The Identity of Indiscernibles

This post distinguishes between substantivalism and relationalism, and how the principle of the identity of indiscernibles threatens substantivalism. Then we’ll evaluate the principle, showing under what conditions it is plausible.

We will assume Leibniz’s view of relationalism. Broadly, this is the view that there are no substances such as space and time. Rather space and time are real only insofar as they are basic relations and properties between material objects – they do not exist independently of material objects. Facts about space and time are derived from material bodies, and without material bodies or events, there simply are no facts about space, time, or their relations. So, what makes it the case that the basketball is five feet away from the hoop is nothing over and the fact that there is a basketball and a hoop that are such-and-such apart.

Substantivalism is the denial of relationalism: space and time are substances which exist independently of any material objects. Consequently the substantivalist can imagine an empty universe, or an empty space/time container, where only facts about space and time obtain. So, what makes it the case that the basketball is five feet from the hoop is that the basketball occupies one region of space and the hoop occupies another, and those two regions are some equivalent of five feet apart. This way we can explain spatial relations without taking them as basic in the sense that relationalism does.

To explain the problem of a Leibniz shifted world, we need to explain the principle of the identity of indiscernibles. This principle states that if any two objects are indiscernible, then those two objects are identical. Two objects are indiscernible if they share all their properties and there does not exist a property belonging to one which does not belong to other (or vice versa) by which you could tell them apart. Jackson and Geoffrey are discernible in that one wears glasses and the other doesn’t. So Jackson and Geoffrey are not identical. Mark Twain and Samuel Clemens, however, are indiscernible. You’ll find they have an identical genetic structure, both occupy the actual world, and both are named both “Mark Twain” and “Samuel Clemens”.

Substantivalism holds absolute time as an ordered set of instants, and the universe must have come into existence in (an arbitrary) one of these instants. These two facts entail that there could be a possible world which would have come into existence at different instant, but otherwise contains all and exactly the same events as our actual world with all the spatial and temporal relations between material bodies being the same. This is one example of a Leibniz shifted world, a world which is identical to ours, except differing in some “absolute” property (e.g. time of instantiation, where that entire world is drifting to the “left” at 5m/s).

Because their relative spatial and temporal relations are identical, the only way they could possibly differ is in an absolute spatial or absolute temporal property. But their arbitrary absolute differences are weak grounds for discernibility. Why should “God” choose to instantiate one world at one time and another identical world at another? Intuitively, there is no reason that God should choose to instantiate two identical worlds at two arbitrary points in time, with some particular duration of absolute time between them. In the spirit of parsimony, the worlds are indiscernible, and so, by the principle of the identity of indiscernibles, they must be identical. But their identity contradicts the claim that there could be a relatively identical world to ours that comes into existence at some other instant of absolute time. If you subscribe to absolute space or time, then your only option is to abandon the principle of identity of indiscernibles.

But is problematic, for this entails the possibility of Leibniz shifted worlds, and this entails an unnacceptable proliferation of relatively identical possible worlds – indeed, we could have an infinite set of these, each differing only in, say, absolute time instantiation. Prima facie, we have better reason to maintain the principle of identity of indiscernibles than to admit the possibility of this proliferation.

The substantivalist might reply by rejecting the principle of indiscernibles. It is logically possible that the universe should have contained nothing but two exactly similar spheres. Every quality and relational characteristic of one holds also of the other, in virtue of the symmetric relations between the two spheres. You might think that the one sphere has the property of being not the other sphere. But this property is also true of the other sphere.

If we introduced an observer, he might name one sphere “A”, and the other sphere “B”. Then A has the property of being -B, a property which B cannot have, so they are discernible and not identical. But there are two considerations here. The first is that by naming them different things, an observer is merely stipulating that they have the property of being different, which is uninformative. The second is that this difference in property is dependent on there being a “namer” in the universe, so this purported difference in property is really more a feature of how observers apply names than a feature of genuine property difference between the two spheres.

It is tempting to think that the spheres differ in virtue of the fact that one is located in a place that the other is not. But their spatial relations are identical, so the only way we could point to this difference in property is if we say that A occupies location R and B occupies location S. But this move can only be made if we admit that regions of space are independently existing things, not merely a consequence of brute spatial relations between objects. So the relationalist would have to concede absolute space to the substantivalist.

