Optimalism and mediocritism

We can think of the optimalist theory of ultimate explanation as the claim:

1. Necessarily, that reality is for the best explains everything.

(I won’t worry in this post about two details. First, whether “reality” in (1) includes the principle of optimality itself—Rescher has suggested that it does, since it’s for the best that everything be for the best. Second, whether “reality” is all the detail of the world, or just the “core” of the world—the aspects not set by indeterministic causation.)

Given that only truths explain, (1) entails:

2. Necessarily, reality is for the best.

Notice that one could accept (2) without accepting (1). One might, for instance, be a Leibnizian and think that there is a two-fold structure to ultimate explanation: first, God’s existence is explained by the ontological argument and, second, God creates the best contingent reality. On this account everything is for the best, but that everything is for the best is not the ultimate explanation, because it does not explain why God exists. Or one might think that reality is necessary and brute, and it brutely has to be like it is. And as a very suprising but non-explanatory matter of fact the way it is is in fact optimal.

I am emphasizing this, because I want to problematize (1). Grant (2). Why should we think that the fact that everything is for the best in fact explains everything?

Suppose that modal fatalism is true, and that it so happens that reality is exactly mid-way between the worst and the best possibility, and is in the only option mid-way between the worst and best. (I assume one can talk of options for reality even given modal fatalism. Otherwise, optimalism falls apart. The “options for reality” may be something like narrowly logically possible worlds.) Then:

3. Necessarily, reality is exactly middling.

Now suppose a “mediocritist” said: “And that reality is necessarily exactly middling explains why reality is what it is.” But why would we buy that? Or suppose that reality is necessarily the only one that is exactly 56.4% of the way up between the worst and the best (where worst would count as 0% of the way up and best as 100%)? Surely we wouldn’t conclude that its being exactly at 56.4% explains why it is the way it is. But if not, then why should its being at 50% explain it, as on mediocritism, or its being at 100% explain it, as on optimalism?

I think what the optimalist ought to say at this point is that analogously to non-Humean pushy laws of nature, there are non-Humean pushy laws of metaphysics. One of these laws is that everything is for the best. It is the pushiness of this metaphysical law that explains reality. But there is something rather odd about pushy laws prior to all beings—they seem really problematically ungrounded.

Open futurism does not save free will

In yesterday’s post, I showed that if an open-futurist is impressed by a certain plausible-sounding logical fatalism argument based on bivalence, and hence opts for truth gaps, then they should also be impressed by another logical fatalism argument based not on bivalence but on truth gaps.

However, there was a weakness to my logical fatalism argument. It was based on the principle:

1. If something true now is incompatible with it’s being true that p, then p is not within your power.

But perhaps our open futurist will deny (1) on the grounds that a present action can be within our power, even though it is presently true that we will do it. (I think this is a problematic concession for the open futurist to make, but let’s bracket that.) Such an open futurist will instead run arguments based on:

2. If q is a past-tensed truth, and q is incompatible with p, then p is not within your power.

Well, here is perhaps a truth value gap counterexample to (2).

• Alice freely ϕs at 5 pm.

• At 1 pm it is true that no indeterministic events will happen between 2 and 4 pm.

(To get the second part, we can suppose that the laws of nature are such that they only allow indeterministic events after 4:30 pm each day, or maybe God just promises not to allow any indeterministic events between 2 and 4 pm.)

So, consider the following complicated past-tensed statement, which is true at 3 pm:

• q: Two hours ago [i.e., at 1 pm], it was true that no indeterministic events would happen between an hour ago [2 pm] and an hour from now [4 pm], while half an hour ago [2:30 pm], it was neither true nor false that Alice freely ϕs at 5 pm.

Now, on the open futurist’s view, time-indexed propositions can only gain truth value as the result of indeterministic events. It logically follows from the ban on indeterministic events between 2 and 4 pm that any time-indexed proposition that was neither true nor false at 2:30, is also neither true nor false at 3 pm. Or to put it in a tensed way, q entails:

3. It is neither true nor false that Alice ϕs at 5 pm.

But (3) is logically incompatible with Alice ϕing at 5 pm, since, necessarily, if Alice ϕs at 5 pm, then it’s true that Alice ϕs at 5 pm. Since q entails (3), it follows that:

4. q is logically incompatible with Alice ϕing at 5 pm.

Hence it follows from (2) (since q is a past tensed truth) that at 3 pm it is true to say:

5. It is not within Alice’s power that Alice ϕs at 5 pm.

Now, I said that “perhaps” this was a counterexample to (2). Besides objecting to the Tarski T-schema, there is one powerful response an open futurist can make. They can just embrace (5) and say: it’s only at 5 pm, or shortly prior to it, that it comes to be within Alice’s power to ϕ.

