Dijkstra's Demon

A distributed system can be described as connected nodes lacking access to global memory.[1] Nodes of a distributed system maintain local variables with contents specifying the state of that node. Local states of the system are characterized in terms of a given node being able to read its own state and the state of a proximally connected - neighbor - node. The global state of the system is the union of all local states of all nodes of the system.

Disconnect between local and global information makes distributed systems susceptible to certain types of failures. For our purposes, faults are disruptions in expected behavior of a distributed system, which may be classified as e.g. permanent, intermittent, or transient. Following Dijkstra, we will focus on transient faults, faults that occur once then disappear but do not affect the global behavior of the system, e.g. message transmission timeout followed by transmission success. In particular, we will examine the notion self-stabilization for a system S with respect to some property P - defined over the global states of S – which identifies the correct behavior of S. Roughly, a system exhibiting self-stabilization can sustain arbitrary transient faults and return to a desirable system state without external intervention. Self-stabilization, in this respect, is much like a spinning top inscribing small concentric circles on a table. Lightly pressing the top – a transient fault – results in a self-stabilizing top inscribing larger concentric circles, before returning to its behavior of inscribing smaller concentric circles.  Similarly, a distributed system exhibiting self-stabilization can weather transient faults without, say, crashing.

Broadly speaking, there are two types of global state for a given distributed system with respect to property P, called legitimate states – those which satisfy P - and illegitimate states – those which do not satisfy P. According to Dijkstra, legitimate states must be such that:[2]

(CLOSURE) Every transition from a legitimate state results only in a legitimate state[3]
(PAIR) Every pair of legitimate states can be connected by transitions from one to the other[4]

From which it is a corollary that each global state in sequence of transitions between legitimate states is itself legitimate.[5] Moreover, legitimate states must be such that:   

(LEGIT) Every legitimate state has at least one privilege present
(PRIV) Each privilege must be present in at least one legitimate state

Where the privilege is a Boolean function defined in terms of a given node’s state and that of its neighbors. If values of a node and its neighbors are input to this Boolean function, then if the function returns the value “true”, then the privilege is said to be present, and “false” otherwise. If (LEGIT) is true with respect to some distributed system, then in any legitimate state of that system there is at least one node for which the privilege function returns “true.” If (PRIV) is true, then every possible output for the privilege function which returns “true” appears in at least one legitimate state.

Definitions in hand, Dijkstra defined a distributed system S as self-stabilizing with respect to P, on the condition that S satisfies the following two behaviors:

(ONE) The system has at most one privilege present
(CONVERGE) Given an arbitrary global state, the global state of S satisfies P within a finite number of state transitions

If (ONE) is true, a self-stabilizing system must have at most one set of state machine and neighbor inputs that result in “true.” A corollary of (LEGIT) and (PRIV), is that a self-stabilizing distributed system with respect to behavior P has exactly one privilege present in any given legitimate state and all privileges will eventually be represented. If (CONVERGE) is true, then the relevant distributed system satisfies P in finite transitions. Combined with (CLOSURE) and (PAIR), any given pair of legitimate states can be connected by a finite sequence of legitimate state transitions. Altogether, a self-stabilizing distributed system will satisfy P in a finite number of transitions, have one privilege, each privilege will be present in some legitimate state which will never transition to an illegitimate state, and each state in between any pair of legitimate states will involve only legitimate states.  Another assumption worth mentioning here – if just to foreshadow - is that Dijkstra posited a central demon for self-stabilizing distributed systems with the ability to select a privileged node to enact a transition. The selection is arbitrary, and once a privileged node enacts a transition, the central demon arbitrarily chooses another among the available privileged nodes to enact the next transition. No node is permitted to enact a transition unless it has been selected by the central demon. Subtleties associated with the central demon assumption will occupy us later.

Before turning to that discussion, however, it is worth specifying Dijkstra’s self-stabilization definition in detail by considering one of three[6] characterizations Dijkstra provided of a self-stabilizing distributed system. Suppose there are N+1 nodes, numbered 0-N in a ring. For any given machine nr.i, where i is an integer between 0 and N, we adopt the following notation:

L: state of the left neighbor of nr.i, i.e. nr.(i-1)mod(N+1)
S: state of machine nr.i
R: state of right neighbor of nr.i, i.e. nr.(i+1)mod(N+1)

For illustration, suppose we have N=3, so there are N+1=4 machines, numbered 0-3 in a ring. Consider nr.0. We have the following:

L: state of the left neighbor of nr.0, i.e. nr.(-1)mod(4)=nr.3
S: state of machine nr.0
R: state of right neighbor of nr.0, i.e. nr.(1)mod(3)=1

To provide conditions under which such a distributed system self-stabilizes, Dijkstra distinguished exceptional machines from all others.[7] In particular, the conditions are, where K is the number of potential assignments to nodes, N the number of nodes, and N ≤ K:

Exceptional Node: If L=S, then assign (S+1) mod K to S
Other Node: If L≠S, then assign L to S

Without loss, suppose nr.0 is the exceptional machine. If there are N nodes each randomly assigned values in K initially, then any node - but the exceptional node - which has distinct assignments from their left neighbor will be privileged. The central demon will arbitrarily select one of these nodes for transition. Suppose nr.3 is chosen. Then nr.3 must have a state distinct from nr.2. But then nr.3 changes its state to that of nr.2, and so nr.3 loses privilege. If, moreover, nr.4 is given privilege, then it will change its own state to be that of nr.3. The procession should be clear. Ultimately, each node that is not exceptional will be in the same state. When this happens, only nr.0 will be privileged, at which point it will initiate a sequence of transitions moving the privilege around the ring.

Recall how Dijkstra’s central demon operates.[8] The central demon selects a privileged node to enact a transition. The selection is arbitrary, and once a privileged node enacts a transition, the central demon arbitrarily chooses another among the available privileged nodes to enact the next transition. No node is permitted to enact a transition unless it has been selected by the central demon. We can divide four distinct assumptions: 

(UNIQUE) A distributed system has only one central demon
(SOLITARY) A central demon cannot choose more than one privileged node
(RANDOM) A central demon chooses among privileged nodes arbitrarily
(LOSS) A central demon cannot grant/remove privilege from a node without that node enacting a transition  

We might wonder whether rejecting one or more of these assumptions undermines self-stabilization for a given distributed system. Suppose, for example, we reject (UNIQUE) while maintaining the other assumptions. Let there be two central demons. Suppose each demon arbitrarily and independently chooses privileged nodes for transition. If each central demon happens to choose the same node, the transition will proceed as if there was only one central demon. So suppose the central demons choose distinct privileged nodes. Then there will need to be some priority ranking which allows the system to decide which of the selected privileged nodes will make the transition first, since both are permitted to make system transitions. We might add a third central demon that arbitrarily selects a privileged node from the two nodes selected by the first and the second central demon, resulting in the selected node making the first transition. Under these conditions, it seems self-stabilization of a distributed system is not violated, since rejecting (UNIQUE) can be plausibly described – if three central demons are permitted – as a two-step implementation of the central demon operation.[15] Specifically, the setup is isomorphic to having a single central demon that selects two distinct nodes, then arbitrarily selects one pair to go first. More generally, this setup would – with n+1 central demons n of which select distinct privileged nodes and one of which arbitrarily orders the results – amount to a single central demon that selects n privileged nodes then orders them arbitrarily. In other words, a legitimate state will ultimately be reached, and will be closed under legitimate states through further transitions given the other central demon assumptions.

            If we reject (SOLITARY) and maintain the rest, we seem to run into trouble since there is no obvious way for multiple privileged nodes selected to transition to determine which nodes will go first. Since we are assuming (UNIQUE), we cannot resolve this issue by appealing to more central demons. But we might adjust the capabilities of the central demon in line with rejecting (SOLITARY) by allowing the demon that arbitrarily chooses several nodes - say, nr.1, nr.2, and nr.3 – may then select among those nodes a priority ranking indicating which node transitions first, second, etc. As with (UNIQUE), since the central demon’s selection was initially among privileged nodes, and the transition of each node results in a loss of privilege for that node and potential gain of privilege for another, then transitioning in groups of ordered privileged nodes will eventually reach a legitimate state if transitioning through one node at a time. Moreover, once in a legitimate state, under these conditions the distributed system will remain in a legitimate state through transitions. Hence, again it seems rejecting one of Dijkstra’s implicit assumptions with respect to the central demon, namely, (SOLITARY) does not affect self-stabilization.

