Leibniz: The Best of All Possible Worlds

According to Leibniz, the actual world is the best of all possible worlds. He outlines a simple argument for this conclusion in The Monadology, §§53-55. The argument proceeds as follows:

  1. God has the idea of infinitely many universes.
  2. Only one of these universes can actually exist.
  3. God’s choices are subject to the principle of sufficient reason, that is, God has reason to choose one thing or another.
  4. God is good.
  5. Therefore, the universe that God chose to exist is the best of all possible worlds.

The argument can be broken down into three parts. Premises (1) and (2) say that God has a choice to make, for there are infinitely many possible worlds, and only one can be chosen. Premises (3) and (4) state that God chooses things with reason (this is the principle of sufficient reason, that is that all things that occur occur for sufficient reasons which fully explain them), and is good – hence, when God makes choices, God chooses that which is most good, or most perfect. Finally, the conclusion puts these two ideas, concluding that in this choice, as with all other choices, God chose that which is best, the best of all possible worlds which could have existed.

The argument is valid, for if there is are infinitely-many choices, and a good, reasonable God has made a choice of one, then that universe is the best. For, if God chose another less-good universe, then God would not be good, God would lack the idea of some universe, or God would not be reasonable, and some premises would be false. (Arguably, one could claim that the argument is invalid on the grounds that its premises may yield a false conclusion if the goodness of universes were identical, and that God did not choose to make any world actual. Clearly, since we know of an existing universe, the claim that none exists would be false, but it is not logically false and hence the argument could have weakness here. However, we will grant Leibniz the tacit assumption that “a universe exists” is a premise.)

Leibniz explains that the reason for the choice of  a world is in its “fitness, or in the degree of perfection that these worlds contain” (76). Hence, the suitability for a world for selection is a function of its level of perfection, and God, being perfect, would choose that world which is most perfect.

Premise (1) follows from the notion of God. God is, by definition all-knowing – a view defended in §48 – and, hence, has the knowledge of what any configuration of the universe would be. So, if God exists, premise (1) is true. Leibniz argues that God must exist in §§44-45 with the argument that “he must exist if he is possible. And since nothing can prevent the possibility of what is without limits, without negation and consequently without contradiction” (74) then God exists. The argument can be symbolized by modal logic as (◊G → □G),  ¬□¬G ∴ G, where G means “God exists”, and is valid.

One may hope to attack premise (2) with the claim that there could be multiple worlds. For if God is a transcendent being, beyond this world, it would seem that he could create all of his possible worlds independently from one another. It may be argued that God would never create anything imperfect, as the other worlds are said to be, but imperfections exist within the actual world even if they are in order with universal harmony. It may be the case that the entire collection of worlds, including the most perfect one, is itself perfect. It is not clear why Leibniz would deny this possibility, though it should also be noted that in this case, we may extend “world” to mean the set of all universes which God is again supreme over, and say that this set is the best of all possible worlds, which would have to be the case since it is the only set in existence.

Premises (3) and (4) seem less controversial. God is defined as being the “ultimate reason” (73) in §38, and hence God is the sufficient reason for things existing. God’s goodness is explained by his perfection in §41.

Hence, it follows from these premises that the actual world is the best of all possible worlds.


Source: Leibniz, G. W. Discourse on Metaphysics and Other Essays. Trans. Daniel Garber and Roger Ariew. Indianapolis: Hackett, 1991. #


In the Pursuit of Truth[1], must one reify? Quine says that “substantial reification is theoretical” (25), beyond the simple observation sentences. We emerge from the “feature-placing” stage (24) and in the persistent recurrence of certain qualitative features we develop a theory that the set of features we regularly observe belong to some consistent, persistent object. These theories are purported to be useful. For the child it helps to recognize Mama as something other than the recurrence of Mama-features, if only for a sense of security. Endless metaphysical thought experiments have us imagining non-identical doubles of things we know, such as twin-Earths and doppelgangers, all with the impression that we’ll recognize that the identity of an object over time is important – seemingly identical objects with the same extension but different causes are purported to be non-identical.

Natural selection seems to have produced reification but is it truth proper to imagine the persistence of a single object between instances of its being observed? The question for the child is how much qualitative difference is acceptable between instances of Mama? If Mama changes her hair or her clothes, has cosmetic surgery or injures her vocal chords, will she still be recognizable as Mama to the child? She’s not strictly identical to the entire set of features previously observed. Observation sentences about her appearance will differ. The theory places her as the same object, but the stimulus meaning of “there’s Mama” has changed drastically since its last utterance. If “Mama” has changed enough, the child may not assent to the observation sentence.