But I think the open futurist’s intuitions behind (2) also support:

6. If q is a past-tensed truth and p is time-indexed, and q is incompatible with p, then p will never be within your power.

(The reason for the restriction to time-indexed p is to avoid this counterexample. Let q be the proposition that there was no wine in the world a minute ago. Let p be the proposition that you are drinking well-aged wine. Then p and q are incompatible. But if you make wine, and age it, then it can come to be the case that drinking well-aged wine is in your power.)

And now (4) and (6) imply:

7. It will never be within Alice’s power that Alice ϕs at 5 pm,

which is just false in our story, since she does ϕ at 5 pm! (Alternate phrasing: replace “within Alice’s power” with “up to Alice”.)

What about open futurists who instead of supposing a truth value gap think that statements about contingent future events are all false? Well, such open futurists will not accept q (at 3 pm). But they will accept:

• q′: Two hours ago [i.e., at 1 pm], it was true that no indeterministic events would happen between an hour ago [2 pm] and an hour from now [4 pm], while half an hour ago [2:30 pm], it was false that Alice freely ϕs at 5 pm.

Again, on their view, time-indexed propositions only change truth value when indeterministic events happen. Thus, q′ entails that presently (i.e., at 3 pm) it is still false that Alice freely ϕs at 5 pm. And the rest of my argument goes through.

So it pretty much seems like I’ve shown that the only person who can accept a principle like (6) is someone who doesn’t believe in the possibility of free will.

Maybe what this is really an argument for is that the open futurist needs to deny the T-schema, which I had used to argue that if something is incompatible with it’s being true that Alice will ϕ at 5 pm, then it’s incompatible with Alice ϕing at 5 pm. Some open futurists do do that (Keith DeRose, for instance; I wonder now: do they do it because of an argument like this one?)

I have to confess a nagging suspicion of an error somewhere. I already found one that I just corrected—I had to restrict (6) to time-indexed truths, which forced me to remove an argument that would work even without the T-schema.

Does denying bivalence get us out of the logical argument for fatalism?

Consider this seemingly standard argument for logical fatalism.

1. It is true that you will ϕ or it is true that you will not ϕ.

2. If something true now is incompatible with it’s being true that p, then p is not within your power.

3. If you are free with respect to ϕing, then it is within your power that you will ϕ and it is within your power that you not ϕ.

4. That you will ϕ and that you will not ϕ are incompatible.

5. So, if it is true that you will ϕ, then it is not within your power that you will not ϕ. (2, 4)

6. So, if it is true that you will ϕ, then you are not free with respect to ϕing. (3, 5)

7. Also, if it is true that you will not ϕ, then it is not within your power that you will ϕ. (2, 4)

8. So, if it is true that you will not ϕ, then you are not free with respect to ϕing. (3, 7)

9. So, you are not free with respect to ϕing. (1, 8)

Many open futurists want to refute arguments for logical fatalism by supposing that in cases of freedom, that you will ϕ is indeterminate (and hence neither true nor false), and that you will not ϕ is also indeterminate, which allows them to deny premise 1 of the above argument.

But now consider this argument.

10. It is now indeterminate that you will ϕ.

11. Necessarily, p if and only if it is true that p.

12. So, it is true that it is now indeterminate that you will ϕ. (10, 11)

13. That it is indeterminate that you will ϕ and that it is true you will ϕ are incompatible.

14. That it is indeterminate that you will ϕ and that you will ϕ are incompatible. (11, 13)

15. If something true now is incompatible with it’s being true that p, then p is not within your power.

16. If you are free with respect to ϕing, then it is within your power that you will ϕ.

17. So, that you will ϕ is not within your power. (10, 14, 15)

18. So, you are not free with respect to ϕing.

Premise 15 of this argument is the same as premise 2 of the first argument. Premise 16 is an even less controversial version of premise 3. So anybody who is impressed by the first argument will be impressed by premises 15 and 16. Premise 13 is obviously true, and is an immediate consequence of the fact that a proposition that is indeterminate is neither true nor false.

Premise 11 is the plausible Tarski T-schema (necessitated, because we can think of the T-schema as an axiom). It has been questioned, but it is still very plausible.

Finally, premise 10 is a commitment of our open futurist.

So, unless our open futurist denies the T-schema, the supposition of indeterminacy leads to fatalism just as determinacy did!

Suppose we deny the T-schema. Nonetheless, even without the T-schema to back them up, 12 and 14 are still plausible as they stand, and so we still have a pretty plausible argument for fatalism, at least one that should be plausible by the open futurist’s lights.

