Showing posts with label incompossibility. Show all posts
Showing posts with label incompossibility. Show all posts

18 Dec 2018

Leibniz (3.405-3.417) Theodicy (The Sextus Pyramid of Incompossibles story), summary

 

by Corry Shores

 

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[The following is summary. Boldface is my own. Proofreading is incomplete, so please forgive my mistakes.]

 

 

 

 

Summary of

 

Gottfried Leibniz

 

Theodicy:

Essays on the Goodness of God, the Freedom of Man and the Origin of Evil

 

Essays on the Justice of God and the Freedom of Man in the Origin of Evil”

 

Part 3

 

Sections 405-417

(The Sextus Pyramid of Incompossibles Story)

 

 

 

 

Brief summary:

(3.405) Leibniz begins with Laurentius Valla’s Dialogue on Free Will (between Antonio Glarea and Laurentius), to set up a discussion about divining and freedom. (3.406) Laurentius will explain how divine foreknowledge can be compatible with human freedom. But he requires that Antonio be satisfied with his answer. (3.407) Antonio argues that since God foresaw Judas betray, that means Judas could not have done otherwise and thus is blameless. Laurentius replies that mere knowledge itself cannot cause things past or present to exist; therefore, knowledge cannot cause future things to exist. (3.408) Laurentius makes a couple distinctions. {1} Foretelling vs. foreknowing. Antonio gives an example where he asks a heathen god which foot he will put forward, then he puts the opposite foot forward (Laurentius explains here that either the god would not foretell, or if he would, then we should expect Antonio to obey the foretelling). {2} Regarding foreknowledge: the necessary vs. the certain. Events that are foreseen could have been otherwise (as their alternatives do not create logical contradictions) and thus they are not necessary, but it is certain they will happen (as they have been chosen by God in advance). “It is not impossible for what is foreseen not to happen; but it is infallably certain that it will happen. I can become a Soldier or Priest, but I shall not become one” (p.371). (3.409) Laurentius says that “Two contradictories are often both possible” (p.372).” He next illustrates why foreknowledge is not causal with a story about Sextus Tarquinius. Sextus goes to the Oracle of Apollo for a prediction. Apollo says that he will die poor and in exile. Sextus objects, asking why Jupiter would be so cruel in choosing for him such a bad fate, when he is innocent and devout. Apollo replies that Sextus will later be proud, adulterous, and a traitor to his country. Antonio agrees that Sextus cannot accuse Apollo of causing these things by foreseeing them. Similarly, Laurentius concludes, Judas cannot complain about God’s foreknowledge of his crimes. (3.410) Laurentius continues the story. Sextus tells Apollo he will not commit the foretold crimes, and he will appeal to the Gods to give him a better heart. Nonetheless, Apollo will notify Sextus that the Gods make creatures with their given traits. The ass is stupid, the lion is courageous, etc. They gave Sextus a wicked soul, and he will act in conformity with his natural disposition; and, Jupiter will accordingly punish his wicked actions. (3.411) Antonio objects that the real crime is caused by Jupiter for having created someone with a wicked nature who will certainly do wrong. Thus Sextus should not be blamed for Jupiter’s crime, as he cannot resist Jupiter’s will. Laurentius says he was able to show that foreknowledge is different from providence and that foreknowledge does not have any causal power. But he also says that he cannot know explain if and how providence restricts freedom. (3.412) Laurentius explains that we will not know why God is hard against one person but compassionate towards another. We simply have to accept that God is very good and wise, and that is enough reason for us to deem his reasons as being good. (3.413) Leibniz now speaks for himself rather than quoting the Laurentius dialogue. Leibniz notes that the dialogue’s defect is it condemns providence, as it makes Jupiter the author of sin. Leibniz now continues the story his own way. Sextus next goes to Jupiter and asks him why he condemned him to be wicked and unhappy, and Sextus asks Jupiter to fix his error and give him a fate where he becomes wise and happy. Jupiter says that Sextus can be wise and happy if he does not go to Rome and thus renounces his kingship. Sextus cannot give that up, so he accepts his doomed fate. Leibniz now adds a new character to the story, Theodorus, a high priest who has been listening to this story. Theodorus tells Jupiter that Jupiter’s worshippers are upset, because Jupiter is the one who decided to give Sextus his evil will (which resulted in him going to Rome even though he now knows it dooms him). Jupiter tells Theodorus that he should visit Jupiter’s daughter Pallas, because she will explain what Jupiter was bound to do when deciding Sextus’ will). (3.414) Theodorus goes to Jupiter’s daughter Pallas. She watches and wards over the palace of fates. It contains not just the actual world, but every possible alternative fate. Jupiter picked the best one, and he  sometimes comes to admire his selection. So at the palace, we can see all the alternative twists in fate. And for any one person, there can be a variety of different lives, and thus there are many Sextuses. Pallas then makes a geometrical illustration for this structure of bifurcating worlds. A locus is a set of points that fulfill certain conditions, but these conditions do not often determine a singular point but rather a set of points forming a line. (For instance, the center of a circle is a focus, and all points equidistant from it is both the circumference of the circle and also the locus of points for that criterion.) Pallas is saying that when you ask for a different condition in the world, like Sextus not going to Rome, then you have defined a whole range of alternative possibilities. She will now show this ranging of various Sextuses.

You see here the palace of the fates, where I keep watch and ward. Here are representations not only of that which happens but also of all that which is possible. Jupiter, having surveyed them before the beginning of the existing world, classified the possibilities into worlds, and chose the best of all. He comes sometimes to visit these places, to enjoy the pleasure of recapitulating things and of renewing his own choice, which cannot fail to please him. I have only to speak, and we shall see a whole world that my father might have produced, wherein will be represented anything that can be asked of him; and in this way one may know also what would happen if any particular possibility should attain unto existence. And whenever the conditions are not determinate enough, there will be as many such worlds differing from one another as one shall wish, which will answer differently the same question, in as many ways as possible. You learnt geometry in your youth, like all well-instructed Greeks. You know therefore that when the conditions of a required point do not sufficiently determine it, and there is an infinite number of them, they all fall into what the geometricians call a locus, and this locus at least (which is often a line) will be determinate. Thus you can picture | to yourself an ordered succession of worlds, which shall contain each and every one the case that is in question, and shall vary its circumstances and its consequences. But if you put a case that differs from the actual world only in one single definite thing and in its results, a certain one of those determinate worlds will answer you. These worlds are all here, that is, in ideas. I will show you some, wherein shall be found, not absolutely the same Sextus as you have seen (that is not possible, he carries with him always that which he shall be) but several Sextuses resembling him, possessing all that you know already of the true Sextus, but not all that is already in him imperceptibly, nor in consequence all that shall yet happen to him. You will find in one world a very happy and noble Sextus, in another a Sextus content with a mediocre state, a Sextus, indeed, of every kind and endless diversity of forms.

(475-476)

(3.415) Pallas takes Theodorus to one of the hall’s in the palace of fates, which displays a whole complete world. In this one, Sextus obeys Jupiter, goes off to a place like Corinth, cultivates a garden, finds treasure, is loved by the city, and dies old. In the hall is this particular world’s book of fate. Sextus has a number on his head. Theodorus follows Pallas’ instruction to find that number in the book, where he finds a more extensive account of this Sextus’ life. Pallas explains that he only needs to point to a line of the text, and its story will come to life. This way, he could see all the characteristics of some part of Sextus’ life. Next they go to another hall, which displays a different possible world. Here, there is another Sextus who also obeys Jupiter, but this time he goes instead to Thrace where he marries the king’s daughter, succeeds the king, and is adored by the subjects. Theodorus and Pallas go to a number of rooms, each time with another possible world and life for Sextus. (3.416) The halls are stacked in the form of a pyramid, with them being better and better worlds as one gets higher and with the one at the apex being the best possible world that Jupiter/God therefore chose as the existing one. But even though there is a certain apex world, the pyramid has no bottom, because the worlds degrade infinitely going down. In the best possible world, Sextus is displayed as he actually is. He goes to Rome, creates confusion and violates his friend’s wife and is then driven out of Rome, beaten and unhappy. But even though choosing that world would have made a happy Sextus, God could not choose it, because then God would be renouncing God’s divine wisdom (which calls him to choose the best of all possible worlds.) So in order to make Sextus actual, he had to choose a world where he was wicked. (For, suppose he did not choose that world; he would either choose no world or a less perfect one. But God is wise and cannot choose a less perfect world. So God must choose the world where Sextus is wicked.) This means that “The crime of Sextus serves for great things: it renders Rome free; thence will arise a great empire, which will show noble examples to mankind.” (So it comes back to God being responsible for Sextus’ wickedness, but God had no better alternative options in the matter.)

