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.

Synthetic A Priori Knowledge

This post discusses what Kant means by ‘synthetic a priori knowledge.’ We will first discuss knowledge, then the a priori, and finally the synthetic.

For Kant, there are two stems of knowledge, viz. sensibility and understanding (B29). Through sensibility, we are presented with ‘objects’ — this can be thought of as perceptual experience. Through understanding, we think, compare, and combine our representations of these objects, and ultimately gain ‘knowledge of objects’ (B1). Understanding, or reason, supplies the rules of thought (B25), and determines how we can relate the items we are presented with in sensibility. Kant, however, acknowledges that all knowledge begins with experience in the sense that our acquaintance with objects gets our cognitive machinery started by affecting our understanding so that we might think or know what we get through sensibility (B1). Sensibility provides you with the ‘raw material’ for knowledge; understanding provides you with the ability to manipulate the raw material. If there is a brown table before me, sensibility provides me with the brownish and tablish features in experience, but understanding allows me to think that ‘there is a brown table before me’ or imagine the brown table being red. So it looks like knowledge is a special kind of relation between one’s representations acquired through sensibility and one’s pure understanding. Understanding endorses some representation(s) as true. Not all our mental representations will be true. But we do know some of them to be true, and the fact we know means we must be able to point to some kind of justification.

There are two ways that knowledge can be justified, viz. a priori or a posteriori. A priori knowledge is ‘any knowledge that is…independent of experience’ (B2). Kant distinguishes this from empirical or a posteriori knowledge, which is dependent on experience (like knowing that most swans are white). By ‘independent of experience,’ Kant means epistemic independence. It is knowledge that never receives its justification from a particular empirical experience, or even from a generalization of particular empirical experiences. An example may help (B2). You see a person digging a big hole beneath their house. A big enough hole will collapse the house. You know before the particular experience of the house collapsing that this person will collapse their house. Your knowledge, nevertheless, is not a priori because knowing that a big hole beneath a house collapses it is knowledge that could only ever be gained through experience. You must have investigated the world before you gained the knowledge that the house would fall. Moreover, Kant must mean epistemic dependence because he recognizes that all knowledge begins with experience (B1) — so the a priori must be independent of experience in some other modality, namely epistemically, not psychologically.

Two criteria for identifying a priori knowledge are (1) that the judgment is necessary and (2) that the judgment carries strict universality (B4). This is tantamount to saying that a priori knowledge brooks no counterexample. It is not possible for a priori knowledge to have been false. Because the a priori is not empirical, a priori judgments/knowledge is generated from the pure understanding or our faculty of knowledge (B5). The knowledge that ‘all bachelors are unmarried men’ is a priori because its justification is absolutely independent of experience. You know the proposition is true in virtue of knowing the meaning of the word ‘bachelor,’ you do not need to empirically investigate the world, checking each bachelor to make sure that he is unmarried. So a priori knowledge is the endorsement of a judgement whose justification does not depend on any empirical investigation.

The analytic/synthetic distinction applies only to judgments or knowledge that admits of a subject/predicate structure, for instance ‘All A’s are B’s’ (B11). In ‘all bachelors are unmarried men,’ the predicate ‘unmarried men’ is (covertly) contained in the concept ‘bachelor,’ making this an analytic judgment. In ‘all bodies have weight,’ the predicate ‘has weight’ is not contained in the concept of ‘body,’ making this a synthetic judgment. So a judgment is analytic if the concept of the predicate is contained within the concept of the subject; if not, then the judgment is synthetic. It is not clear, however, what Kant means by ‘containment.’ He provides some clues, namely that analytic judgments are those which connect subject and predicate through the law of identity, that the rest entirely on the principle of contradiction (Pro. 17) regardless of whether their concepts are empirical, but what is the law or principle operating on?

It cannot be identity of extension. Consider two sets: (1) the set of all creatures with hearts and (2) the set of creatures with livers. These two sets are coextensive. If extensional identity was all Kant had in mind, then the judgment ‘all creatures with hearts have livers’ would be analytic. But recall that all analytic judgments are a priori. We could imagine a counterexample, namely a creature that has a heart and no liver, but then this would contradict the definition of a priori. But Kant does not admit analytic a posteriori judgments, so analytic judgments based on the law of identity are not based on identity of the extensions of the predicate and the concept.

If B is not contained in A in virtue of their extensions, then perhaps B is contained in A in virtue of their intensions. Recall that knowledge is going to consist in some relation between our representations and our understanding. We might think of the intension of ‘creature with a heart’ as something like our completed mental representation of hearted-creatures. The essential features will be the concept of ‘heart’ and concept of ‘creature’ somehow united in our understanding. So the intension of ‘creature with a liver’ will be something else. We’ll have a mental representation that unites the concepts of ‘liver’ and ‘creature’ in understanding. So a proposition like ‘all bachelors are unmarried men’ is analytic (and a priori) in the sense the mental representations of ‘bachelors’ and of ‘unmarried men’ are identical — that is to say the judgment is explicative, the predicate adds no content the cognition of the concept; they are one and the same.