I am not an open futurist. I just get out of the arguments by denying 2 and 15. Easy.

An observation about the backwards-infinity branching view of possibility

In my dissertation, I defended a causal power account of modality on which something is possible just in case either it’s actual or something can bring about a causal chain leading to its being actual. I noted at the time that unless there is a necessary first cause, this leads to an odd infinite branching view on which any possible world matches our world exactly once you get far enough back, but nonetheless every individual event is contingent, because if you go back far enough, you get a causal power to generate something else in its place. Rejecting this branching view yields a cosmological argument for a necessary being. To my surprise when I went around giving talks on the account, I found that some atheists were willing to embrace the branching view. And since then Graham Oppy has defended it, and Schmid and Malpass have cleverly used it to attack certain cosmological arguments.

I want to note a curious, and somewhat unappealing, probabilistic feature of the backwards-infinite branching view. While it is essential to the view that it be through-and-through contingentist, assuming classical probabilities can be applied to the setup, then the further back you go on a view like that, the closer it gets to fatalism.

For let S_t be a proposition describing the total state of our world at time t. Let Q_t be the conjunction of S_u for all u ≤ t: this is the total present and past at t. Here is what I mean by saying that the further back you go, the closer you get to fatalism on the backwards-infinite branching view:

1. lim_{t→− ∞} P(Q_t) = 1.

I.e., the further back we go, the less randomness there is. In our time, there are many sources of randomness, and as a result the current state of the world is extremely unlikely—it is unlikely that I would be typing this in precisely this way at precisely this time, it is unlikely that the die throws in casinos right now come out as they do, and so on. But as we go back in time, the randomness fades away, and things are more and more likely.

This is not a completely absurd consequence (see Appendix). But it is also a surprising prediction about the past, one that we would not expect in a world with physics similar to ours.

Proof of (1): Let t_n be any decreasing sequence of times going to  − ∞. Let Q be the infinite disjunction Q_t1 ∨ Q_t2 ∨ .... The backwards-infinite branching view tells us that Q is a necessary truth (because any possible world has Q_t is true for t sufficiently low). Thus, P(Q) = 1. But now observe that Q_t1 implies Q_t2 implies Q_t3 and so on. It follows from countable additivity that lim_n→∞ P(Q_tn) = P(Q) = 1.

Appendix: Above, I said that the probabilistic thesis is not absurd. Here is a specific model. Imagine a particle that on day  − n for n > 0 has probability 2⁻ⁿ of moving one meter to the left and probability 2ⁿ of moving one meter to the left, and otherwise it remains still. Suppose all these steps are independent. Then with probability one, there is a time before which the particle did not move (by the Borel-Cantelli lemma). We can coherently suppose that necessarily the particle was at position 0 if you go far enough back, and then the system models backwards-infinite branching. However, note an unappealing aspect of this model: the movement probabilities are time-dependent. The model does not seem to fit our laws of nature which are time-translation symmetric (which is why we have energy conservation by Noether’s theorem).

The fixity of the past and laws

Suppose an ever-truthful dictator tells you that he is interested in the truth value of a proposition p solely about the laws of nature and how the world was like 1000 years ago. He tells you that in an hour he will infallibly find out whether p is true. If so, he will execute you. If not, he will let you go free.

Unless you have a time machine or a God who answers prayers before they are made is on your side, fatalism is surely the appropriate attitude. There is nothing you can do about whether you will be executed.

Next suppose that determinism is true. That shouldn't affect what was just said. Determinism does not create new supernatural powers to affect the past.

Now add that your identical twin is told by the dictator that he will be executed if and only if he scratches his head in an hour.

Finally suppose that your proposition p is the proposition that one thousand years ago the universe was such as to nomically determine that in an hour you will scratch your head, and suppose that the dictator's infallible method for finding out whether p is true is simply to see if you scratch your head. Then you are in the same boat as your twin! Each of you will be killed if and only if he scratches his head. Since fatalism is true for you, it's true for your twin. Thus he can't do anything about his execution, and in particular he has no freedom about scratching his head. And so compatibilism is false.

A curious fact about open future views

Here is a curious fact. Open futurists and fatalists both are committed to the claim that

1. It is not true that tomorrow I will freely choose what to eat for lunch.

But they agree for different reasons. Fatalists think this is so because they think no one will ever freely choose. Open futurists think this is so because whether I will freely choose what to eat for lunch depends on various future contingencies, such as whether I freely choose to stay up until 10 am tomorrow, and then sleep from 10 am to 4 pm tomorrow. It is only the closed futurist non-fatalist who gets to affirm that tomorrow I will freely choose what to eat for lunch.

