversity of meanings of one and the same word, and given that a word can have various meanings, the fallacy of equivocation arises, as for instance: "All dogs can bark. But the Dog Star is a dog, therefore a star can bark."
17. To refute this, let us refer to cameras BFC. B tells us that there is a difference between an animate body and an inanimate one. F says that animate and inanimate bodies cannot be lumped together as if they were of the same species. C tells us that animate bodies have sensual correlatives and that inanimate bodies do not have any sensual correlatives. And thus the artist can tell where the fallacy lies in the faulty syllogism and point out its impossibility, and by reason of this knowledge, the intellect knows that a logician cannot stand up against a natural philosopher, especially one using this art to point out impossibilities. For instance, a star cannot possibly belong to the same natural genus as a barking animal.
18. Further, by applying camera DFE and the other cameras, we can detect more flaws in the false syllogism: by the second species of D, a dog can bark because it consists of elementative, vegetative and sensitive powers, but a star cannot bark because it does not have these constituent principles. The second species of rules C and D show this, as does the ladder of the medium, or middle.
Article II: Amphyboly
19. The deception of amphyboly arises from the fact that one and the same sentence can be construed as having two different meanings. For instance, let us take this false syllogism: "Whatever is Aristotle's is owned by Aristotle. But this is Aristotle's book, therefore it is owned by Aristotle."
20. To refute this fallacy, let us refer to camera DFH where D, with its third species, tells us that this book is not owned by Aristotle because it can only be owned by a man joined to the elementative, vegetative, sensitive, imaginative and rational powers, as the second species of rule D shows. Now F signifies the medium of measure, conjunction and continuity in the subject in which it exists, and H signifies that the now existing book is not owned by Aristotle because Aristotle is dead. And the same is shown by camera BFG where B shows the difference between a dead man and a living one, and F posits the conjunction between sensual and intellectual which is non existent in a dead man. G posits appropriation: now Aristotle did write this kind of book, but it is no longer his property, because he is dead.
Article III: The Fallacy of Composition
21. The fallacy of composition is a deception due to the multiple meanings of some sayings whose parts can be differently associated with one another. Here is one such paralogism: "Whatever has the possibility of being white can be white, but black has the possibility of being white, therefore black can be white."
To refute this, let us refer to camera DFE, where D indicates contrariety, and F says that black and white cannot be constituted by any medium of conjunction between extremes of color. With E we understand that things are possible only when they consist of their own constituent principles, as the first species of rule E shows, and therefore the conclusion is that it is impossible for white to be black. And we can also detect the deception by applying camera GFH, where G signifies that anything whose proper habit is white cannot be habituated with black, F tells us that whiteness and blackness do not constitute any medium of conjunction, measure or continuity between extremes, because if they did, they would set up opposition within the object. With H, we understand that it is possible that a cloth presently habituated with whiteness can at some later time be habituated with blackness.
Article IV: The Fallacy of Division
22. The fallacy of composition is a deception due to the multiple meaning of a saying whose parts can be dissociated from each another in different ways. For instance, take thia paralogism: " All animals are either rational or irrational. But not all animals are rational, therefore all animals are irrational."
23. Let us apply camera CFG to this deception. With C we know that when a statement about one subject is made in concordance with the subject's correlatives as signified by the second and third species of rule C, the statement means one thing. But when, on the contrary, a statement does not respect the subject's correlatives, the meaning of the statement is altered and divided, as shown by the ladder of C in the second figure. With F, we know that opposite beings, such as rational and irrational ones, cannot be joined together nor measured or compared as members of the same species through any medium of continuity. G tells us that laughter is proper to rational beings, not to irrational ones. The deception can also be detected by using camera CFI, CF tell us the same as above, and I signifies that truth does not truly posit that diverse things are identical, nor does equality posit that they are of the same species or that they occupy the same place at the same time.
Article V: The Fallacy of Accent
24. The fallacy of accent is a deception arising from the fact that the same utterance pronounced with different emphasis can mean different things, as in the following paralogism: "All the spectators at the wrestling match who yell 'Kill Bart!' want Bart to lose. But some of Bart's most loyal fans are also yelling 'Kill Bart!' Therefore some of Bert's most loyal fans also want him to lose the match."
25. Let us apply camera BFC to this deceptive argument, or paralogism. With B and with the conjunction and measure of F we understand the difference in emphasis, and with C we understand the concordance of different utterances in one meaning. Those who yell "Kill BART!" are encouraging his opponent, but Bart's fans are yelling: "KILL, Bart!" to encourage Bart to defeat his opponent. Camera B also serves to detect the deception: the emphasis is different, and F shows that the voice does not join or measure the words in the same way in both cases. K indicates a disregard for the emphasis that conveys divergent meanings by emphasizing different syllables.
