Sorglose Nacht

Overview

Primary Truths was written shortly after Leibniz’s famous Discourse on Metaphysics, which places it about ten years after Freedom and Possibility, five before A New System, and almost twenty five before the mature position in the Monadology and the Principles of Nature and Grace.

This essay importantly develops at least two of Leibniz’s fundamental principles, the so-called “Predicate-in-Notion Principle” (PIN: that the notion of the predicate is in some way included in that of the subject - cf. §2.a below) and the Principle of the Identity of Indiscernables (PII), which he indicates here is derivable from combination of the Principles of Sufficient Reason (PSR) and Contradiction (PC) (cf. §4 below).

Brandon Look explains the implicit argument nicely:

1. Suppose there were two indiscernible individuals, a and b, in our world, W.
2. If this were the case, then there must also be a possible world, W^*, in which a and b are "switched".
3. But if this were the case, then God could have had no reason for choosing W over W^*.
4. But God must have a reason for acting as he does. (PSR)
5. Therefore, our original supposition must be false. There are not two indiscernible individuals in our world. (PII)

Outline

1. The primary truths are identities (A is A, everything is similar or equal to itself).
2. All other truths are reducible to these identities by resolving their definitions into their (progressively simpler) component propositions. This is called an a priori proof.
   1. Predicate in Notion Principle (PIN): Since all truths follow from primary truths, it follows that in any true proposition the predicate is always in the subject.
   2. This is the case for every (necessary or contingent) affirmative truth, and this tells us something about the nature of contingency and the challenges in thinking necessity (the fate of the free, e.g.).
3. The principle of sufficient reason
   1. Take this axiom: “There is no effect without a cause/Nothing is without reason.” (PSR, see Overview) If this were false, then there would be a truth that couldn’t be proved a priori (couldn’t resolve into identities). So, if this is false, Leibniz’s theory of truth is false. So, this follows from Leibniz’s theory of truth.
   2. This also applies to symmetries: Symmetry will follow from symmetry.
   3. Finally, there is even a reason about eternal truths. Imagine that we live in a world constituted by tiny spheres. There still needs to be a reason why they aren’t cubes.
4. The principle of the identity of indiscernibles
   1. From these considerations, it follows that in nature there can’t be two things that differ in number alone. (PII, see Overview)
   2. The basic idea in this argument seems to be that if x is identical to y in every way but in the fact that it one a second instance of the other, then there is no reason for them both to exist.
5. It also follows that there are no purely relational properties - that is, all properties are properties of things, and relational properties are grounded in non-relational ones. This, I think, is meant to follow from (2.a): Since all P’s of a given S are contained within S, it would seem to follow that if relational predicate R is attributable to S, then it would have to be contained in S, or at least in some P of S.
6. Any complete notion of a substance contains all its predicates: past, present and future. (If an S will have P, then it is now has T where T = “it is true now that it will have P”).
   1. This is a complete (perfect) notion of a substance, and from this we are meant to understand that God, who has knowledge of the possibilities for each of infinitely many potentially actual complete notions, would choose the ones that it, in its supreme wisdom, thought best.
7. Every individual substance contains in its complete notion the entire universe.
   1. For any given things x and y, there is a true proposition about how x relates to y only if they are related to each other.
   2. Since there are no purely relational predicates, both x and y must contain a predicate that explains their relationship.
   3. This must be the case for x viz. every other thing in the universe.
8. This means that all created substances are mirrors of the entire universe, which is to say, God, the universal cause. These expressions vary in perfection.
   1. This implies that every time any created substance changes, it changes all the others.
   2. However, strictly speaking, this does not mean that any created substances exercises metaphysical action or influence on anything else. This is to say that there is no inter-substance causal relationship, because each substance already contains within itself the entire universe, past, present, and future, which means that substances just harmoniously change without any sort of meaningful interaction.
   3. This theory also cleanly accounts for the correspondence of soul and body, without having to provide a medium of transport. By the nature of their complete concepts, they are simply in harmony already.
   4. Further, this implies that there is no atom (no body that could not be split). If there were atoms, there would be no cause to explain the effects of (e.g.) their size and shape. Every material thing requires smaller material things to explain its various properties.
   5. This means that every particle in the universe contains a world of infinitely many creatures.
   6. It also means that there is no determinate shape in actual things, because there is infinite complexity in any materially instantiated thing. Therefore, perfect circles, etc. exist only in our thoughts.
9. Bodies, Monads
   1. Since things have no determinate shape, this means that bodies are just extension and motion (which are “not substances, but true phenomena”)
   2. That means that something unextended is required for bodies, because material, extended stuff (as infinitely complex) can’t deliver unity. Since this can’t be atoms, all that remains is something analagous to souls.
   3. Corporeal substance comes into existence through creation (as opposed to construction) and leaves through annihilation (as opposed to dispersal), because there is no reason for them not to last forever. (Luckily, we know this argument gets better.)
   4. Therefore, animate things don’t come into or go out of existence entirely, but are merely transformed.