In fact, just as fatalists are, open futurists may be committed to the claim that

2. It is not true that I will ever make any indeterministic free choices.

For surely whether I will ever make any indeterministic free choices depends on future contingencies, such as whether in the next moment God chooses to take me off to my eternal destiny and remove all indeterminism from my future (or, if one is an atheistic open futurist, whether quantum events rip me to shreds next moment).

Of course, the agreement between open futurists and fatalists only goes so far. Typical open futurists will say that in the past I made some free choices, while fatalists will deny that. Also, fatalists are going to replace the "not true" in (1) and (2) with "false", which some open futurists will resist. But there is still an irony that a view motivated by a desire to maintain one's freedom makes it impossible to say that one will make a free choice.

Logical fatalism, compatibilism and theism

In my previous post, I discussed logical fatalism and the options available. One of these options I labeled as "compatibilism" which I defined as the denial of the principle:
(1) If it is now necessary that I will do A, then I will not be freely doing A.
I was wrong to label the denial of this "compatibilism". It is possible to deny (1) and still hold that free will and determinism are incompatible, as long as one holds:
(1*) If a present state of affairs outside of me deterministically causes me to do A, then I will not be freely doing A.
Someone who denies (1) but accepts (1*) will still be an incompatibilist as long as we assume that in a deterministic system earlier states of affairs not only determine later ones but deterministically cause the later ones, so that if determinism holds, the state of the universe prior to my conception would deterministically cause all my actions, and hence vitiating my freedom. (C deterministically causes E provided C causes E and the occurrence of C cannot but cause E.)

Thus, there is a nice variant of the option I called "compatibilism" available: deny (1) but hold on to (1*). It is also worth noting that theists have independent reason to do this. It is necessarily true that God does not choose evils. We then need to deny (1) (or its variant for non-actions, but the same goes for it) in order to hold on to the idea that God is responsible for not choosing evils. And we can hold on to (1*), because nothing external to God causes his actions.

So while I find (*) implausible, denying (1) but holding on to (1*) may be the best solution since by holding on to (1*) one gets to maintain most of our incompatibilistic intuitions about free will.

Logical fatalism -- the options

This post is just an attempt by me to work something out for myself. Maybe it doesn't interest anybody else.

People who accept an Aristotelian open future because of concerns about logical fatalism do so on the strength of the intuition that if I freely do something, it was possible for me not to do it, and that:
(*) If it is now the case that I will do A, then it is now necessary that I will do it.

So, the question is: What are the options for getting out of the argument from logical fatalism. One option is just to deny (*). This, I think, is by far the best option. Call someone who accepts (*) an "Open Futurist". What logical options does an Open Futurist have?

Well, to see that, let's sketch a logical fatalism argument based on (*):

1. If it is now necessary that I will do A, then I will not be freely doing A. (Premise, justified via Principle of Alternate Possibilities)
2. If it is now necessary that I will not do A, then I will not be freely refraining from doing A. (Premise, same justification)
3. If it is now necessary that I will do A, then I will not be freely refraining from doing A. (Premise)
4. If it is now necessary that I will not do A, then I will not be freely doing A. (Premise)
5. If it is now necessary that I will do A, then I will not be freely doing A and I will not be freely refraining from doing A. (By (1) and (3) and the principle that if p→q and p→r, then p→q&r.)
6. If it is now necessary that I will not do A, then I will not be freely doing A and I will not be freely refraining from doing A. (By (2) and (4) and the principle that if p->q and p→r, then p→q&r.)
7. If I will do A, then I will not be freely doing A and I will not be freely refraining from doing A. (By (5) and (*).)
8. If I will not do A, then I will not be freely doing A and I will not be freely refraining from doing A. (By (6) and (*).)
9. Either it is the case that I will do A or it is not the case that I will do A. (By Law of Excluded Middle)
10. If it is not the case that I will do A, then I will not do A. (Premise)
11. Therefore, either it is the case that I will do A or it is the case that I will not do A. (By (9) and (10) and the principle that if p or q, and q→r, then p or r.)
12. Therefore, I will not be freely doing A and I will not be freely refraining from doing A. (By (7), (8) and (11), together with the principle that if p→r and q→r and (p or q), then r.)

So what are the at all plausible options if we accept (*) (which we shouldn't)?
(I) Compatibilism: Deny (1) (and (2)--they are surely in the same boat).
(II) Intuitionistic Logic: Deny the Law of Excluded Middle, thereby allowing the denial of (9).
(III) Not-will / will-not distinction: Deny (10), holding on to Law of Excluded Middle.
(IV) Deny the principle that if p→r and q→r and (p or q), then r.
(V) Deny one of the other rules of inference used.