Article VI: The Fallacy of Figures of Speech
25. The deception in the fallacy of figures of speech is due to the fact that some utterance is similar to another utterance, as in the following paralogism: "Whatever you saw yesterday is what you see today. But yesterday you saw white, therefore you see white today."
Let us apply camera BFG to this paralogism. With B we understand the difference between quiddity and quality while F shows that they are neither joined nor measured to one numerically identical object on account of their diversity. G shows that quiddity has to have its own meaning, as does quality, and the deception is in the improper appropriation in which the principles do not rest in their proper end. Camera DFH also serves to reveal the deception: D signifies contrary ends whereby quiddity is transformed into quality, and F shows that there is no continuity between a past "now" and the present "now". H indicates time, and by the fourth species of rule C and the first of D, quiddity means one thing while quality means another, because quiddity refers to substance and quality refers to accidents.
About Fallacies in the Subject Matter
27. Fallacies in the subject matter are different from fallacies in the word because the former have their root cause in the voice whereas the latter arise from the subject matter.
Article VII: The Fallacy of Accident
28. The deception in the fallacy of accident arises from the improper identification of two things as one on account of some accidental feature they have in common, as for instance in this paralogism: "I know Socrates, but Socrates is arriving, therefore I know who is arriving."
Let us apply camera BFD to this deception. B indicates the difference between sensual and sensual. Now Socrates is one person, and whoever is arriving can be someone else. F indicates that Socrates and whoever is arriving are extremes without any continuous medium between them, by C we understand that Socrates could be sitting by the roadside while someone else arrives. Further, camera GFH reveals the deception: G says that Socrates has his own identity as does the other man who is arriving, and that the term "is arriving" is falsely attributed to Socrates. F says that Socrates is not joined or identified by any measure to anyone else who may be arriving, and H tells us that while Socrates is sitting, he is not arriving.
Article VIII: The Fallacy of Overgeneralizing
29. The deception in this fallacy occurs when a statement made with reference to something is taken in an absolute sense, as in the following syllogism: "Negroes have white teeth, therefore Negroes are white."
30. Let us apply camera CFI to this deception, or paralogism: by the fourth species of rule C we understand that Negroes have white color in their teeth, eyes and nails, and black color in their skin. F says that the white color in Negroes does not extend continuously to the rest of their bodies and I indicates that they are white in some places and black in others. The deception is further unmasked by camera GFK: G tells us that they do have white teeth and it would seem by appropriation that Negroes are entirely white, if we accept this false conclusion. F tells us that a Negro is a subject comprised of many discrete quantities, like the quantity of his teeth and the quantity of his feet, and that his teeth are habituated with white coloring and his feet with black. K tells us that a Negro's teeth are colored with white and his feet with black.
Article IX: The Fallacy of Ignoring the Elenchus
31. In the fallacy of ignoring the elenchus, the deception arises from ignoring the things needed to define an elenchus and especially the contradiction it entails. An elenchus is a contradicting syllogism, and it can comprise either one or two syllogisms. It comprises one syllogism when the syllogism reaches a conclusion contrary to a previously stated proposition, as occurs when the statement "Some animal is incorruptible" is followed by the syllogism: "All things composed of contraries are corruptible. But all animals are composed of contraries, therefore all animals are corruptible." This conclusion contradicts the previous statement.
An elenchus can also be made of two syllogisms whose conclusions contradict each other, for instance, taking the previous syllogism, we add: "Nothing holy is corruptible. But some animal is holy, therefore some animal is incorruptible." Thus, an elenchus is always patterned on a syllogism and a contradiction, and whatever contradicts the definitions of syllogism and contradiction also contradicts the definition of an elenchus. Now let us take this paralogism: "Two is the double of one, but two is not the double of three, therefore two is both a double and not a double". This is invalid: if we stop considering everything in the same respect, there is no contradiction, as we can see with the second species of rule C.
32. Let us apply camera BFC to this deception. B tells us that two and one are different from each other; with F we understand that two has greater discrete quantity than one; C tells us that two agrees with even numbers and three with odd numbers. Camera DFE further reveals the deception: D tells us that two, an even number, is made of two units, by the second species of rule D, and that one is the beginning of numbers according to the first species of rule D. With F we know that two and one are not equally measured by the first species of rule E because two is a double whereas one is not a double.
