Literature and science

I think we learn at least as much about ourselves as persons from literature as from science. This is surprising if physicalism is true.

Against the incredulous stare objection to our coming into existence at conception

There are two main kinds of arguments against abortion: Those based on the idea that we begin existing at conception and those based on the idea that personhood begins at conception.

One of the main objections to thinking that our existence begins at conception is the incredulous stare: How can that single cell be me?!

Here my recent geometrical observations about how I will be very small in almost every reference frames become relevant. Exactly the same argument establishes that in almost every reference frame, I start out really small. In almost every reference frame, I start out less than a nanometer in size (any non-zero size can be substituted here), and hence much smaller than a single cell.

Thus, it seems we are simply stuck with a counterintuitive result about what we are like at our beginning. Even if we don’t begin at conception, in almost all reference frames we begin as something much smaller than a single cell.

Can the geometrical observations show that personhood begins really small, too, and thereby undercut the incredulous stare at the idea that a single cell is a person?

Now, if we are essentially persons, given that by the previous argument we begin smaller than a cell, then indeed something smaller than a cell is a person.

So the remaining case to consider is views on which we are only accidentally persons, and we pre-exist our personhood. A typical view in this family will say that we are animals that come into existence at conception or implantation, and that about 1.5-2 years after our beginning, we come to have the property of personhood.

In the previous argument, I looked at the set K of all the spacetime locations of my body, and it followed that for almost every reference frame F, there was a time t in F and near my beginning such that the t-slice of me was really tiny. The obvious analog is to look at the set K^* of all spacetime locations of my personal body—i.e., of my body at times at which I am a person—and repeat the argument. The problem with this move is that whether a spacetime location is within my body is intuitively independent of reference frame, but whether a spacetime location is within my personal body could more plausibly depend on the reference frame, if my 4D personal body is not all of my 4D body.

So at this point, I don’t have a version of my smallness argument against the view that to be a person I have to be big, when that view is coupled with the idea that I can exist without being a person.

God's hiddenness

If God is closer to me than I am to myself, how can he be hidden from me?

But don't I learn from Hume that my self is also hidden from me?

A variant on an argument of Unger

1. In some ordinary reference frames, there are times at which I am less than a nanometer in size. 
2. If I am fully material, I cannot ever be less than a nanometer in size in an ordinary reference frame.
3. So, I am not fully material.

The same argument applies to dogs, fish and trees, and not just people. And I embrace that conclusion, since I think they all have form, and form is not material. But it is less of a bullet to bite to deny the existence of dogs, fish and trees than to deny one's own existence.

I will be very small

I have a counterintuitive view that our bodies can be extremely defective, to the point that we can exist with a body that’s just a couple of atoms. But counterintuitive as this view is, I have an argument for it.

Start with this little geometric result about Minkowski spacetime. Think of a reference frame F as a maximal set of spacelike hyperplanes called F-times. If T is an F-time, and K is a region of spacetime, then the T-slice of K is the intersection of K and T.

Proposition. Let K be a bounded non-empty region of spacetime. The following is true for almost every reference frame F. For every ϵ > 0, there are F-times T₁ and T₂ less than ϵ apart, with the properties that (a) all of K is temporally before T₂ (according to F), (b) the T₁-slice of K is non-empty, and for any F-time T between T₁ and T₂ inclusive, and any two points w and z in the T-slice of K, the F-distance between w and z is less than ϵ.

(This follows from the result here. We can identify a reference frame with wthe future-facing unit normal vector of its times, and then “almost every” is understood with respect to the Lebesgue measure on the unit sphere.)

For simplicity, and as the approximation is surely appropriate, assume that special relativity is right. Let K be the four-dimensional region occupied by my body during my life. Assume K is bounded, which sure seems intuitively plausible (there are some quantum issues here which I will ignore for now). Then it follows from the Proposition that, according to almost every reference frame, there is a time T₂ within a nanosecond of my death such that the T₂-slice of my body (or the region K occupied by it) is less than a nanoneter in size.

So not only can I be really small, but I will be really small, according to most reference frames.

Autonomy and God

We have much in the way of autonomy rights against other people. Do we have autonomy rights against ourselves? I think so. There are ways of constraining our future selves that are contrary to our dignity.

Here is a thesis I find plausible:

1. We have no autonomy rights against God.

Of course, and importantly, God has reasons for action based on the value of our autonomy. But I think it’s still true that these reasons are not going to be conclusive in the way that they would be if we had autonomy rights. (They might be conclusive in some other way, say if God promised us autonomy in some area. I take it that a right to have a promise fulfilled is not an autonomy right, perhaps pace Kant.)

Claim (1) seems to be a thesis about God’s authority. It paints a picture of God as an authoritarian being with infinite normative power, and the picture is not so attractive to modern sensibilities.

