Leibniz
Sunday, April 18, 2010


Leibniz

I’m returning to the St. John’s reading list with three short works by Liebniz. Many people know him through Voltaire’s slanderous presentation of him as Dr. Pangloss in Candide, but his optimism is not really Panglossian.

For some reason Liebniz didn’t make it into The Great Books of the Western World, and he’s hard to find in the local library, so I’m using texts that I found on the Internet.

Discourse on Metaphysics—This is a short piece on metaphysics in which he sets forth a series of 37 propositions. I’m going to comment on those that I find most interesting.

Proposition I: Concerning the divine perfection and that God does everything in the most desirable way. Liebniz says in the course of this proposition that “This is because the number which is the greatest of all (that is, the sum of all the numbers), and likewise the greatest of all figures, imply contradictions. The greatest knowledge, however, and omnipotence contain no impossibility. Consequently power and knowledge do admit of perfection, and in so far as they pertain to God they have no limits.” This is interesting because while there may be some truth to what he says if it is confined to all positive numbers, it can be demonstrated that the sum of all integers and the sum of all reals is 0. Think of a number. Multiply it by -1. Whatever number you think of will have a corresponding negative value that when added to it will cancel it out. The contradiction lies in having a non-zero number that is the sum of all numbers since that number would be included in the set of all numbers so it would include itself in the sum, which is an obvious impossibility. I think the same thing happens when you hear talk of the set of all sets.

Proposition II:  Against those who hold that there is in the works of God no goodness, or that the principles of goodness and beauty are arbitrary. “This is confirmed by the fact that it is in reflecting upon the works that we are able to discover the one who wrought.” This is the argument from design, that the works reveal the worker. Hume and Kant will call this proposition into question, and Kierkegaard will postulate the leap of faith in response to the skeptical position.

Proposition III:  Against those who think that God might have made things better than he has. “I think that one acts imperfectly if he acts with less perfection than he is capable of. To show that an architect could have done better is to find fault with his work.” God never has an off day.

Proposition IV: That love for God demands on our part complete satisfaction with and acquiescence in that which he has done. “The general knowledge of this great truth that God acts always in the most perfect and most desirable manner possible, is in my opinion the basis of the love which we owe to God in all things; for he who loves seeks his satisfaction in the felicity or perfection of the object loved and in the perfection of his actions.” Liebniz assumes that we owe love to God on a rational basis. I think this idea may be contradicted on an experiential basis. In the depths of the dark nights, as experienced by St. Therese of Lisieux or Blessed Teresa of Calcutta, one goes on loving despite any rational basis for loving, or any feeling of reciprocated love.

Proposition VI: That God does nothing which is not orderly, and that it is not even possible to conceive of events which are not regular. “Because, let us suppose for example that some one jots down a quantity of points upon a sheet of paper helter skelter, as do those who exercise the ridiculous art of Geomancy; now I say that it is possible to find a geometrical line whose concept shall be uniform and constant, that is, in accordance with a certain formula, and which line at the same time shall pass through all of those points, and in the same order in which the hand jotted them down; also if a continuous line be traced, which is now straight, now circular, and now of any other description, it is possible to find a mental equivalent, a formula or an equation common to all the points of this line by virtue of which formula the changes in the direction of the line must occur.” I’m not sure what Liebniz means here. Any collection of data can be analyzed, and a trend line can be drawn that shows an idealized equation, but not all the points will be on that line. If he means that you can formulate equations for AB, BC, CD, and so on then the point seems valid, but trivial. If you click on the picture at the top left of this paragraph, the larger image will show you that some of the points lie outside of the moving average. You’ll also notice that the plot is not one that can readily be reduced to a simple equation. The chart for Apple, shown in the second picture, is also not amenable to a single exact equation that will generate every data point.