The halls rose in a pyramid, becoming even more beautiful as one mounted towards the apex, and representing more beautiful worlds. Finally they reached the highest one which completed the pyramid, and which was the most beautiful of all: for the pyramid had a beginning, but one could not see its end; it had an apex, but no base; it went on increasing to infinity. That is (as the Goddess explained) because amongst an endless number of possible worlds there is the best of all, else would God not have determined to create any; but there is not any one which has not also less perfect worlds below it: that is why the pyramid goes on descending to infinity. Theodorus, entering this highest hall, became entranced in ecstasy; he had to receive succour from the Goddess, a drop of a divine liquid placed on his tongue restored him; he was beside himself for joy. We are in the real true world (said the Goddess) and you are at the source of happiness. Behold what Jupiter makes ready for you, if you continue to serve him faithfully. Here is Sextus as he is, and as he will be in reality. He issues from the temple in a rage, he scorns the counsel of the Gods. You see him going to Rome, bringing confusion everywhere, violating the wife of his friend. There he is driven out with his father, beaten, unhappy. If Jupiter had placed here a Sextus happy at Corinth or King in Thrace, it would be no longer this world. And nevertheless he could not have failed to choose this world, which surpasses in perfection all the others, and which forms the apex of the pyramid. Else would Jupiter have renounced his wisdom, he would have banished me, me his daughter. You see that my father did not make Sextus wicked; he was so from all eternity, he was so always and freely. My father only granted him the existence which his wisdom could not refuse to the world where he is included: he made him pass from the region of the possible to that of the actual beings. The crime of Sextus serves for great things: it renders Rome free; thence will arise a great empire, which will show noble examples to mankind. But that | is nothing in comparison with the worth of this whole world, at whose beauty you will marvel, when, after a happy passage from this mortal state to another and better one, the Gods shall have fitted you to know it.

(377-378)

(3.417) Theodorus awakes from this dream being even more convinced of his beliefs, and he carries out his priestly duties zealously. Leibniz explains that this Sextus story fills out what is missing in Valla’s dialogue. Valla discussed God’s knowledge of vision (of the future) which concerns beings that exist. But Pallas shows knowledge of simple intelligence, which embraces all that is possible (that is, knowledge not just of the existing world but of all other possibilities). Leibniz ends by saying that the source of things should be sought in this second kind of knowledge.

 

 

 

 

 

Contents

 

3.405

[Using the Laurentius Valla Dialogue on Freedom]

 

3.406

[Laurentius’ Agreement to Answer]

 

3.407

[Knowledge as Having No Power to Cause Existence, Particularly Knowledge of the Future]

 

3.408

[The Foreknown as Certain but Not Necessary]

 

3.409

[Apollo’s Foreknowledge of Sextus Tarquinius’s Crimes as Not Causing Them]

 

3.410

[Sextus as Having the Hope or Intention to Change His Ways but Still Failing to Do So]

 

3.411

[The Crime as Seeming to Lie with Jupiter and Not Sextus]

 

3.412

[Our Inability to Know Why God Treats Some People Badly and the Need to Simply Trust that God Is Being Good Nonetheless]

 

3.413

[Theodorus as Being the One Who Will Learn Why God Must Make Some People Wicked]

 

3.414

[Jupiter’s Daughter Pallas as Guarding the Palace of Fates, Which Holds Every Alternative Fate for the World]

 

3.415

[The Different Rooms with Different Worlds, Fates, and Sextuses]

 

3.416

[The Best of All Possible Worlds is One Where Some People Are Made as Wicked and Suffer]

 

3.417

[God’s Foreknowledge as Being More Than Mere Foreseeing the Events of This World but Instead as Knowing all Events in All Worlds]

 

 

 

 

 

 

 

Summary

 

3.405

[Using the Laurentius Valla Dialogue on Freedom]

 

[Leibniz begins with Laurentius Valla’s Dialogue on Free Will (between Antonio Glarea and Laurentius), to set up a discussion about divining and freedom.]

 

[Leibniz will give comments on free will contra Boethius. He will do it by quoting in the abstract a dialogue, Laurentius Valla’s Dialogue on Free Will. In it, a Spaniard named Antonio Glarea asks Laurentius to elaborate on the difficulty of free will, because justice and injustice, punishment and reward, in this life and the next, depend upon it.  Laurentius’ point is that we must accept that we have a certain ignorance with regard to free will, and we must come to terms with it like how we must accept that we do not wave the wings of birds. (Note: In the following quotations, “Ant.” is for Antonio and “Laur.” is for Laurentius.)]

405. I intended to finish here after having met (as it seems to me) all the objections of M. Bayle on this matter that I could find in his works. But remembering Laurentius Valla’s Dialogue on Free Will, in opposition to Boethius, which I have already mentioned, I thought it would be opportune to quote it in abstract, retaining the dialogue form, and then to continue from where it ends, keeping up the fiction it initiated; and that less with the purpose of enlivening the subject, than in order to explain myself towards the end of my dissertation as clearly as I can, and in a way most likely to be generally understood. This Dialogue of Valla and his books on Pleasure and the True Good make it plain that he was no less a philosopher than a humanist. These four books were opposed to the four books on the Consolation of Philosophy by Boethius, and the Dialogue to the fifth book. A certain Spaniard named Antonio Glarea requests of him elucidation on the difficulty of free will, whereof little is known as it is worthy to be known, for upon it depend justice and injustice, punishment and reward in this life and in the life to come. Laurentius Valla answers him that we must console ourselves for an ignorance which we share with the whole world, just as one consoles oneself for not having the wings of birds.

(370)

[contents]

 

 

 

 

 

 

3.406

[Laurentius’ Agreement to Answer]

 

[Laurentius will explain how divine foreknowledge can be compatible with human freedom. But he requires that Antonio be satisfied with his answer.]

 

[Antonio references Boethius and says we can still obtain wings like Daedalus, and so please enlighten us a little about free will, Laurentius. Specifically, we want to know how to reconcile foreknowledge with freedom. Laurentius agrees to give an answer, so long as Antonio makes his curiosities satisfied with it and will not ask another question after it.]

406. Antonio—I know that you can give me those wings, like another Daedalus, so that I may emerge from the prison of ignorance, and rise to the very region of truth, which is the homeland of souls. The books that I have seen have not satisfied me, not even the famous Boethius, who meets with general approval. I know not whether he fully understood himself what he says of God’s understanding, and of eternity superior to time; and I ask for your opinion on his way of reconciling foreknowledge with freedom. Laurent—I am fearful of giving offence to many people, | if I confute this great man; yet I will give preference over this fear to the consideration I have for the entreaties of a friend, provided that you make me a promise. ant.—What? Laur.—It is, that when you have dined with me you do not ask me to give you supper, that is to say, I desire that you be content with the answer to the question you have put to me, and do not put a further question.

(370-371)

[contents]

 

 

 

 

 

 

3.407

[Knowledge as Having No Power to Cause Existence, Particularly Knowledge of the Future]

 

[Antonio argues that since God foresaw Judas betray, that means Judas could not have done otherwise and thus is blameless. Laurentius replies that mere knowledge itself cannot cause things past or present to exist; therefore, knowledge cannot cause future things to exist.]

 

[Antonio states the crux of the problem with the example of Judas. Suppose God foresaw Judas committing treason. If God foresaw it, then it is necessary that Judas betray (because God cannot be wrong, including about the future, so it cannot be otherwise), and thus it is impossible for Judas not to betray. Now, since there is no obligation to do the impossible, Judas did not sin (having not broken any obligation even in having betrayed), and thus he did not deserve to be punished. So generally speaking, if God foresees such things, then there is no justice or religion and no fear of God. Laurentius replies that even though God foresaw the sin, he did not compel people to commit the sin. For, sin is voluntary. Antonio restates that since the will to sin was foreseen, it was necessary. Laurentius replies that knowledge cannot cause things past or present to exist, therefore, knowledge cannot cause future things to exist. ]

Ant.—I promise you. Here is the heart of the difficulty. If God foresaw the treason of Judas, it was necessary that he should betray, it was impossible for him not to betray. There is no obligation to do the impossible. He therefore did not sin, he did not deserve to be punished. That destroys justice and religion, and the fear of God. Laur.—God foresaw sin; but he did not compel man to commit it; sin is voluntary. Ant.—That will was necessary, since it was foreseen. Laur.—If my knowledge does not cause things past or present to exist, neither will my foreknowledge cause future things to exist.