If we introduce an asymmetric observer, however, one sphere will be on the “right” and the other on the “left”. Then the spheres would have different properties. So it is logically possible that the spheres have different properties. The substantivalist admits this, but holds it is in virtue of newly acquired relational characteristics. But the relationalist might argue modal properties are real properties.

Here’s how that argument might run. The substantivalist holds that A and B have the same properties. The spheres are equivalent in that they both satisfy all the same propositions. Each sphere must bear a reflexive relation to itself and a symmetric relation to the other. But the substantivalist admits that if there were an asymmetric observer, then the two spheres might have different properties. But we can say something stronger. For an asymmetric observer must be an observer which is closer to the center of one sphere than the center of another, and so it is necessary that the spheres would have different properties (qua to the observer).

So the substantivalist has admitted that it is possible that it is necessary that A and B are not equivalent. This, together with A and B being symmetric, entail that it is not the case that A and B are equivalent, by the axiom of symmetry.1 But if A and B are not equivalent, then they cannot be identical, contrary to the substantivalist’s supposition.

But the substantivalist might reply as follows. In instantiating the asymmetric observer, the spheres are no longer symmetrical in all their spatial properties. Using the axiom of symmetry, then, is not valid.

At this point, it’s hard to see who is right. Because the relationalist might think that it is possible that there is an asymmetric observer before we move to instantiate one. And from that observer’s perspective, it would be necessary that the two spheres are distinguishable in virtue of a spatial-relational property. So before we have disrupted the purported symmetry, there is already a difference in (modal) properties between the two spheres.

The tension here is that discernibility seems to essentially involve the idea of some observer doing the discerning, whereas identity is an objectively necessary condition for this being this, regardless of observation. Two things are indiscernible iff it is logically impossible for an observer to tell them apart. The asymmetrical observer can discern between the spheres (so it is logically possible). But when left out, it is logically impossible to discern between them, so the relationalist cannot explain why they are not identical. (There’s a certain antimony here.)

The notion of a point of view is required for discernibility to be logically possible, if the two spheres are not in fact one and the same. I am not sure what resources the relationalist has to be able to make sense of “point-of-viewness” – without positing an observer – in this situation. But if he can make sense of this, then he will have a means of discerning between the two spheres and so can explain why they are not identical. But if he cannot, then we really can conceive of two spheres which are indistinguishable but not identical. That would falsify the principle of the identity of indiscernibles, and so defang Leibniz shifted worlds.

1 Axiom of symmetry: <>[]p → p

Intuition, Space, and The Singularity Argument

This post will interpret what Kant means by ‘intuition’ and then explain his singularity argument for space’s being a pure intuition.

Intuition is an immediate relation between a mode of knowledge and an object, to which all thought is directed (A19).  By ‘immediate’ we mean that intuitions do not relate to by means of some other thing (e.g. another representation, conceptual or otherwise).  Rather, if I am intuiting some object K, my thought is immediately directed to the K-ness of K; my mind is directly aware of K.  We intuit an object only insofar as the object is ‘given to us; an object cannot be given to us unless our mind is affect in the right way (A19).  We are given objects via sensibility (B34).  This means only sensibility can give rise to intuitions, for an intuition is a direct relation to an object and objects are only given through sensibility.  There is a post before you: you stand in an immediate awareness relation to it: you are intuiting an object, namely my Kant post.

Intuition is to be distinguished from concept.  My concept of K refers to k(s) indirectly — that is, ‘mediately by means of a feature which several things may have in common’ (B377).  Call it the generality criterion.  My concept of an elf refers to Galadriel (and Legolas and Haldir) by means of feature(s) they share, e.g. pointy ears or forest-frolicking, (and not by my representation of the totality of elves).  So I can indirectly refer to Galadriel and Haldir by considering and representing the concept of pointy eared forest-frolickers.

This means that intuitions must be singular representations, in the sense that they always present a particular, single object.  Why?  Because in intuition the relation between knowledge and object is direct unmediated.  If your relation were indirect, then you would be representing features that a set of objects share, not that particular object as it appears to your sense organs (and so this could not be called a singular representation).  Your intuition of an object is brought about from a particular object affecting your sense organs, consequently it must be a representation of that object producing those sensations — that is to say, it must be a singular representation.  Call this criterion for intuition ‘the singularity criterion’.