Proposition XIX: The utility of final causes in physics. “As I do not wish to judge people in ill part I bring no accusation against our new philosophers who pretend to banish final causes from physics, but I am nevertheless obliged to avow that the consequences of such a banishment appear to me dangerous, especially when joined to that position which I refuted at the beginning of this treatise. That position seemed to go the length of discarding final causes entirely as though God proposed no end and no good in his activity, or as if good were not to be the object of his will.” Liebniz here anticipates the arguments of the anti-Darwinians, such as Samuel Butler and George Bernard Shaw, who rejected the Darwinian version of evolution on the grounds that it “banished mind from the universe.” Liebniz gives the viewpoint of the natural theologians. “All those who see the admirable structure of animals find themselves led to recognize the wisdom of the author of things and I advise those who have any sentiment of piety and indeed of true philosophy to hold aloof from the expressions of certain pretentious minds who instead of saying that eyes were made for seeing, say that we see because we find ourselves having eyes. When one seriously holds such opinions which hand everything over to material necessity or to a kind of chance (although either alternative ought to appear ridiculous to those who understand what we have explained above) it is difficult to recognize an intelligent author of nature.” Liebniz believes that you can get from nature to statements about nature’s God. The problem is that while you may be able to prove the watchmaker, you may not be able to prove that the watchmaker and the designer are one. What if there isn’t a single watchmaker, but a committee that designs, and a watchmaker who carries out? Can you get from nature to a monotheistic concept of deity? Hume argued in his dialogues on natural religion that you couldn’t.

Proposition XXIII: Returning to immaterial substances we explain how God acts upon the understanding of spirits and ask whether one always keeps the idea of what he thinks about. “First of all it will be in place to remark that the wrong use of ideas occasions many errors. For when one reasons in regard to anything, he imagines that he has an idea of it and this is the foundation upon which certain philosophers, ancient and modern, have constructed a demonstration of God that is extremely imperfect. It must be, they say, that I have an idea of God, or of a perfect being, since I think of him and we cannot think without having ideas; now the idea of this being includes all perfections and since existence is one of these perfections, it follows that he exists. But I reply, inasmuch as we often think of impossible chimeras, for example of the highest degree of swiftness, of the greatest number, of the meeting of the conchoid with its base or determinant, such reasoning is not sufficient.” Liebniz here re-instantiates the ontological argument that we saw with Anselm. The major problem here is that it is possible to imagine things that do not exist. We can imagine unicorns, but unicorns have no real existence. My office at home is an ugly shade of green, painted that way by the previous owners, but I can imagine it as the blue of Wedgwood Jasperware. I can even use Photoshop and produce a picture of a blue office. The blue office has no real existence. On the other hand it can be said that while the unicorn is not real, the rhinoceros is real, and that the unicorn is a misunderstanding of, or a bad report of the real thing, the unicorn. My office is real, and blue is real, so I can imagine the combination of the two. Can I imagine something that is unreal? Even science fiction monsters are in some sense developments of real things. So saying that because I can conceive of something that does not exist may not be that meaningful.

Proposition XXX: How God inclines our souls without necessitating them; that there are no grounds for complaint; that we must not ask why Judas sinned because this free act is contained in his concept, the only question being why Judas the sinner is admitted to existence, preferably to other possible persons; concerning the original imperfection or limitation before the fall and concerning the different degrees of grace. “This evil will be more than overbalanced. God will derive a greater good from it, and it will finally turn out that this series of events in which is included the existence of this sinner, is the most perfect among all the possible series of events.” The maxim that God draws straight with crooked lines puts it a bit more succinctly. I think that Liebniz would be on better ground if he were to argue that a world in which it was not possible for Judas to betray Christ would be a worse world than one in which it was possible and in which Christ was betrayed. He would probably have to resort to the idea of the fortunate fall, that the graces produced as a result of the fall, and the death and resurrection of Christ surpass those that would have occurred without the fall. He would also be on better ground, to my mind, if in discussing evil he were to say that a world in which God does not permit evil, necessitating continuous Divine intervention, would be a chaotic world, and not one with natural laws.

Principles of Nature and Grace—Liebniz begins by speaking about monads. These are similar to atoms, but are non-material. These monads have no parts and have neither beginning nor end. It’s not clear here whether he is asserting that they are co-eternal with God or not. That proposition is not one that is consistent with the usual Christian tradition. He asserts that monads will never go out of existence: “They cannot naturally either begin or end, and therefore they last ·for ever, that is· as long as the universe (which will alter but will never go out of existence).” Liebniz may be on shaky ground here. Some cosmologists are speculating on the possibility of a “big rip.” Some trillions of years in the future, assuming that expansion keeps up, the very fabric of the universe, down to the level of strings, may pull apart into a vast nothingness.