This is where Quine later drew a distinction between perceptual and full reification. In a passage from a late manuscript cited by Peter Hylton in his text on Quine[2], by way of Leonardi and Santambrogio[3], Quine clarifies the terms:

Prior cognition of a recurrent body—a ball, or Mama, or Fido—is on par with our recognition of any qualitative recurrence: warmth, thunder, a cool breeze. So long as no sense is made of the distinction between its being the same ball and its being another like it, the reification of the ball is perceptual rather than full.

For Quine, the child is capable only of perceptual reification, rather than the full reification one that is present in a theory. I take this to be a sort of family resemblance between stimulus meanings. A child can recognize certain sets of stimuli that, in a criss-crossing mesh include various patterns that trigger recognition, representing something perceptually for that child even if the child lacks a theory of persons, minds, bodies or persistence of an object.

Hylton takes the question of reference to be “how we can get from observation sentences to a mastery of language that is clearly about particular entities”[4] My question is, in a world of bits where language refers to various arrangements of those bits, why must language be about entities in the strict sense? Why must we pass from the perceptual reification that occurs when those bits are arranged in familiar ways to the full reification that says that there is some entity there? It seems to me that we can preserve a tasty desert landscape without reification of anything beyond a fundamental bit. At the end of this chapter, Quine expresses his preparedness to bail on the traditional concept of existence (36). If existence can go by the board, the entity can follow.

I know I’m taking a step away from the point of this chapter when I zero in on this, and I had prepared a commentary on Quine’s indistinguishable, isomorphic ontologies but I read it over and wasn’t sure there was sense to any of it. Indeed we can build fairly successful theories with varying versions of the ontology. But I find the reification game a little superfluous, especially if we’re taking a behaviourist account of things. We can build our ontology around dogs, around sets of {dog} or their absolute complements like  ∁{dog}, and each adopt our own isomorphic ontology and I can talk about dogs meaning dogs, and Smith can talk about dogs meaning {dog} singletons and Jones can play around with his ∁{dog} complements – just as my red could be your blue and, I don’t know, maybe there’s magic. Perhaps I need to be reminded that reference even needs to be successful – why can’t it just be a game of resemblance and recognition? What seem to be entities over time swap out their bits with other bits and it barely matters if the bits are the same bits so long as whatever bits are there are behaving in similar ways. We’ll quickly assent to the same observations when the bits move around. Twin Earth is Earth or not Earth and, sure, XYZ can be water if you want it to be and now I sound like a pragmatist so I’ll fall just short of that and say that I don’t see a difference made.

We can all have our own brain-bits differently-arranged and equally assent to the same observation sentences and whenever we generally agree on the borders around sets of bits we’ll call it an entity. Or, better still, we’ll each list off all of the types of entities that we think actually exist as fundamental and with each one take a sip of scotch. Whoever is left standing wins.


[1] Quine, W. V.  Pursuit of Truth. Revised Edition. Cambridge, MA: Harvard University Press, 1992. Print.

[2] Hylton, Peter. Quine. New York: Routledge, 2007. §5, V.

[3] Leonardi, Paolo and Marco Santambrogio, eds. On Quine. Cambridge: Cambridge University Press, 1995). p. 350.

[4] Hylton. Quine. §5, V. #


In Book I, Chapter VII of his Confessions[1], Augustine makes some comments on the innocence of infants. I’m not a huge fan of religious philosophy, but I found this passage kind of amusing.

Augustine says that the actions of infants are “reprehensible” (8), the way they cry loudly for nourishment, constantly demanding the attention of their mother. Infants become intolerant of others, their parents and strangers, who do not obey them, often lashing out “with sheer will to hurt” (9). They also complain and demand things that aren’t even in their best interests. Augustine remarks that such actions would not be tolerated of an adult; in fact, an adult behaving in such an infantile manner would rightfully be the subject of scorn and ridicule. One cannot blame infants for the way they cry, of course, since they do not know what is wrong with their behaviour. However, Augustine says that such behaviour is clearly wrong, for as the child grows up there is an attempt to put an end to such behaviour, creating a more calm and polite child. Were it correct, it would be allowed to continue as the child matures.

