Gottfried Leibniz
  • Mathematics is the Scientific Ideal
    • deductive elaboration
    • of intuitive grasp of innate ideas of
      •  line, plane, point, circle, triangle, square, etc.
  • Metaphysics: {4}
    • deductive elaboration
    • of intuitive grasps of innate ideas of {C1}
      • substance, attribute, cause, etc. 
      • mind, matter, God, etc. {1} {2}
  • Contrast Spinoza
    • where Spinoza saw the indissolubly interconnected oneness of It All
    • Leibniz saw a radically disconnected multiplicity
    • Conservatism
      • RE: Aristotelian teleology {3}
      • RE: Judeo-Christian theology
  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)


in every

the souls 
of atoms

attraction to 
other atoms

perception = 
sensitivity to
influence of 
other atoms, e.g.,
to be 
to them in 
proportion to
the square of
their distances

  • Simple Substances {1}
    • Atomic {2} & Indestructible {4}
    • Units of force (conatus)
  • Immaterial Intelligence's 
    • extension cannot be an attribute of substance since it involves plurality {3}
    • so the ultimate individual "atoms" of which things are made must be immaterial agencies or intelligences {8} {A2}
  • Self-contained or "windowless" {5}
    • not subject to material effects (obviously)
    • not subject to mental effects (no telepathy)
  • Unique: Identity of Indiscernibles {7} {6}
  • Interaction problems between substances 
  • Descartes 
    • problem about mind-body interaction
    • due to their being essentially unlike type substances
      • problem about mind-mind interaction: different tokens of the same type. 
      • minds affect minds via matter
      • not telekinesis
  • Leibnizian solution to m<~>b: parallelism due to preestablished harmony of monads {17}
  • Preestablished harmony of monads: m<~>m: parallelism of minds.
    • each "reflects" the whole of reality
    • each a world apart independent of every other
    • coordinated due to prestablished harmony {12}
    • like synchronized virtual realities {13} {14}
    • bodies = "shared" images in virtual "space" {15}
  • Hierarchy of Monads
    • some are superior to others in the clearness and distinctness with which they mirror the universe {11}
    • for every living body there is a dominant monad which, in humans and animals called the soul of the body {16}
    • has clearest perceptions of the monads composing ones body -- oversight of them, as it were.
    • voluntary motions of ones body pursue the purposes of this dominant monad
  • The Inner Life of Monads
    • have no parts or internal structures
    • do have qualities
    • aim, purpose, Appetite 
    • unconscious entelechies in lower monads
    • perception: a reflection of -- & unique perspective on -- the whole universe in each
    • unconscious in lower monads: e.g., the mere situatedness of bodies 
    • conscious in higher monads
    • our perception is more distinct and is accompanied
      • memory
      • reason equipped with innate ideas {11}
      • reflective self-awareness: consciousness or apperception
  • Panprotopsychism or panvitalism {18} {19}
  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)
& Theodicy


Q: How many
letters above?

A: 3 tokens,
1 type.

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.

of Fact

Some bachelors 
are unhappy.

Today is Tuesday.

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 
There is no God.

Logic and Monads

  • The Concept of Substance
    • root Aristotelian notion: a subject or ground in which attributes or qualities or properties inhere
    • problem of the bare substratum
    • Spinoza's token Monism (cf. Parmenides): It bes
    • Leibniz's Objection: to be is to be some way {B6}
  • Token Pluralism
    • Leibniz a type monist but token pluralist 
    • Type monist: only minds
    • token pluralist (different individuals)
    • Problem of Individuation sans substratum
  • Individual Essences as complete and total descriptions
  • Bundle Theory of Individuals
    • properties don't inhere in a bare substratum
    • properties cohere in uniquely identifying ways 
  • Identity of Indiscernibles
    • For there are never in nature two beings which are exactly alike. {B7}
    • Contrary = Indiscernibility of Identicals Principle

Contingency & Necessity

  • Two great truths {2} {3}
    • Principle of Contradiction (PC): for every judgment J
      • J & not-J is false
      • if J is false then not-J is true
    • Principle of Sufficient Reason (SR): 
      • nothing happens or is without a reason
      • though we may not know the reason 
  • Two kinds of truth {4}
    • Truths of Reason {5}
      • are necessary: their opposites are impossible
      • sufficient reason for their truth that their denial would involve a contradiction 
    • Truths of Fact 
      • are contingent: their opposites are possible
      • sufficient reason for their truth = their causes {10}
        • efficient: for physical events
        • final: for mental events


  • Cosmological Proof {6} {7}
    • intermediate causes not ultimately sufficient
    • a self-sufficient first cause (i.e., God) is needed
  • Ontological Proof {8} {9}
    • God is absolutely perfect & unlimited
    • Real possibilities require some self-realized possibility (God) as their ground {8}
    • Such a self-realizing possibility (God) is possible
    • Such a self-realizing possibility (God) exists
  • Argument from Prestablished Harmony
  • Contingency and Necessity Revisited
    • Eternal truths not dependent on God's choice
    • Contingent truths depend on God's choosing & willing them
  • Theodicy {11}
    • Infinity of Possible Worlds
    • But not all compossible {12}
    • This it the best of all possible worlds.
  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")

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