Synthetic propositions are not analytic or explicative. They are ampliative in that the predicate adds content to the cognition of the concept; the predicate extends our knowledge of the concept beyond what is merely ‘thought in’ or ‘contained in’ the concept. Indeed Kant puts it, ‘we are required to add in thought a particular predicate to a given concept’ (Pro. 19). That creatures with hearts have livers extends our knowledge of creatures with hearts.

So synthetic a priori knowledge will amount to the following. It is the endorsement of the truth of a mental representation (like a judgment), where the justification of the endorsement is epistemically independent of experience, and the predicate of the judgment is not intensionally contained within the concept.

Information, Mind, and Dretske

This post aims to present the pith of the first three chapters of Fred Dretske’s Naturalizing the Mind, namely the Representational Thesis (RT) and how it accounts for the qualitative, subjective, first-person aspect of mental life; raise some interpretive questions, and some possible responses.

1

The Representational Thesis has two central claims, (1) all mental facts are representational facts and (2) all representational facts are facts about information functions.  The mind being the ‘representational face of the brain.’  So now we ought to get a grip on the meaning of ‘representational fact’ and the meaning of ‘information function.’

Dretske characterizes representation in the following way, a system S: represents a property F, iff S has the function of indicating (providing information about) the F of a certain domain of objects.  S performs its (representational) function by occupying some different states $s_1,...s_n$ corresponding to the determinate value(s) of $f_1,...f_n$ of F.

An initial question: what makes a particular function an information function?

Dretske uses a speedometer as an initial example of representation.  A speedometer S, represents speed F, of a car.  S’s function is to indicate the F of the car.  The representational fact is that S has a speed indicating function, e.g. pointing at ’37’ is supposed to carry the information that the car is going 37mph.  The nonrepresentational fact is that S is connected to the axle by a cable.  The mere (nonrepresentational) fact about the cable connection does not imply that this physical arrangement has a function.  The representational fact is true in virtue of the fact that S is designed to carry that information.

So we may have a partial answer to our initial question.  The representational fact is true in virtue of the fact S is designed.  So design (or perhaps, intentionality?) is characteristic of representation functions.  The mere fact of the physical connection does not imply that S has a function, however, even if it does not have a function, S would still carry the information that the car is moving at (some speed equivalent to) 37mph.  This suggests (a) that the flow of information does not constitute a function, and (b) information and some function (which must in some sense be designed) are both necessary for representation.  What remains unanswered (at this point) is: what separates an information function from a representation function?  Moreover, it is prima facie the case that information is an output of some kind.  You don’t have one bit of information until you flip the coin and it lands ‘heads’ or ‘tails’.  At this point, I see no reason to discriminate between information functions and representation functions — if not addressed, this may become problematic.

2

Dretske emphasizes three ‘pivotal’ distinctions. (1) Natural vs. conventional representations, (2) representational states vs. representational systems, and (3) represented properties vs. represented objects. Conscious experience is a case of natural representation.

So, for instance, I am a representational system in virtue of the fact that I occupy representational states, like seeing the color blue or hearing the crescendo of an opera. There are two categories of representational system, viz. conventional and natural representational systems. Conventional representations are things like language or measured marks on a beaker (amounting to Gricean nonnatural meaning [meaning$_{nn}$]). Natural representations, however, come in one of two varieties, viz. sensory systems and conceptual systems. Sensory systems are things like experiences, sensations, or feelings. Conceptual systems are things like thoughts, beliefs, or judgments. Dretske implicates that sensory systems are natural to the system or simply part of the system, whereas conceptual systems are acquired by the system. This makes some sense, infants are born with their sense organs functioning (to some degree) while it takes years for them to learn to think, believe, and judge. In a certain sense, these natural representations seem to be varieties/instances of Gricean natural meaning (meaning$_n$). Dretske holds that the difference between naturally acquired and conventionally assigned functions entails the difference between natural and conventional representation.

Dretske explains the distinction between conventional and natural representations in the following way. Consider the fact that the size of an object is correlated with the temperature of that object. With the right background knowledge, one could look at a paperclip or a flagpole and (maybe with some calculation), calculate the temperature. A thermometer works similarly, the volume of the mercury expands or contracts in accordance to the temperature. Paperclips and flagpoles, however, do not represent temperature; thermometers do represent temperature (in the conventional sense). Paperclips and flagpoles do not represent anything. This is because we have not assigned paperclips or flagpoles the function of indicating the temperature. When an object’s informational or representational function is derived from the intentions of its designers, the resulting representations are conventional. From this we can infer that natural representations, and representational functions, are not derived from something with an intentional character. It’s worth noting that conceptual awareness, like thoughts and beliefs, will be classified as experiences and natural representations on this picture.

This raises the question, however, of how intention and design are related to each other. Dretske wants to maintain that something can be designed to have a certain function, without there being intention anywhere in the picture. After all, kidneys have a function (for we have no problem discerning whether or not they are functioning properly), but we do not think that some entity with intentions (which, I think, are a quality of mental life) designed our kidneys, or humans at all — natural evolutionary processes seem to account for that. It would be nice if Dretske provided a more robust explanation of how there can be any genuine design without an intention behind it. After all, the notion of design seems to imply some kind of vision (which is hoped to come to fruition), some end goal, or else some construction that is, in some sense, deliberate. More explanation here would importantly clarify and elucidate Dretske’s distinction between natural and conventional representation.