(371)

[contents]

 

 

 

 

 

 

3.408

[The Foreknown as Certain but Not Necessary]

 

[Laurentius makes a couple distinctions. {1} Foretelling vs. foreknowing. Antonio gives an example where he asks a heathen god which foot he will put forward, then he puts the opposite foot forward (Laurentius explains here that either the god would not foretell, or if he would, then we should expect Antonio to obey the foretelling). {2} Regarding foreknowledge: the necessary vs. the certain. Events that are foreseen could have been otherwise (as their alternatives do not create logical contradictions) and thus they are not necessary, but it is certain they will happen (as they have been chosen by God in advance).]

 

[Antonio tries to show that were the future foreknown, it is fixed and necessary. (But his illustration is odd, because it seems to show a different point, namely, that the future cannot be foreknown.) We think of a heathen god who claims to know the future. We ask, which foot will we put forward? Whichever he foretells, we do the opposite. Laurentius says that there is a false supposition here, namely, that God would answer Antonio’s question in the first place; and if He did, then Antonio would obey Him. But at any rate, Laurentius says, we have changed the issue here, because now we are speaking about foretelling rather than foreknowing. For foreknowledge, we must distinguish the necessary from the certain. “It is not impossible for what is foreseen not to happen; but it is infallably certain that it will happen. I can become a Soldier or Priest, but I shall not become one.”]

408. Ant.—That comparison is deceptive: neither the present nor the past can be changed, they are already necessary; but the future, movable in itself, becomes fixed and necessary through foreknowledge. Let us pretend that a god of the heathen boasts of knowing the future: I will ask him if he knows which foot I shall put foremost, then I will do the opposite of that which he shall have foretold. Laur.—This God knows what you are about to do. Ant.—How does he know it, since I will do the opposite of what he shall have said, and I suppose that he will say what he thinks? Laur.—Your supposition is false: God will not answer you; or again, if he were to answer you, the veneration you would have for him would make you hasten to do what he had said; his prediction would be to you an order. But we have changed the question. We are not concerned with what God will foretell but with what he foresees. Let us therefore return to foreknowledge, and distinguish between the necessary and the certain. It is not impossible for what is foreseen not to happen; but it is infallibly sure that it will happen. I can become a Soldier or Priest, but I shall not become one.

(371)

[contents]

 

 

 

 

 

 

3.409

[Apollo’s Foreknowledge of Sextus Tarquinius’s Crimes as Not Causing Them]

 

[Laurentius says that “Two contradictories are often both possible” (p.372).” He next illustrates why foreknowledge is not causal with a story about Sextus Tarquinius. Sextus goes to the Oracle of Apollo for a prediction. Apollo says that he will die poor and in exile. Sextus objects, asking why Jupiter would be so cruel in choosing for him such a bad fate, when he is innocent and devout. Apollo replies that Sextus will later be proud, adulterous, and a traitor to his country. Antonio agrees that Sextus cannot accuse Apollo of causing these things by foreseeing them. Similarly, Laurentius concludes, Judas cannot complain about God’s foreknowledge of his crimes.]

 

[Antonio says that “The philosophers’ rule maintains that all that which is possible can be considered as existing.” [(Antonio’s idea might be the following, but I am not certain. He might be appealing to Diodorus’ Master Argument. Quoting Epictetus (and note the final sentence):

The ‘Master’ argument appears to have been proposed on the basis of some such principles as these. Of the following propositions, any two imply a contradiction to the third. They are these. That everything that has happened is necessarily true; that the impossible cannot be a consequence of the possible; and that something is a possibility which neither is nor ever will be true. Diodorus, perceiving this contradiction, made use of the probability of the two first to demonstrate this conclusion: nothing is possible which neither is nor ever will be true.

(Epictetus 1995: 122, boldface mine. See Long trans at Perseus)

) Antonio next says: “But if that which you affirm to be possible, namely an event different from what has been foreseen, actually happened, God would have been mistaken.” (Maybe the idea here is the following. Assume God cannot be mistaken. So whatever God foresees must happen. We want to know if there can be more than one possible future and thus if there can be freedom. We established (the Diodorus Master Argument idea) that whatever is possible must exist (and so the only possible outcomes are the ones that in fact will come about, and their alternatives were thus never possible). But if we affirm that one of two alternatives is possible but it does not happen, then that means something which is possible (and thus that will happen) in fact did not happen, and (supposing God foresaw it) than God was mistaken. (So, since God cannot be mistaken, it cannot be that anything deemed possible does not happen. So only one thing can happen, with the alternative options being impossible, and thus we have no freedom, because we have no options or choices to make. I am guessing this is a Master sort of argument like this, but I am not sure. Please see the quotation below.) Laurentius replies that “The rules of the philosophers are not oracles for me. This one in particular is not correct.” (Maybe he is saying that he does not accept Diodorus’ assumptions, because they are wrong.) For, he continues: “Two contradictories are often both possible.” Laurentius then wonders if two contradictories can both exist. (As we will see, it seems they cannot both exist, but they can coincide as possible worlds.) He then begins a story of Sextus Tarquinius (wiki), who comes to Delphi to consult the Oracle of Apollo. The oracle says, “Exul inopsque cades irata pulsus ab urbe (You will die poor and in exile, driven in anger from your fatherland). A beggared outcast of the city’s rage, Beside a foreign shore cut short thy age.” Sextus is disappointed. Apollo says he is merely foretelling what will happen; he is not causing it to come about. Apollo says that if Sextus has any complaints, he should take them to Jupiter and the Parcae (the fates). So, Laurentius says, Sextus would be ridiculous if he continued to complain to Apollo. Antonio says that Sextus will ask why Jupiter would be so cruel, when he is innocent and devout. Laurentius explains that Apollo would reply that Sextus will later be proud, adulterous, and a traitor to his country. Antonio agrees that Sextus cannot accuse Apollo of causing these things by foreseeing them. Similarly, Laurentius concludes, Judas cannot complain about God’s foreknowledge of his crimes.]

Ant.—Here I have you firmly held. The philosophers’ rule maintains that all that which is possible can be considered as existing. But if that which you affirm to be possible, namely an event | different from what has been foreseen, actually happened, God would have been mistaken. Laur.—The rules of the philosophers are not oracles for me. This one in particular is not correct. Two contradictories are often both possible. Can they also both exist? But, for your further enlightenment, let us pretend that Sextus Tarquinius, coming to Delphi to consult the Oracle of Apollo, receives the answer:

Exul inopsque cades irata pulsus ab urbe.

A beggared outcast of the city’s rage,

Beside a foreign shore cut short thy age.

The young man will complain: I have brought you a royal gift, O Apollo, and you proclaim for me a lot so unhappy? Apollo will say to him: Your gift is pleasing to me, and I will do that which you ask of me, I will tell you what will happen. I know the future, but I do not bring it about. Go make your complaint to Jupiter and the Parcae. Sextus would be ridiculous if he continued thereafter to complain about Apollo. Is not that true? Ant.—He will say: I thank you, O holy Apollo, for not having repaid me with silence, for having revealed to me the Truth. But whence comes it that Jupiter is so cruel towards me, that he prepares so hard a fate for an innocent man, for a devout worshipper of the Gods? Laur.—You innocent? Apollo will say. Know that you will be proud, that you will commit adulteries, that you will be a traitor to your country. Could Sextus reply: It is you who are the cause, O Apollo; you compel me to do it, by foreseeing it? Ant.—I admit that he would have taken leave of his senses if he were to make this reply. Laur.—Therefore neither can the traitor Judas complain of God’s foreknowledge. And there is the answer to your question.

(371-372)

[contents]

 

 

 

 

 

 

3.410

[Sextus as Having the Hope or Intention to Change His Ways but Still Failing to Do So]

 

[Laurentius continues the story. Sextus tells Apollo he will not commit the foretold crimes, and he will appeal to the Gods to give him a better heart. Nonetheless, Apollo will notify Sextus that the Gods make creatures with their given traits. The ass is stupid, the lion is courageous, etc. They gave Sextus a wicked soul, and he will act in conformity with his natural disposition; and, Jupiter will accordingly punish his wicked actions.]