            If we reject (RANDOM), then the central demon may exhibit a pattern of privilege selection, say, in order of nearest to the exceptional node, say, nr.0, in terms of counterclockwise rotation. For example, if the privileged states include nr.2, nr.7, and nr.8, then the central demon will select nr.2. On this ordering, the central demon’s selection being non-arbitrary will again not have an effect on whether the relevant distributed system will ultimately reach a legitimate state for reasons comparable to those involving the discussion of (UNIQUE) and (SOLITARY). Moreover, once in a legitimate state, the distributed system will not be led into an illegitimate state, since there will be only one privileged node to select, and so only one pattern for the central demon to employ.    

            The preceding discussion was warmup; if we reject (LOSS), then the central demon may arbitrarily alter the state of a node without enacting a transition, as well as arbitrarily choose a privileged state to enact a transition. There are broadly two ways in which this might affect self-stabilization. First, the central demon might remove privilege from a node; second, the central demon might grant privilege to a node. We consider each in turn.

            Suppose the central demon is permitted to remove privilege from a node. Suppose nr.0 is the exceptional privileged state. Then f(nr.0)=f(nr.N). Suppose the central demon removes privilege from nr.0. Then f(nr.0)≠f(nr.N), but also f(nr.0)≠f(nr.1), and so nr.1 will be privileged. In this case, if the relevant distributed system is in a legitimate state, then it remains in a legitimate state despite the central demon’s action. Similar remarks apply to non-exceptional nodes with privilege. On the other hand, suppose there are two privileged nodes, f(nr.1)≠f(nr.2) and f(nr.3)≠f(nr.4), while f(nr.0)≠f(nr.N), f(nr.4)=f(nr.5), f(nr.5)=f(nr.N), and f(nr.2)=f(nr.3). Suppose the central demon removes privilege from nr.1, so that f(nr.1)=f(nr.2)=f(nr.3). Again, the actions of the central demon in this context will neither undermine reaching a legitimate state nor force a transition from a legitimate state to an illegitimate state. These observations suggests rejecting (LOSS) by allowing the central demon to arbitrarily remove privilege from a node does not undermine self-stabilization.

            However, interpreting (LOSS) as allowing the central demon to arbitrarily grant privilege to a node does undermine self-stabilization. To illustrate, suppose there are two privileged nodes, f(nr.1)≠f(nr.2) and f(nr.3)≠f(nr.4), while f(nr.0)≠f(nr.N), f(nr.4)=f(nr.5), f(nr.5)=f(nr.N), and f(nr.2)=f(nr.3). Suppose the central demon’s actions repeat in the following manner: (1) grant privilege to nr.j for some j in N where j≠0, i.e. not exceptional; (2) reverse the transition of nr.j by granting nr.j privilege, e.g. altering the assignment of nr.j. If the central demon operates according to such a pattern – which is reasonable sequence given our rejection of (LOSS) and maintenance of the other assumptions – then a distributed system in an illegitimate state will not necessarily transition to a legitimate state. Moreover, rejecting (LOSS) in this manner makes trouble for maintaining closure over legitimate states as well. To illustrate, suppose a distributed system is in a legitimate state, e.g. f(nr.0)=f(nr.2)=f(nr.1) for N=2 and nr.0 the exceptional node. The central demon might grant nr.0 privilege, resulting in a transition to f(nr.0)≠f(nr.2)=f(nr.1) and nr.1 being privileged, but then alter nr.2 so that f(nr.0)=f(nr.2)≠f(nr.1), resulting in each of nr.0, nr.1, and nr.2 being privileged, i.e. an illegitimate state. This clearly violates (CLOSURE).  

Our focus here Dijkstra’s commitment to a central demon. We identified features of this commitment, distinguishing several of which seem incidental to the maintenance of a self-stabilizing system. However, we did identify one crucial assumption, namely, that the central demon not be able to introduce privilege to the ring, which if rejected would undermine self-stabilization. This seems of particular importance when thinking about the security of networks and fault tolerance, since it seems plausible allowing a central demon to grant single privilege to a system might simulate a type of subtle attack on an otherwise self-stabilizing system, which might go unnoticed due to its maintenance what we identified as incidental central demon assumptions.

[1] Kshemkalyani, A.D. & Singhal, M. (2007). Distributed Computing: Principles, Algorithms, and Systems.
[2] Dijkstra, E.W. (1974). Self-Stabilizing Systems in Spite of Distributed Control. Communications of the ACM. 17(11): 643-644.
[3]More carefully: For any legitimate state s at transition point t, and state s’ at transition point t’, if t<t’, then s’ is a legitimate state.
[4]More carefully: For any legitimate states s, s’’ at respective transition points t, t’’, there is a state s’ at transition point t’ such that t<t’<t’’.
[5]More carefully: For any legitimate states s, s’’ at respective transition points t, t’’, if state s’ at t’ is such that t<t’<t’’, then s’ is a legitimate state.  Proof: Suppose state s’ at t’ is such that t<t’<t’’. There is such an s’ by (PAIR) and s’ is a legitimate state by (CLOSURE).
[6] Dijkstra, E.W. (1986). A Belated Proof of Self-Stabilization. Distributed Computing. 1:5-6. 
[7]This is an assumption worth exploring in more detail, but I focus on other aspects of Dijkstra’s algorithm in what follows. Hence, my not giving this assumption its own name here.
[8]Explanation of the central demon follows (Dijkstra, 1986) closely, supplemented by remarks in (Kshemkalyani & Singhal, 2007). I did not find any similarly detailed analysis of the various aspects of the central demon assumption.
[9]Indeed, since the selection of privileged nodes is arbitrary with Dijkstra’s assumptions, it seems the only difference that arises by rejecting (UNIQUE) is that some two-step (or n-step where n is less than or equal to the number of privileged states when the selection is made) will result in longer transition sequences leading to a legitimate state than others. Nevertheless, central demons selecting groups of privileged nodes to operate in what we might think of as ‘transition chunks’ will ultimately lead to a legitimate state as far as I can see.

Locke's New Negro and the Harlem Renaissance

Marx's (Essence) Alienation Argument

Marx isn’t concerned with any state of nature myth. His boots are firmly on the ground at the rise of capitalism and he’s an astute observer of economic progress and woes.

As I understand him, Marx is an economic determinist, which is to say that he believes economic developments under certain conditions are deterministic. The economic component doesn’t bring with it a moralistic force. It’d be hard to see how that would even be possible with determinism in the picture. The economic determinism articulated by Marx is one of class struggles leading ultimately to classless society, since each class struggle will result in new classes necessarily bringing into existence other classes that will ultimately overcome them, until there is no class. This is the basic picture.

Suppose *you* are a member of the bourgeoisie though, and I’m some proletariat coming to kick down your door and seize the means of production. I barge in ready to perhaps kill you, and you say “Hey, wait! This was all determined! Don’t hurt me and my family. It wasn’t our fault! We’re determined!” I might respond “Me too!” But this shouldn’t sound like a convincing sort of explanation of the situation. While we may both be involved in an economically determined system, we both get to choose our actions. It’s compatible with Marx’s picture, I believe, that individuals may be blameworthy or praiseworthy for what they choose to do. There is some room then for morality.

But then return to our story. *You* say “Wait, what if I change? Maybe if I pay my workers more, and we create a middle class, then you’ll be happy too, right? Surely not everyone can be wealthy and own the means of production, but if you let me manage the means, then we can all be better off. A rising tide raises all boats!”

(Q1) What can a member of the proletariat say in response to this claim, supposing what the member of the bourgeoisie says is true

I ask this question to get at the heart of justification for agents to engage in class struggle. I think Marx has a compelling argument to this conclusion. I will pitch it in terms of capitalism. Let’s walk through the premises slowly though, since each reveals an important feature of Marx’s – labyrinthine – theory.

Marx’s Alienation Argument (Essence Version)

(1)   Creativity is necessary for human flourishing
(2)   If creativity is necessary for human flourishing and x inhibits humans from manifesting creativity, then x is harmful to humans
(3)   Wage labor inhibits humans from manifesting creativity
(4)   Hence, wage labor is harmful to humans
(5)   Capitalism invariably leads to wage labor
(6)   If x invariably leads to y and y is harmful to humans, then it is justifiable to resist x in proportion to its harmfulness to y
(7)   Hence, it is justifiable to resist capitalism in proportion to its harmfulness to humans

Let’s walk through:

            (Q2) Do you think premise (1) is true?

