Legitimate and illegitimate authority

It is tempting to think that legitimate and illegitimate authorities are both types of a single thing. One might not want to call that single thing “authority”. After all, one doesn’t want to say that real and fake money are both types of money. But it sure seems like there is something X that legitimate and illegitimate authorities have in common with each other, and with nothing else. One imagines that a dictator and a lawfully elected president are in some way both doing the same kind of thing, “ruling” or whatever.

But this now seems to me to be mistaken. Or at least I can’t think what X could be. The only candidate I can think of is the trivial disjunctive property of being a legitimate authority or an illegitimate authority.

To a first approximation, one might think that the legitimate and illegitimate authorities both engage in the speech act of commanding. One might here try to object that “commanding” has the same problem as “authority” does: that it is not clear that legitimate and illegitimate commands have anything in common. This criticism seems to me to be mistaken: the two may not have any normative commonality, but they seem to be the same speech act.

However, imagine that Alice is the legitimate elected ruler of Elbonia, but Bob has put Alice in solitary confinement and set himself up as a dictator. Alice is not crazy: when she is in solitary confinement she isn’t commanding anyone as there is no one for her to command. Alice is a legitimate authority and Bob is an illegitimate authority, yet they do not have commanding, or ruling, or running the country in common. (Similarly, even without imprisonment, we could suppose Alice is a small government conservative who ran on a platform of not issuing any orders except in an emergency, and no emergency came up and she kept her promise.)

One might think that they have some kind of dispositional property in common. Alice surely would command if she were to get out of prison, after all. Well, maybe, but we need to specify the conditions quite carefully. Suppose she got out of prison but thought that no one would follow her commands, because she was still surrounded by Bob’s flunkies. Then she might not bother to command. It makes one look bad if one issues commands and they are ignored. Perhaps, though, we can say: Alice would issue commands if she thought they were needed and likely to be obeyed. But that can’t be the disposition that defines a legitimate or illegitimate authority. For many quite ordinary people in the country presumably have the exact same disposition: they too would issue commands if they thought they were needed and likely to be obeyed! But we don’t want to say that these people are either legitimate or illegitimate authorities.

We might argue that Alice isn’t a legitimate authority while imprisoned, because she is incapacited, and incapacitation removes legitimate authority. One reason to be dubious of this answer is that on a plausible account of incapacitation, insanity is a form of incapacitation. But an insane illegitimate dictator is still an illegitimate authority, and so incapacitation does not remove the disjunctive property legimate or illegitimate authority, but at most it removes legitimacy. Thus, Alice might still be an authority, but not an illegitimate one. Another reason is this: we could imagine that in order to discourage people from incapacitating the legitimate ruler, the laws insist that one remains in charge if one’s incapacitation is due to an act of rebellion. Moreover, we might suppose that Bob hasn’t actually incapacitated Alice. He lets her walk around and give orders freely, but his minions kill anybody who obeys, so Alice doesn’t bother to issue any orders, because either they will be disobeyed or the obeyers will be killed.

Perhaps we might try to find a disposition in the citizenry, however. Maybe what makes Alice and Bob be the same kind of thing is that the citizens have a disposition to obey them. One worry about this is this: Suppose the citizens after electing Alice become unruly, and lose the disposition to obey. It seems that Alice could still be the legitimate authority. I suppose someone could think, however, that some principles of democracy would imply that if there is no social disposition to obey someone, they are no longer an authority, legitimate or not. I am dubious. But there is another objection to finding a common disposition in the citizenry. The citizenry’s disposition to obey Bob could easily be conditional on them being unable to escape the harsh treatment he imposes on the disobedient and on him actually issuing orders. So the proposal now is something like this: z is a legitimate authority or an illegitimate authority if the citizenry would be disposed to obey z if z were to issue orders backed up credible threats of harsh treatment. But it could easily be that a perfectly ordinary person z satisfies this definition: people would obey z if z were to issue orders backed up by credible threats!