 

[Antonio is now satisfied with Laurentius’ reply and story. But Laurentius says they should take the story a little further. We now suppose that Sextus will tell Apollo that he will not commit the foretold crimes. Antonio says that God (Apollo) would then proclaim that he is not a liar and that Sextus will in fact do the foretold things. Laurentius then claims that Sextus may try to alter his fate by praying to the Gods and asking them to give him a better heart. Antonio says that the answer the Gods would give him is that they cannot make God’s foreknowledge be a lie (Desine fata Deum flecti sperare precando / Hope not that the fates of the gods may be turned aside by prayers. (Virgil, Aeneid, VI, 376)), and so there is nothing they can do to change his fate. And thus Sextus would complain that therefore he is not free, and it is not in his power to follow virtue. Laurentius says that Apollo would tell Sextus that the Gods make creatures with their given traits. The ass is stupid, the lion is courageous, etc. They gave Sextus a wicked soul, and he will act in conformity with his natural disposition; and, Jupiter will accordingly punish his wicked actions.]

Ant.—You have satisfied me beyond my hopes, you have done what Boethius was not able to do: I shall be beholden to you all my life long. Laur.—Yet let us carry our tale a little further. Sextus will say: No, Apollo, I will not do what you say. Ant.—What! the God will say, do you mean then that I am a liar? I repeat to you once more, you will do all that I have just said. Laur.—Sextus, mayhap, would pray the Gods to alter fate, to give him a better heart. Ant.—He would receive the answer: |

Desine fata Deum flecti sperare precando.

He cannot cause divine foreknowledge to lie. But what then will Sextus say? Will he not break forth into complaints against the Gods? Will he not say? What? I am then not free? It is not in my power to follow virtue? Laur.—Apollo will say to him perhaps: Know, my poor Sextus, that the Gods make each one as he is. Jupiter made the wolf ravening, the hare timid, the ass stupid, and the lion courageous. He gave you a soul that is wicked and irreclaimable; you will act in conformity with your natural disposition, and Jupiter will treat you as your actions shall deserve; he has sworn it by the Styx.

(472-473)

[contents]

 

 

 

 

 

 

3.411

[The Crime as Seeming to Lie with Jupiter and Not Sextus]

 

[Antonio objects that the real crime is caused by Jupiter for having created someone with a wicked nature who will certainly do wrong. Thus Sextus should not be blamed for Jupiter’s crime, as he cannot resist Jupiter’s will. Laurentius says he was able to show that foreknowledge is different from providence and that foreknowledge does not have any causal power. But he also says that he cannot know explain if and how providence restricts freedom.]

 

[Antonio then notes that the real crime lies in Jupiter for having created someone who will certainly be wicked. So there again is no grounds to punish Sextus, as he is the victim of Jupiter’s crimes, and Sextus is powerless to resist Jupiter’s will. Laurentius then notes that he cannot say much more here. He distinguished Apollo and Jupiter so to distinguish foreknowledge and providence. He has shown that foreknowledge does not impair freedom, but he cannot explain if and how providence does not impair freedom. Antonio notes that even though Laurentius helped with one matter, he created an equally intractable one that still needs resolution. Laurentius reminds Antonio about the agreement: Antonio must not ask further questions (so he cannot ask about providence and free will).]

Ant.—I confess to you, it seems to me that Apollo in excusing himself accuses Jupiter more than he accuses Sextus, and Sextus would answer him: Jupiter therefore condemns in me his own crime; it is he who is the only guilty one. He could have made me altogether different: but, made as I am, I must act as he has willed. Why then does he punish me? Could I have resisted his will? Laur.—I confess that I am brought to a pause here as you are. I have made the Gods appear on the scene, Apollo and Jupiter, to make you distinguish between divine foreknowledge and providence. I have shown that Apollo and foreknowledge do not impair freedom; but I cannot satisfy you on the decrees of Jupiter’s will, that is to say, on the orders of providence. Ant.—You have dragged me out of one abyss, and you plunge me back into another and greater abyss. Laur.— Remember our contract: I have given you dinner, and you ask me to give you supper also.

(372)

[contents]

 

 

 

 

 

 

3.412

[Our Inability to Know Why God Treats Some People Badly and the Need to Simply Trust that God Is Being Good Nonetheless]

 

[Laurentius explains that we will not know why God is hard against one person but compassionate towards another. We simply have to accept that God is very good and wise, and that is enough reason for us to deem his reasons as being good.]

 

[Antonio says that Laurentius deceived him. Laurentius admits that he has resorted to something that cannot be explained. But this is something we have to accept. We will not know why God is hard against one person but compassionate towards another. We simply have to accept that God is very good and wise, and that is enough reason for us to deem his reasons as being good. And moreover, God is just, because he makes it such that his decrees and operations do not destroy our freedom. We must think of Jesus Christ and put our trust in God’s divine mercy.]

Ant.—Now I discover your cunning: You have caught me, this is not an honest contract. Laur.—What would you have me do? I have given you wine and meats from my home produce, such as my small estate can provide; as for nectar and ambrosia, you will ask the Gods for them: that divine nurture is not found among men. Let us hearken to St. Paul, that chosen vessel who was carried even to the third heaven, who heard there unutterable words: he will answer you with the comparison of the potter, with the incomprehensibility of the ways of God, and wonder at the depth of his wisdom. Nevertheless it is well to observe that one does not ask why God foresees the thing, for that is understood, | it is because it will be: but one asks why he ordains thus, why he hardens such an one, why he has compassion on another. We do not know the reasons which he may have for this; but since he is very good and very wise that is enough to make us deem that his reasons are good. As he is just also, it follows that his decrees and his operation do not destroy our freedom. Some men have sought some reason therein. They have said that we are made from a corrupt and impure mass, indeed of mud. But Adam and the Angels were made of silver and gold, and they sinned notwithstanding. One sometimes becomes hardened again after regeneration. We must therefore seek another cause for evil, and I doubt whether even the Angels are aware of it; yet they cease not to be happy and to praise God. Boethius hearkened more to the answer of philosophy than to that of St. Paul; that was the cause of his failure. Let us believe in Jesus Christ, he is the virtue and the wisdom of God: he teaches us that God willeth the salvation of all, that he willeth not the death of the sinner. Let us therefore put our trust in the divine mercy, and let us not by our vanity and our malice disqualify ourselves to receive it.

(373-374)

[contents]

 

 

 

 

 

 

 

3.413

[Theodorus as Being the One Who Will Learn Why God Must Make Some People Wicked]

 

[Leibniz now speaks for himself rather than quoting the Laurentius dialogue. Leibniz notes that the dialogue’s defect is it condemns providence, as it makes Jupiter the author of sin. Leibniz now continues the story his own way. Sextus next goes to Jupiter and asks him why he condemned him to be wicked and unhappy, and Sextus asks Jupiter to fix his error and give him a fate where he becomes wise and happy. Jupiter says that Sextus can be wise and happy if he does not go to Rome and thus renounces his kingship. Sextus cannot give that up, so he accepts his doomed fate. Leibniz now adds a new character to the story, Theodorus, a high priest who has been listening to this story. Theodorus tells Jupiter that Jupiter’s worshippers are upset, because Jupiter is the one who decided to give Sextus his evil will (which resulted in him going to Rome even though he now knows it dooms him). Jupiter tells Theodorus that he should visit Jupiter’s daughter Pallas, because she will explain what Jupiter was bound to do when deciding Sextus’ will).]

 

[Now Leibniz is talking. He notes that this dialogue’s defect is it condemns providence, as it makes Jupiter the author of sin. So Leibniz will take the story a little further. Sextus leaves Apollo and Delphi and seeks out Jupiter at Dodona. He asks Jupiter, why have you condemned me to be wicked and unhappy? Change my fate and my heart, and acknowledge your error. Jupiter replies that if Sextus renounces Rome, the Parcae (the Fates) will spin him a different fate where he becomes wise and happy. (“Renouncing Rome” seems to mean not going there to become King and thus not committing his subsequent crimes.) Sextus then asks Jupiter, why do I need to renounce the hope of the crown? Why can I not be a good king? Jupiter says that he “knows what is needful for you”, and so if he goes to Rome, he is lost. (The idea might be that given Sextus’ nature, if he puts himself in that situation, he will certainly act wickedly. So he needs to remove himself from those influences in order to be good. This seems similar to Stoic co-fatality. See Goldschmidt Le système stoïcien et l'idée de temps section 2.1.4.3.49) Sextus could not sacrifice his hopes of becoming a king, so he accepts his fate. Now we have a new character, Theodorus, who is a high priest and who was listening to this discussion. Theodorus says to Jupiter that Jupiter shows that the unhappiness Sextus receives will be the result of his own evil will, and he no longer has any right to complain. But now, Theodorus continues, the followers of Jupiter are upset, because it was still Jupiter’s decision to have given Sextus this evil will to begin with rather than a better one. Jupiter then tells Theodorus that he should now visit Jupiter’s daughter Pallas, because she will explain what Jupiter was bound to do (when deciding Sextus’ will).]