Marx seems to believe that creativity is essential for human flourishing, i.e. (1). Note, he also thinks that autonomy is essential, and this should make sense since creativity comes along with autonomy. It’s also worth noting Marx emphasizes creativity while Rousseau emphasized autonomy, so in that respect these authors differ.

            (Q3) Do you think premises (2) and (3) are true?

(2) seems true, since inhibiting human flourishing is plausibly a harm. It also seems (3) is true. Think of labor as intimately bound up with creativity; creating is what well-functioning humans do, and labor is how they do it. Humans take items from their imagination, that great wide interior world, and through labor bring those things into existence. Wage labor is a way we attach an abstract ratio to labor, so that we may sell it in the market, as if it were corn. Think about that for a moment. Marx is suggesting wage labor – which is intimately bound up with your essential creativity – makes it easy for you to think of that important aspect of yourself as just another good to be sold on the market.

Let me press the point further: I had a student who once claimed he believed it was permissible to sell himself into legitimate slavery. My first thought on hearing this was “How deep have the capitalist tendrils crept into you that you think you can literally sell yourself on the market like you’re corn.” You’re not corn, and your essential nature shouldn’t be for sale as if it is.

(Q4) Do you think premises (5) and (6) are true?

Here’s where Marx’s economic determinism seems to have force. The very nature of capitalism seems to involve abstracting away from products on the market so that capital can circulate and drive innovation. Put another way, free market capitalism of the sort I’m imagining here requires innovation. Bartering is insufficient to drive innovation, so more abstract means are needed and have been developed, e.g. money. Labor is required to drive innovation, so a natural step in the progress of capitalism is using money to purchase whatever is needed by innovation, in this case labor. This very brief history suggests (5) is true.

With (6), we have what I take to be a compelling premise. Humans can proportionally resist what harms them. But this is more forceful than it might first appear. The sort of harm capitalism engenders in alienating you from your essential nature is significant. Capitalism makes it far too easy to be alienated from who you are and who you should be. Because of the depth of this harm, the proportionality constraint in the consequent of this premise suggests to me we’re justified in doing a great deal to resist capitalism. This, moreover, is precisely what I would say in response to the bourgeoisie who claimed a rising tide raises all boats. This platitude is of course trite because it’s true, as most platitudes are. Nevertheless, it’s plausible to think that while we might be able to survive under capitalism, and we may even be able to live an okay life, it’s not obvious we can thrive under capitalism, and thriving is – as I’m using it here – synonymous with human flourishing. 

Lorde, Lugones, and Change

What follows are notes from a discussion I recently led on Audre Lorde’s The Uses of Anger and Maria Lugones’ World-Traveling and Loving Perception:

Lorde claims anger can be used as a tool. What she seems to mean is that anger can be used as a tool to convey information to others.  Moreover, Lorde maintains that anger can be justified or not. That is, you can be justifiably angry, say, if the target of your anger is appropriately blameworthy, or unjustifiably angry, say, if you’re angry at someone who is not blameworthy or you’re angry for illegitimate reasons. Lorde rightly observes anger as a response to racism is always justified.

Lorde claims anger is distinct from hate. Hate can also be used as a tool to convey information, and hate may be justified in some circumstances, e.g. when one attempts to correct persistent, explicit, racism, and presumably unjustified in others. But note, then conveying information can't be the only feature of anger, since it doesn’t distinguish anger from hate. 

(Q1) What does Lorde think distinguishes anger from hate?

Anger is distinguished from hate based on how it is used and under what conditions it is justified. With respect to how anger and hate are distinguished by what they signal:

• Anger is used to signal judgment recognition of failure to live up to commonly accepted expectations, e.g. black feminist angry with white feminist's self-serving or ignorant behavior

• Hate is used to signal recognition of rejection of expectations, e.g. an intransigent and harmful racist who refuses to change

And with respect to how anger and hate are distinguished by conditions under which they're justified:

• Anger emerges between peers in disagreement, when negotiation and discussion is possible

• Hate emerges among recalcitrant disputants who are unwilling to negotiate

Anger and hate then have different goals. This should remind you a bit of some differences we discussed recently. Take the view of anger and hate we've uncovered when discussing Lorde and:

(Q2) Use them to characterize the dispute between MLK (in Message to Grassroots) and Malcolm X (in Letter from Birmingham Jail).

It's plausible to think X was under the impression there could be no room for negotiating, since whites were recalcitrant racists, often saying one thing and doing another. This suggests the attitude he seemed to bear - in Lorde's terms - is one of hate. In contrast, MLK found enough common ground to desire negotiation. Recall, he used a moral argument in his letter to support non-violent resistance. This was an appeal to common ground - morality - among disputants. He was nevertheless angry, and justifiably so.

There are standard hallmarks of justifiable attitudes, namely, justifiable attitudes are typically such that, using anger to illustrate:

(1) If you judge action A was a mistake, then you should suspend anger

(2) If you judge the agent in A is not a member of the moral community, then you should suspend anger

These features are often associated with justifiable attitudes because justifiable attitudes presuppose responsibility. For example, if you are justifiably angry with someone, then it seems to follow they're an appropriate target for your anger, i.e. they've some responsibility that's been violated. The idea is supposed to be captured in (1) and (2). Suppose Sam spoils a TV show for me by telling someone nearby, not knowing I could hear. I might be angry, but if I recognize Sam made a mistake, then I shouldn't hold on to that anger. It wouldn't be justified. This accords with (1). On the other hand, if my cat spills my water (assuming cats aren't entities which bear responsibility) then I'm not justified in being angry with my cat. This isn't to say my feelings aren't valid. Rather, it's just to say I can't hold my cat responsible, since she's not a member of the moral community. This accords with (2).

I say this to point to a perhaps puzzling feature of Lorde's characterization of anger. Recall, Lorde writes:

"Anger is the appropriate attitude to racist attitudes, as is fury when the actions arising from those attitudes does not change."

Lorde's speech is largely directed at white academic feminists who plausibly are peers worth negotiating with who have similar interests in refraining from harming each other. Lorde claims anger is justified. But justified anger must align with (1), it seems. But plausibly white academic feminists listening to Lorde made mistakes in their hurtful comments that led to Lorde's experiences of anger. It’s not like they were intentionally being ignorant or racist. But then it seems if anger is justified, then these cases aren't going to count as justified anger.

(Q3) What do you think Lorde would say in response?

I came up with two options, which are surely not exhaustive:

• One might say Lorde isn't rejecting (1), but instead reject the premise that white academic peers are simply making mistakes. This is a response on epistemic grounds, that white academics should correct their beliefs. They have plenty of evidence indicating they should be more open and less reactive, and less afraid of black women and their concerns. You might say this if you want to preserve Lorde understanding anger as a reactive attitude, while satisfying (1). In this case, reactive attitudes such as anger presuppose responsibility.

• On the other hand, you might reject (1) and claim even if white academics are simply making mistakes, they’re blameworthy on moral grounds, because people are being harmed and mistreated, and anger is a useful attitude in these contexts to effect change. Put this way, anger wouldn't get its justification by satisfying (1) and (2), but rather it would be justified by its effects, namely, by correcting or preventing moral failings. We might then say that targets of reactive attitudes need not be responsible for their actions to be appropriate targets. A white academic who genuinely makes a mistake that results in the appearance of a racist attitude is nevertheless the appropriate target of anger.

I think given how underspecified the case I gave was, either option might be available. But I'm inclined to think the latter is the better interpretation. First, Lorde doesn't qualify when anger is appropriate to racist attitudes; it's always appropriate. Second, I think it's plausible white academics in the audience agreed anger was appropriate when responding to racism. The problem was they didn't see what they were doing as racist.

This brings us back to what anger is used to convey. Lorde seems - like Truth, Douglass, Walker, and others - to observe inconsistency in implicit and explicit beliefs. Rather than employ irony, interrogatives, etc., Lorde points to a signal white academics can use to recognize the inconsistency they exhibit. The idea seems to be, when you see an angry black woman, don't be afraid.

(Q4) Rather than fear, what do you think Lorde is suggesting white academics do instead?