After laying out the aforementioned distinctions, Dretske states his working assumption: There naturally acquired functions and, consequently, naturally acquired representations.

This assumption merits some discussion. The idea is that if a function can be naturally acquired, then a representation can be naturally acquired, and, moreover, functions can be naturally acquired. Recall my earlier question about the distinction between information functions and representation functions, for now it seems especially pertinent. Suppose that information functions are equivalent to representation functions. Then there are functions that are naturally acquired which are not information functions. That is, there are functions that amount to brute physical processes, devoid of any semantic/informational/representational component. But it is unclear how this is supposed to entail that there are natural representations or representation functions. Contained in the assumption without any defense, on this interpretation, is the idea that isolated physical processing can give rise to representational functions or representations — these notions are semantic, and there seems no reason to suppose that some collection of purely natural (which is, presumably, physical) processing can catalyze the emergence of something a fundamentally distinct, uniquely semantic character. If someone like me is to be convinced by Dretske’s Representational Thesis, then there must be some defense of this assumption’s implication.

But suppose, instead, that information functions and representation functions are not equivalent. Then we can ask ‘are the (antecedent) natural functions informational, or no?’ If they are not, then I figure a more accurate working assumption would be: there are naturally acquired functions, and so there are naturally acquired information functions, and so there are naturally acquired representation functions. If, however, this is so, then the same question as in the preceding paragraph is raised. Namely, how do we get from the pure physical stuff to the stuff with semantic character? But suppose there can be just informational functions, and it is these which give rise to the representational functions. This interpretation of his working assumption seems more tenable; that there are naturally acquired information functions which give rise to naturally acquired representation functions is a straightforward inference, for they both are essentially semantic in character.

There is a lingering question, however, concerning the status of information functions and how the idea of information should fit into the ontological picture. If this does not resolve itself, then we will have more to discuss. (Especially if it turns out that information is not an output of a function [or input, or relation between input and output], as Dretske implies, for then it is not clear where the information comes from.)

3

So certain things have representational functions and, unsurprisingly, their functions are to produce such-and-such representations.  A representation is a particular (token) state or event.  A token state, i.e. a representation, is representative — that is, has an indicator function — in virtue of two sources.  (1) The token state’s representational status is derived from the system of which it is a state with an indicator function (=function$_s$).  And (2) The token state’s representational status is derived from the type of state of which it is a token (=function$_a$).  The former is the systemic function and the latter is an acquired function.  Not all systemic functions are acquired functions.  Experiences — having your senses impinged upon — are identified with functions$_s$.  Concepts, however, are functions$_a$.  This is because, for example, when we are born our senses are operational and yet we have no concepts whatsoever.

At the risk of adumbration, I’ll respond with the following question.  Why should a physical system need a representational function at all, regardless of whether it is function$_s$ or function$_a$?  And further, at the risk of appearing flippant, what is the ontological status or constitution of a representational system and how, if at all, does it differ from other systems?

Dretske further elaborates on representation and also enumerates the two ways that a representation, e.g. experience, can misrepresent.  That S represents $k$ implies the representational fact that for some F, S represents the F of $k$.  That Phil represents the blue mug implies the representational fact that for some property, e.g. blueness, Phil represents that blueness of the blue mug.  This is a fact purely about Phil’s representation/representing.  That S represents $k$, however, also implies a hybrid (a fact part about the representation and part not), namely that $k$ stands in a certain kind of relation, relation C, to S.  This is a hybrid fact because it involves a fact about the object of representation, not merely about the representation, namely that it relates to the representational system in the relevant way.  This brings us to the two ways that an experience, i.e. a representation, can misrepresent.  (1) There can be a genuine object connected to the representational system in the right way, but the system misrepresents the relevant property of the object.  For instance, I am looking at an object, a blue mug, but I see a yellow mug instead.  (2) There can be no object of representation (for instance, a hallucination).  I look at the table and see a blue mug, when there is in fact no mug (nor object with pseudo-blue-mug-like properties).

So what exactly is C?  C is the contextual relation which determines the object of representation for the system, which is to say that C is the relevant external causal or contextual relation which makes the representation of the object veridical (that is, not a misrepresentation).  For instance, the speedometer, whose function is to represent the speed of my car, is hooked up properly to the axle of my car.  That it is hooked up properly is essential to the speedometer’s representation, like the needle pointing to ’37’, being veridical.  To see this, suppose someone severed the cord connecting the speedometer to the axle.  If I had absolute faith in my speedometer, I could be blazing across the countryside at 80mph totally unwittingly, while I’m focused on the speedometer reading ‘0’.  This speedometer is not truthfully representing the speed of my car, and so constitutes a misrepresentation.

It should be noted that things with indicator functions have the function of conveying information about a specific property, not information about the vast array of properties which may be present.  Drestke notes that an instrument can have a pressure indicating function without having a temperature indicating function even when it cannot deliver information about pressure without delivering information about pressure.  The thermometers function is to detect temperature, not pressure.  We can imagine artificially holding pressure constant while increasing the temperature of a room — intuitively, the thermometer will accurately represent the temperature without misrepresenting the pressure, as we haven’t given it made its indicator sensitive to pressure, but rather temperature.