There is always an object of thought — something to which the thought is directed (A19?).  This means that all thought must, directly or indirectly, relate to intuitions (B34).  For objects are given to us only through sensibility, and sensibility alone produces intuitions.  So if a thought could not relate, in some way, to an intuition, then there could be no object of the thought — and a contentless thought is no more a thought than a blank square of glossy paper is a photograph.

An object affecting our faculty of representation is a sensation (B34).  An intuition is empirical iff relates to an object of sensation.  (The [undetermined] object of an empirical intuition is an appearance [B34].)  So in experience there is an appearance which affects my sense faculties, producing sensations of, e.g. browness, bitterness, warmth. (A cup of coffee?)

That quality of an appearance which allows its (that is, the appearance or sensations) being ordered in a certain way is the form of appearance (B34).  Sensation is not the form/arrangement/ordering of sensation — to say that sensations are ordered is not to say that sensations are an ordering or arrangement.  Because the form of appearance is divorced from the sensation of the appearance, the form of appearances must given to us a priori. For objects affect our sense-faculties and are given through sensibility, giving rise to sensation, but sensations are not orderings — only effects of objects on our mind.  So the ordering cannot come from experience of objects — it cannot be a posteriori — and so it must be a priori, in the mind (B34).

A pure or a priori intuition is an intuition-sans-sensation.  (Consequently, pure intuitions are present even in the absence of all appearances.)  That is, a pure intuition contains nothing (or rather, is of nothing) but the form of sensibility.  The form of sensibility is a feature of our minds which determines the manner in which we necessarily must represent things.  It gives rise to two pure intuitions, (1) the representation of space and (2) the representation of time. We say representation of space/time because pure intuitions, as containing nothing but the form of sensibility, are mind-dependent and not mind-independent features of the world.
We’re now in a position to explain Kant’s singularity argument for space’s being a pure intuition, as opposed to a general concept (e.g. a general concept of the particular spatial relations of things).  Recall that intuitions are singular representations: they are not representations of features which a set of objects might share; they are always representations of singular/particular objects.  Kant’s aim is to show that space is a particular representation which contains nothing but the form of sensibility.

Kant’s first premise is that ‘we can represent to ourselves only one space’.  By ‘space’ here, Kant has in mind the representation of the single all-embracing space.  That is, the space in which all our intuitions of outer sense take place or are seemingly represented.  (If Kant did not mean the ‘all-embracing space’ then this first premise would not make sense, because we represent particular objects in particular spatial locations and arrangements, and so there would in fact be multiple spaces we represent, contrary to his opening premise.)

Because we can represent to ourselves only one space, the representation of space must be an intuition.  Why?  If we can only represent one all-embracing space, then our representation of space can only be of one, single thing.  This means that it is a representation of a particular thing.  Representations of particular things are always intuitions, by the singularity criterion.  Our representation of space is not a conceptual representation of general features of space that all spaces or spatial things share, rather it is the particular manifold upon which my sensations of particular objects take place (B34).

Prima facie, this looks like a misapplication of the singularity criterion.  Consider our representation of God (a maximally perfect being).  God is certainly not an empirical intuition (nor is She an a priori intuition).  Rather, our representation of God is formed from conceptual representations finitely and relatively perfect beings (presumably we relate these conceptual representations in such a way as to form a concept bearing maximal perfection as a feature.  In a similar way, you might think that our representation of all-embracing space is formed from the conceptual representation of a finite space (or spaces).  That is, the concept of our all-embracing space is formed from considering and representing the aggregate of all objects falling under the general concept of space, in order create a sort of infinite ‘all-embracing’ space (B40).

But the subsequent portion of the singularity argument aims to overcome this objection.  A part of space cannot be prior to the singular, all-embracing space.  Therefore, parts of space are not constituents composing the all-embracing space, but rather we can only think of parts of space as being in the all-embracing space (A25).  Consequently, we cannot build a general concept of space out of the concept of a space.  Why is the all-embracing space prior to a part of space?  For Kant, space is ‘essentially one’ (A25).  All things in space (parts of space, empirical intuitions, etc…) depend on placing ‘limitations’ on space.  To bring this out, consider your representation of a particular region of space.  In representing this, you must also represent it as having bounds.  In representing it as having bounds, you represent it as being surrounded by \psi.  The only plausible candidate for \psi is the all-embracing space.  Therefore, the representation of all-embracing space is necessary for any particular representations within its manifold.  This entails that the intuition of all-embracing space is a condition on our representing particular spaces (and things in them).