This dialogue of Valla’s is excellent, even though one must take exception to some points in it: but its chief defect is that it cuts the knot and that it seems to condemn providence under the name of Jupiter, making him almost the author of sin. Let us therefore carry the little fable still further. Sextus, quitting Apollo and Delphi, seeks out Jupiter at Dodona. He makes sacrifices and then he exhibits his complaints. Why have you condemned me, O great God, to be wicked and unhappy? Change my lot and my heart, or acknowledge your error. Jupiter answers him: If you will renounce Rome, the Parcae shall spin for you different fates, you shall become wise, you shall be happy. Sextus—Why must I renounce the hope of a crown? Can I not come to be a good king? Jupiter—No, Sextus; I know better what is needful for you. If you go to Rome, you are lost. Sextus, not being able to resolve upon so great a sacrifice, went forth from the temple, and abandoned himself to his fate. Theodorus, the High Priest, who had been present at the dialogue between God and Sextus, addressed these words to Jupiter: Your wisdom is to be revered, O great Ruler of the Gods. You have convinced this man of his error; he must henceforth impute his unhappiness to his | evil will; he has not a word to say. But your faithful worshippers are astonished; they would fain wonder at your goodness as well as at your greatness: it rested with you to give him a different will. Jupiter—Go to my daughter Pallas, she will inform you what I was bound to do.

(374-375)

[contents]

 

 

 

 

 

 

3.414

[Jupiter’s Daughter Pallas as Guarding the Palace of Fates, Which Holds Every Alternative Fate for the World]

 

[Theodorus goes to Jupiter’s daughter Pallas. She watches and wards over the palace of fates. It contains not just the actual world, but every possible alternative fate. Jupiter picked the best one, and he  sometimes comes to admire his selection. So at the palace, we can see all the alternative twists in fate. And for any one person, there can be a variety of different lives, and thus there are many Sextuses. Pallas then makes a geometrical illustration for this structure of bifurcating worlds. A locus is a set of points that fulfill certain conditions, but these conditions do not often determine a singular point but rather a set of points forming a line. (For instance, the center of a circle is a focus, and all points equidistant from it is both the circumference of the circle and also the locus of points for that criterion.) Pallas is saying that when you ask for a different condition in the world, like Sextus not going to Rome, then you have defined a whole range of alternative possibilities. She will now show this ranging of various Sextuses.]

 

[Theodorus then goes to Athens, sleeps in the temple of the Goddess Pallas. In his dream, Pallas appears at the gate of a great palace, with the quote, Qualisque videri, Coelicolis et quanta solet: In the guise and grandeur in which she is wont to appear before the denizens of heaven. (Virgil, Aeneid, II, 591-592). She touches Theodorus’ face with an olive branch so he can converse with her. Pallas says to Theodorus that this is the palace of fates, and she keeps watch and ward over it.  In it are the representations not only of what happens, but also of all that which is possible. Jupiter surveyed all these possibilities at the beginning of the existing world, he classified the possibilities into worlds, and chose the best of all. He sometimes comes to the palace to enjoy his selection. So because we can also see whole alternate worlds with a different fates, we can know what would happen if any particular possibility should attain into existence. “And whenever the conditions are not determinate enough, there will be as many such worlds differing from one another as one shall wish, which will answer differently the same question, in as many ways as possible.” (So if in the alternate one change somewhere along the line creates a path that itself admits of further determinations and thus many further alternative outcomes, then we can see all those ramifying possibilities too.) Pallas then makes a geometrical illustration for this structure of bifurcating worlds. A locus is a set of points that fulfill certain conditions, but these conditions do not often determine a singular point but rather a set of points forming a line. (For instance, the center of a circle is a focus, and all points equidistant from it is both the circumference of the circle and also the locus of points for that criterion.) Pallas is saying that when you ask for a different condition in the world, like Sextus not going to Rome, then you have defined a whole range of alternative possibilities. She will now show this ranging of various Sextuses.]

Theodorus journeyed to Athens: he was bidden to lie down to sleep in the temple of the Goddess. Dreaming, he found himself transported into an unknown country. There stood a palace of unimaginable splendour and prodigious size. The Goddess Pallas appeared at the gate, surrounded by rays of dazzling majesty.

Qualisque videri

Coelicolis et quanta solet.

She touched the face of Theodorus with an olive-branch, which she was holding in her hand. And lo! he had become able to confront the divine radiancy of the daughter of Jupiter, and of all that she should show him. Jupiter who loves you (she said to him) has commended you to me to be instructed. You see here the palace of the fates, where I keep watch and ward. Here are representations not only of that which happens but also of all that which is possible. Jupiter, having surveyed them before the beginning of the existing world, classified the possibilities into worlds, and chose the best of all. He comes sometimes to visit these places, to enjoy the pleasure of recapitulating things and of renewing his own choice, which cannot fail to please him. I have only to speak, and we shall see a whole world that my father might have produced, wherein will be represented anything that can be asked of him; and in this way one may know also what would happen if any particular possibility should attain unto existence. And whenever the conditions are not determinate enough, there will be as many such worlds differing from one another as one shall wish, which will answer differently the same question, in as many ways as possible. You learnt geometry in your youth, like all well-instructed Greeks. You know therefore that when the conditions of a required point do not sufficiently determine it, and there is an infinite number of them, they all fall into what the geometricians call a locus, and this locus at least (which is often a line) will be determinate. Thus you can picture | to yourself an ordered succession of worlds, which shall contain each and every one the case that is in question, and shall vary its circumstances and its consequences. But if you put a case that differs from the actual world only in one single definite thing and in its results, a certain one of those determinate worlds will answer you. These worlds are all here, that is, in ideas. I will show you some, wherein shall be found, not absolutely the same Sextus as you have seen (that is not possible, he carries with him always that which he shall be) but several Sextuses resembling him, possessing all that you know already of the true Sextus, but not all that is already in him imperceptibly, nor in consequence all that shall yet happen to him. You will find in one world a very happy and noble Sextus, in another a Sextus content with a mediocre state, a Sextus, indeed, of every kind and endless diversity of forms.

(475-476)

[contents]

 

 

 

 

 

 

3.415

[The Different Rooms with Different Worlds, Fates, and Sextuses]

 

[Pallas takes Theodorus to one of the hall’s in the palace of fates, which displays a whole complete world. In this one, Sextus obeys Jupiter, goes off to a place like Corinth, cultivates a garden, finds treasure, is loved by the city, and dies old. In the hall is this particular world’s book of fate. Sextus has a number on his head. Theodorus follows Pallas’ instruction to find that number in the book, where he finds a more extensive account of this Sextus’ life. Pallas explains that he only needs to point to a line of the text, and its story will come to life. This way, he could see all the characteristics of some part of Sextus’ life. Next they go to another hall, which displays a different possible world. Here, there is another Sextus who also obeys Jupiter, but this time he goes instead to Thrace where he marries the king’s daughter, succeeds the king, and is adored by the subjects. Theodorus and Pallas go to a number of rooms, each time with another possible world and life for Sextus.]

 

[The Goddess Pallas then leads Theodorus to a hall of the palace, which is no longer a hall, but a world, with the quotation Solemque suum, sua sidera norat: A sun of its own it knew, and stars of its own. Here, Sextus obeys Jupiter and goes to some city resembling Corinth between two seas; he cultivates a garden and discovers treasure, is esteemed and beloved by the city, dying old. Theodorus sees Sextus’ life unfold like a stage production. Theodorus then notes a great volume of writings in this hall. Pallas explains that it is the history of this world; it is its book of fates. Sextus had a number on his head. Pallas says, look for that number in the book. Theodorus does that, and he finds an even more extensive history of this Sextus’ life. Pallas then says that Theodorus need only point to a line of text, and its story will come to life, and so by pointing to one, he saw all the characteristics of one particular part of Sextus’ life. They then go to another hall, which presents another possible world. Here there is another Sextus who also obeys Jupiter, and he goes to Thrace. There he marries the king’s daughter, succeeds the king, and is adored by the subjects. Theodorus and Pallas go to a number of rooms, each time with another possible world and life for Sextus.]

Thereupon the Goddess led Theodorus into one of the halls of the palace: when he was within, it was no longer a hall, it was a world,

Solemque suum, sua sidera norat.