Note, it can't just be 'think more about what you said'. It has to be something deeper. I say this because, if you recall, Lorde has no use for guilt. Guilt arises when you do something that's judged wrong. Guilt is easy to alleviate. You just apologize or pay penance, etc. It's easy because guilt isn't about you; it's about your actions. I think Lorde is suggesting white academics do more than feel bad. They need to re-evaluate their own values. To get a handle on what she might have in mind, consider:

(Q5) What's the difference between guilt and shame?

Guilt concerns actions; shame concerns you. When you're guilty, you can pay for it, brush it off, but it's not about you. When you recognize shame, you recognize you're broken. That's not about what you do; it may be correlated though. It's much more personal. Also, it's much harder to alleviate. You can pay a fine to get over guilt. To get over shame, you either have to change as a person, or ignore it altogether.

For Lorde, that likely justifies using anger to reveal to white academics that they've exhibited racist attitudes. White women didn't realize they were being racist because shame hides. Even when presented with the anger of black women, it's easier to interpret that as something wrong with black women, so that it's unjustified, rather than as justified anger indicting them because they're racist. This is why, I think, white academic women are "more afraid of the anger of black women than of their own racist attitudes." They're focusing on the wrong thing because shame is too painful. This, I think, is why Lorde ends the speech by inviting those in the audience to join the discussion beyond guilt. Recognition of the uses of anger is a way to get there.

There's much more to say about the uses of anger, and I've only guided us along one strand here. But where we've ended up might leave you wondering if spotting anger is enough. It would be little help to have white women constantly on the lookout for anger so they can reactively correct their own values. To be fair, I don't think Lorde is suggesting that's all that should be done. But she doesn't say much more. Fortunately, Lugones provides further assistance through world-traveling.

(Q6) Remind yourself of Lugones, in particular the difference between arrogant and loving perception

Here we have recognition of the failing each of us have in applying stereotypes to other individuals. In many ways we're inclined to treat others as objects rather than subjects. That is, we tend to treat individuals are carrying the same properties with them no matter what world they inhabit. But importantly, we should recognize that each of us inhabits many worlds, and ha many properties that vary by context. There is no single unifying element. We're the intersection of worlds, if anything. Lugones discusses this generally, for each of us, but it's easily applied to the white academics we just discussed. What's needed is not simply recognition of inconsistencies, but awareness of the many ways in which individuals inhabit different worlds. What's needed is openness and vulnerability to being wrong, and willingness to change one's mind. World-traveling seems crucial to developing integrity, since world traveling seems precisely how one might develop integrity.

Lugones observes that being comfortable in one world is dangerous. This is because one might instill values that are never contradicted. This might emerge in white academics not being able to see their own ignorance, which is a topic we examine in more detail next time.

Rousseau's Reductio of the State of Nature Myth

Rousseau is often read as engaged in the same project as Hobbes and Locke, namely, employing the state of nature myth as a way to distinguish what humans have by nature - and so what doesn't need political justification or explanation in political philosophy - and what is gained by governance - and so what does require political explanation or justification. Indeed, Rousseau in the Discourse seems to be claiming Hobbes and Locke just didn't take the state of nature myth seriously enough, and if they had, they'd have started with primitive man, a creature full of possibility - in the form of potential dispositions - but lacking instincts one might find among animals. Among these potential dispositions is the ability to reason, but importantly, this isn't something primitive man comes equipped with; it must be cultivated at the outset like any disposition. On this way of reading Rousseau, he incurs a significant explanatory burden, having to - like Hobbes and Locke before him - provide a plausible story for how one gets from the so-called primitive individuals to modern individuals. Hobbes and Locke claim inhabitants in the state of nature come equipped with the ability to reason, which makes the transition stories offered more plausible. Rousseau’s explanation, however, seems much less plausible…

Simply put, it is not at all clear how a non-reasoning entity, only perceiving tokens, lacking language, with its limited drives, ever develops such characteristics as we find them in modern individual. Of course, it might simply be argued this transition must have occurred, since modern individuals clearly exist. But while it's obvious modern individual exist (hello!), it's not so clear they made this transition from primitive individuals. These observations, along with what I take to be Rousseau's rather dismissive putative explanation of the transition, coupled with his emphasis on the problems one finds in moderns society while suggesting we can't return to our primitive state, suggest to me we should read Rousseau in a slightly different way. Namely, as providing a reductio argument against the very idea of employing a state of nature myth as Hobbes and Locke had. On this reading, Rousseau is not engaged in the same project as these philosophers. Rather, he's undermining a core starting position of their respective theorizing. He's then turning to concrete problems that come from governance to indicate since we can't separate ourselves from governance, we should focus on ourselves under governance.

More specifically, the argument I have in mind is the following:

Rousseau’s Reductio of the State of Nature Myth

(1)   SUPPOSE: The state of nature myth reveals basic human nature
(2)   If (1), then primitive individuals exhibit basic human nature
(3)   If primitive individuals exhibit basic human nature, then transition from primitive individual to modern individuals is possible
(4)   Hence, transition from primitive individuals to modern individuals is possible
(5)   Transition from primitive individuals to modern individuals is not possible
(6)   Hence, the state of nature myth does not reveal basic human nature

The first premise is assumed by Hobbes and Locke. (2) is Rousseau’s contribution, since he claims taking the state of nature myth seriously entails primitive individuals - as he understands them - will be the appropriate sort of entity to reveal basic human nature. If this is so, then the transition to modern individuals must be possible, i.e. (3), and so by logic the consequent follows, i.e. (4). But I claim Rousseau believes (5) as well, i.e. he doesn’t think it is possible for this transition to occur. If so, then since we’ve derived a contradiction from our assuming (1), we must take that back, and so we have (6) which is the negation of (1).

That said, premise (5) is – I think – ambiguous, and this may make it seem less plausible than it is. Consider the following three ways to read “possible” in this premise:

• Metaphysical – As a matter of fact, independent of what humans think about it, it is impossible for primitive individuals to transition to modern individuals

• Epistemic – The putative transition from primitive individuals to modern individuals is not something we could know about

• Nomological – It is incompatible with the laws of nature that it’s possible for primitive individuals to transition to modern individuals

If we read (5) in the metaphysical sense, then it’s clearly false. The world doesn’t care what we know or don’t.

If we read (5) in the epistemic sense, then it seems (5) might be true, but then I think Rousseau would reject (3). Simply put, there’s no reason to think there is a connection between the existence of primitive individuals and what we could or couldn’t know about them.

However, if we read (5) in the nomological sense, then it seems (5) might be true, and (3) might be as well. With respect to the former, Rousseau would be claiming the laws of nature rule out this transition, and he might motivate this by reflecting on the difficulties inherent in bridging a non-reasoning creature to the sort of reasoning creatures we are, among other things. Additionally, (3) might still be accepted since there’s plausibly a link between primitive individuals revealing basic human nature and nomological possibility.

I’ll let you sort out whether you find the preceding convincing or not.

Sketches of Love

What follows treats love as consisting entirely of desires and motivational profile:
x loves y just in case x desires goods for y up to and greater than what x takes y to deserve
We might have as a dual:
x hates y just in case x desires bad for y up to a greater than what x takes y to deserve

Clarification 1: When John loves Sally, John wants good things to happen to Sally in general. John might want goods for Sally even if John isn't involved in Sally obtaining said goods.

Clarification 2: When John merely likes Sally, John wants good things for Sally that Sally deserves. Note, John not wanting Sally to receive goods greater than what John thinks Sally deserves is not equivalent to John wanting Sally to not receive goods greater than what John thinks Sally deserves. The latter - but not the former - would lead to John being upset if Sally did receive such goods.

Clarification 3: One might hold - as Velleman does - that John desires goods for Sally out of respect for her capacity for practical reasoning. I would not accept this though. It seems to me love for another person is love of that other person's qualities, because that's all there is to the other person. I can't imagine a table absent extension, color, shape, etc.; I can't imagine Sally absent all her qualities, so how could I love such a thing?

• Response 1: If one loves another only for their qualities, then since these qualities can be instantiated elsewhere, the beloved is not unique, and that seems counterintuitive.