So space must be an a priori intuition, for two reasons.  (1) Our representation of all-embracing space is singular, so it must be an intuition.  (2) Our representation of space is the condition on our having empirical intuitions, but the representation of space itself does not depend on any particular mind-independent objects and as such cannot be empirical.  Therefore, it is a priori.

Briefly on Modality and Possibility

Consider statement \alpha, ‘McCain could have won the 2008 election.’  What makes statements about what is possible (but not actual) true or false?  You might say that, ‘there exists a way things could have been, such that McCain was the winner of the 2008 election.’  One interpretation of what it is for that to be true is to read, ‘there exists a possible world where McCain wins the 2008 election.’  This raises the question ‘what is a possible world?’  We will discuss two views addressing this, (1) linguistic ersatzism [LE] and (2) modal realism [MR].

A possible world is like a ‘worldbook’; something that describes to the very last details everything that is true of the world.  Think of a worldbook as a maximally complete and consistent set of propositions.  Proposition \beta, ‘McCain is the winner of the 2008 election’ is an element of a consistent set of propositions — it cannot include \neg \beta, e.g. \gamma, ‘Obama is the winner of the 2008 election’, because then the set would be inconsistent.  So the  complete and consistent set that includes \gamma must be different than the set that includes \beta, and so each set must be describing a different possible world.  In contrast, saying that ‘it is necessary that Obama wins the election’, means that in every possible world Obama wins the election — though this is likely false.

LE sits nicely with this.  An ersatz possible world is an abstract formulation of a possible world, namely a set of propositions (abstract like the set of natural numbers).  To define a set of propositions, a world making language is used, e.g. the lagadonian language.  Let each object and property in the actual world be name for itself, e.g. if there is a grey table, then it also represents the proposition ‘the table is grey.’  We can recombine objects and properties in conceivable ways (like ‘the table is blue’), each recombination defining a possible world.  So all possible worlds will be some recombination of the objects and properties of our actual world, to be identified with abstract, complete, and consistent sets.

On LE, to say \alpha means that there exists a complete and consistent set of propositions which contains \beta.  Crucially, there is no commitment to the abstract set actually being instantiated somewhere in reality.

MR, championed by David Lewis, maintains that the possible worlds must be real, concrete entities, as opposed to abstract sets.  (With ersatz possible worlds being the mere abstractions of the concrete possible worlds.)  Lewis cannot conceive of our actual world as a mere set of consistent sentences; consequently, he cannot conceive of possible worlds as being mere abstractions.  This is prima facie parsimonious: we are not asked to believe in any strange, new kind of thing, but rather just an infinity of things of exactly the same kind of thing as our own universe.  On this view, each possible world is as real as our own, and each is causally and spatiotemporally isolated from the other.  ‘Possible’ is to be contrasted to ‘actual’ insofar as ‘actual’ is treated as an indexical.  That is, ‘the actual world’ refers to this world, the one occupied by us.  When a person in a different world says ‘actual’ they are referring to their world.  A possible world is the same kind of thing as the actual world, but with varying degrees of differing facts.

On MR, when I say \alpha, I am saying that there exists a possible world where a counterpart to the John McCain in the actual world wins the 2008 election.  A counterpart is an entity in a possible world bearing the relevant similarity relation to the entity-in-question in the actual world.  Relevant similarity is dependent on the context of the modal statement, for the similarity between any two objects is dependent on the aspect of their comparison.  So \alpha means there is a possible world where a counterpart McCain wins the election — the actual McCain and the counterpart being united by their relative similarities insofar as, e.g., being a senator, a war vet, or such-and-such age.  But if I say that \neg \alpha, then any would-be counterpart of McCain who does win the election is not a genuine counterpart, because for me the relevant similarity relating them is not just that he is a senator, but also that he loses the election.  So on MR, what makes it possible that \phi could be \psi is that there exists a possible world, just as real as the actual world, where a counterpart-\phi is in fact \psi.

Neither MR nor LE, however, is palatable.  Analyzing modal statements in terms of possible worlds is unintuitive and a mistake.