Let’s try one more thing. What fake and real money have in common is that they are both objects made to appear to be real money. Could we say that both Alice and Bob claim have this in common: They both claim to (“pretend to”, in the old sense of “pretend” that does not imply “falsely” as it does now) be the legitimate authority? Again, that may not be true. Alice is in solitary confinement. She has no one to make such claims to. Again, we can try to find some dispositional formulation, such as that she would claim it if she thought it beneficial to do so. But again many quite ordinary people would claim to be the legitimate authority if they thought it beneficial to do so. Moreover, Bob can be an illegitimate authority without any pretence to legitimacy! He need not claim, for instance, that people have a duty to obey him, backing up his orders by threat rather than by claimed authority. (It is common in our time that dictators pretend to a legitimacy that they do not have. But this is not a necessary condition for being an illegitimate authority.) Finally, if Carl is a crazy guy who claims to have been elected and no one, not even Carl’s friends and family, pays any attention to his raving, it does not seem that Carl is an illegitimate authority.

None of this denies the thesis that there is a similarity between illegitimate authority and legitimate authority. But it does not seem possible to turn that similarity into a non-disjunctive property that both of these share. Though maybe I am just insufficiently clever.

Disjunctions and differential equations

It is plausible that:

1. Some of the fundamental dynamic laws of nature are given by differential equations.

2. All fundamental dynamic laws of nature provide fundamental causal explanations.

3. Facts that involve disjunction do not enter into fundamental causal explanations.

But one cannot believe (1)–(3). For:

4. Facts about derivatives are facts about limits.

And:

5. Facts about limits are infinite conjunctions of infinite disjunctions of infinite conjunctions.

For the limit of f(x) as x → y equals z if and only if every neighborhood N of z there is a neighborhood M of x such that for all u ∈ M we have f(u)∈N. Universal quantification is a kind of conjunction and existential quantification is a kind of disjunction.

I am inclined to reject (1).

A tale of three horses

Consider three horses: Alexander's Bucephalus, Gandalf's Shadowfax and Dawn. Here, I am using "Dawn" as the name of a horse that has come into existence just now, so that it is now the first moment of existence for Dawn. (Imagine the claims about Dawn all being made at the first moment of its existence.)

Intuitively, there is something Bucephalus and Dawn have in common with each other that they don't have in common with Shadowfax, namely reality.

The eternalist can take this at face value and say: Bucephalus and Dawn both exist, while Shadowfax does not.

But it is difficult for the presentist to say what Bucephalus and Dawn have in common which they don't share with Shadowfax. According to presentism, neither Bucephalus nor Shadowfax exist. Of course Bucephalus did exist, but on the other hand it is false that Dawn did exist: it is Dawn's first moment. So on presentism, Bucephalus and Dawn have neither existence nor past existence in common. And they don't have future existence in common either, since Bucephalus presumably has no future (unless there is a resurrection for brute animals, which we can suppose for the sake of argument there won't be). Nor do they have timeless existence in common, since none of the three is a timeless entity.

Of course, it is true that both Bucephalus and Dawn did-or-do-exist. But that's a disjunctive property, and a similarity in respect of a merely disjunctive property is not a real similarity. Perhaps the presentist can argue that it is a disjunctive property, but not a merely disjunctive one. But barring some sort of account of the similarity this seems ad hoc. We might as well say that Shadowfax and Bucephalus have this in common, that each fictionally-or-actually-exists.

Intending a disjunction that has an evil disjunct

This may take back the central part of my argument about tautologously equivalent intentions.

Suppose that Sally is a crime boss who really hates Fred and really likes fresh salmon. So she tells a henchman: "I need some sparkle in my day. I need you today to either kill Fred or find me some fresh salmon." Sally's intention is that

1. Fred is killed or Sally[note 1] gets fresh salmon.

It seems, then, that (1) is a wicked intention for Sally to have. What makes it wicked is that one of its disjuncts is an evil.