A second example.  Our eyes are sensitive to color, but not other forms of radiation.  We visually represent color without visually representing the rest of the radiation spectrum, even when certain colors may entail facts about other, present radiation.  It’s worth emphasizing that we represent the properties of the objects of experience, not the objects themselves.  I’m on the pier looking out on the lake and see what appear to be two white ducks.  Unbeknownst to me, one of them is a decoy.  This is because the decoy duck is meant to produce some of the same experiences of the duck, like shape and color.  My visual experience of the duck and the decoy are virtually the same, even though the objects are of entirely distinct kinds.  The decoy is designed to have the same color properties of the duck, without actually being a duck.  So our sense modalities are sensitive to certain, specific properties of objects, not the objects themselves.  This also explains the aspectual character of representation.  When I see a tomato, I visually experience the side facing me, an aspect of the the tomato, not the whole thing itself, front, back, inside, and out.

Objections to Verificationism and ‘It-From-Bit’

Schlick’s verificationism is vulnerable to a number of objections.  In light of the similarities between informationism and verificationism, we might wonder whether informationism falls prey to the same sort of objections.  We will now discuss some objections to the given and see if the sort of informationism held by Wheeler can overcome them.

The most immediate objection to Schlick’s verification principle is that the verification principle itself is not logically verifiable.  Fortunately for Wheeler, this will not be a problem for informationism.  Wheeler is not committed to the meaning of his statements relating to some atomic properties of perception.  Meaning is the joint product of all the evidence that is available to those who communicate.  Evidence can be either direct or indirect.  There is no recourse to unanalyzable, non-theoretical features of perception because instead, Wheeler relies on the notions of the kind of question asked and the digital response.  A digital response need not be an atomic response.

Another concern for both verificationism and informationism might be, how can we have third person scientific knowledge if all scientific knowledge is based on 1st person statements?  Fortunately, there is agreement in third person scientific knowledge between scientists.  Supposing that each has a different experience, the fact that they all agree in the way that they communicate suggests that there is a structural similarity between each’s first-person experience.  Scientific knowledge and theory are intimately connected.  And theory is about the structure of relations between those things that feature in our experience.  The description of the structure may (and should) be identical, regardless of the organization of the features of experience for each individual.  And, indeed, this makes a great deal of sense on Wheeler’s picture.  This is because all ‘reality’ for each subject is information-theoretic.  And the information is constituted by the relations between its components, without ever being committed to saying what those components actually are.  Objective, third-person, scientific knowledge is information-theoretic — it strives to capture the formal relations between phenomena, regardless of what the character of the phenomena is to any particular individual.

A larger problem, raised by Plato’s ‘Theaetetus,’ regards the fact that if atomic statements are verifiable by an individual, then those statements will always be true.  And if those statements are always true (and so trivially true) then they can have no descriptive content.  It is as if someone were to say, ‘I’m sensing the thing that I sense over there in the manner that I typically sense it.’  This is completely and totally uninformative.  We will now elaborate on this.

Prima facie, on Wheeler’s view, knowledge and perception and intimately connected.  Knowledge comes from recording the binary responses of our measurement devices (and interpreting the responses in such-and-such way).  So it seems that ‘man is the measure of all things.’  We grant existential status only to those things which we can measure to be so.  This may be problematic.

Take six dice.  They number more than four by a half.  But compared to twelve dice, the six are fewer by a half.  It is both more and less.  But nothing can become greater or less while remaining equal to itself.  The number of dice is either ‘is greater’ or ‘is less’ depending on the frame of reference that it is considered in.  The veridicality of the ascription of the predicate depends not on the properties of the object under question, but more upon its mode of consideration.  This seems an impoverished notion of knowledge, for it does not seem to give us insight into the actual properties of the object.

Moreover, intuitively, it seems that perception is the union of capacity for sensation and an object of sense.  Perception depends on some connection between an agent with a capacity for certain kinds of sensations and an object with a capacity for producing those kinds of sensations.  But on Wheeler’s picture, it seems like the (‘physical’) object of perception has no (independent) existence until it is united with the subject (for instance, the scientist).  There can be no one, self-existent thing.  Rather, everything is related within the information space.  Each component in the space depends on its existence on the structure of the rest of the components of the information space.  There is a potential infinity of ‘physical’ objects and subjects (which can come together in perception) — each combination of object and subject produces a result which is not the same, but different.  This is because each perception is defined by the unique identities of both the object and the subject.  My capacity for perception, $\phi$, meets with an object with a capacity to produce certain perceptions in virtue of its identity, $\alpha$, to produce the unique perception, $(\phi + \alpha)$.  Another agent with capacities for perception, has his own identity $\psi$.  When he meets $\phi$, the perception is uniquely defined as the resultant of $(\psi + \alpha)$.  And there can be no justification for the claim that $(\phi + \alpha)$ is identical with $(\psi + \alpha)$.  Consequently, there is no other object I could encounter which should give me the same perception, for another object will correspond to a different agent-patient relation and so the perception must be different.  Nor can any object which affects me in a certain way, if it should meet with some other subject, produce the same perception.  For that perception will be uniquely defined by that other subject and the object.