Bureaucratic Note

Finally, I should note that this ends my dalliance with pre-Kantian rationalism. Although I plan to come back to Spinoza at some point, for now, in order to push through to modernity, I’m going to take a step back to the roots of Kant’s other wellspring, British empiricism, and take a look at some bits of at least Locke and Hume, before finally arriving at Kant himself, who will represent the start of the period of philosophy in which I am most interested, German idealism. So, up next: John Locke.

Overview

Leibniz’s famous 1695 essay (in long form: A new system of the nature and communication of substances, and also of the union that exists between the soul and the body) was the introduction to a broad European readership of his original metaphysical ideas (many of which he had come to a decade earlier).

Outline

1. This paper is published in a scholarly journal - it is not written in the popular style.
2. Physics needs more than the concept of matter (”extended mass”), it also needs an operative concept of force.
3. At first, Leibniz favored an idea of matter and empty space (because it gives us a physics we can always “picture”).
   1. The matter itself, he realized, doesn’t yield any real unities. Because matter, by its nature is always divisible into smaller matter, and thus never a unity per se.
   2. Likewise, he thinks, geometrical points can’t yield existential unities, because points aren’t real extant stuff.
   3. In order to get a unity (a thing that’s deep down really just one thing), he needed a “real and living” point.
      1. These points, he realized, must be something like our idea of a soul - must be a force - that is, like appetition (desire and its low-grade analogs) and sentiment (belief, feeling).
      2. We can use these substantial forms to solve general (not particular) problems in natural science. Indeed, they are what Aristotle calls ‘first entelechies’.
      3. Leibniz calls them ‘basic forces’ for intelligibility, and because they involve actuality and activeness.
4. These forms and souls had to be indivisible.
   1. However, since this is the case, it also had to be the case that they were created and annihillated (rather than assembled/dismantled).
   2. This means that all substances were created with the universe, survive its duration, and will die with it.
5. There are at least two types of simple substances, though: rational souls (minds) and other souls. Compared with the latter, our minds are “like little Gods.”
   1. So, where God has imposed an order on matter, minds have special laws that raise them above that, or that matter works for minds (the punishment of the wicked, and the happiness of the good).
6. Since we are saying that souls (rather than atoms) last forever, one might be disposed to imagine that they pass from body to body. Because of microscopic observation, Leibniz is rather inclined to conclude that the animal simply begins and then just adds on other bits to itself in growth and development.
7. But what about the end of the animal, then? Since it is unreasonable to assume that souls just occupy a chaotic material station after death, the only tenable position is that not merely the soul but the animal is conserved (albeit in much smaller form) after death.
   1. This entails that rather than a transporting of souls, there is merely a continuous transforming, and that there is no death in a metaphysical sense.
8. God, however, has provided for rational souls so well that nothing can ever make them lose the “moral qualities of their personhood”.
   1. Thus it can be said that everything tends to not merely the perfection of the universe in general, but of these creatures in particular (who are destined to reach such a high degree of happiness that it affects the universe as a whole!)
9. Leibniz now attributes something like this view (that things don’t die, just appear and disappear) to Hippocrates, Parmenides, and Melissus.
10. The moderns take there to only be a quantitative difference - i.e. large and small - between the machines of nature and of humans, rather than a qualitative one. This is too far.