Here’s why.  Intuitively, when we say ‘\phi could have been \psi‘ we are stating a (modal) fact about this world that we inhabit.  We are trying to evaluate something about the potentialities of our universe; we are not trying to evaluate the truths of other worlds, but rather about our world (what is possible for it).  On both LE and MR, our modal statements will not be about our world at all — and this is why they are unsatisfying.  According to MR, saying \alpha is just to say ‘in another spatiotemporally/causally isolated world, \beta.’  So a modal statement in our world is not actually about our world at all — rather, it states a fact about some other world, failing to say anything insightful about our world.  Knowing that something is true in a possible world does not entail that that thing is possible in our world, for the spatiotemporal and causal isolation between worlds makes it such that there cannot be a meaningful relation between worlds.  So facts in one world entail nothing about facts in another world, the mere fact that \phi in world \Gamma entails nothing about \phi in world \Delta.  Intuitively, that \phi is a possibility for our world is a fact about our world.  Enumerating the facts of other worlds can tell us nothing about our own.

This applies equally to LE.  When I want to know whether something is possible, I do not want to know whether it is part of an abstract, consistent, and complete set.  Rather, I want to know whether events in this world could have unfolded such that some other thing could have occurred.  We may be able to define a complete and consistent set where the gravitational constant is $1/g&bg=e7e5e3$ (instead of $g&bg=e7e5e3$) — but this does not entail that that is a genuine possibility for this world.  In this way, LE equivocates conceivability and possibility.  But we seem to be saying something different when we say something like ‘it is possible that \phi‘ versus ‘it is conceivable that \phi‘.  The latter does not entail the former.

So how do we think of \alpha without the aid of possible worlds?  Prima facie, \alpha, if true, suggests there was a time in this world where things could have turned out such that \beta.  But what does it mean for \alpha to be true in this world, where \neg \beta obtains?  What facts, without possible worlds, make something like \alpha true?


Interested in other thoughts.  May update with my own.

Hobbes’ Commonwealth

In this post I will interpret Hobbes’ explanation of commonwealth via institution (C_I) as a means of escaping the ‘state of war’ (S_w).  Subsequently, I will consider an objection regarding the feasibility of forming a C_I in S_w, and then consider how Hobbes might reply.

A state of nature (S_n) is where there is no authoritative power to constrain people, no obligations nor civil laws, and all have a natural right (R_n) to do whatever he can to ensure his own self-preservation (SP) (103).  In S_n, all people have natural equality; each of us has the power to kill anyone else — no one is so superior to anyone else that they can, individually, ensure their SP (99).1

Three factors cause the S_n to evolve into S_w, viz. (a) competition, (b) diffidence, and (c) glory.  (a) People often desire the same things; natural equality means each person has reason to believe that they have a chance to attain their desires over others, leading to fighting, promoting S_w.  (b) A person realizes that at some point they may have to compete with others, and inaction just allows others to grow stronger as they compete, subdue, and acquire their desires; immediate action allows the person to strike when others are still weak.  But if a person can think this, then it is like that everyone can think this.  So everyone realizes that immediate action, going on the attack, is in their best interest.  And if everyone is predisposed toward aggression, then no one can be trusted, promoting S_w.  (c) Some are disposed toward vanity; they overestimate themselves, and think they are capable of, and that they enjoy, subduing others — they are easily dishonored, so take offense easily, thus promoting S_w.  Clearly, S_w promotes no one’s SP (99).

From R_n we rationally derive two descriptive conditions on behavior (the ‘laws of nature’ [Ln]. L1: we will do whatever we believe we need to in order to survive.  L2: we accept constraints on our conduct if we believe that others will accept similar constraints (104).2  A contract is a mutual transfer of rights (106).  Hobbes asserts that a contract becomes invalid as soon as one party doubts that the other party will uphold his end (108).3    A covenant is a kind of contract, namely a promise to be kept at a later time.  The third ‘law of nature’ (L3) is that men perform their covenants.  This straightforwardly follows from L1 and L2, for the person who breaks his covenant will not be covenanted with in the future, which bodes ill for SP, conflicting with L1 and L2.4  Injustice consists in breaking your covenants.  An obligation is a duty to obey another, only acquired through voluntary consent (for we are [initially] naturally free and equal [165]).  Because S_w is owed to natural equality and (a)(b)(c), to escape S_w, we must voluntarily consent to obligate ourselves to an artificially unequal power, a sovereign, with two attributes: the unlimited, unique, and virtually unconditional (1) right to command others and (2) the right to act (in whatever way).5  (1) Means that others have a duty to obey the sovereign, regardless of the nature of his command.6  (2) Means there is nothing the sovereign has a duty not to do, giving him the power to decide on and enforce his law.  The sovereign’s rights quench (a)(b)(c), and glory because the sovereign becomes the justly agreed on arbiter of resources and acceptable action (via right to command) and, moreover, has the power to enforce his will unconditionally such that all are compelled to obey, through voluntary consent (via right to do).  In addressing (a)(b)(c), we remove ourselves from S_w to the obeisance of an unequal, artificial power.