But actually (1) is not a wicked intention as such for Sally to have. Let's say I am the henchman. But yesterday I repented of my sins and confessed them all, and then I went to the FBI. The FBI asked me to remain in Sally's service for a few more days while they gather more evidence. So there I am: Sally wants me to kill Fred or find her some fresh salmon. I go and find her some fresh salmon. Why? In order to fulfill her order by killing Fred or getting her some fresh salmon. In other words, I am finding her some fresh salmon as a means to (1), which in turn is a means to having Sally be satisfied with me for a couple more days. My intention is morally upright.

There is nothing wrong, then, with acting to make true a disjunction that has an evil disjunct as long as I do so by means of making true a non-evil disjunct. There is something wrong with acting to make true a disjunction that has an evil disjunct indifferently between the disjuncts, as Sally does or as a henchperson passing Sally's unchanged order to a lower-down henchperson would be doing.

Notice a crucial difference between my and Sally's action plan. If I were to kill Fred, that would not fulfill my action plan. For my plan was to make the disjunction true by making the salmon disjunct true. But it would fulfill Sally's action plan.

Here is a tough question: What intention does Sally have that makes her action wicked and mine upright? Of course Sally has a desire that Fred die, and that makes her, we may suppose, a wicked person. But that does not make her action wicked. Sally wants to please herself. I want to please Sally. So far our intentions are the same. Sally wants to please herself by making (1) true. I want to please Sally by making (1) true. Our intentions are still the same. I have an additional intention: to make the salmon disjunct true. Sally doesn't care how (1) is made true. But that's a matter of her lacking an intention. Is that what makes her action wicked?

If so, then this would be an interesting example of a thought I've explored in other contexts, that certain actions are only permitted with certain intentions. For instance it is only permitted to participate in some of the sacraments if one has an appropriate intention. Or perhaps it is only permitted for spouses to make love with the intention of uniting or the intention of reproducing. Or maybe it is only permissible to assert with the intention of avoiding asserting a falsehood. To these kinds of cases (which are controversial, of course) one would add: one is only permitted to intend a disjunction with an evil disjunct if one additionally intends a non-evil disjunct (or intends that a non-evil disjunct be true or something else of like nature).

In "The Accomplishment of Plans", I've suggested that it's wrong to act in such a way that an evil might be accomplished by one. (Not everything one causes is accomplished. Paradigmatic cases of unintended side-effects are caused but not accomplished.) This would also explain the difference between Sally and me. Sally's plan is such that she might end up accomplishing Fred's death through it. But my plan is not like that. While I might accidentally kill Fred while driving to the airport in order to fly to a place where they have fresh salmon, Fred's death wouldn't be an accomplishment of mine.

A Gricean theory of indicative conditionals

The theory consists of two theses and two definitions. I will use → for indicative conditionals. And all my disjunctions will be inclusive.

1. MatCond: "p→q" expresses the same proposition as "~p or q".
2. NonTriv: A use of "p→q" normally implicates that "~p or q" is an evidentially non-trivial disjunction for the speaker.
3. Definition: "a or b" is an evidentially non-trivial disjunction for an agent x if and only if x has non-negligible evidence for the disjunction that goes over and beyond evidence for ~p and evidence for q.

I don't here commit to any particular view of evidence, and if there are non-evidential justifications, one can probably easily modify the theory.

Here is an interesting consequence of the theory which I think is just right. When my evidence that at least one of ~p and q is true is simply the evidence for ~p (or for q), I don't get to say "If p, then q." But if I tell you that at least one of ~p and q is true, then normally you get to say "If p, then q". For when I tell you that at least one of ~p and q is true, then "~p or q" comes to be an evidentially non-trivial disjunction for you: my testimony is evidence for the disjunction and this evidence does not derive for you from evidence for the one or the other disjunct.