    1. For Leibniz the machines of nature and of humans differ not only by degree, but in kind. He isolates three differences:
       1. Nature’s machines are so well equipped as to never succumb to accidental destruction.
       2. Nature’s machines have a truly infinite number of parts.
       3. Nature’s machines remain the same, although they are (beautiful here:) “folded together differently.”
11. Furthermore, the soul is a true unity (which is what we call the ‘I’). Where human machines are more like armies of parts, and thus require unified parts somewhere.
    1. Since these unified parts clearly can’t be material (which for Leibniz is infinite in its compositional complexity). Rather we need something like “atoms of substance” (contra atoms of matter).
    2. These atoms of substance are:
       1. the sources of activity
       2. the basic reason for the composition of things (the explanation for material unities)
       3. the ultimate elements in the analysis of substantial things
    3. They might be called metaphysical points. They are not merely mathematical points because they have something alive in them (a kind of perception).
    4. So where material points seem indivisible but are not, and mathematical points are indivisible but are not things, only forms or souls/metaphysical points are both exact and real.
12. This generates a problem viz the soul’s communion with the body. The Cartesian/Malebranchean position is that senses and the motor behind actions is that God manually coordinates our activity/sensation with our volition, as well as causality in general.
13. Leibniz thinks that this is motivated right (its negative argument is good), but that its positive argument is wrong.
    1. In other words, it’s right that one created thing has no real influence on another and that all things are continually produced by the power of God, but relying on a deus ex machina is ostensibly the same as relying on miracles.
    2. Leibniz wants to explain how God coordinates causality.
14. Leibniz thinks that this happens because God initially created each soul to be spontaneous (aka. not causally affected by other monads), but meanwhile to just be in perfect conformity to things outside it.
    1. This entails that the internal perceptions of our souls are purely mental phenomena. The constitution of the soul “gives the substance a representative nature”: or, each substance reflects the entire universe in itself according to its particular point of view.
    2. Thus, the interaction of the body and the soul works by means of a universal spontaneous coordination that is the property of every substance.
    3. This theory has the charm of explaining how the soul resides in the body: e.g. in the same way that a unity is in a multitude.
15. Why couldn’t souls be like formal, free automatons? (This question will turn out not to answer itself.)
    1. Since the soul represents the entire universe (although with differing degrees of clarity), conversely, the body is adpated to the soul, and this gives us the sense of causal mind-body interaction.
16. It also has the advantage of showing that we are not susceptible to any kind of material causal determinism.
    1. Every mind is like a world apart: self-sufficient, independent of every other created thing, involving the infinite, and expressing the universe.
    2. It is also meant to be another proof of God that so many interacting substances do so harmoniously, a fact which implies that they share a common cause.
17. This system finally also allows us to understand “x acted on y and z” as “A change occurred in x which intelligibly explains changes in y and z, in such a way that we can conclude that when God was decreeing what substances were to exist he chose y and z so as to fit with the already chosen x.”
    1. That is, if matter is not substance, then something like this story is the only coherent way to explain the appearance of material causality.
18. This will prove useful in physics, despite its metaphysical character.