We cannot escape S_w and form C_I without obligating ourselves to the sovereign.  For everyone covenanted with each other to live peacefully, without installing a sovereign, then there is no external force to which they are obligated or can compel them.  Without this force, I have reason to doubt others’ veracity, and so the covenant is invalidated.  But to form a C_I is to install a sovereign who can punish those who do not keep their covenants makes it such that the everyone’s adherence to the covenant is in the interest of R_n.  When we covenant to form an institution, each person covenants which each other person to create a sovereign to whom they are all obligated by way of voluntary consent and whom is not obligated to them.  They cede their natural freedom to the sovereign; natural equality gives way to artificial obligation as the sovereign is created and ascribed these authoritative rights via voluntary consent.  Disobeying the sovereign to whom you are obligated constitutes injustice.  Crucially, this is not a covenant between the people and the sovereign — the sovereign is not a party to the covenant.  For if he were, then there would be condition on the sovereign’s power, namely that he uphold his end of the covenant.  And if anyone felt he had violated the covenant, then the whole covenant between the people and the sovereign would become invalid.  So in order to preserve the institution, there cannot be anything that the sovereign does which constitutes a breach of covenant; this means that he cannot be party to the covenant.  (Consequently, nothing the sovereign can do can release us from our obligation to him, and for any subject to fail to recognize the sovereign performs injustice, for the covenant is to recognize and obey the whomever the majority of the convention agree upon.)  Everyone can be assured that everyone else will keep the covenant — that is, obey the sovereign — as the sovereign has the right to command and do and so will punish anyone who breaks the covenant (recalling that breaching a covenant constitutes injustice).

Hobbes’ explanation of C_I relies on the derivation of L3 from L1 and L2, for without L3, there is no reason to expect anyone else to keep their covenant and so it is immediately invalidated.  But this derivation is tenuous.  L1 and L2 are both firmly grounded in human desire for SP.  This means L3 must be firmly grounded in the same.  But L3, as stated, doesn’t straightforwardly trace back to SP — it is not as though keeping covenants is entailed by your desire for SP.  The justification for L3 is that if you keep your covenants, people will covenant with you in future, which is better for your SP than not.  But intuitively, it is possible that breaking a covenant is better for your SP — albeit if only for temporary, short-term SP, rather than ‘the long run’.  But intuitively, people will only covenant with you if they believe that you keep your covenants, regardless of whether or not you actually do.  So what we can actually derived from L1 and L2, insofar as they trace to SP, is that men intend to appear as if they keep their covenants (L3*) — not that they actually do.

So in S_n, I know I am assure of L3*, but not L3.  But if I know this, and I know that everyone else knows L1 and L2, then I know anyone else is assured of L3*, but not L3.  If this is so, then diffidence must invalidate the covenant of C_I — regardless of our self-preservatory contract to obey the sovereign.  For there is no reason I shouldn’t suspect that someone is irrationally vain, overestimates himself, and plans to act as if he will uphold the covenant (publicly) — with know intention of keeping it (privately) — then he will take everyone else unaware, subdue them, and achieve the fulfillment of his own natural desires or SP).  If I know anyone else knows this, then I know everyone else has a reason to doubt the covenant, and the mutual doubt invalidates the covenant ipso facto.

You might think that such a vainglorious betrayal is antithetical to SP, for there is no reason to think that you might survive such an attempt.  Consequently, there is no reason for me to think that anyone would attempt such a coup — especially given the artificial strength and rights of the sovereign — it would be simply irrational.  So for Hobbes’ explanation of C_I to work, we need an additional assumption, namely each person assumes that each other person is rational (and would not get caught up in feckless vainglory).  Assuming rationality is importantly different from assuming the desire for SP.  Though Napoleon was irrationally vainglorious, he surely desired SP.  Clytemnestra publicly upheld her covenants, only to privately slay Agamemnon.  It was not that she didn’t desire SP, it’s that she mistakenly (and perhaps irrationally) thought that she could keep up her appearance to everyone else.  So in order to derive L3 from L1 and L2, we must further assume that no one becomes irrationally mistaken or vainglorious, not just that everyone desires their SP.