When I perceive something, I must be the percipient of something.  For there could be no such thing as perception without some thing being perceived.  In the words of Socrates, ‘nothing can become sweet which is sweet to no one.’  So on Wheeler’s view we can only be bound to one another.  The existence of all things depend on their relation to something else — no thing can be absolute.

Moreover, if this is so, then all my perceptions must be true to me.  And if this is so, then how could I ever fail to know that which I perceive?  For if truth is found only in perceptual experience (or sensation), and no man can know another’s feelings better than he, then each is to himself the sole judge — and everything that he judges must be true.  There is no need for us to consult each other, for each is the God of his own perception and consequently determines what is true of his own reality.

Three points are crucial here.  (1) That there be some intersubjective agreement on matters of fact, (2) Wheeler does not mean to deny that there is some object of our perception, and (3) if we take the primacy of information spaces seriously, then that ‘there can be no one, self-existent thing’ is not as counterintuitive as you may suppose.

With regard to 1, while each individual may be the final arbiter of the character of his own perceptual experience, this only entails that his (honest) reports about the character of his experience be true — not that his (honest) reports with respect to his inferences from his perceptual experience be true.  I say, ‘such-and-such looks green to me,’ and this may be true, regardless of whether or not the object I am referring to actually is green.  But if I say, ‘such-and-such is green,’ then I am not reporting my experience, but rather reporting a fact inferred from my perceptual experience.  It is often the case that such inferences are false.  It does not matter that no identity can be drawn between $(\phi + \alpha)$ and $(\psi + \alpha)$; what does matter is that $\phi$‘s report and $\psi$‘s report be in agreement, not that they be identical.

With regard to 2, Wheeler, unlike Schlick, does not straightforwardly dismiss the notions of an internal or external world.  Rather, to confirm an object of reality, we just need some empirical justification, direct or indirect.  That there are objects of our perception is not denied.  What is denied is that they really are ‘physical,’ for the word ‘physical’ is itself a theoretical term.  It does not matter that perception requires the union of a subject and an object, for Wheeler allows there to be independent objects.  (He is just reluctant to make a definitive claim to their ontological status.)

With regard to 3, we must first consider Wheeler’s views on space and time.  Wheeler claims that there is no space, nor no time.  He cites both Leibniz, ‘…time and space are not things, but orders of things…,’ and Einstein, ‘Time and space are modes by which we think, and not conditions in which we live.’  He goes on to describe Einstein’s notion of spacetime, saying that on this theory, predicted fluctuations grow so great at distances on the order of the Planck length, that ‘they put into question the connectivity of space and deprive the very concepts of ”before” and ”after” of all meaning.’  So for Wheeler, spatial and temporal concepts are modes of thought, not features of reality.  This sort of view is lent support by the establishment of nonlocality and absolute simultaneity in quantum mechanics.  Split a pion to produce an electron and a positron.  The outcome of the measurement of the electron collapses the associated positron (into the opposite value), regardless of the distance between the two particles — the effect is absolute simultaneity, and that causes need not operate locally.  Absolute simultaneity entails that local realism is false, and if local realism is false then realism about special relativity is false, too (space and time are not part of reality).  Now recall how an information space is constructed.  There are difference relations between information states embedded in an information space, and the relations can be transmitted down some causal pathway.  You might think that there has to be some self-existing thing, that there must be some loop like this: physics gives rise to observer-participancy, observer-participancy gives rise to information, and information gives rise to ‘physics.’  So first, there is something that exists, which causes there to be observers, and only then can the information relation be constituted, wherein we can then access ‘physical’ knowledge.  This line of reasoning presupposes that time is a feature of reality and not a mode of thought.  There is something thought to ‘exist before’ which at some time later gives rise to observer-participants.  But if time is not a feature of reality, and reality is just an information space, then we cannot make sense of a real temporal relation between physical processes giving rise to observers.  Here’s one way to think about it.  All ‘reality’ is at once instantiated — objects, subjects, and relations, all.  You, as a subject instantiated someplace is the information-space of reality, perceive time to give order to your perceptual interactions with objects in the information space.  Objects do not precede you in time, they are instantiated alongside you in the information space and are experienced in a certain order.  As such, there is no need to talk about some unobserved/unobservable feature of reality prior to observation which gives rise to observers.

So it seems like informationism does, in fact, overcome the objections to verificationism that we’ve been discussing.  This looks promising for Chalmers.  However, there is a larger, more powerful objection to this kind of view which is clearly articulated by Sellars, and we will discuss next.

Informationism and Verificationism – A Comparison

Wheeler’s informationism should remind us of Schlick’s verificationism and the old school of logical positivism.  Schlick shares with Wheeler this sort of hardline empiricism.  This section will explore the similarities and differences between the two.  As a first order of business, we should briefly explain Schlick’s verificationism.  (Note that this explanation can also be found in the above Schlick link.)

The main thrust of verificationism is this.  A statement is meaningful only insofar as it is logically verifiable.  Any statement that is not logically verifiable is not meaningful.  The only statements that are logically verifiable or knowable are those which reduce to some description of the given.  The given is the domain of all that is knowable; it is roughly your perceptual experience at some particular point in time.  The given should not be confused with the terms ‘the internal world’ and ‘the external world,’ both of which are meaningless for the verificationist.  This is because propositions like ‘there is an external world,’ will turn out to be not logically verifiable.1 All difference in the given is detectable.  Because the given is what is presented to you in perceptual experience, there can be nothing in the domain of the given that is undetectable.