• Rejoinder: While true qualities can be instantiated elsewhere, quality combinations are rarer. There are many blue-eyed individuals, but fewer blue-eyed brown-haired individuals. Attending to the configuration of a beloved sharply restricts the likelihood of another individual exhibiting the same quality set. Moreover, everyone has a height, but each person has a specific height. For each quality, each person has both a determinable and determinate aspects. Focusing on the determinate aspect sharply restricts the likelihood of another exhibiting the same determinate quality set. It is not simply that Sally has blue eyes, brown hair, etc., but that Sally has this shade, hue, and saturation, along with her many other features, which make her rather rare.

• Response 2: If a beloved perished but all the beloved's qualities were found in a duplicate, would we love the duplicate? Likely not, so there must be something beyond the mere qualities.

• Rejoinder: I’m not sure what to make of this exotic thought experiment, but I’m inclined to say – if all the properties are the same, including memories, etc. – then ‘yes’. Cp. Hurka who asks if our beloved is replaced with a clone with all the same properties would we still feel a sense of loss. He infers from answering this affirmatively that there is something special about the beloved beyond properties. I think this inference is fallacious. Of course I’d still feel a sense of loss, someone has died. Death is a loss. This doesn’t yet show there’s something beyond the properties of my beloved.

Clarification 4: Some qualities we dislike are found in those we love. John might dislike when others interrupt him in general, but dislike it much less when one interrupts him in a charismatic or charming manner. Similarly, things we dislike in general we might even enjoy if done by our lover because we generally like when things are done, say, cleverly or charismatically, and we find our lover clever or charismatic.

Fake Coins Puzzle

Question

There are 12 coins before you, one of which is fake. The fake coin is either heavier than or lighter than the other 11 coins. The legitimate coins all weigh the same. You have a balance scale you can use to weigh the coins. You can use the scale at most three times. How do you find the fake coin?

Answer

Number the coins 1-12. Separate the coins into a pile of 1,2,3,4, a pile of 5,6,7,8, and a pile of 9,10,11,12. Let "f" denote the fake coin. Let the predicate "H" denote heavy and the predicate "L" denote light.

Weigh 1: 1,2,3,4 x 5,6,7,8. There are three possible outcomes:
Outcome I: 1,2,3,4 = 5,6,7,8. f is among 9,10,11,12.
Weigh 1.2: 1,9 x 10,11, where 1 is clearly not f. There are three possible outcomes:
Outcome I: 1,9 = 10,11. f is 12. DONE.
Outcome II: 1,9 > 10,11. Either H(9) or L(10) or L(11).
Weigh 1.2.3: 10 x 11. There are three possible outcomes:
Outcome I: 10 = 11. Then f is 9. DONE.
Outcome II: 10 > 11. Then f is 11. DONE.
Outcome III: 10 < 11. Then f is 10. DONE.
Outcome III: 1,9 < 10,11. Either L(9) or H(10) or H(11).
Weigh 1.2.3: 10 x 11. There are three possible outcomes:
Outcome I: 10 = 11. Then f is 9. DONE.
Outcome II: 10 > 11. Then f is 10. DONE.
Outcome III: 10 < 11. Then f is 11. DONE.
Outcome II: 1,2,3,4 > 5,6,7,8. f is either H(1), H(2), H(3), H(4), L(5), L(6), L(7), or L(8).
Weigh 1.2: 4,5,6,7 x 8,9,10,11. There are three possible outcomes:
Outcome I: 4,5,6,7 = 8,9,10,11. Then f is either H(1) or H(2) or H(3).
Weigh 1.2.3: 1 x 2. There are three possible outcomes:
Outcome I: 1 = 2. Then f is 3. DONE.
Outcome II: 1 > 2. Then f is 1. DONE.
Outcome III: 1 < 2. Then f is 2. DONE.
Outcome II: 4,5,6,7 > 8,9,10,11. Then f is either H(4) or L(8).
Weigh 1.2.3: 1 x 4. There are two possible outcomes:
Outcome I: 1 = 4. Then f is 8. DONE.
Outcome II: 1 < 4. Then f is 4. DONE.
Outcome III: 4,5,6,7 < 8,9,10,11. Then f is either L(5) or L(6) or L(7).
Weigh 1.2.3: 5 x 6. There are three possible outcomes:
Outcome I: 5 = 6. Then f is 7. DONE.
Outcome II: 5 < 6. Then f is 5. DONE.
Outcome III: 5 > 6. Then f is 6. DONE.
Outcome III: 1,2,3,4 < 5,6,7,8. f is either L(1), L(2), L(3), L(4), H(5), H(6), H(7), or H(8).
Weigh 1.2: 10,11,12,1 x 2,3,4,5. There are three possible outcomes:
Outcome I: 10,11,12,1 = 2,3,4,5. Then f is either H(6) or H(7) or H(8).
Weigh 1.2.3: 6 x 7. There are three possible outcomes:
Outcome I: 6 = 7. Then f is 8. DONE.
Outcome II: 6 > 7. Then f is 6. DONE.
Outcome III; 6 < 7. Then f is 7. DONE.
Outcome II: 10,11,12,1 > 2,3,4,5. Then f is either L(2) or L(3) or L(4).
Weigh 1.2.3: 2 x 3. There are three possible outcomes:
Outcome I: 2 = 3. Then f is 4. DONE.
Outcome II: 2 > 3. Then f is 3. DONE.
Outcome III: 2 < 3. Then f is 2. DONE.
Outcome III: 10,11,12,1 < 2,3,4,5. Then f is either L(1) or H(5).
Weigh 1.2.3: 1 x 4. There are two possible outcomes:
Outcome I: 1 = 4. Then f is 5. DONE.
Outcome II: 1 < 4. Then f is 1. DONE.

Garbage Logic

Question

One sunny afternoon John asks Sally how she's doing, and Sally responds that she isn't happy. Sally then quotes the song by the band Garbage - "I'm only happy when it rains." John then claims Sally has committed a fallacy. Is John correct?

Answer

To get a feel for the question, consider whether you think the following is a good inference:

(i) S is only happy if it rains
(ii) It does not rain
(iii) Hence, S is not happy

Let "It rains" be denoted by Q and "S is happy" by P. If you think (i) has the form (Q->P) then this will be invalid. You might think this because "if" on its own seems to be introducing "It rains" as the antecedent of a material conditional. Then (i) is equivalent to: "It rains, only if S is happy." That is:

(1) It rains only if S is happy (Q->P)
(2) It does not rain (~Q)
(3) Hence, S is not happy (~P)

On the other hand, if you think (i) has the form (P->Q), then the argument is valid. You might think this because "only if" is typically taken to introduce the consequent of a material conditional, and "S is only happy if..." is plausibly read as "S is happy only if...". Then (i) is equivalent to "S is happy only if it rains." That is:

(4) S is happy only if it rains (P->Q)
(5) It does not rain (~Q)
(6) Hence, S is not happy (~P)

There are two further options as the setup permits another reading:

(iv) S is only happy if it rains
(v) S is not happy
(vi) Hence, it does not rain

So that taking "if" to introduce the antecedent, we have the valid:

(7) It rains only if S is happy (Q->P)
(8) S is not happy (~P)
(9) Hence, it does not rain (~Q)

And if you take "only happy if" to introduce the consequent, we have the invalid:

(10) S is happy only if it rains (P->Q)
(11) S is not happy (~P)
(12) Hence, it does not rain (~Q)

So, whether a fallacy has been committed depends on whether Sally intended to infer "it does not rain" or "Sally is not happy, as well as whether "Sally is only happy if it rains" should be read as "Sally is happy only if it rains" or "It rains only if Sally is happy."

Concerning the first, I take Sally to be supporting the claim "I'm not happy" by appealing to the fact that it is not raining, which is common knowledge. If this is correct, then the second premise of the argument should be "It does not rain." So we can rule out setup (vi)-(vi).

Concerning the second, I take Sally to be claiming that if she's happy, then it rains. That is, Sally is making a valid argument and John is incorrect. This reading is also consistent with Sally not being happy, but it raining nevertheless. In other words, all we know is that if Sally is happy then it's raining, and if it's not raining then Sally isn't happy. This is also a bit sadder. Sally isn't even happy all and only those times it rains. Rather, Sally is only happy some of the times it rains.

Exhaustive Paradox

Question

John asks Sally if she is tired.
Sally responds: "I'm not tired, I'm exhausted."
John responds: "Well, I'm glad to hear you aren't exhausted!"

Sally is perplexed. But so is John. Explain both perplexities.

Answer

Clearly, what Sally means is that she is not just tired. That is, she is both exhausted and tired. So John suggesting she is not exhausted is perplexing to Sally.