Consequently, Hobbes’ justification of political authority hinges on whether this assumption is plausible — whether we are entitled to L3* or L3.  Intuitively, it seems hard to justify.  Indeed, a person intends to privately break a covenant only if they do not think their breach will become public.  If they succeed, there will be no consequence, and all will continue to (publicly) keep the covenant.  Situations where someone intends to privately break their covenant are easily imaginable.  Suppose the sovereign commanded that you must spin three times before stepping in the shower.  You know that if you don’t, it’ll be injustice.  But sometimes you are reasonably confident that no one is watching, so you step in without the spins, figuring no harm no foul.  And maybe you’re right.  The point is that private breaches of covenants are intuitively plausible.  And if this is so, then I am assured only of L3*, not L3.  I have no reason to suppose that people won’t try to privately break their covenants, nor reason to suppose that they won’t sometimes succeed.  Therefore, I have reason to doubt that the covenant will be upheld by others, and others have reason to doubt me, and so our covenant must be invalid.  If this is so, then it seems we cannot get C_I off the ground.


  1. Agamemnon, intellectually and physically capable, returned home from a victorious war, and was slain in the bathtub by his wife, Clytemnestra — he could not ensure his preservation despite his capability. 
  2. I give up my right to nuclear force iff (I believe that) you, too, will give up your right to use nuclear weapons.  Renouncing the right to use nuclear weapons is good for everyone’s SP.  L1 amounts to natural freedom; L2 amounts to voluntary duty or obligation. 
  3. Suppose we duel.  If you cede me your right to bring a knife to our fist fight, I’ll cede mine.  If we agree, but I come doubt the contract (perhaps I see a knife hidden in your boot), then our contract is invalid and I can use whatever means at my disposal in our duel. 
  4. In S_w, there is reason to suspect covenants made, because there is no salient external force to compel people to keep their covenants. 
  5. No one else will have these rights. 
  6. Though its worth noting that you are not obligated to, e.g. kill yourself if commanded, for that violates L1. 

The Doctrine of the Mean

In this post I will explain Aristotle’s doctrine of the mean.  Subsequently, I will consider an objection that not all virtuous actions conform to the doctrine.  Then I will reinterpret Aristotle such that he can reply to the objection.

Moral virtue is a state of character regarding the passions, actions, and choices of the agent.  Passions are feelings like anger or lust, typically accompanied by pleasure or pain (handout).  When an agent chooses an action, he is intellectually endorsing it or setting it as his intended action.  An action is what is actually done.  To be in a virtuous state will be to have the right balance within and between the passions, actions, and choices — it is to feel $\phi$ toward the right object, at the right time, to the right people, with the right motive, in the right way (30).

Aristotle observes that it is ‘the nature of things to be destroyed by excess and defect’ (25).  Consider the virtue of courage.  The man deficient in courage never stands his ground against anything, and in so doing becomes a coward.  The man who ‘overshoots’ courage (that is, acts with excess courage) and never fears anything is rash.  But the man who knows when to stand his ground and when to withdraw and acts accordingly has the right about of courage and can rightly be called courageous.  To emphasize this, Aristotle points out that we call a work of art ‘good’ when there is no element of the work that we could either add or take away without diminishing the work.  That is, a good work of art is destroyed by excess or defect.  Virtue, as a similar good, will strive for the intermediate in the same way — that is, virtuous action is destroyed by excess or defect.  An action is virtuous or ‘good’ if that action would not be made better by the addition of something like (a passion, or a more extreme action) or the subtraction of something.  So a virtuous action is destroyed by excess or defect.  It looks like virtuous action admits of degrees, that it is a point on a continuous and divisible scale continuous and divisible.  For Aristotle, in all things that are continuous and divisible, it is possible to have more, less, or equal.  An agent acts courageously, but just before the act it was possible for him to have acted cowardly or rashly.  Aristotle takes the ‘equal’ amount to be that which is intermediate between excess and defect — the mean lies between the two extremes.