But I think there is a different way of thinking and feeling about (1). We can, instead, think of (1) as consequence of the ways that

2. God is infinitely close to me—closer than I am to myself.

There are many ways in which I am “not that close to myself”. I am ignorant of much that goes on in me, even in my mind. I don’t love myself as much as I should. My future is murky and my past is fading. And, above all, I don’t have being in myself, but being by participation in another, God. God is closer to me than I am to myself. And a consequence of this closeness is that I have even less in the way of autonomy rights against God than I do against myself.

Related to (1) is an interesting hypothesis. Everyone agrees:

3. God has infinite power.

It intuitively sounds plausible that:

4. God has infinite normative power.

I am not sure what exactly (4) means, or how it is true. But doesn’t it sound right?

A tweak to Bohmianism

I think there is a sense in which it is correct to say that:

1. Bohmian quantum mechanics is only known to work empirically if we suppose that the initial configuration of the particles is fine-tuned.

Yet there are famous results that show that:

2. For typical initial configurations, Bohmian quantum mechanics yields standard quantum Born rule predictions, which we know to work empirically.

It seems that (1) and (2) contradict each other. But that is not so. For the typicality in (2) is measured using a typicality measure P^ψ defined in terms of the initial wavefunction ψ of the universe (specifically, I believe, P^ψ(A) = ∫_A|ψ(q)|²dq for an event A). And a configuration typical relative to P^ψ₁ need not be typical relative to P^ψ₂. In fact, if ψ₁ and ψ₂ are significantly different, then a P^ψ₁-typical configuration will be P^ψ₂-atypical.

The fine-tuning I am thinking of in (1) is thus that the initial configuration of particles needs to be fitted to the initial wavefunction ψ: a configuration typical for one wavefunction is not typical for another.

I think there is an interesting solution to the Bohmian fine-tuning which I haven’t heard discussed, either because it’s crazy or because maybe nobody else worries about this fine-tuning or maybe just because I don’t talk to philosophers of quantum mechanics enough. Suppose that the wavefunction of the universe (or, more precisely, the aspect of physical reality that is representated by the mathematics of the wavefunction) has a special causal power in the first moment of its existence, and only then: an indeterministic power to produce a particle configuration, with the power’s stochastic propensities being modeled by P^ψ.

This adds a little bit of metaphysical complexity to the Bohmian story, but I think significantly increases the explanatory power in two ways: first, by giving us a proper stochastic ground for the statistic probabilities and, second, by unifying the cause of the initial particle configuration and the cause of the dynamics (admittedly at the expense of a complexity in that in that cause there is a causal power that goes away or becomes irrelevant).

(Maybe this is not necessary. Maybe there are, or can be, some typicality results that don’t require fine-tuning to the initial wavefunction. Or maybe I just misunderstand the framework of the typicality results. I don’t know much about Bohmianism.)

A curious but common art form

A curious art form that blends nature with artifice is endemic in our culture, and likely a cultural universal. Many people modify their bodies (e.g., muscle building, hair-styling, etc.) and then combine them in harmonious ways with other physical objects attached to the body, such as paint, clothing, jewelry, etc., deliberately to create a work of art that is a hybrid of a living thing and typically (but not always) non-living accessories.

A large proportion of our population engages in this art form on a daily basis, but I don’t know a good name for the works of this art in the languages I know. We have two English words that come close, “fashion” and “cosmetics”, but both are specific to aspects of the art rather than the work as a whole. We might try to explain this odd lack by saying that there is a sense in which the work is the person (for, after all, normally when we imagine a person, we imagine them accoutred). We might call the art form "anthropocosmetique", using the archaic spelling to hearken back etymologically to earlier English uses (evoking shades of Bulwer's use of "cosmetique" and his specific contexts) that may be closer to the Greek roots, but also emphasizing the human component in the work.

An interesting feature of the works of anthropocosmetique art is their diachronic character. They are often created for a specific occasion—a day, a party, a liturgical celebration—and disassembled into their constituents afterwards, typically without any feeling that one has destroyed something of great value in disassembly.

At the same time, some people engage in a larger art form, one spread over multiple occasions, consisting of sequences of the anthropocosmetique art, with similarities and differences from occasion to occasion in the particular works of each occasion being aesthetically relevant perhaps in something like the way that themes and variations are the warp and weft (not respectively) of music.

Sometimes there is a melding between the anthropocosmetique and other art forms, especially performance arts like dance.

And another curious fact is that many of the most famous works of fine art are actually meta-art: they are themselves portrayals of the works of the anthropocosmetique art.

Aquinas on per se and accidentally ordered causal series

Famously, Aquinas thinks that an accidentally ordered infinite causes is possible, but a per se ordered one is not. The difference is that in a per se ordered series ..., A₋₂, A₋₁, A₀, item A_n − 1 (for n <  − 1) is not only the cause of A_n, but is the cause of A_n’s causing of A_n + 1. But in an accidentally ordered series, A_n − 1 is not the cause of A_n’s causing of A_n + 1. Aquinas illustrates the distinction with a sequence of an infinite sequence of fathers and sons, since a grandfather is not the cause of the father’s conceiving of a son.