Still, claiming to not be tired and to be exhausted is an odd way to claim to be both tired and exhausted. At least, John thinks so. He reasons that for any agent S, if S is exhausted then S is tired, since being exhausted is an extreme form of being tired. Hence, to claim:

1. S is exhausted

Entails:

       2. S is tired

So claiming, in addition:

       3. S is not tired

Is inconsistent. But John is trying to be charitable, and so’d rather not attribute an inconsistency to Sally. Rather, John takes Sally at her word when she claims "I'm not tired." Moreover, John believes, as is plausible:

        4. S is not tired

Entails:

        5. S is not exhausted

And since John is a nice guy, he's glad to hear Sally isn't exhausted given that she isn't tired. Of course, that still leaves Sally as speaking inconsistently, since she explicitly says she is exhausted, and this conflicts with (5). In other words, if John assumes Sally speaks consistently then either Sally is not tired and not exhausted or tired and exhausted, either of which conflicts with Sally’s expressed claim. John is perplexed because he seems forced to conclude his friend Sally is inconsistent.

Whistling

Consider the task of teaching someone to whistle. A natural strategy when teaching someone to whistle is to describe to your pupil how they should hold their mouth, tongue, etc., so that they may imitate the sound you make when you successfully whistle. This is not, however, a very successful pedagogical strategy. This strategy amounts to throwing true claims at the pupil and hoping they stick. A less natural strategy, a better strategy I think, is to have the pupil attempt to whistle themselves and, of course, fail. As they fail to whistle, however, you manipulate your mouth, tongue, etc., so that you imitate the sound they produce in their failure. Once you are able to imitate their sound, do so while slowly manipulating your mouth, tongue, etc., to the whistle position you have mastered. Once you understand the steps, describe each step to your pupil so they see how to get from their noise to your whistle. In other words, teach them how to whistle from what they already know, not from what you already know. 

For the Sake of Argument...

I had an instructor who thought hard about formal systems that might underwrite analysis of speech acts like supposition and asserting. He argued as a matter of logic, asserting entailed supposing, though supposing did not entail asserting. For example, the following would be counted as valid:

1. John AST(The store is open)

2. Hence, John SUP(The store is open)

While the following would not count as valid:

1. John SUP(The store is open)

2. Hence, John AST(The store is open)

I agree with the latter not counting as valid. Asserting seems clearly associated with a norm of truth in every case, while supposing does not. John might claim to know p while supposing not p, without intuitive conflict. In contrast, John claiming to know p while asserting not p, seems a misuse of asserting, i.e. a lie. He's surely asserted, but he's violated a norm.

Does this make trouble for the first argument too? Not obviously. John asserting p comes with a norm of assertion, and if it's entailed John supposes p as well, we might think John's supposing in this case comes with a norm of assertion as well. That doesn't mean John can't suppose without the norm, and indeed, in many cases he will do just that.

That said, I do think there's trouble holding the first entailment. Supposing as an attitude seems to me to involve - in every case - direction towards some further goal. John doesn't simply suppose the store is open. Rather, John supposes the store is open for a reason. This is clearest, I think, in situations where one might suppose something for the sake of contradiction, i.e. reductio proofs. John might suppose p with the intention of drawing out some inconsistency in a premise set combined with background logical constraints. This strikes me as how supposing works in natural language as well. When John supposes the store is open, it's natural to ask - if you aren't already party to reason for the supposition - why John is supposing such a thing, e.g. do you need milk? do you have a shift today?

This feature of supposing in mind, return to the first argument. If John asserts the store is open, then if this argument is valid, it follows John supposes the store is open. But if John supposes the store is open, then there is some goal X John has in mind which motivates this supposition. Hence, in every case of assertion, there is some goal X agents have in mind which motivates the assertion. I find this implausible.

I'll detail why in another post. In the meantime, what do you think?

A Simple Question

Setup

Mathematician S is thinking of a number which is either 1, 2, or 3. Mathematician P can ask S only one question to determine which number S is thinking of. S can only answer "Yes", "No", or "I don't know" to the question posed by P.

Question

What question might P ask to determine which number S is thinking of?

Answer

There are many questions P might ask to determine S's number. I'll share what I'd ask S: If n is an odd integer larger than any you've divided any number into, is n divisible without remainder by the number you're thinking of? Let m be S's number. There are three options:

1. S knows n is divisible without remainder by m iff m is 1
2. S knows n is not divisible without remainder by m iff m is 2
3. S does not know whether n is divisible without remainder by m or not iff m is 3

To see other question P might ask, check out the forum where I came across the puzzle here.

Chicago Area Consortium Plato Conference

The Chicago Area Consortium in Ancient Greek and Roman Philosophy will be holding a conference on Plato, focusing on Eros, Polis, and Cosmos on October 19 and 20. It looks like a banger. Details here.

Two Stones Puzzle

Puzzle

Frank owes the merchant Jack a large sum, which Frank is unable to pay. Jack offers Frank a deal: “Convince your daughter Sally to marry me, and I’ll drop the debt.” Frank asks Sally if she’ll marry Jack, but Sally is uninterested. When Jack relates this to Frank, he responds: “I still may be able to help you out. I’ll drop the debt if you convince Sally to agree to the following deal. We all three go to the nearby river. I’ll grab two stones from the river bank, one white and one black. I’ll place the stones in a bag, then hand the bag to Sally. Sally will then pull a single stone from the bag. If Sally draws a black stone, then we’ll be married. If Sally draws white, then we won’t be married. In either case, I’ll drop the debt.” Jack tells Sally the new offer. Sally agrees given the new chances to save her father. However, while at the river Sally sees Jack put two black stones in the bag instead of one black and one white. Sally doesn’t want to ruin the deal by calling Jack out, but she also doesn’t want to marry Jack. What does Sally do?

Answer

After I came up with a solution, I looked at others. The standard solution (if there is one), seems to be: Sally draws a stone and quickly drops it into the river before anyone can tell what color it is. Sally then observes the group could determine the color of the stone she dropped by looking at the remaining stone in the bag.

That’s fine; it might work. But I’m not a fan of this solution, as it relies on dropping the stone before anyone can see its color.

I prefer my solution: Sally claims she is superstitious, and that drawing a black stone to start a marriage courts bad luck. Sally proposes that rather than she and the merchant marrying if she draws a black stone, they marry if she draws a white stone. Had the merchant been fair, there would be no reason for him to prefer one color over another, so he should have no grounds for rejecting Sally’s proposal.

Symposium: Socrates Responding to Agathon

Just prior to his speech, Socrates disputes Agathon's claim that Love is beautiful and good:

1. There is some x such that Love loves x or there is no y such that Love loves y

2. It is not the case there is no y such that Love loves y

3. Hence, there is some x such that Love loves x

4. If there is some x such that Love loves x, then Love desires x

5. If Love desires x, then Love does not possess x

6. Love loves/desires what is beautiful

7. Hence, Love does not possess what is beautiful

8. If Love does not possess what is beautiful, then Love is not beautiful

9. Hence, Love is not beautiful

10. Love loves/desires what is good

11. Hence, Love does not possess what is good

12. If Love does not possess what is good, then Love is not good

13. Hence, Love is not good

14. Hence, Love is neither beautiful nor good

(1) is plausible by law of excluded middle. Agathon grants (2), so (3) follows. Agathon grants (4) as well, presumably since loving is plausibly understood as a species of desiring. Socrates argues for (5) by observing infelicities, e.g. a bald man desiring to be bald, and accompanied by an explanation of putative counterexamples, e.g. what the bald man desires is that he continue to be bald. Agathon claimed (6) and (10); note I've collapsed the link between loving and desiring from (4) when characterizing these premises. (7) and (11) follow. Socrates motivates (8) and (12) by shifting from possession of an object with a quality to being an object with a quality. (9), (13), and (14) follow.

Why accept (4)? To be fair, I think it's right to say that if S desires x then S does not possess x, so I'm happy to grant the related (5). Desire seems motivational, and so intimately tied to action. If S desires something S already possesses, there seems little motivation or guidance for action on offer unless one appeal to something like continued possession, as Socrates points out. That said, (4) treats loving as a species of desiring. But it doesn't seem as obvious that, say, loving is motivational. S might love x without that love motivating or guiding action, e.g. love of an ancestor, love of a mathematical proof. Yet, this must be the case if loving is a species of desiring.