Because of this clear wrongdoing on the part of infants, Augustine wonders why it is that infants are thought to have innocence. He concludes that it must not be anything having to do with the mind of an infant, since as has been shown, infants are not in possession of finer human qualities like humility and patience. Quite to the contrary, infants are selfish, impatient and impolite, and thus can rightfully be labelled as sinners. Instead, Augustine says, they must be innocent only in the sense that they are helpless.

He goes on to provide further evidence that the state of the infant’s mind is sinful, by means of demonstrating infant jealousy. He says that he has seen a case of a baby who was watching another feeding at a breast. The child who was watching was “livid with anger” (9), despite being too young to even speak. This jealousy shows an unwillingness to share readily-available milk with a child that will not survive without it, though the child likely doesn’t understand this. Still, this shows that infants can be guilty of jealousy and of gluttony. For Augustine, referring to infants as innocence seems to refer to “an odd kind of innocence” (9).

On this account, infants get away with their behaviour and allowed to act in the manner they do not because their behaviour is correct or sinless, but because it “will pass with the years” (9). Adults only allow infants their sins because they are short-lived.

So how about that? Normally we think that infants are innocent because of their ignorance — though ignorance doesn’t count as a defense later in life.

It turns out, they’re just awful.


[1] Augustine. Confessions. Second Edition. Trans. F. J. Sheed. Ed. Michael P. Foley. Indianapolis: Hackett, 2006. pp. 8-9. Print. #

Epistemology, Metaphysics, Philosophy

In his Mind and World, McDowell contrasts three positions in his concerns with spontaneity and intentional states in general. These are what he calls bald naturalism, rampant platonism and naturalized platonism, the last of which he defends. What McDowell calls ‘bald naturalism’ I will argue for, but I will refer to it more favourably, as ‘naturalism proper’.

The proper naturalist position counts the mind as part of the world, as McDowell wants to do. What a naturalist proper cannot coherently talk about is the Kantian subject. Instead, there are only objects. For those who would say that things are only objects in the sense that they are the object of some subject, then we may use the word ‘substance’, in the earlier Greek sense, to talk about physical things. Thus, the naturalist position is that everything is a substance; in Heidegger’s terminology, everything is essentially present-at-hand[1] and though further supposed properties or features of substances (readiness-to-hand, the existence of Dasein, the mind, intentionality, subjectivity) are reducible to that raw substance. In contemporary physics, that substance is identified with particles, though the details may be somewhat more complex than that[2]. The manifest image of the world[3], the normative space in which intentionality and morality are thought to lie, is composed of that same physical substance that makes up the brains of those who experience and project outwards.

So, for the naturalist proper, the space of reasons is not a realm outside of the natural or physical world, as it is in rampant platonism, nor is it an autonomous space within the world as it is in McDowell’s naturalized platonism. Rather, all rationality, normativity and intentionality is identical with brain states. There is no one space of reasons with which human beings have a connection; rather, each human being can be thought to have their own space of reasons. This space is not especially private, though. It can be seen physically by examination of the neurological states of the brain, and with the proper technology, those states may even be translatable into intelligible images. In another sense, it is not fully private, since glimpses into its content can be seen through behaviour.

‘Content’ needs qualification in that last remark. Intentional mental states are mental states that are about something else in the world. But they are neither a metaphysical link through some imaginary (or real) space to other substances which they are about, nor are they really representations of the substances they seem to be about. They are not the former because such space doesn’t exist in any important way. They are not the latter because, of course, the neurological features of our brain do not form a structure that mimics the outside world. Rather, they form a structure that allows us to have a mental state (which is identical with that brain state) such that we think we have a representation of the substance we are thinking about. So, when I close my eyes and picture the CN Tower, I do not obtain or summon some representation of that object. That object may be gone, moved, or different than I remember. Instead, my brain generates a certain arrangement such that it looks like the CN Tower to itself.[4] All of the qualia, ‘what it’s like to be’[5] and private world phenomena that philosophers expect to find in a separate mental world are  merely what the brain’s activity looks like from the point of view of that very brain.

Against the rampant platonist, the naturalist’s response is brief. Whatever attitudes one has towards the empirical observations with which one is presented, one does not survive without indulging in them. With a proper account of naturalism, any reason to favour a platonic account dissolves. Naturalism proper offers an explanation of intentionality, removes the “spookiness” (McDowell 92) of a separate space of reasons that McDowell complains of. We don’t need to add anything ontologically, and we have a hope to answer the how questions about mental states and intentionality through study of the brain. Spontaneity doesn’t need any explanation here, either, because it is not sui generis, if it’s counted as existing at all. We’re better off with the naturalist account.