It is important to note, however, that what is the ‘equal’ or ‘intermediate’ amount is not the same for all.  Indeed, ‘equal’ or ‘intermediate’ amount is relative to the agent.  With respect to courage, compare me to Superman.  The courageous action for Superman may involve fighting evil and saving the day.  But I don’t have superpowers; if I were to confront evil like Superman, I may be defeated and (even worse) evil might prevail — I would be a victim of my vicious, rash action.  For me, the intermediate is more likely to be braving some minor danger so that I may call 911 or Superman for help, so that the day may be saved without endangering myself or others.  In this way, the intermediate action is relative to the agent (and that agent’s characteristics or abilities).  So the doctrine of the mean amounts to something like ‘do the right thing relative to yourself, in the right way, to the right people, in the right context’ — that is, do what is appropriate to the occasion, and not every occasion responds to the same treatment.

Having explained the doctrine of the mean, we’ll now consider the following objection.  Not all passions, actions, and choices (and the balancing between them) conform to the doctrine. To press the point, some actions just don’t seem to admit of degrees.  For example, consider the virtue of justice.  How can we make sense of an excess or deficiency of justice?  You might think that a deficiency of justice is a kind of iniquity where a few get all the goods and most are impoverished, while an excess of justice is a kind of iniquity where all get an equal amount of the goods but not all are equally deserving, and that in this way justice will lie between two extremes.  The problem with this view, however, is that we cannot make sense of individual action in this way.  Actions promoting the iniquity of resources are generally actions taken by the polis, not by an individual agent.  And the kind of virtue we are interested in is the kind that is ascribed to individuals.  How could an individual act with an excess of justice?  What kind of action could possibly embody the mean amount of justice?  It seems that one simply acts justly or unjustly.  If this is so, then not all purported virtues conform to Aristotle’s doctrine of the mean.  And if not all passions, actions, or choices fit into Aristotle’s doctrine, then there must be more to virtue than merely striving for intermediate action (even if a virtuous action can sometimes be thought of as a mean).  That is, virtue does not always strive for the intermediate.  Therefore, the doctrine of the mean, the thesis that virtue strives for the intermediate, must be false.

We might defend Aristotle with the following reinterpretation.  A person acts virtuously iff he strikes the right balance between passions and choices, is not externally inhibited in his action, and does in fact act.  In this way, the virtuous action is the product of the virtuous/right balancing of passions and choices, with the addition of nothing inhibiting the agent’s execution of the action.  What is important here is that the virtuous action flows from the right balance between passions and choices, not that the action itself is part of the calculus-of-virtue.  So we need not always be able to place an action in between two extreme actions.  Indeed, Aristotle recognizes this when he notes that it would be absurd to expect that in self-indulgent action there should be a mean (e.g. you end up with excess of excess) (31).  Similarly, we might think it absurd that one could act with an excess of justice.  So how does just action work?

A just action will not be between deficiently and excessively just actions, but rather will be the result of someone’s passions and choices being balanced in the right way.  An example.  Sam has eight cookies and he is deliberating over how to divide them between Tom, Dick, Harry, and himself.  His antipathy for Tom is palpable, but he’s clearly friendly with Harry; and he’s never met Dick before.  To divide the cookies justly, Sam must balance his various passions toward Tom, Dick, Harry, and himself.  And he must identify the right choice amid the manifold of chooseable actions.  Having done this, if he is not externally inhibited, he will perform the just, virtuous action.  For suppose he does not balance his passions the right way.  He let’s his antipathy get the better of him and gives Tom 0 cookies, while his friendship for Harry and his like for himself earns each of them 3 cookies.  His apathy to Dick earns Dick 2 cookies.  This inequitable distribution cannot be said to be the result of a just action, and the iniquity is attributable to the misbalance of the passions.  Or suppose Sam can manage his passions, he achieves a mean between his desire to stiff Tom, and his desire to give extra to himself and his friend, Harry.  But he cannot identify the right choice, and so he cannot equitably distribute the cookies.  This, too, cannot be called just.  However, suppose Sam balances his divergent passions, chooses to award everyone 2 cookies, and no external thing inhibits his ability to execute this choice.  Then there is an equitable distribution of cookies and Sam acted justly.  So we aim for the mean of our passions, identify and endorse the choice that brings our intentions about, and, if not externally inhibited, the virtuous action emerges as a consequence.  In this way, we can preserve Aristotle’s doctrine of the mean.