Article X: The Fallacy of Begging the Question
33. In the fallacy of begging the question, the deception arises from proving something with the same expressed in different words. For instance, take this paralogism: "Rational animals run, but men are rational animals, therefore men run."
34. Let us apply camera EFH to this deception. E shows us that the principle in the major premise is not proved, it is merely a supposition. F says that the major and minor premises are disconnected, because the major premise is a supposition and the minor premise requires a proven major premise. H tells us that rational animals do not always run. And camera EFG further serves to unveil the deception: with G we understand that a true syllogism must have a proven major premise, F says that the major and minor premises must be connected and measured with proof, I tells us that they do not carry equal weight in the conclusion.
Article XI: The Fallacy of Affirming the Consequent
35. The deception in the fallacy of affirming the consequent occurs when the consequent is deemed to be entirely identical to the antecedent, as in the following paralogism: "Lions are animals; but you are an animal, therefore you are a lion." This is invalid, because the consequent is not identical to the antecedent.
36. Let us apply camera BFD to this deception: with B we understand that lions and rational animals do not belong to the same species, because the difference between sensual and sensual is not the same as the difference between sensual and intellectual; F says that the sensual and intellectual species are joined together in man as his constituent parts; D tells us that the sensual and intellectual species are joined in men but not in lions. Camera DFE tells us more about the deception: D tells us that a supposite consisting of sensual and sensual cannot convert with a supposite consisting of sensual and intellectual; by F we know that men and lions are not connected through any continuous medium between extremes; F tells us that men exist in order to understand, which is not the case for lions.
Article XII: Fallacy of the Specious Reason
37. The fallacy of the specious reason occurs when some proposition that merely appears to be a reason but has no valid bearing on the conclusion is inserted between the premises leading to the conclusion, as in the following paralogism: "Given that soul and life are identical, death and life are contraries, and generation and corruption are contraries, now if death is corruption, then life is generation, and to live is to be generated." However, this is impossible, because the rational soul is alive, although it is not generated.
38. Let us apply BFC to this deception: with B we understand the difference between soul and life and that life is something more universal found in irrational animals made of a continuum of the vegetative and sensitive souls as well as in man who is made of a rational soul joined to a body. F tells us that the life of the rational soul is not one by any means with the life of irrational animals; with C we understand that in the rational soul, life has great continuation of the intellect, will and memory, which is not at all the case for irrational animals or plants.
Camera DFE tells us more about the deception: D says that life in plants and irrational animals consists of corruptible correlative parts but this is not so in the rational soul, because it is not made of contrary parts; F says that a specious reason about a supposite is not by any means the same as a true reason, with E we know that the soul lives and has repose in its end, which is God.
Article XIII: The Complex Question Fallacy
39. The deception in the complex question fallacy lies in giving a single answer to a question that inquires about several things, just because they are all included in a single question, as in the following paralogism: "Do you suppose that men and lions are rational animals?" If you answer "no", the reply is: "Men and lions are not rational animals, therefore man is not a rational animal."
40. Let us apply camera BFC to this deception. With B we understand that the difference between sensual and sensual is different from the difference between sensual and intellectual, and for this reason, a man and a lion cannot be the same. With F we understand that men and lions do not stand within any continuous medium between extremes. C tells us that a man and a lion do not belong to the same species and cannot be the same individual. Camera DFG tells us more about this deception: D tells us that a man consists of three souls, namely the vegetative, sensitive and rational, which is not the case for a lion that consists only of the vegetative ans sensitive souls. F says that a man can have a habit of thinking scientifically, but a lion cannot. G says that laughter is a passion proper to man, and that man has substantial intelligibility; lions do not have these things because they are not made for them.
Article XIV: The Fallacy of Contradiction
41. The fallacy of contradiction (which we expounded more broadly in the New Logic discovered through the mode of the General Art) is a deception that arises and derives from the abovementioned fallacies which seem to reach contradictory conclusions where there is no real contradiction, as in the following paralogism: "No stone is visible, but some stone is visible, therefore some stone is both visible and not visible."
42. Let us apply camera BFC to this paralogism. With B we understand that there is a difference between a visible and an invisible stone because an invisible stone has no innate visible part of its own as it is not habituated with the habit of sense, whereas a visible stone is accidentally visible, as the sight habituates itself with its color and situation. F tells us that when a stone is invisible it is not joined to the species of visibility, but when it is visible, it is. C tells us that sight is not active in an invisible stone, and by the fourth species of C, the stone has no passion under the power of sight; but we can say the contrary of all this about a visible stone.