At the command of Pallas there came within view Dodona with the temple of Jupiter, and Sextus issuing thence; he could be heard saying that he would obey the God. And lo! he goes to a city lying between two seas, resembling Corinth. He buys there a small garden; cultivating it, he finds a treasure; he becomes a rich man, enjoying affection and esteem; he dies at a great age, beloved of the whole city. Theodorus saw the whole life of Sextus as at one glance, and as in a stage presentation. There was a great volume of writings in this hall: Theodorus could not refrain from asking what that meant. It is the history of this world which we are now visiting, the Goddess told him; it is the book of its fates. You have seen a number on the forehead of Sextus. Look in this book for the place which it indicates. Theodorus looked for it, and found there the history of Sextus in a form more ample than the outline he had seen. Put your finger on any line you please, Pallas said to him, and you will see represented actually in all its detail that which the line broadly indicates. He obeyed, and he saw coming into view all the characteristics of a portion of the life of | that Sextus. They passed into another hall, and lo! another world, another Sextus. who, issuing from the temple, and having resolved to obey Jupiter, goes to Thrace. There he marries the daughter of the king, who had no other children; he succeeds him, and he is adored by his subjects. They went into other rooms, and always they saw new scenes.

(376-377)

[contents]

 

 

 

 

 

 

3.416

[The Best of All Possible Worlds is One Where Some People Are Made as Wicked and Suffer]

 

[The halls are stacked in the form of a pyramid, with them being better and better worlds as one gets higher and with the one at the apex being the best possible world that Jupiter/God therefore chose as the existing one. But even though there is a certain apex world, the pyramid has no bottom, because the worlds degrade infinitely going down. In the best possible world, Sextus is displayed as he actually is. He goes to Rome, creates confusion and violates his friend’s wife and is then driven out of Rome, beaten and unhappy. But even though choosing that world would have made a happy Sextus, God could not choose it, because then God would be renouncing God’s divine wisdom (which calls him to choose the best of all possible worlds.) So in order to make Sextus actual, he had to choose a world where he was wicked. (For, suppose he did not choose that world; he would either choose no world or a less perfect one. But God is wise and cannot choose a less perfect world. So God must choose the world where Sextus is wicked.) This means that “The crime of Sextus serves for great things: it renders Rome free; thence will arise a great empire, which will show noble examples to mankind.” (So it comes back to God being responsible for Sextus’ wickedness, but God had no better alternative options in the matter.)]

 

[The halls are stacked up into a pyramid, and as Theodorus and Pallas proceed through them, they ascend toward the structure’s apex, with each new hall representing yet a more beautiful world. Finally they reached the top one, which was the most beautiful of all. Such a best one is needed, for otherwise God would have no basis to choose one to be the existing world. (This is an important point as we will see. If there were no best possible world, there would be no basis to choose one, namely, that best one ((and note that Jupiter cannot choose more than one! There seems to be a non-contradiction constraint in Leibniz’s metaphysics)).) However, there are an infinity of lesser and lesser perfect worlds, so the pyramid, while having a determinate apex, had no ultimate base. When Theodorus enters this highest world, he is entranced in ecstasy, and Pallas needs to give him some divine medicine to restore him. Here we see Sextus as he actually is. He leaves the temple of Jupiter (or Apollo?) in rage and scorns the council of the gods. He goes to Rome, creating confusion and violating his friend’s wife. He is then driven out of Rome with his father, beaten and unhappy. Yet if Sextus were to be happy at Corinth or king of Thrace, it would no longer be this most perfect world but another, less perfect one, altogether. But even though choosing that world would have made a happy Sextus, God could not choose it, because then God would be renouncing God’s divine wisdom (which calls for God to choose the best of all possible worlds.) So in order to make Sextus actual, God had to choose a world where he was wicked. For, suppose God did not choose that world; God would either choose no world or a less perfect one. But God is wise and cannot choose a less perfect world. So God must choose the world where Sextus is wicked. (This seems similar to providence in Stoic theology. See for instance Goldschmidt, système stoïcien, section 2.1.4.1.37.5). This means that “The crime of Sextus serves for great things: it renders Rome free; thence will arise a great empire, which will show noble examples to mankind.” (So it comes back to God being responsible for Sextus’ wickedness, but God had no better alternative options in the matter.)]

The halls rose in a pyramid, becoming even more beautiful as one mounted towards the apex, and representing more beautiful worlds. Finally they reached the highest one which completed the pyramid, and which was the most beautiful of all: for the pyramid had a beginning, but one could not see its end; it had an apex, but no base; it went on increasing to infinity. That is (as the Goddess explained) because amongst an endless number of possible worlds there is the best of all, else would God not have determined to create any; but there is not any one which has not also less perfect worlds below it: that is why the pyramid goes on descending to infinity. Theodorus, entering this highest hall, became entranced in ecstasy; he had to receive succour from the Goddess, a drop of a divine liquid placed on his tongue restored him; he was beside himself for joy. We are in the real true world (said the Goddess) and you are at the source of happiness. Behold what Jupiter makes ready for you, if you continue to serve him faithfully. Here is Sextus as he is, and as he will be in reality. He issues from the temple in a rage, he scorns the counsel of the Gods. You see him going to Rome, bringing confusion everywhere, violating the wife of his friend. There he is driven out with his father, beaten, unhappy. If Jupiter had placed here a Sextus happy at Corinth or King in Thrace, it would be no longer this world. And nevertheless he could not have failed to choose this world, which surpasses in perfection all the others, and which forms the apex of the pyramid. Else would Jupiter have renounced his wisdom, he would have banished me, me his daughter. You see that my father did not make Sextus wicked; he was so from all eternity, he was so always and freely. My father only granted him the existence which his wisdom could not refuse to the world where he is included: he made him pass from the region of the possible to that of the actual beings. The crime of Sextus serves for great things: it renders Rome free; thence will arise a great empire, which will show noble examples to mankind. But that | is nothing in comparison with the worth of this whole world, at whose beauty you will marvel, when, after a happy passage from this mortal state to another and better one, the Gods shall have fitted you to know it.

(377-378)

[contents]

 

 

 

 

 

3.417

[God’s Foreknowledge as Being More Than Mere Foreseeing the Events of This World but Instead as Knowing all Events in All Worlds]

 

[Theodorus awakes from this dream being even more convinced of his beliefs, and he carries out his priestly duties zealously. Leibniz explains that this Sextus story fills out what is missing in Valla’s dialogue. Valla discussed God’s knowledge of vision (of the future) which concerns beings that exist. But Pallas shows knowledge of simple intelligence, which embraces all that is possible (that is, knowledge not just of the existing world but of all other possibilities). Leibniz ends by saying that the source of things should be sought in this second kind of knowledge.]

 

[(ditto).]

At this moment Theodorus wakes up, he gives thanks to the Goddess, he owns the justice of Jupiter. His spirit pervaded by what he has seen and heard, he carries on the office of High Priest, with all the zeal of a true servant of his God, and with all the joy whereof a mortal is capable. It seems to me that this continuation of the tale may elucidate the difficulty which Valla did not wish to treat. If Apollo has represented aright God’s knowledge of vision (that which concerns beings in existence), I hope that Pallas will have not discreditably filled the role of what is called knowledge of simple intelligence (that which embraces all that is possible), wherein at last the source of things must be sought.

(378)

[contents]

 

 

 

 

 

 

 

 

 

 

From:

 

Leibniz, Gottfried. 2007. Theodicy: Essays on the Goodness of God, the Freedom of Man and the Origin of Evil. English translation by E. Huggard. Charleston, S.C.: BiblioBazaar.

 

 

For Latin translations, I consulted also:

Jorgensen, L.M. 2008. “PHIL 375: Advanced History of Philosophy”. Available at:

https://docslide.net/documents/phil-375-advanced-history-of-philosophy-ljorgensteachrestheodicy-packetpdfleibnizs.html

and

Leibniz, Gottfried. Philosophical Writings. English translation by Mary Morris. London: Dent. New York: Dutton. Available at:

https://archive.org/details/in.ernet.dli.2015.214800

 

 

 

 

 

 

31 Mar 2015

Somers-Hall, (1.10), Deleuze’s Difference and Repetition, ‘1.10 Leibniz (43–4/54, 46–52/56–63)’, summary


by
Corry Shores
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[The following is summary. All boldface, underlining, and bracketed commentary are my own. Proofreading is incomplete, so please forgive my typos and other distracting mistakes. Somers-Hall is abbreviated SH.]