Features in the given are describable with atomic words or atomic sentences.  Atomic words, like green, pain, and so on, can only be known by ‘pointing’ to some feature of our perceptual experience.  They cannot be understood in terms of other words.2  I point or otherwise gesture to a grassy knoll and say ‘that green.’  The word’s meaning is established by the agreement of the reactions of others, e.g. that other react by observing, ‘green.’  That is, the use of the word occupies the same relational-role in the given}as it is experienced by each of us.  For the verificationist, the question of whether the phenomenal quality of his green-experience is identical to the phenomenal quality of my experience, is meaningless.  This is because that fact is not logically verifiable.

Atomic sentences are composed of atomic words.  All complex propositions, like ‘there is a deer by the bush,’ are made of atomic sentences, like ‘there is a brown spot with such-and-such features by that green spot arranged in so-and-so way.’  So complex propositions are reducible to (some sequence of) atomic words, whose meaning directly describes the given.  To see this, suppose that a proposition’s meaning is something over and above its determining some state of affairs in our perceptual experience.  If this additional meaning is expressible, then it would be a (complex) proposition (and so nothing over and above an atomic description of some feature of our perceptual experience).  But if the meaning is not expressible, then it cannot mean anything, for that which expresses nothing means nothing.  So the truth or falsity of a proposition must correspond to a difference in the given in order to be meaningful.

It follows from this that the meaning of a proposition is identical with its verification in the given.  The meaning of ‘there is a deer by the bush’ is just whether or not there is a familiar arrangement of brown situated by another familiar arrangement of green, and perhaps some audible rustle — for these are the features of our perceptual experience which verify and are associated with the presence of a deer.  So if we cannot conceive of some verification in the given of the fact, then the fact means nothing.  So, a proposition is meaningful only insofar as it is logically verifiable.  A meaningful statement says that under certain conditions, certain data appear.3

Here are the similarities between Wheeler and Schlick.  Prima facie, both seem to share the verification principle — that is, the only statements that are meaningful are those which are logically verifiable.  For both Schlick and Wheeler, if something is meaningful, it must correspond to some empirical indication of fact.  Consequently, both Schlick and Wheeler grant existential status only to those things that have some possible effect on our perceptual experience — for something to exist, it must be meaningful.

They also share a sort of ‘atomism’ about reality.  For Schlick, meaning comes from the atomic features of our perceptual experience.  For Wheeler, meaning comes from the binary answer to a question.  But these binary answers are a lot like the ‘atoms’ of Schlick, as for both reality bottoms out at something that is impenetrable to further investigation or analysis.  The ‘atoms’ of Wheeler are fundamental digital questions/answers, while the atoms for Schlick are atomic words that directly ‘point to’ features of perceptual experience.  They differ in how and when they ‘bottom out,’ but they agree on ‘bottoming out’ somewhere upon which the entirety of our discourse gets its meaning.

Both the ‘it-from-bit’ doctrine and verificationism, at heart, are deeply antimetaphysical views.  For Wheeler, physical objects have the status of ‘theory’ because they are the result of an interpretation of a binary item in our perceptual experience.  Because reality is theoretical, we ought not make metaphysical claims about it and, moreover, at any rate, such claims will be meaningless.  Likewise Schlick, in explaining the given, emphasizes his avoidance of any commitment to an internal or external world — for such concepts are meaningless.  Metaphysical statements are not verifiable, and so not meaningful; whence the antimetaphysicalism.  But if we take physical objects to be objects in the external world, then Schlick will see physical objects as the same sort of ‘convenient’ myth as Wheeler and Quine (for, for Schlick, there is no external world — any talk of the [objects of] the external world can only be taken as heuristic).

The differences between Wheeler and Schlick primarily revolve around (1) space and time, and (2) meaning.  For Schlick, space and time will be features of the given, their reality easily ‘verified’ by the mere fact of the given at all.  In contrast, Wheeler sees space and time as modes of thought, not part of reality.  If space and time are modes of thought, then there must be something that we are thinking about.  This seems to imply that there is something external to us or mind-independent that our thoughts try to ‘reach out and grasp,’ or represent — but this kind of talk is forbidden on Schlick’s account.

For Wheeler, meaning is the joint product of all the evidence available to communicators.  For Schlick, meaning is identical with method of verification in the given.  Prima facie, these views are rather similar.  But for Schlick, all meaningful statements must be reducible to some concatenation of atomic words, directly referring to the immediately apprehensible features of the given.  Wheeler doesn’t explicitly commit himself to such reductionism (to atomic words).  Rather, evidence is more broadly construed so that we can actually talk about theoretical entities without talking about only our phenomenal experience. For Wheeler, to say that there is a forcefield is to infer a theoretical fact about reality from a set of registrations on some device.  Schlick, in contrast, maintains that just to say that there is a forcefield is to say that such-and-such a device registers so-and-so in a particular way — and does not ascribe reality to the forcefield itself.  The differences in their respective accounts of meaning will be important going forward.