Camera FGH tells us more about the deception: with G we know that visibility is not a passion proper to a stone, rather, sight accidentally appropriates visibility to it because color, shape and situation are the objects of sight. F tells us that a stone is not joined to the sensitive power; H says that a stone can be sometimes visible and sometimes invisible.
43. We have dealt with the fallacies applied to the rules, so that the deceptions in the fallacies can be known. And by the things we said, the intellect knows that a logician using fallacies cannot stand up against a natural philosopher, because if we suppose that the logician is telling the truth, all kinds of impossibilities would follow according to the nature of things, as shown by the nature of the definitions of the principles and rules. And here the intellect knows that when one logician debates with another logician, they can never reach the end of their debate because they never come down to the realities of things as they deal only with words and likenesses of things with the definition of contrariety. But if the logician debates with a natural philosopher, the truth of the matter is quickly found and resolved, because the logician has no way of denying the experience of his senses, imagination and reason, as we said above.
Chapter V: Techniques for Learning
44. The fourth figure is more apt than the others to provide modes for acquiring other sciences more easily and quickly, like Theology, Philosophy, etc. which is done by finding a medium that is neither entirely general nor entirely specific. This is because this science has ultimately general principles as well as ultimately general rules, whereas other sciences have subordinate principles, so that their means are imperfect without this science. This is why people spend a long time learning them with difficulty and when doubts arise, they have no ultimately general principles that they can artificially invoke as does an artist of this art.
45. Further, other sciences can be learned with this art by forming cameras with F as the middle term and by expounding on the authorities with the camera according to the way F can apply to the authorities by reducing them to a syllogism following the doctrine given in Chapter 3 above. Let me give the following example: in Theology, we read that God is a pure act. This authority can be proved with two cameras, namely BFC and DFE. Now with B we have goodness and difference. C says that goodness is a great reason with good, great and distinct innate correlatives that are eternal and primordial according to D and repose in their end by rule E. By the second species of rule D and by the first of E, they are necessary, and by F they are well united and measured infinitely and eternally, and separated from all accidents. And this exposition clearly shows that God is a pure act in existence and action.
46. Further, in Philosophy we read that nothing can be made from nothing. Let us expound upon this authority by applying camera DFE. First, with the first species of D we explain that nothing is not a principle because if it were, nothing would be something. The same is understood with the third species, now if nothing were subject to something, it would be something. F also says, or signifies that nothing can be made from nothing and nothing cannot have any middle, for if it had one, it would be something. With E we understand that nothing cannot be a material, formal, efficient or final cause and cannot be habituated with any power, because if it could, it would be something. And thus the authority has been explained and expounded with the said camera.
47. This does not mean that the world is eternal, rather, it is new and has a beginning, as proved above. And the authority that says the world was created from nothing can be expounded with the same camera: now D says that God is primordial in eternity, power and intellect, and by the third species of rule D, God is not subject to his own power, and thus God can understand that the world, that was neither in potentiality nor in actuality in nothingness, was in his power to produce from nothingness. Therefore it follows that the world is in actuality through creation as God measures his infinite power, intellect, primordiality, etc.
48. Further we read that being and oneness are convertible, as are oneness and good, oneness and truth etc. These authorities can be expounded with camera BFC as well as the other cameras. And B tells us that there are differences between some sensual things and others, as oneness is one thing in a stone, another thing in a plant, another in sentient beings and the same applies to goodness, truth, etc. These kinds of unity, goodness and truth are not convertible, for if they were, difference would be destroyed, and consequently the medium as well as concordance, which is impossible; now there is one mensuration in a stone, and one continuous medium, and one quantity, and another in a plant etc. Now these authorities cannot be taken literally because the camera cannot enter into the authorities to expound them literally, but it enters with the allegorical sense by using rule G because the correlatives of unity are not properly the same as the correlatives of entity, truth, or goodness but only in an appropriated sense, because each principle communicates with the others so that the principles can still be differentiated, concorded and mediated as qualitative reasons, and each principle has its own repose and its own essence and act, and thus there is no contradiction, and rule B consents to this as do all the other rules.
49. Following the examples we gave using Theology and Philosophy by expounding and clarifying them with the cameras, other sciences can also be treated, such as medicine, law, morals etc. because if there is any truth in an authority, the cameras of the fourth figure can enter into it with their definitions and species through affirmation or negation, and if they cannot, the authority cannot possibly be true. No authority constituted of primordial, true and necessary principles can contradict reason. And this rule is infallible and necessary.