Summary of


Henry Somers-Hall


Deleuze’s Difference and Repetition:
An Edinburgh Philosophical Guide


Part 1
A Guide to the Text

 

Chapter 1. Difference in Itself

1.10 Leibniz (43–4/54, 46–52/56–63)





Brief summary:

Leibniz presents an infinite representational system. The world is composed of monads with predicates. This means the world takes on the subject-predicate structure of judgments, and is thus representational. Each monad is in some relation to every other monad, and these relations are expressed in a monad’s predicates. Therefore each monad expresses the world in its entirety. There are infinitely many monads, so there are infinitely many predicates for each one, and thus what each monad represents in its predication is infinite. Since we have a world of coexisting differences, we would think in Leibniz’ system that we might have non-oppositional difference. However, we have just one world with its own defined limits, since it stands opposed to other possible worlds that have inconsistencies and thus were not created. So while within this world there is non-oppositional difference, between this world and the others that God did not create there is in fact an oppositional difference.

 



Summary


[A while ago we examined Aristotle’s system of classification and definition. We examined the issue and problems of the highest genus or genera. Given that this is the most encompassing level of classification, we called it the Large, and problems regarding it we called the problems of the Large. In the prior section we saw Hegel’s infinite representation and dialectical movement. All categories of thought come about through this movement. The movement is somehow infinite. It is infinite either because it has no beginning or end (however, it would really seem to have a beginning and end, namely, indeterminate being and the absolute), or because at each stage there is a sort of unlimitedness. For example, at the beginning being and nothing seem to ceaselessly revolve one into the other in a movement that is genetic of a third concept, becoming (it is not clear to me if there are determinate stages and thus not endless interaction at each stage, or if it is one ceaseless interaction after another, all adding together and remaining in motion). At any rate, we need somehow to conclude that this dialectical movement is infinite. It is still representation, because it generates the categories of understanding that we use to make judgments, which have the form of representation. And also, we have a structure similar to the representational structure of genus-species. In Hegel we have something more like a process-product or pattern-instance structure. This is as clear as I can conceive matters at this point, but surely there is a better explanation. It would seem that since Hegel is dealing with the movement that generates all categories, then we are dealing with the Large, that is, with something roughly equivalent to the most basic category. SH will then speak of “the notion of contradiction as the largest difference” (48). I am not entirely sure what is meant by “largest difference”, but perhaps it can be understood in this way. What makes the dialectic movement the largest is that it is inherent to each stage and each instance of production. Also, at each stage, contradiction is like a motive force in the movement. Since contradiction is a motive force at each stage and in each production, it is also ‘largest’ in that sense of being all-encompassing. At any rate, Hegel introduces the infinite into the Large by saying that somehow it is ceaseless. Each stage is finite, but the entire process is infinite. In that way, Hegel introduces the infinite into the finite. Leibniz will also introduce the infinite into the finite, but this time on the level of the Small, that is, of the individual rather then of the highest grouping.] Deleuze has a problem with understanding the world by means of judgments, which normally take the subject-predicate form [exactly what is wrong with representation seems just to be the unresolved problems it creates. I am not sure if there are any other motivations to oppose representation. For example, I am not sure if there is an anti-totalitarian political motivation to be against systems that organize all their parts around some fixed center of power and that use fixed meanings in symbolic language to convince people of the legitimacy of that centralized power.] Leibniz, [like Hegel and Aristotle, is a representational thinker, because he] “holds to the view that all truths take the form of subject-predicate judgements” (48). We already saw for example: “man is a rational animal”. [So the first step we are now taking in our thinking here is to claim that such predicative formulations can be true. The next step is to say that if they are true, then they correspond to some reality in the world, Thus,] this means that in reality, there are things which can take predicates, since they are things with properties. [We should distinguish the language of predication we are using here from the way we were using it for Aristotle (and Porphyry). In that prior case, we said that the genus serves as a predicate to its species: “man (species) is an animal (genus) that reasons (specific difference).” Now instead in this current section, we are not thinking of the genus being a predicate. Rather, we are thinking of specific things having properties, and those properties being ‘predicated’ to the thing. We might for example say something like, ‘This apple is red’. Here the ‘subject’ of the sentence is the individual apple, and its predicate is something like ‘has redness’ or ‘is a red thing’ or ‘is something which is red’ or just of course ‘is red’.]

At the beginning of this chapter, we saw how Deleuze’s central claim is that we need to find an alternative way of conceptualising the world to that provided by judgement. Now Leibniz holds to the view that all truths take the form of subject-predicate judgements: ‘In every categorical proposition (for from them I can show elsewhere that other kinds of propositions can be dealt with by changing a few things in the calculus) there are two terms, the subject and the predicate’ (Leibniz 1989b: 11). It is certainly the case that some truths take this form, such as the claim that ‘man is a rational animal’, or that ‘seven is a prime number’. If we hold that our judgements are able to accord with the world, then it is going to be the case that the basic elements of existence are also going to be substances of some form possessing properties (what Leibniz calls monads).
(SH 48)

[Now we will address a problem that arises were we to suppose all this that we said above. Some predicates place the subject into a reciprocal relation with another thing. For example, Paul is taller than Peter. Our basic claim is that there are individuals that have predicates. The problem here is apparently that reciprocal relations like this make it confusing which is the subject and which is the predicate, because our example sentence means the same as John is smaller than Paul. I do not understand exactly what the problem is yet. It seems we have two individuals, Paul and John, both of which have properties, being smaller or larger than the other. Why is it that if something is found in the predicate of something else, then it cannot itself be a subject with reciprocal properties? But we need to figure this out in order to proceed to the next idea. One reason I can think of is that for some reason being in another’s predicate is to eliminate one’s own individual existence. So we have monads. We assume Paul and Peter are monads. If we put Paul into the predicate of Peter, we either have two Paul’s, which is  impossible, or we removed Paul from the world of monads and inserted it into Peter. The other reason I can think of is that we are claiming that all things fit a subject-predicate judgment form without any ambiguity, but for relational predicates there is no clear subject. Again, it is still not evident to me why even under this assumption we cannot have two clearly discernible individuals, Peter and Paul, both having a predicate that places each in relation to the other. Maybe the problem is that there is one relation but it is expressed with two different and opposite predicates. There is just one relation of largerness/smallerness between Peter and Paul, so there should be just one predicate for some reason, but in fact we have two. Still it is unclear why one relation cannot have two expressions depending on the perspective taken. There must be some better reason to explain the problem here. We have to assume it is a problem for all relational predicates, which include cause and effect. For, if x is the effect of y, then y is the cause of x. Which then is the subject (assuming there can only be one for each relation). We are going with this idea that this is so problematic as to call into question the viability of the judgment of cause and effect, and thus somehow no objects can be understood as causes of any other objects. This is very interesting, but I cannot grasp the reasoning for it yet.]

If we see the basic substances in existence as purely defined in terms of substances and properties, however, we encounter a problem when we deal with relations between substances, since these don’t seem to fit this structure. If we say, for instance, that ‘Paul is taller than John’, then it doesn’t seem clear what is the subject and what is the predicate (we might want to say that ‘Paul’ is the subject, and ‘is taller than John’ is the property, but what about if we rephrase the proposition as ‘John is shorter than Paul’?). Similarly, relations of cause and effect seem to involve two subjects and a relation between them. If all propositions can be reduced to judgements, therefore, we seem to be left with a world of non-causally interacting entities – ‘the monads have no windows through which something can enter or leave’ (Leibniz 1989a: §7).
(SH 48)

We now need to explain two problems. 1) [For the first problem, we are working with the notion that we cannot explain causality on the basis of relations. This still is not evident to me why, but it has something to do with the fact that our mode of subject-predicate judgment fails with reciprocal relations like cause-effect. X has the predicate ‘causes y.’ Y has the predicate, ‘is the effect of x. The claim is that we cannot answer, who is the subject? It cannot be X, since for the same relation, Y is also the subject when the relation is reformulated. For some reason, they both cannot be subjects even though they both are monads and even though there are no logical inconsistencies in these reciprocal formulations. At any rate, the first problem requires two ideas, a) we cannot explain causal interactions on the basis of relations between causing things and effected things, and b) the world is a system of causality that needs to be explained.] “First, how do we explain interactions without relations, given that we appear to live in a world of causally interacting substances” (48d). [SH will then tell us what the solution is, but I am unable to grasp it very well right now. The conclusion we will arrive at is that all things will contain relational properties to all other things, including causal relations. The way we get to this conclusion is by recognizing the above point that we have causality but we cannot understand causal interaction using the notion of relations. I do not grasp yet how this inference is made. If I wanted to come to this conclusion, I think I would first recognize that there are predicates expressing reciprocal relations, then next I would establish that for certain reasons all things in one way or another relate to all other things. One possible way are spatial relations of physical things. Each monad, if it lies in space, is to one side or another of some other monad, which is to one side or another of some other, and all are somehow spatially related. Another would be to see everything in the world as in a system of physical causality, where on the local level there are proximate causal interactions, but given that chains of effects spread that influence throughout the system, all things are either directly or indirectly related causally. I will quote.]