Overview

The Principles is among the last philosophical texts of Leibniz. It provides a short summary written in lay style of his philosophy. Taken together with the Monadology, Theodicy and the New System, Leibniz found it to be a coherent and comprehensive statement of his philosophy. (cf. Pauline Phemister, Leibniz and the Natural World pp. 7-8)

Outline

1. Substances
   1. A substance is a being that is capable of action.
   2. Substances can be simple (having no parts) or composite (collection of simple substances, monads).
   3. Simple substances = unities; Composite substances = multiplicities
   4. Lives, souls, and minds are simple substances, and therefore where there is simple substance there is life.
   5. Since the whole world is built out of simple substances, life is everywhere in nature.
2. Monads
   1. Because monads have no parts, they can’t be made/unmade.
   2. They also cannot come into or go out of existence. They last as long as the universe does.
   3. They can’t have shapes or sizes (since for this they would need parts).
   4. Therefore, they must be distinguished by their qualities (perceptions) or actions (appetitions).
   5. A simple substance can be in many states at once since these states match up with its various relations to things outside it. (E.g. a geometrical point is simple, but is at the center of infinitely many angles.
3. Causes
   1. Nature is totally full of simple substances, which are separated by their actions, and in a constant state of change relative to one another.
   2. A body is an infinite number of monads clustered around a central monad.
      1. If we can think this, then we can think that the central monad corresponds with the states of the body.
      2. This means that a body is a collection of progressively complex machines, a natural automaton.
      3. In turn, this means that every monad is a living mirror which represents the universe in accordance with its own point of view.
      4. “Living” refers to a monad’s being its own source of activity.
      5. Deleuze loves this bit.
   3. A monad’s perceptions arise out of its other perceptions by the laws of appetites (the final causes) just as changes in bodies arise from the laws of movement (the laws of efficient causes). [Note: formal and efficient causes in the Aristotelian sense.]
4. Animals, Subconscious Perceptions
   1. Since every organism is made up of smaller forms of life (less complex monads, say, organs), and so are these, and so on, then not only is life everywhere, but there are “infinite levels of life.”
   2. A sufficiently complex (?) lifeform is called an animal, and its (central?) monad is called its soul.
   3. Non-reasonable animals (”bare life”) have unelevated monads for souls. They don’t have distinct enough perceptions to be remembered.
      1. Here’s a distinction between perception (say, mere perception or sentience) and awareness (say, reflective knowledge or sapience).
      2. Awareness is not given to all souls and no soul has it all the time.
      3. Here’s where Cartesians went wrong - they didn’t grok le petit perceptions (we now say: subconscious perception).
5. Minds
   1. Animals have interconnected perceptions in a way that is not quite by reason. (A dog remembers a stick with which it has been beaten.)
      1. This is to say that it is grounded only in the memory of effects, without knowledge of causes.
   2. The kinds of animals that can understand causes (and therefore other analytic principles) are rational animals. Their soul-monads are called minds. Minds are capable of reflective acts (self-knowledge, science).
6. Death
   1. The ancients believed that life emerged from chaos, but we now know that it comes from organized systems (seeds), and therefore from other forms of life.
   2. Since this is the case, since animals do not emerge out of nowhere when they are born, it is unlikely that they disappear completely when they die. There is no metempsychosis, rather merely metamorphosis.
7. Since nothing comes about without sufficient reason, and since things do exist, we should be able to give a reason why there being something is preferable to there being nothing.
8. God
   1. The sufficient reason for the existence of the universe can’t be found in the order of contingent things (bodies and their representations in souls).
      1. It can’t be in bodies because there’s never a reason in matter for its own motion. The material reasons for the motion of matter are causal, and as we know, if we follow this chain, we regress infinitely.
   2. Therefore the sufficient reason for the universe must lie outside of the causal chain. It must be something that exists necessarily and without cause.
