Gottfried Leibniz
  1. Now this is the axiom which I utilize, namely, that "no event takes place by a leap."  This proposition flows, in my view, from the laws of order and rests on the same rational ground by virtue of which it is generally recognized that motion does not occur by leaps, that is, that a body in order to go from one place to another must pass through definite intermediate places. (222)
  2. I do not believe that extension alone constitutes substance, since its conception is incomplete.  . . . We we can analyze it into plurality, continuity, and coexistence (that is simultaneous existence of parts).  . Hence I believe that our thought of substance is perfectly satisfied in the conception of force and not in that of extension.  . . .  Since activity is the characteristic mark of substances, extension on the contrary affirms nothing other than the continual reiteration or propagation of an already presupposed effort and counter-effort, that is, resistant substance, and therefore extension cannot possibly constitute substance itself.  (222-223)
  3. We . . . attain here an understanding of the traditional Aristotelian doctrine of entelechies . . . . (223)
  4. We must, in addition to purely mathematical principles, recognize metaphysical ones [in physics]. (224)
& Mind

"To those who
thought prestablished 
harmony odd, Leibniz
pointed out what 
admirable evidence
it afforded of the 
existence of God"
[who was needed to synchronize the
infinitude of souls] 
(Russell, p.584)

no psychokinesis
no telekinesis

Macrocosm in every

Example: the souls 
of atoms
their distinctive
causal powers,
e.g., gravitational 
attraction to other atoms
perception = differential
sensitivity to influence of 
other atoms, e.g.,
to be attracted
to them in inverse 
proportion to the square of
their distances apart.

  1.  The Monad . . . is nothing else than a simple substance, which goes to make up composites; by simple we mean without parts. (§1)
  2. There must be simple substances because there are composites; for a composite is nothing else than a collection . . . of simple substances. (§2)
  3. [W]here there are no constituent parts there is possible neither extension, nor form, nor divisibility. These Monads are the true Atoms of nature, and, in fact, the Elements of all things. (§3)
  4. [T]here is no way a simple substance can perish through natural means. (§4)
  5. There is no way of explaining how a monad can be altered or changed in its inner being by any other created thing . . .. The Monads have no windows through which anything can come in or go out. . . . [N]either substance or attribute can enter from without into a monad. (§7)
  6. Monads must needs have some qualities, otherwise they would not even be existences. (§8)
  7. Each Monad . . . must be different from every other. For there are never in nature two beings which are exactly alike. (§9)
  8. The passing condition which involves or represents a multiplicity in the unity, or in the simple substance, is nothing else but perception, which must be distinguished from apperception or consciousness, as will appear in what . Here it is that the the Cartesians especially failed, having taken no account of the perceptions of which we are not conscious.  It is this also which made them believe that . . . there are no souls of brutes or of other entelechies. (§14)
  9. [Appetite is] the action of the internal principle which brings about the change or the passing from one perception to another." (§15)
  10. There is nothing besides perceptions and their changes to be found in the simple substance (§17)
  11. [K]nowledge of eternal and necessary truths is that which distinguishes us from mere animals and gives us reason and the sciences, thus raising us to a knowledge of ourselves and God. (§29)
  12. [I]t is only through the primal regulation [of God] that one [monad] can have dependence on another. (§51)
  13. [God's primal regulation] brings it about that every simple substance has relations which express all the others and that it is consequently a perpetual living mirror of the universe" (§56)
  14. [The harmony of monadic perceptions is much] as the same city regarded from different sides appears entirely different, and is, as it were multiplied respectively. (§57)
  15. The Monad is by its . . . nature representative (60)
  16. God alone is without body (§72)
  17. [T]he soul follows its own [final causal] laws, and the body also its own [efficient causal] laws. They are fitted to each other in virtue of the pre-established harmony between all substances. (§78)
  18. Whence we see that there is a world of creatures, of living being, of animals, of entelechies in the smallest particle of matter. (226)
  19. Each portion of matter may be conceived of as a garden full of plants, and as a pond full of fishes.  But each branch of the plant, each member of the animal, every drop of its humors is also such a garden or such a pond. (226)
Logic,  Theology
& Theodicy

BBB: How many letters? 
3 tokens, 1 type.

Truths of Reason

  • All bachelors are unmarried.
  • Either today is Tuesday or not.
  • The square on the diagonal is twice
  • the are of the original square.
Truths of Fact
  • Some bachelors are unhappy.
  • Today is Thursday.
  • Hauser illustrated the diagonal theorem in class.
Argument from Evil

1. God is all knowing,  all powerful, and perfectly good.
2. There is evil.
3. If there is evil then either
(A) God doesn't know about it, or
(B) can't prevent it, or (C) is unwilling to prevent it. 
4. If (A), God is not all knowing;
if (B), not all powerful; 
if (C), not perfectly 
Conclusion: There is no God.

  1. If is also through the knowledge of necessary truths, and through their abstract expression, that we rise to acts of reflection, which make us think of what is called I, and observe that this or that is within us: and thus, thinking of ourselves, we think of being, of substance, of the simple and the compound, of the immaterial, and of God Himself, conceiving that what is limited in us is in Him without limits. And these acts of reflection furnish the chief objects of our reasonings. 
  2. Our reasoning is based on two great principles: first, that of Contradiction, by means of which we decide that to be false which involves a contradiction and that to be true which contradicts or is opposed to the false. (§31)
  3. And second the principle of Sufficient Reason, in virtue of which we believe that no fact can be real existing and no statement true unless it has a sufficient reason why it should be thus and not otherwise. Most frequently, however, these reasons cannot be known by us. (§32)
  4. There are also two kinds of Truths, those of Reasoning and those of Fact. The Truths of Reasoning are necessary, and their opposite is impossible. Those of Fact, however, are contingent, and their opposite is possible. (§33)
  5. When a truth is necessary, the reason can be found by analysis in resolving it into simple ideas and into simpler truths until we reach those that are primary. (§33)
  6. Therefore, the sufficient or ultimate reason [for any contingent thing] must be outside the sequence or series of these details of contingencies, however infinite they may be. (§37)
  7. It is thus that the ultimate reason for [contingent] things must be a necessary substance . . . and this substance we call God. (§38)
  8. [I]n God is found not only the source of existences, but also that of essences, in so far as they are real. In other words, he is the source of whatever there is real in the possible. (§43)
  9. Therefore, God alone (or the Necessary Being) has this prerogative that if he be possible he must necessarily exist, and as nothing is able to prevent the possibility of that which involves no bounds, no negation, and consequently no contradiction, this alone is sufficient to establish a priori his existence. (§44)
  10. Souls act in accordance with the laws of final causes through their desires, ends and means. Bodies act in accordance with the laws of sufficient causes or of motion. (§79)
  11. [I]f we were able to understand sufficiently well the order of the universe, we should find that it surpasses all the desires of the wisest of us, and that it is impossible to render it better than it is, not only for all in general, but also for each one of us in particular, provided that we have the proper attachment for the author . . . as our Lord and Final Cause, who ought to be the whole goal of our will, and who alone can make us happy. (§90)
  12. It does not seem possible for all possible things to exist, they get in one another's way. (Leibniz, "On Contingency")

Next: Locke: Knowledge & Empiricism

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