1. The truth or falsity of the reality of the external world has no impact on your perceptual experience.  If we are all in the internal world and this should be some fantastic dream, there is no empirical matter of fact you could ever come across which would verify that you are in an internal or an external world.
2. For such a description of pain can only amount to something like, ‘pain hurts,’ ‘pain is the opposite of pleasure,’ or ‘pain is what makes you recoil.’  The first is a tautology, the second is almost as trivial, the third overbroad and not necessary, and none of them convey any nontrivial knowledge about what pain actually is to the person who has never experienced it.
3. For such a statement to be verified re vera, is for there to be consistent agreement in the reactions of a sufficient number of persons to a given stimulus — an agreement that under certain conditions, certain data appear.  (In this way, hallucinations and illusions will not be verifiable.)

It from Bit, Information as Fundamental

The main problem that leads Wheeler to propose his ‘it-from-bit’ doctrine is the mysterious nature of the fifth axiom of quantum mechanics, viz. the collapse postulate, which we will discuss later.  ‘It-from-bit’ is an antimetaphysical thesis.  The motivation for holding an antimetaphysical thesis is that it provides a clearer notion of truth and a definite, methodical path to getting there.

Wheeler’s central distinction is between ‘its’ and ‘bits.’  An it is a thing (that is, something that we ascribe existence to).  This class includes particles, forcefields, the spacetime ‘continuum,’ and your mother’s rosebush.  A ‘bit,’ is an apparatus-elicited answer to a yes-or-no question (that is, a binary choice); e.g. the counter registers a click in a specified second, indicated ‘yes’ for ‘photon.’1   Every ‘it’ derives its function, meaning, and existence from ‘bits.’  The reality of every ‘it’ is derived and established from the affirmative answer to a binary/digital question.  I establish the reality of my coffee mug by asking ‘is there a coffee mug on the table?’, looking to it and registering the familiar shape of the cup and handle, and the characteristic deep blue color, in my visual experience (resulting in an affirmative answer), and then I can say, ‘there is a coffee mug on the table.’

Wheeler says that ‘It from bit symbolizes the idea that every item of the physical world has at [very] deep bottom…an immaterial source and explanation;…reality arises in the last analysis from the pose of yes-no questions and the registering of equipment evoked response.’  This amounts to: all things physical are information-theoretic in origin — that is, information is in some sense ‘prior to’ the physical world.  We can break most things down and explain them in terms of their component parts — and take those component parts and do the same.  But eventually we will bottom out somewhere (binary).  Suppose we reach the most fundamental physical particle — some physical point — call it $\omega$.  At that point, the only question we can ask is the brute question, ‘is an $\omega$ there?’ as we cannot explain it in terms of other things (or anything else more fundamental).  If we can measure its presence, and in the affirmative, then that is the brute bottom of our explanation of $\omega$.  But the reality of $\omega$ comes from being able to measure its presence.  The information precedes the ascription of existence to the physical object.

Wheeler shows how this comes out in a number of ways.  Take a putative physical object, like a forcefield.  We measure the strength of a forcefield by using a device which measures shifts in interference patterns by representing the number of ‘fringes’ in the pattern.  But all the fringes can possibly stand for is a statistical pattern of yes-no registrations.  Or consider how we determine the existence of a photon.  We ask a question like, ‘did a counter register a click during a specified second?’  If so, we say, ‘a photon did it,’ thus ascribing existence to the putative physical object on the basis of binary information.  Blackholes furnish a particularly interesting example.  Consider the following discovery by Bekenstein.  The surface area of the horizon of a blackhole measures the entropy of the blackhole.  Thorne and Zurek explain that, in performing an operation on the value of the surface area we get $N$, the number of binary digits (‘bits’) required to specify in all detail the constituents of the blackhole.  Entropy is a measure of lost information.  No outside observer can determine which of the $2^N$ configurations of bits compose the blackhole.  So the size of a blackhole (an ‘it’) is defined by the number of ‘bits’ lost within it.  Finally, a more ordinary example.  You wish to determine whether or not your tea is too hot to drink.  If you taste it and burn your mouth then ‘yes’ it is too hot to drink.  If you taste it and do not burn your mouth, then ‘no’ it is not too hot to drink.  In this way, the evaluation of a putatively physical property like temperature is reduced to a binary choice, and so the information precedes the ascription of the property.

What this means is that physics can be cast in terms of information.  Wheeler calls (physical) reality a ‘theory.’  We can make each physical item a (metaphysically neutral) element (in some arbitrary state — either 0 or 1) in an information space, and characterize the relations (and their similarities and differences) between elements without ever being committed to a metaphysical claim about what those elements actually are.  Physics does not require a commitment to physicalist metaphysics.