Why accept (8) and (12)? Socrates seems to shift from the lack of possession of an object to the lack of having whatever quality that object exhibits possesses. If this conditional is true, it's nevertheless irrelevant, since there seems little connection between, say, my not possessing a red apple and so thereby not being red. That is, it seems plausible Love might lack beautiful things, yet still be beautiful. Moreover, Love might seek out beautiful things because Love is beautiful, if one assumes - as many of the speakers seem to - that like attracts like.

Symposium: Speech of Pausanias

Pausanias provides an analysis of what he means by accepting a lover in the Heavenly manner:
It is honorable for a young man Y to accept a lover X iff

1. X realizes he's justified in performing P for Y who returns the favor by performing Q
2. Y understands he's justified in Q for X because X can make Y virtuous and wise
3. X can make Y virtuous and wise
4. Y is eager to be taught by X

The idea is that it is honorable for a young man to accept a lover just in case the lover realizes he can provide services for the young man who returns services in kind, and they both understand they are justified in this interaction with the eager young man gaining wisdom and virtue from the deal, and both can gain what they desire.

One worry to have about this is the transactional nature of honorable acceptance of a lover. For a young man to accept another as lover, the young man must essentially be engaged in cost-benefit analysis. Consider, according to this analysis the following holds: It is honorable for young man Y to accept lover X where,

1. X realizes he is justified in performing P for Y who returns the favor by performing Q
2. Y understands he's justified in Q for X because X can make Y virtuous and wise because X knows Z who is virtuous and wise, and while X tells Y he does not intend to lead Y to Z, Y holds out hope any way
3. X can make Y virtuous and wise through Z
4. Y is eager to be taught by X because Y hopes X will teach Y what X has learned from Z or will introduce Y to Z  

Pausanias might respond that Y loves virtue and wisdom. My quarrel here is not that, however, but rather that this should not count as honorable acceptance of a lover. Rather, it’s honorable acceptance of wisdom and virtue. The lover is incidental. Related, it seems counter-intuitive to claim love is never for the sake of an individual – the lover – rather than as some instrument.

Symposium: Speech of Phaedrus

Phaedrus sets the tone for the Symposium, complaining no poet praises Love. From Phaedrus, we learn Love is ancient – not the oldest – and one of the earliest gods to exist. Love has no parentage, though Love is said to have started to exist at some time. Phaedrus rests on authority in this origin myth, adding both humanity and the gods stand in awe and praise of Love.

We also learn Love is the greatest good for humans. Here, it seems Phaedrus is providing something of an argument, though as you’re no doubt aware he’s sees no reason to provide support for his claims, or consider potential counterexamples or difficulties. Rather, Phaedrus claims Love is the greatest guidance or motivator for humans, because whether lover or beloved, being shamed in a lover or beloved’s eyes is something we all seek to avoid and being admired is something we all seek. In fact, Phaedrus claims avoiding shame and seeking admiration effected through the lover-beloved pairing is a much better guidance or motivator than anything deriving from kinship, wealth, or even honor. Putting this point another way, if we are to seek to achieve great things, we require great guidance and motivation, and Love provides the best source of such guidance and motivation.

I pause here to point out the intuitive plausibility of this claim. Most of us no doubt can empathize with the sting of hearing those words from a lover “I’m disappointed in you.” Feeling that you’ve disappointed one you love – even if that love falls short of the sort of lover-beloved relationship Phaedrus has in mind here – is not enjoyable, and one feeling the sting is likely spurred to ensure they are not stung similarly in the future. In other words, the recipient will likely change their behavior to avoid disappointing their love. On the other hand, most of us likely know how good it feels to be admired by a lover, and to admire. Admiration by a lover spurs one to seek out further admiration, by achieving great things perhaps. We may even do quite drastic, perhaps unhappy, things for to acquire admiration and avoid shame. But I’m getting ahead of myself; let’s return to Phaedrus.

Phaedrus illustrates his understanding of Love as a great motivator with the example of the army of lovers. He claims, hyperbolically, that an army of lovers would be invincible, perhaps capable of taking over the world. I can’t help but think of Thebes’ Sacred Band, elite troops who loved, fought, and often died together, who respected one another as lovers might. They posed a considerable threat on the battlefield, from what I understand. I’m not sure which came first, the Symposium or the band. It’s not that important though. What is important is that this thought experiment seems well-motivated.

Phaedrus goes on to claim Love is the reason we are willing to make great sacrifices, with the greater sacrifice in the right context leading to the greater blessings from the gods. He provides three examples to illustrate. The first is of a lover Alcestis who sacrifices herself to save the life of her beloved – her husband. Alcestis is returned to life by the gods, a blessing provided for her great sacrifice. Note too in this example, the callback to how poorly kinship pales as a motivator for great sacrifice, as the husband’s parents are not even willing to sacrifice their lives for their son.

Contrast this with Orpheus, a lover who only caught a glimpse of his beloved, since he wasn’t willing to sacrifice himself. The gods did not praise Orpheus, but punished him with a mere image of his beloved. This is because Orpheus was unwilling to do what a lover should: sacrifice.

Where both Alcestis and Orpheus are examples of a lover sacrificing or not, Phaedrus’ third example is that of Achilles who he understands as the beloved of Patroclus. Even so, Achilles sacrificed himself by avenging the death of Patroclus by killing Hector, and consequently the gods gave him one of the highest prizes – the Isle of the Blessed. This is so even though Achilles was – as Phaedrus claims – the beloved and not the lover.

In fact the gods, Phaedrus claims, delight more with a beloved cherishes their lover, than when the lover cherishes the beloved. I suspect the point here trades on loving not being a symmetric relation. That is, just because x loves y it doesn’t follow that y loves x. Anyone can love, and one who loves may be motivated to do rather unacceptable things if that love is unrequited. This should be expected, as love is – again – a great motivator. But it seems paradigmatic cases Phaedrus has in mind of loving are those where love is symmetric, i.e. where the lover is loved in return. This is perhaps why the gods delight more with a beloved who cherishes their lover, than with a lover who cherishes the beloved. The latter may be had too easily, while the former secures a good.

Before closing his speech, Phaedrus says something rather puzzling: the lover is more like a god than the beloved. This is so because the lover is inspired by the gods. I can think of two ways to understand this passage.

1. The implication here is that the beloved is not inspired by the gods. I think this is a problematic reading of the passage. If the lover is inspired by the gods, while the beloved is not, but the gods delight and bestow more honors on the beloved, then it seems the gods praise something more than what they inspire. More concretely, the gods praise Achilles the beloved for his sacrifice more than they praise Alcestis the lover for hers, though they make similar sacrifices. But Alcestis was inspired by the gods in her sacrifice, since she was a lover. There seems tension here, since this seems to imply that the gods praise something as greater than themselves. I take this consequence to speak against reading the passage as having the implication that the beloved is not inspired by the gods.
2. But we can mitigate by claiming the beloved is not directly inspired by the gods, though the beloved is indirectly inspired. Achilles – after the death of Patroclus – acts as a lover would act, and so acts as if he’s inspired by a god. Because Achilles sacrifices himself, the way a lover would despite the fact that he is not a lover, he is more praiseworthy than Alcestis. Note: on this reading it is important only to claim Achilles acts as a lover. We can’t, for instance, go so far as to say Achilles – in acting as he does – becomes a lover. This is because if Achilles becomes a lover through his action, then Alcestis – who was already a lover – should receive just as much praise. Since she doesn’t, according to Phaedrus, we seem limited to saying Achilles acts as a lover would, but is not himself a lover. Ultimately then, the implication from the passage should be that the beloved is not inspired directly by the gods, but is inspired indirectly.

Summary aside, there are patent worries one should have about Phaedrus’ characterization of Love. Most clearly, Phaedrus simply assumes that Love guides lovers towards things that are good. This is not obviously true. We can illustrate the point in several ways.