Liebniz postulates an infinity of animals such that larger animals grow out of smaller animals: “And what I have just said about large animals applies also to the generation and death of those spermatic animals themselves; that is to say, they have grown up out of other still smaller spermatic animals, in relation to which they would count as large! For everything in nature goes on to infinity, ·including the nested series of ever smaller animals.”

Swift makes this observation:

“So, naturalists observe, a flea Has smaller fleas that on him prey; And these have smaller still to bite ’em; And so proceed ad infinitum.”

Liebniz goes on to contend that “God is supremely perfect,” and draws a number of conclusions from this:

it follows that in producing the universe he chose the best possible design—a design in which there was •the greatest variety along with the greatest order, •the best arranged time and place, •the maximum effect produced by the simplest means, •in created things the highest levels of power, knowl- edge, happiness and goodness that the universe could allow.

Note that he does not assert that there is no evil in the world, only that there is a minimum amount of evil.

Voltaire mocked Liebniz, rather unfairly, in Candide. The Lisbon earthquake of 1755 is generally supposed to have been partly behind the rejection of Liebnitzian optimism. The devastation brought on by the earthquake generally had a disillusioning effect upon theologians and philosophers. If God is good and omnipotent, how could He allow the earthquake and its devastation to occur?

To my mind this question arises because of the insertion of man into the question, and the unconscious belief that he is somehow apart from the natural world. If the earthquake is looked at not from our perspective, but from the perspective of the earth, the quake is neither good nor evil but a process that involves the release of energy due to the overlap of two tectonic plates. These processes were there, at least implicitly, at the planet’s formation, and continue to the present day. To demand God’s intervention is to demand that rather than ordered, natural processes there be random, unordered processes controlled by either our whim, or by God’s whim.

Liebniz goes on to assert that we should love God, and that He is “very lovable and a source of very great pleasure.” In this context he mentions that, “Martyrs ·who go happily to their deaths· show what the pleasures of the mind can do. (The same is true of fanatics, though in their case the emotion is out of control.)” Again, this is a matter of perspective. I regard suicide bombers as fanatics, while they regard themselves as martyrs.

The Monadology—This is a relatively short work of 90 paragraphs in which Liebniz puts forth a variety of propositions.

In 17 he asserts that perception cannot be explained in terms of “mechanistic causation,” but through simple substances.

In 53 he asserts that “there is an infinity of possible universes among God’s ideas, and only one of them can exist, there must be a sufficient reason for God’s choice, which determines him to the one rather than to the other.” There is one interpretation of quantum physics that holds that there is an infinity of worlds, and that separate universes exist. So there may be some universes in which I am president, others in which I’m dead, and others in which I am a great novelist, or even a great saint. In some I’m married to my childhood sweetheart, while in this, and possibly others, I’m married to the woman who is actually my wife. This interpretation, to the extent that it thinks about God at all, would assert that God lets all of the possible universes come into being in what it calls a multiverse.

In 61 he asserts that there is communication among these bodies even over vast distances: “But in a plenum, every motion has some effect on distant bodies in proportion to its distance. So each body also registers what happens to its neighbours’ neighbours, through their mediation. It follows that this communication extends to any distance whatever.” This means, according to Liebniz, that it is possible for someone who sees everything to read what happened in the past, and what will happen in the future.

In 74 he mentions the rejection of the idea of spontaneous generation, and that organic bodies are always the result of seeds, i.e., reproductive processes.

In 81 and 82 he deals with the relation of soul and body. He finds that each acts as if the other did not exist while at the same time acting as if each were an influence upon the other.

In 87 he asserts that there is a harmony between efficient and final causation. He describes God as “the designer of the machine of the universe,” and as “the monarch of the divine city of spirits.”

In 90 he asserts that good and evil are rewarded, and makes the assertion that “Everything must come out right for those who are good — that is to say, for those who are not rebels against this great state; who trust in providence after doing their duty; and who love and imitate the Author of all good as they ought to.” Paul puts it more succinctly in Romans 8:28, “And we know that all things work together for good to those who love God, to those who are the called according to [His] purpose” (NKJV). It is in recognizing God as “our master, and the final cause which must constitute the whole aim or our will, and which alone can constitute our happiness.”

Next up, David Hume and The Treatise on Human Nature.