We now have to deal with two problems. First, how do we explain interactions without relations, given that we appear to live in a world of causally interacting substances; and second, how do we differentiate different monads? The solution to the first problem is to see each of these monads as somehow containing the relations between different substances as properties. This | means that ‘taller than John’ will be a property of Paul, and ‘shorter than Paul’ will be a property of John. If causal interactions are going to be understood purely as properties of each subject, then each monad will have to contain all of its causal interactions with the rest of the world. Leibniz therefore writes that [the following up to citation is Leibniz quotation]:

This interconnection or accommodation of all created things to each other, and each to all others, brings it about that each simple substance has relations that express all the others, and consequently, that each simple substance is a perpetual, living mirror of the universe. (Leibniz 1989a: §56)
(SH 48-49)

[So, by means of relational predicates, each smallest individual in the world express the entirety of the all other individuals in the world. [It seems we also assume that the world is infinite, thus] the infinite in a sense is contained in each monad. [Now, since each such relation is a relation of difference,] all the world’s difference in all its variety is contained in each smallest part.

Each monad is therefore made up of an infinite number of properties which together describe the totality of what would be its relations with the universe, and hence, in a sense, the universe itself. To this extent, the infinite, in the sense of even the smallest elements of the universe, is contained within each monad. The whole variety of difference is therefore brought into the notion of the essence of each particular monad. Deleuze writes that: ‘The inessential here refers not to that which lacks importance but, on the contrary, to the most profound, to the universal matter or continuum from which essences are finally made’ (DR 47/58).
(SH 49)

2) [The reasoning for the next problem is also a little hard for me to grasp. It seems like it goes like this. Suppose that each monad contains relational predicates that express its relation to every other part of the world, that is, to every other monad. Each one expresses the world in its entirety. Perhaps somehow then there is no way to distinguish each monad, since they all express exactly the same thing, the whole world. To continue our reasoning, recall the specific relational predicate Peter is taller than Paul. There is just one relation of size comparison between them, but two predicates, ‘is taller than’ and ‘is smaller than’. Both Peter and Paul can be the subject, so which is the subject? Well, it depends on which perspective you take. If we take Paul’s perspective, we make him the subject, and the appropriate predicates follow, and likewise for Peter. So return to the idea that each monad expresses every relation with every other monad. Each relation can put one or another monad as the predicate. Perhaps the idea is that if we take one monad and all its predicates, we can reexpress those predicates such that they become identical to the predicates of any of the other monads. Think of the simple world where there are just two monads, Peter and Paul.

(Peter > Paul) = (Paul < Peter).

So Peter can have this predicate: Peter is taller than Paul

And Paul can have this predicate: Paul is smaller than Peter.

Yet, the inverse is true for both.

So Peter can keep his predication: Peter is taller than Paul.

And Paul can invert his predication: Paul is smaller than Peter. Peter is taller than Paul.

Now, think of a world with infinitely many monads. The predicates for each can be made identical with the predicates for any, and thus, all others. All relational predicates of all monads can be made identical. So for monads, what distinguishes them is not what their predicates express, since they all express the sum of all differences constituting the world; rather, what distinguishes them is each one’s unique perspective, which might orient all the predications such that instead of taking the above third personal form, they instead substantiate their own selves in the formulations in a first personal way. So for example, Peter’s predication might be “I (Peter) am taller that Paul”. And Paul would say “I (Paul) am shorter than Peter”. But Paul’s predication would never be: Peter is taller than Paul (like in our substitution above), since we are taking his perspective and not Peter’s and so Paul will take the subject place of the sentence. Now, we need somehow to get to an idea of the distinct and confused expression of relations. This part I cannot follow well. But it seems that from one monad’s particular perspective, one can have clear knowledge of how it interacts with those other monads it is directly in relation to, but confused knowledge of its relation to all the other monads it is only indirectly related to, as mediated through the transitive chain of relations between continguously related monads. Thus perhaps we may say now that what distinguishes each one on the level of their predicates is that each will have some clear predicates and many other confusedly stateable predicates. But since each one takes a different relative position to the others and thus has different direct and different indirect relations, each monad will have as its ‘signature’ its own unique set of clearly stateable predicates. I am saying ‘clearly stateable’, because from the perspective of God, who created all the monads and their relations, I would think all is clear. The only way the predicates that a monad has, which were endowed by an omniscient being, would be unclear is if we think of the predicates being understood by means of a limited mind taking that particular limited perspective and stating the predicates as clearly as possible from that perspective. So for example, we can say that the earth’s gravity pulls on us and we on it to some much lesser extent. And we might also then say that at the furthest distance from us in the cosmos, we gravitationally influence those distant bodies but at some remarkably slight amount. We cannot however state what those bodies are, how we influence them, and so on.]

The second question was, how do we differentiate monads given that each expresses the whole of the universe? While each monad expresses the entire universe, each does so from a particular perspective, and so only that which is proximal to the monad is expressed distinctly. Events which are at some remove from the monad are only perceived confusedly [the following up to citation is Leibniz quotation]:

Monads are limited, not as to their objects, but with respect to the modifications of their knowledge of them. Monads all go confusedly to infinity, to the whole; but they are limited and differentiated by the degrees of their distinct perceptions. (Leibniz 1989a: §60)

[new paragraph] The difference between monads is therefore the difference between different perspectives on the world.
(SH 49)


[Note here that two monads relate without being opposed. It would seem then that we can have judgment without oppositional difference in Leibniz’ system. However, all the predicates must be consistent with one another for Leibniz. There is one consistent world to which all the monad’s perspectives are in harmony. We thus have a logic of identity, since we can only have one world and not many which are incompatible with that world. Somehow Deleuze sees there being as many worlds as there are perspectives, but the perspectives are all of one world. It is not clear to me how there are both many worlds and just one world at the same time, instead of there being one world with many perspectives.  Hopefully this idea becomes clearer as we proceed.]

Different perspectives are not opposed to each other, and so Leibniz appears to have succeeded in coming up with a form of non-oppositional difference which explains all of the accidents of entities. If he had done so, then he would have developed a conception of non-oppositional difference founded on judgement, thus providing an alternative to Deleuze’s philosophy. In the end, however, this project fails, because the concept of difference is still founded on an identity. If we ask what these different perspectives | are perspectives of, then we are given the answer that they are perspectives of the universe. The notion of the universe itself has to pre-exist the different perspectives of it, since it is through this notion that God determines which of the monads can exist and which cannot. Only those which are compossible, that is, can simultaneously co-exist within the same world, can exist. We cannot have a world in which Adam both sinned and did not sin, as this would be a contradiction, nor a world in which different monads see the world in such radically different ways, as then the impression of causality would break down. ‘There are, as it were, just as many different universes [as there are monads], which are, nevertheless, only perspectives on a single one’ (Leibniz 1989a: §57). Leibniz’s notion of difference therefore still relies on the convergence of these different perspectives on a single identity, the universe itself [the following is quotation of Deleuze]:

Leibniz’s only error was to have linked difference to the negative of limitation, because he maintained the dominance of the old principle, because he linked the series to a principle of convergence, without seeing that divergence itself was an object of affirmation. (DR 51/62)
(SH 50)

 

 

 

 

 

Citations from:

Somers-Hall, Henry. Deleuze’s Difference and Repetition. An Edinburgh Philosophical Guide. Edinburgh: Edinburgh University, 2013.



Or if otherwise noted:


DR:
[Deleuze] Difference and Repetition, trans. Paul Patton, New York: Columbia University Press, 1994/London: Continuum, 2004.


 

Leibniz, Gottfried Wilhelm (1989a), ‘The Principles of Philosophy, or, the Monadology’, in Roger Ariew and Daniel Garber (ed. and trans.), Philosophical Essays, Cambridge: Hackett Publishing, 213–24.


Leibniz, Gottfried Wilhelm (1989b), ‘Samples of the Numerical Characteristic’, in Roger Ariew and Daniel Garber (ed. and trans.), Philosophical Essays, Cambridge: Hackett Publishing, 10–19.