1. Consider first a lover who is not cherished by his beloved. It is easy to imagine a lover doing all sorts of terrible things for the sake of the beloved, because they aren’t cherished or perhaps because the beloved cherishes someone else.
2. Consider second Phaedrus’ army of lovers not directed at admirable ends, but instead, say, genocide in the name of racial purity. Put another way, were Nazi’s lovers, I’d hope Phaedrus is incorrect about whether the resulting force was “invincible.” An army of lovers may achieve great things, but pure motivation need not be directed at a good end. 
3. Consider third Achilles and Patroclus. Achilles seemed motivated by wrath and revenge rather than love. Indeed, it seems his love was an instrument for his wrath rather than the other way around, i.e. love was the justification but vengeance was the end. I take Achilles’ desecration of Hector’s body after killing him – parading him in view of his family and Troy – illustrates this point. Perhaps more telling is the fact that the gods had to intercede to force Achilles to stop, i.e. give Hector’s body to his father Priam for proper burial. Surely then the gods did not find this action praiseworthy. This again illustrates that Love understood by Phaedrus has no valence, it’s directed – but not much more.

Objections aside, I think Phaedrus’ speech is valuable for three reasons.

1. First, Phaedrus provides Love a motivational character, which is taken up by subsequent speakers in the Symposium.
2. Second, Phaedrus seems to play the role of a foil for later speakers. This is particularly apparent with the subsequent speech of Pausanias who begins his speech by making a philosophical distinction, something Phaedrus noticeably does not do throughout his speech. Phaedrus instead prefers to make claims, rely on myth, and basically play the role of a rhetorician. Pausanias doesn’t merely show Phaedrus as being a mere rhetorician by making philosophical distinctions where Phaedrus didn’t, but also tells by distinguishing between two sorts of love: one better than the other. I take this to be Pausanias picking up on the lack of direction towards the good that Phaedrus’ account of Love employs. In that, I think Pausanias is correct to make this distinction, as Love perhaps should be more than pure motivation; it should be directed towards something good.
3. Third, Phaedrus’s speech isn’t merely a foil, but is a natural starting point for discussion to follow. Phaedrus’ account is wrong, but it’s by virtue of realizing his mistakes that we make progress towards the truth. Isn’t it plausible masses of people can be moved by mere rhetoric of the sort exhibited by Phaedrus – without reflecting much on its content? Of course. This is common enough in our lives today. It is common enough now, and likely was common enough then, to be worthy of being addressed directly. Phaedrus provides a case to dispute, but in doing so provides our base camp from where we begin our ascent towards understanding the nature of Love. It’s a starting point for dissent, which is a starting point for ascent.

Virtue in Rags: Virtue Requires Friendship

In Chapter 9 of the Nichomachean Ethics Aristotle defends - with a rather tortured argument - the claim that a virtuous friend is naturally desirable for a virtuous individual. I’ve attempted to extract his argument here (Let “John” and “Sally” designate distinct virtuous individuals):

(1) John exists
(2) If x exists then x perceives/thinks
(3) If x perceives/thinks then x perceives that x perceives/thinks
(4) If x perceives that x perceives/thinks then x perceives that x exists
(5) Hence, if x exists then x perceives that x exists                                                                                                     (from 2-4)
(6) John perceives that John exists                                                                                                                                     (from 1,4)
(7) If x exists then x's existence is intrinsically good/pleasant for x
(8) John's existence is intrinsically good/pleasant for John                                                                                    (from 1,6,7)
(9) If z is intrinsically good/pleasant for x & x perceives z, z seems good/pleasant for x
(10) Hence, John's existence seems good/pleasant for John                                                                                    (from 6,8,9)
(11) If y is x's friend, then whatever is intrinsically good/pleasant for x is intrinsically good/pleasant for y
(12) Sally is John's friend
(13) Hence, whatever is intrinsically good/pleasant for John is intrinsically good/pleasant for Sally   (from 11,12)
(14) Hence, John's existence is intrinsically good/pleasant for Sally                                                                   (from 8-13)
(15) If y is x's friend, then whatever seems intrinsically good/pleasant for x seems intrinsically good/pleasant for y
(16) Hence, John's existence seems intrinsically good/pleasant for Sally                                                          (from 12,15)
(17) If y is x's friend, then x is y's friend
(18) Hence, John  is Sally's friend                                                                                                                                         (from 12,17)
(19) Hence, Sally's existence is intrinsically good/pleasant for Sally                                                                   (repeat 1-8 replacing "John" with "Sally")
(20) Hence, Sally's existence seems intrinsically good/pleasant for Sally                                                         (repeat 1-10 replacing "John" with "Sally")
(21) Hence, whatever is intrinsically good/pleasant for Sally is intrinsically good/pleasant for John   (from 11,18)
(22) Hence, Sally's existence is intrinsically good/pleasant for John                                                                   (from 19-21)
(23) Hence, Sally's existence seems intrinsically good/pleasant for John                                                          (from 15,18)
(24) If z is intrinsically good/pleasant for y & z seems intrinsically good/pleasant for y, then z is desirable to y
(25) Hence, Sally's existence is desirable to John                                                                                                          (from 22,23,24)
(26) Hence, John's existence is desirable to Sally                                                                                                          (from 14,16,24)

Virtue in Rags: Vicious Friends

Several arguments in Aristotle's Nicomachean Ethics – in particular Chapter 9 – suggest Aristotle thinks virtuous individuals need friends because, as a second self, friends provide a route to self-knowledge. That sounds correct, but seems too limited. Consider the following: During a long-term relationship years ago, I tried in vain to be friendly with my lover's best friend, call her E. E and I did not get along, and were around each other often. Reflection on why suggested to me that E and I shared many qualities, but those qualities we shared were qualities I didn't like about myself, e.g. pride, aggressiveness, etc. Meeting with E reminded me of what I disliked about myself. In fact, I learned quite a bit about myself that I didn’t like from E, who I wouldn’t consider a friend.

Now, neither of us was virtuous, and it doesn’t seem Aristotle would count this relationship as a friendship, e.g. neither of us felt goodwill towards the other, etc. Nevertheless, E provided an effective route to self-knowledge because she was, in a sense, a second self – reflecting vicious qualities of mine at the time. This leads me to think where Aristotle thinks virtuous individuals need friends because their second-self provides self-knowledge, less-than-virtuous individuals might need less-than-virtuous relationships – not necessarily friendships - because these second-selves also provide self-knowledge.    

Moderate Modal Skepticism

Philosophers frequently motivate claims as possible based on conceivability.[1] It is then natural to wonder whether conceiving is a reliable method for generating justified beliefs in possibility claims. Yablo argued[2] conceiving proposition p as possible provides evidence that p is, in fact, possible.[3] Less optimistic philosophers, such as van Inwagen,[4] claim conceiving proposition p as possible provides no evidence that p is possible. If van Inwagen is correct, philosophical arguments relying on possibility claims motivated solely by conceivability are suspect. Given how widespread such philosophical arguments seem to be, van Inwagen’s claims are worth examining in detail. 

            In Section 1 of this paper, we extract and evaluate van Inwagen’s argument for Moderate Modal Skepticism, the view that while agents have justified beliefs in some – rather commonsensical – modal claims, agents do not have justified beliefs in many other – rather philosophical – modal claims. Having outlined van Inwagen’s position, in Section 2 we note a long-standing objection to van Inwagen’s argument – that it can be generalized to undermine justified beliefs in commonsensical modal claims as well as philosophical modal claims – fails, but a related worry – that van Inwagen’s argument relies on an under-motivated distinction between basic and non-basic modal claims – does not. Two responses are offered on behalf of van Inwagen, though neither are entirely satisfying. Additionally, we note van Inwagen’s argument implausibly requires agents justified in believing a given modal claim is true in every case know the modal claim is true. Having observed costs of van Inwagen’s characterization of the relationship between conceivability and possibility, in Section 3 we examine Yablo’s well-known alternative, which does not rely on an obscure distinction between basic and non-basic modal claims, and which allows justified belief and knowledge concerning modal propositions to come apart. Since there are independent reasons to prefer Yablo’s proposal to van Inwagen’s as an appropriate analysis of the link between conceivability and possibility, and since – pace van Inwagen – Yablo’s proposal does not entail Moderate Modal Skepticism, we conclude the various philosophical arguments targeted by van Inwagen are not threatened by his skeptical thesis.

[1](Putnam, 1980)’s super-Spartans; (Putnam, 1975)’s twin-earth; (Lewis, 1980)’s pained Martians; (Jackson, 1986)’s Mary; (Chalmers, 1996)’s zombies, etc.
[2]Cp. (Chalmers, 2002); others tie modal knowledge to counterfactual reasoning (Williamson, 2007), (Kroedel, 2017).
[3](Yablo, 1993).
[4](Van Inwagen, 1999).