   3. This is called God.
9. God’s Perfection
   1. This simple, primal substance must have in a higher form the perfections of those things derivative from it.
   2. Directly this means that God has perfect power (omnipotence), knowledge (omniscience), and will (is supremely good). From this follows perfect justice (goodness + omniscience).
   3. Whatever imperfections earthly stuff has, they don’t derive from God, but rather from their own limits as created things.
10. The Most Perfect Universe
    1. Since God is perfect, it follows that he chose the best design for the universe. One with:
       1. The greatest variety and orderliness.
       2. The best arranged time and place (and terrain).
       3. The maximum effect produced by the simplest means.
       4. The highest levels of power, knowledge, happiness and goodness in created things that the universe allowed.
    2. This all follows since things must lay claim to existence where their claim is in direct proportion to their perfections.
11. The Most Perfect Physics
    1. God’s perfection is also exemplified in the laws of motion, which hang together the best and are the most comprehensible to metaphysical reasoning.
    2. Leibniz, who himself discovered some laws of nature, notes that these cannot be justified merely by means of (efficient) causality, and rather require appeal to final causes, a fact which provides yet another evident proof of God.
12. The Harmony of the Monads
    1. From the perfection of the universe (by way of the perfection of its author) it follows that every living mirror (monad/substantial center) must have its perceptions and appetitions ordered in the most perfect way qua compatibility with the rest of the monads.
13. The Fold
    1. So monads are ordered in perfect harmony with one another. This implies a serious kind of determinism (Leibniz nicely says “The present is big with the future, the future could have been read in the past, and distant things are expressed in what is nearby.”)
    2. If we could unfold any individual soul, we could see the beauty of the entire universe.
    3. But, since most of a soul’s perceptions are confused, and since the soul can only know its clear and distinct perceptions, which are /much/ fewer, individual souls know very little of the universe at a given time. Only God can have distinct perceptions of everything.
    4. Leibniz is obviously getting romantic here. He waxes poetical that in the roar of the ocean, he has many confused perceptions of distinct waves.
14. Imperfect Works and the Mirror of the Creator
    1. A rational soul is not merely a mirror of the universe, but also a likeness of its creator.
    2. It not only perceives God’s works, it can reproduce something like them on a smaller scale.
15. The City of God
    1. This means that all minds, entering into a kind of harmony with God, are members of the City of God - the most perfect and judicious state, with many fine characteristics:
       1. no crime without punishment
       2. no good deed goes unrewarded
       3. “as much virtue and goodness as possible”
    2. God achieves this City by means of a pre-established harmony between the kingdoms of nature and of grace, between God as the architect and God as the monarch.
    3. Nature leads on to grace, while grace perfects nature while at the same time making use of it.
16. Love of God
    1. Reason can’t tell us about the next life, but it can assure us that things have been done in a perfect way.
    2. In loving God, we can take pleasure in his perfections, which are … perfect … and so love for God must give us the most pleasure of which we are capable.
17. Pleasure without Sensory Input
    1. It is easy to love this God. There is nothing mysterious about taking pleasure from something imperceivable. Supporting arguments:
       1. People get pleasure from honors.
       2. Martyrs show the power of the pleasures of the mind in going happily to their deaths.
       3. The pleasures of the senses, in the end, are intellectual pleasures. Their sensory character is just our confusion (the real pleasure of music is in the numbers, e.g.).
       4. Again, very poetic Leibniz: “We are not aware of the numbers of these beats, but our soul counts them all the same!”)
18. The Pursuit of Happiness
    1. Loving God is its own reward, and gives us a foretaste of our future happiness.
    2. Finally, since God is infinite, and thus never knowable in its entirety, our happiness in loving it won’t ever consist in a mind-numbing complete enjoyment with nothing left to desire, but rather in “a perpetual progression towards new pleasures and new perfections.”