Against McDowell’s naturalized platonism, the proper naturalist has to say that McDowell is wrong about naturalism. He argues against his ‘bald naturalist’, saying that “knowing one’s way around the space of reasons, the idea of responsiveness to rational relationships, cannot be reconstructed out of materials that are naturalistic” (McDowell 77). But the naturalist proper doesn’t want to reconstruct a space of reasons, really. The naturalist proper holds that all reasoning, all intentionality, all communication—the entire manifest image—takes place between physical substances across physical substances. The naturalist isn’t committed to reconstructing any intentional state beyond this because she doesn’t hold it to exist. What counts as intentionality for a naturalist proper is evidenced through behaviour, and it consists of a brain processing incoming information. The space of reasons, the finer points of language, art, morality, knowledge and so forth can be talked about as abstractions. They are useful in the processing that the brain must do; they result in digestible inputs. But the naturalist proper is ever-mindful that these are not things in themselves, but that they are always identical with and reducible to the states of the brain. The same holds of spontaneity. The naturalist counts human judgments to be determined (in a deterministic or indeterministic sense[6]) by the physical processes that cause them. Thus, spontaneity can be said either to not really exist, or at least to be denied status as sui generis, as is the case with the other ideas McDowell wants to preserve. Where McDowell wants to say that human beings are free to choose their beliefs, to take their experiences and spontaneously form judgments about them, the proper naturalist denies this. For the naturalist proper, sometimes brain states will have the disposition to respond to the stimulus of a red bench and form the belief that there is a red bench. Sometimes, because of other beliefs, brain states will not have such a disposition and will not form such a belief. Whether or not this happens is not an act of spontaneity, but a function of the states of the brain, including the stimulus received and the beliefs already held.

By positing an autonomous space of reasons, and a second nature with which humans can access it, the naturalized platonist gains little in the way of explanation and much in the way of recalcitrant philosophical questions. McDowell thinks that he gets out of the “threat of supernaturalism” (78) by saying that scientific advancements don’t clarify nature as a whole, but only the realm of law. This step does not work; it only redefines “nature” to include what the naturalist counts as supernatural. McDowell renames nature as the realm of law, says that the platonic heaven, the space of reasons, also exist, and says that there’s this new thing, now called nature, previously called existence, which encompasses all of them. The connection between the realms of laws and reasons is as sketchy as ever, and it is only through proper naturalism of intentionality and spontaneity that the confusion is finally dissolved.


[1] See: Heidegger, Martin. Being and Time. Trans. John MacQuarrie and Edward Robinson. New York: Harper & Row, 1962. p. 98; p. 69 in the original German.

[2] String theories and wave-particle duality in physics play a role here, but they are beside the point. Scientific skepticism about what substances are physically is important. Equally important is the fact that extra-physical phenomena haven’t turned up at all. That is, the naturalist account is the best lead we have.

[3] From Sellars.

[4] …because we are always our physical selves and are never apart from our brains.

[5] From Nagel.

[6] Indeterminism as is afforded by quantum mechanics offers a sort of natural spontaneity, but it is not immediately clear how, or even if, this would impact judgments. #

Logic, Philosophy

Here’s a tautology in propositional logic:

⊨(P → Q) ∨ (Q → R)

Try throwing that into English. Here’s a reading using some propositions I just came up with:

“I’ll die if I’m immortal, or I’ll live if I die.”

Obviously, neither of those are the case. But this formula, (P → Q) ∨ (Q → R), is both provable and self-implied in classical propositional logic.

Here’s a syntactic proof by means of natural deduction using some basic rules of inference:

Continue Reading #

Epistemology, Logic

In his essay “Empiricism and the Philosophy of Mind” (1955-56), Wilfrid Sellars launches an attack against sense-datum theorists. I don’t want to defend sense-data because I think that’s a flawed concept, but I do want to point out a misstep that Sellars makes in this paper.

This objection has probably been made before, but for the sake of my notes I’m spelling it out as I read it.

In the paper, Sellars runs through a set of three propositions that he believes that sense-datum theorists must hold, but that Sellars believes is inconsistent.
Continue Reading #