For Wheeler, the notions of ‘meaning’ and ‘existence’ are intertwined.  Meaning is ‘the joint product of all the evidence that is available to those who communicate.’  So for something to be meaningful it must be (1) communicable and (2) empirical.  Let’s explain 1 first.  It’s plausible to say that anything expressible is communicable (and vice versa). If something that is meaningful were not expressible, then it could not mean anything, for that which expresses nothing clearly means nothing.  So for something to be meaningful it is necessary that it be expressible. Now let’s explain 2.  Something that is meaningful must make an empirical difference — that is, there must be some item in possible perceptual experience, which is logically possible to access, that corresponds to the thing’s truth-value.  This notion of meaning is not as impoverished as you might expect, for there is quite a bit of evidence available to communicators.  Even with regard to the past, an intrepid crew of investigators, armed with the right equipment, will be able to establish that such-and-such happened so-and-so long ago in the past, based on some chain or network of physical evidence.  Their findings will contribute to the establishment of that past event’s meaning.  Here’s how this importantly ties into existence.  If a $\phi$ is not meaningful, then it is meaningless to assert something like, ‘$\phi$ exists.’  (Attach any other predicate you choose, and it will nevertheless presuppose the existence of $\phi$.)  For suppose I do assert that ‘$\phi$ exists.’  That entails there must be some possible item in my perceptual experience which ‘verifies,’ so to speak, the existence of $\phi$.  If there isn’t anything that I could see, or smell, or taste, or hear as some result of $\phi$‘s existence, then it means nothing to say that $\phi$ exists.  What would it mean to ascribe existence to something which could never impinge upon our perceptual experience?  Its existence or lackthereof will never affect the truth-value of any proposition of this world.  So if something is not meaningful, any assertion of its existence is meaningless; therefore we can only grant existential status to those things which are meaningful.

Chalmers’ observes that this sits nicely with the idea of Shannon information.  In Shannon information, where there is information, there are information states embedded in an information space — where an information space is a structure of (difference) relations between its components.  Differences may be transmitted down some causal pathway.  Notice how this sits nicely with how Wheeler thinks that past events are meaningful.  Consider the infamous tree that fell in the forest with no one to hear it.  Nevertheless, its fall will leave some kind of evidence (like a depression in the ground, scattered needles, etc…) which some investigators may happen to stumble across (and so make the fall meaningful).  On this picture, the tree in the forest, prior to its fall, is an information state (to be defined in terms of its relations to other trees, perhaps).  The information space evolves, differences are transmitted, and some information relates to the tree in such a way that it falls (its fall constituting continuous differences down a causal pathway).  When the information corresponding to the falling tree is related to the ground, there are changed information states corresponding to the depression it leaves and the needles which scatter.  The information is finally communicated when our intrepid explorers see the depression and so receive the information of the tree having fallen.

Physical ‘its’ must come from ‘bits,’ which are discrete, for there is no continuum in physics.  There is no continuum in physics because there can be no continuum in mathematics.   Of the number continuum, Weyl says ‘belief in this transcendental world taxes the strength of our faith hardly less than the doctrines of the early Father of the Church.’  Likewise there can be no continuum of/for physical objects; they must be discrete.  Quine articles this point quite well, ‘Just as the introduction of the irrational numbers… is a convenient myth [which] simplifies the laws of arithmetic… so physical objects are postulated entities which round out and simplify our account of the flux of existence…  The conceptual scheme of physical objects is a convenient myth, simpler than the literal truth and yet containing that literal truth as a scattered part.’  (1) That physics is discrete in this way means that it must yield to digital questions and consequently physics will be information-theoretic.  (2) I think that the phrase, ‘conceptual scheme of physical objects’ is particularly telling.  We interpret empirical evidence through a particular theory or conceptual lens — to call an object ‘physical’ is just to conceptualize a feature of our perceptual experience in a certain way.  We reserve the word ‘physical’ just for those meaningful, empirical items in our perceptual experience.

So on Wheeler’s account, ‘reality’ has the status of theory.  Reality is constructed out of the kinds of questions we ask about the world, and the ways in which we interpret those binary answers.  To press the point, consider how we measure the spin-properties of electrons.  Suppose I have an electron.  I cannot ascribe either ‘black’ or ‘white’ or both (or neither) until I shoot the electron through a color-box.  If the color-box does its job right, the outcome of the measurement will be with ‘black’ or ‘white’ (each with exactly $1/2$ probability).  But my choice to measure color disrupts the electron’s hardness value — that is, I can never predicate a definite hardness property and a definitely color property to the same electron at the same time.  The moral is that the choice of question (e.g. what is the hardness? vs. what is the color?) and the choice of when the question is actually asked play (some [but not the whole]) part in deciding what we can justifiably assert about reality or ‘the World.’  So to say that reality is a theory isn’t as unintuitive as it may first appear.

So if information is primary to physical objects — and, indeed, the status of physical objects is merely theoretical — then it seems like something which must be fundamental is perceptual experience.  This is the notion which led Chalmers to suggest something like Wheeler information as the fundamental constituent of reality.  Our conscious perception of ‘the World,’ or of things underlies all other empirical (and even metaphysical) knowledge.  Without it, reality wouldn’t even speakable.  So on this picture, physics has a distinct theoretical quality, whereas perceptual experience is non-theoretical and most fundamental.

1. Here’s the reason why I put scarequotes around ”photon.”  We ascribe existence to the thing we think caused the counter to register a click.  But a photon is a theoretical entity (you can never actually see a photon — only its causal influence).  If we conducted the experiment within a different theoretical/conceptual framework, we may attribute the registering of a click to some other theoretical entity.