Overview

This early (1680) paper by Leibniz details a two-pronged theory of truth. Certain truths are necessary because their contraries are self-contradictory, and certain (existential) truths are necessary because of a free choice of God for the more perfect existence.

This theory seems to be meant to address a problem of freedom and determinism (or, as Leibniz calls it “future contingents”) - namely, because of the latter kind of truth, God can have future directed omniscience without future events being analytically necessary.

Outline

1. Premises
   1. In God everything is spontaneous.
   2. It can “hardly be doubted” that people have free will.
   3. A volition is a conscious attempt to act, and an act necessarily follows from the will and ability to do it.
   4. If the conditions pro and con for an action exist, a volitional equilibrium is reached, and thus, a person won’t act.
2. Analytic Propositions
   1. In every true proposition there is a connection between the subject and the predicate (”S is P”) and so every true proposition can be proved a priori.
   2. There are two primary propositions/truths:
      1. Necessary ones: whatever implies a contradiction is false. All truths of metaphysics (and logic, geometry, etc.) are necessary.
      2. Contingent ones: Whatever is more perfect or has more reason to be true.
   3. This cashes out to the idea that the principle of necessary truths is the principle that applies to essences, and the principle of contingent truths applies to existences.
3. Modality into Freedom
   1. God is the only being whose existence is not contingent. Which is to say that his existence is analytically entailed by his essence.
   2. For most contingent things (x), x’s definition shouldn’t explain its existence, because if it did, its nonexistence would be a contradiction.
   3. Contingent things that exist do so because they are more perfect than the possible rivals for existence. Now, if x’s nonexistence is a contradiction, then it could not be the case that there are other competing possibilities qua existence.
   4. This means that we need a notion of possibility according to which some things are not necessary and do not actually exist.
   5. If this kind of possibility exists, it implies a certain freedom on the part of a free mind to choose one thing rather than another (for its perfection, as God does, or from our imperfection).
4. Modality, God’s Actions and Existence
   1. God’s Free and Necessary Actions (God must have two types of actions)
      1. Example of a necessary action: God loves himself. This can be demonstrated from the definition of God.
      2. Example of a free action: God makes whatever is most perfect. There’s nothing contradictory in the contrary proposition (if it were, non-existent possibles would in fact be impossible).
   2. A similar conclusion (about modality) derives from the nature of existence:
      1. Take A and B. Only one of these can exist. Assume A is more perfect than B.
      2. Now, A exists because of this, and this fact can be demonstrated, or rendered certain by the nature of the case.
      3. If being certain were the same as being necessary, we’re in trouble.
      4. But, A’s existence has merely a hypothetical necessity. This means that it is necessary that if God always chooses what is most perfect, then A exists.
      5. This is to be distinguished from the (absolutely necessary-type) proposition that it is necessary that A exists.
      6. Again, if A were absolutely necessary, B would be impossible.
   3. So we must hold that:
      1. What has some degree of perfection is possible.
      2. What is more perfect than its opposite actually exists. (Perfection is an “urge for existence.”)
   4. This means that extant things are products of God’s will rather than of necessity.
   5. But: Does god will by necessity (because of his nature) or freely (because of his will)?
      1. It must be by necessity, since if he has to will to will something, this entails an infinite regress.
      2. Does this demean God? With Augustine: Such necessity is blessed.
5. Possible Things
   1. So, things are possible even if God does not will them into existence, because they are not in themselves contradictions.
   2. Or, a possible thing is “something with some essence or reality, that is, something that can be clearly understood.”
   3. This means that if there is never an instantiation of a perfect circle, a circle is still possible, but just possesses less perfection (i.e. less reality) than the things that do exist.
   4. So that “No perfect circle ever did or will exist” is a necessary proposition is true, but “No perfect circle exists” (the timeless proposition) is a necessary proposition is false.
      1. This is so because Leibniz denies that the timeless proposition can be demonstrated.
      2. Basically, Leibniz wants to distinguish between propositions that cannot be solved because they are self-contradictory (e.g. find x where x^2=9 and x+5=9) and where they are merely possible/imaginary (e.g. find x where x^2 + 9 = 3x).
6. Future Contingents
   1. This is meant to remove the problem about the foreknowledge of future contingents.
   2. God can formulate propositions about future contingents that are:
      1. necessary, given the state of the world that has “been settled once and for all”
      2. necessary, given the harmony of things.
   3. But future contingents are not necessary in the analytical sense. This lets God have foreknowledge of them even though they are not necessary.
   4. This entails that it is possible for the imperfect rather that the more perfect to exist. This is fine since we can accept “what God doesn’t will to exist doesn’t exist” without asserting the necessity of this proposition.
   5. [Near the end of this paper Leibniz has an incomplete sentence which he probably meant to turn into something saying:] The only existential proposition that is absolutely necessary is God exists.