I think (V) is not attractive--all the other rules of inference seem really hard to deny. Option (IV) is pretty radical. It means that we will no longer accept arguments like: "If Bob is telling the truth, George is guilty. If Fred is telling the truth, George is guilty. Either Bob or Fred is telling the truth. So, George is guilty." The principle denied in (IV) follows from the axioms of intuitionistic logic, and I think is also going to hold in supervaluationist settings.

If this is right, then an exhaustive list of our at all plausible options with regard to the logical argument for fatalism is:

1. Denial of free will
2. Denial of (*)
3. Compatibilism
4. Denial of excluded middle
5. Denial of the claim that not-will implies will-not

I rank the attractiveness of these as follows, in order of most to least attractive: 2, 3, 5, 4, 1. Why list 1 last? Because free will is central to the things that matter most in life. How to justify the rest of the ordering? Well, we should be least willing to give up general rules of all reasoning, like excluded middle. We should be more willing to give up rules about particular kinds of reasoning, such as the tensed logic rule that not-will implies will not. We should be more willing yet to give up intuitions about modal or concrete concepts, since there things get difficult by everybody's lights, and so 2 and 3 are even more attractive as options than 5, 4 and 1. Why take 2 as more attractive than 3? Well, that's a judgment call on my part--I find compatibilism deeply implausible, and I suspect that most people who find (*) plausible find the denial of compatibilism even more plausible.

Excluded Middle and an Open Future

Some people deny the Law of Excluded Middle (LEM--for all p, p or not-p) because they are convinced it leads to fatalism. But they really shouldn't deny LEM.

Suppose Helga is convinced that utilitarianism is true. You offer Helga a reductio argument against utilitarianism on the assumption that the hedonistic theory of happiness holds and another reductio argument against utilitarianism on the assumption that the hedonistic theory of happiness does not hold. Helga accepts both reductios and comes to deny hedonistic utilitarianism and non-hedonistic utilitarianism, but continues to accept utilitarianism. Pressed on how Helga's new position squares with logic, Helga asserts that based on her belief that utilitarianism holds, and her new beliefs that if hedonism holds, utilitarianism is not true, and if hedonism doesn't hold, utilitarianism is not true, she has concluded that LEM does not hold. There seems to be something irrational about this. Surely, she should either find fault with at least one of the reductios or abandon her belief in utilitarianism. It is hard to imagine premsies whose plausibility should trump LEM.

Arguments the depend on LEM are not, I think, uncommon in philosophy. If Molinism is true, evil and the existence of God are compatible (by Plantinga's free will defense). If Molinism is not true, evil and the existence of God are compatible (by Adams' free will defense). Hence, evil and the existence of God are compatible. It is pretty likely that Helga uses LEM-based arguments in other contexts, and it is pretty likely that the defender of the Open Future who denies LEM also uses LEM in other contexts.

Could they both say that LEM applies in some contexts (e.g., non-normative ones in Helga's case, or in ones that do not involve the future in the freedom case) but not others? Yes. But once we denied the plausible view that LEM follows from the meaning of the words "or" and "not", and denied the general intuition that between p and not-p tertium non datur, it seems that we have undercut the grounds we could have for thinking LEM holds even in those contexts in which it is supposed to hold in. Besides, the defender of the Open Future who denies LEM presumably does so on the basis of something like a temporalized modal logic according to which if p already holds, then not-p is no longer possible. But surely the principles of classical non-temporal non-modal logic are more plausible and more deeply embedded in our thinking than those of temporalized modal logic.

Anyway, it seems much better to hold on to LEM, and just deny the principle that if not(will(p)), then will(not-p), where "will(p)" means p will hold. The principle that if not(will(p)), then will(not-p) is a dubious one if we see "will" as a modal-type operator, maybe akin to "would" except for being a one-place operator, and that is precisely how we will see "will" if we have presentist or growing-block intuitions. Moreover, it is a principle that is less central to our thinking than LEM, particularly because it applies only to our thinking about the future, while LEM applies to all our thinking. It seems clear to me that this is what the person impressed by the argument for logical fatalism should say, boldly holding that there is a fact of the matter whether Jones will mow the lawn tomorrow: it is false that Jones will mow the lawn tomorrow, just as it is false that he will fail to mow the lawn tomorrow. And God's omniscience will be unrestricted: he knows that it is false that Jones will mow the lawn and that it is false that he will not mow the lawn.

Of course, it's best to hold on to both LEM and if not(will(p)), then will(not-p).