Notice that "has non-negligible evidence for the disjunction" has some vagueness to it. Moreover, negligibility is contextual, and that is how it should be. If I tell you that at least one of the following is true: snow is not purple and 2+2=4, then "If snow is purple, then 2+2=4" does not generally become assertible for you. For while you do gain additional testimonial evidence for the disjunction that snow is not purple or 2+2=4 from my speaking to you, the gain is normally negligible over and beyond your earlier evidence that 2+2=4. But if you respond to my assertion with "So, if snow is purple, then 2+2=4", you are speaking quite correctly, since the use of "So" and the conversational context makes the evidence I just gave you salient and hence non-negligible. (Perhaps "salient" or "relevant" could be used in place of "non-negligible" in (3).)

The theory explains why it is that paradoxes of material implication can almost always be made to cease to be paradoxes of material implication as soon as one fills out the evidential backstory in a creative enough way. Take, for instance, the paradox of material implication:

4. If the president will invite me for dinner tonight, I will have dinner with the president in my pajamas.

The antecedent is false, so the material conditional is true, but (4) sure sounds bad (it sounds bad to assert and seems to be saying something bad about my manners). Yes, but now suppose that an epistemic authority has just handed me two numbered and folded pieces of paper, with a sentence written on each and folded in half, and told me that either at least the first paper contains a falsehood or they both contain truths. I puzzle out what she says, and I conclude, very reasonably:

5. If the sentence on the first piece of paper is true, the sentence on the second piece of paper is true.

I then unfold the pieces of paper, and notice that the first piece contains the sentence "The president will invite me for dinner tonight" and the second contains "I will have dinner with the president in my pajamas." And so I reasonably infer from (5):

6. So, if the president will invite me for dinner tonight, I will have dinner with the president in my pajamas.

(And, moreover, I now gain a new piece of evidence that the president won't invite me for dinner tonight—for it would be absurd to suppose I'd have dinner with him in my pajamas.) With this epistemic backstory, the paradoxical conditional is quite unparadoxical. That's because with this epistemic backstory, the corresponding disjunction

7. The president won't invite me for dinner tonight or I will have dinner with the president in my pajamas (or both)

is epistemically non-trivial. But in normal circumstances, (7) is epistemically trivial, since my only evidence for (7) is evidence for the first disjunct.

A similar kind of epistemic backstory can be given for any of the standard paradoxes of material implication, thereby turning paradoxical sentences into non-paradoxical ones (cf. this post). Our Gricean theory (1)-(3) explains this phenomenon neatly. So do theories on which indicatives are non-cognitive and ones on which they are subjective. But the Gricean theory is, I think, simpler.

Notice that in this Gricean theory we haven't brought in non-material conditionals through any back door, because we have explained the implicated content entirely in terms of disjunctions. Furthermore, (2) is basically a consequence of (1) plus the very plausible claim that disjunctive sentences normally implicate the epistemic non-triviality of the disjunction.

Disjunction introduction

The following argument is valid by disjunction introduction:

1. I won't play the lottery.
2. I won't play the lottery or I'll win the lottery.

But the conclusion sounds wrong.

Now, here is a hypothesis. The wrong-sound of the or-sentences corresponds precisely to the appearance of falsity in the conditional:

3. If I play the lottery, I'll win the lottery.

Now if the indicative conditional is the material conditional, then (3) is true assuming I won't play the lottery. This is one of the standard objections to taking the indicative conditional to be a material conditional. But I think this objection is weakened if (2) also sounds wrong, since (2) is the material conditional analysis of (3). If (3) sounds wrong, and (2) is the analysis of (3), then if one of them sounds wrong, so should the other. And that's what we observe.

The following would be an interesting test. Consider this argument:

4. I won't play the lottery.
5. So: I won't play the lottery or I'll win the lottery.
6. So: If I do play the lottery, I'll win the lottery.

Where would ordinary folks situate the apparent fallacy? Would it be at step (5) or at step (6)? I don't know. But if only at (5), then the material conditional analysis of indicative conditionals is not challenged by the apparent wrongness of (3).

On the other hand, (3) sounds false to ordinary folks (unless the lottery is rigged!), but I don't know if (2) sounds false to ordinary folks.

Truth, logic and explanation

Consider the following two very plausible explanatory intuitions:

1. Roses are flowers or violets are yellow because roses are flowers.
2. "Roses are flowers or violets are yellow" is true because "Roses are flowers" is true or "Violets are yellow" is true.

Now, the intuition in (1), when generalized to the general principle that if p and not q, then p or q because p, yields:

3. "Roses are flowers" is true or "Violets are yellow" is true because "Roses are flowers" is true.

Explanation may or may not be transitive in general, but it seems correct in the case at hand to move from (2) and (3) to:

4. "Roses are flowers or violets are yellow" is true because "Roses are flowers" is true.

Observe that (1) and (4) are parallel. Now suppose we agree with the deflationist about truth that:

5. "Roses are flowers or violets are yellow" is true because roses are flowers or violets are yellow.

We now have two paths to explaining why "Roses are flowers or violets are yellow" is true. One explanation is (4) and the other is (5). Unless one of these two explanatory paths subsumes the other, it seems that we have a case of explanatory overdetermination. But neither path subsumes the other. First, the explanans in (4) does not explain the explanans in (5), since that "Roses are flowers" is true does not explain why it is that roses are flowers or violets are yellow, as the former is a fact about a sentence (we can also make the argument go with utterances, statements or propositions) while the latter is a fact about flowers. Second, the explanans in (5) does not explain the explanans in (4)—for that "Roses are flowers" is true may be explained by roses being flowers, but is surely not explained by roses being flowers or violets being yellow.

Thus, the deflationist who accepts (1) and (2) is pressed to accept that (4) and (5) are an overdetermining pair of explanations. But that is unappealing. Probably the deflationist will have to deny the Tarskian intuition in (2). I don't know how great the cost of that is.

So what should we say if we accept (1)-(4), and we are inflationists? We still have a bit of a puzzle, even if we deny (5). The problem is that the explanations in (1) and (4) are exactly parallel. But, we ask, what explains this parallelism? It seems too much to separately explain the truth of the disjunction by the the truth of the true disjunct, and to explain the disjunction by the true disjunct. There should be a way of unifying this. One way would be:

6. (a) Roses are flowers or violets are yellow because "Roses are flowers or violets are yellow" is true; (b) "Roses are flowers or violets are yellow" is true because "Roses are flowers" is true; and, finally, (c) "Roses are flowers" is true because roses are flowers.

(Or we can give a propositional variant. That would probably be better, but I'll stick to the linguistic here so I don't have to keep on saying "the proposition that...". And maybe to explain "Roses are flowers" being true we need a few more steps on the linguistic side—but maybe not, since it may be a logically simple claim about the natural kinds rose and flower rather than a quantified claim.) On this perhaps weird approach, the explanation in Tarski's Schema (T) sometimes goes in one direction and sometimes in the other. I don't fully like this weird approach, though, because step (b) is troubling. The obvious way to justify the explanation in step (b) seems to be: (bi) "Roses are flowers or violets are yellow" is true because "Roses are flowers" is true or "Violets are yellow" is true; and (bii) "Roses are flowers" is true or "Violets are yellow" is true because "Roses are flowers" is true. However, if (bii) has no further intermediate steps, then, by the same token, (1) shouldn't have any further intermediate steps, and (6) is wrongheaded. And if (bii) has further intermediate steps, then these steps will need to be expanded in the fashion of (6), which will result in circularity.

Maybe, though, we can get away with just making (6b) be immediate in the case where "Roses are flowers" is true. In that case, what makes certain complex apparently worldly facts true is stuff on the linguistic side, finally combined with something more basic on the worldly side. I suppose this is basically what Tarski was up to. A lesson of this approach would be that logically complex facts, like the fact that roses are flowers or violets are yellow, are very different from simpler ones.

Of course, if it can be shown that "explains" is used equivocally in (1)-(4), or that the instances of transitivity that I employed are unjustified, all of this goes out the window. But I do think that this may give some reason to be an inflationist about truth.