Now suppose we replace the people in Aquinas’s example with self-reproducing robots (von Neumann machines), each programmed by its predecessor to reproduce. Then we have a per se ordered series.

The following seems to me to be very plausible:

1. If a backwards infinite reproductive series of humans is possible, a backwards infinite reproductive series of robots is also possible.

Yet this seems to be something that Aquinas is committed to by his example of the accidentally ordered series.

Suppose one bites the bullet and denies (1). What is the relevant difference between the humans and the robots? It is presumably the determinism in the robots. Very well, then let’s suppose that each of the robots has a little hidden switch whose position is permanently set at the time of manufacturing. When the switch is in the D position, the robot is determined to reproduce at specific points in its life; when it is in the N position, at those points in its life, the robot performs an internal indeterministic quantum coin flip, reproducing on heads but not on tails.

It seems absurd to suppose that one could have a backwards infinite reproductive series of robots with the switches in the N position, but not in the D position. Yet that implausible conclusion seems to be what Aquinas’s position commits him to.

Here a suggestion for what Aquinas could do.

Aquinas thinks there is a very good metaphysical argument for rejecting backwards infinite per se ordered series. Suppose that argument is sound. Then Aquinas could say that this argument does not apply to the accidentally ordered case. But nonetheless there is a good argument based on a rearrangement principle or a principle of modal uniformity that:

2. If a backwards infinite series of robots with the switch in the N position is possible, so is a backwards infinite series of robots with the switch in the D position.

3. If a backwards infinite series of humans is possible, a backwards infinite series of robots with the switch in the N position is possible.

Given the impossibiliy of the series with the switch in the D position, it follows that the the backwards infinite sequence of humans is impossible. Aquinas can then simply say that he was wrong about his example (something that he is willing to concede anyway, due to an argument from al Ghazali specifically against an backwards infinite sequence of humans). But nothing in Aquinas’s theory commits him to the claim that every describable accidentally ordered backwards infinite sequence is possible. (An accidentally ordered backwards infinite sequence of square circles is not possible.)

At this point, Aquinas can do one of three things. First, he can say that while the backwards infinite sequence of humans or N-robots is impossible, we should remain agnostic whethere there are some backwards infinite accidentally ordered sequences are possible.

Second, he can give a plausibilistic argument that if the backwards infinite sequence of N-robots is impossible, probably all accidentally ordered backwards infinite sequences are impossible as well. (One might think this would require Aquinas to reject the possibility of an infinite past. This is not clear. He might still hold that an infinite past is possible as long as it doesn’t generate a backwards infinite causal sequence—imagine that every day in the past God creates a rock so far apart from all the other rocks that the rocks never interact).

Third, Aquinas could try to construct a new example of a backwards infinite accidentally ordered series that is possible. My intuition is that the best bet for trying to do this would be to construct a backwards infinite sequence where each item gets only a very slight causal contribution from its predecessor, and most of the explanation of the item’s existence involves God or some other single timeless being.

I myself like the second option.

It's official! Fastest mile on a climbing wall (male) record

 Guinness has just approved my record from July for fastest mile on an indoor climbing wall (male), officially at 1:42:57.95. For technical details and links to video, see my writeup from July.

Thinking about this made me realize just how much this was a team effort. I am grateful to everyone who made this possible, especially:

• My family for encouragement and patience with me over the summer as I trained for this.
• Benjamin Sadler doing the official measurements of the route, correcting for the angle of inclination.
• Mitchell Minyard and Libby Regnerus for being witnesses for the route measurement.
• Madelyn Hayden, Dominic Pruss and Gabriella Williams for being in charge of my safety during the attempt and/or outside-of-regular-Rock-hours training sessions.
• Rock staff for watching out for my safety during regular hours, for extending the route so that 112 climbs would be enough for a mile, and constant encouragement.
• Rich Eva and Libby Regnerus for spending 1¾ hours of their Saturday holding stopwatches to provide an official time.
• Mitchell Minyard and Gabriella Williams for witnessing the attempt and working hard to log the start and end times of each of 112 climbs. 
• Gym management staff Rachel Burduroglu, Zac Huston and Cody Schrank for much encouragement, practical help, patience with many requests, and especially allowing me to use the facility outside of hours.
• The audience (notably including President Linda Livingstone and First Gentleman Brad Livingstone) for their great encouragement.
• All the members of the Baylor rock climbing community for being such a welcoming community over the past eight years, and having taught me pretty much all I know about climbing.
• Baylor Moody Media Lab for lending me equipment for recording the attempt.
• And Guinness World Records for patiently answering all my nitpicking questions and taking the time to review a massive amount of evidence in a fair and trustworthy way.

Exhibiting character flaws

Take a science fiction movie scenario. Carl is trapped near a device set to explode, and cannot be freed until too late. However, it is possible to go and defuse the device. Unfortunately, getting to the bomb requires going through a tunnel where one will get a dose of radiation that will result in severe injury within a day.

Alice and Bob are bystanders with no special obligations to the trapped people. They also know what effects the radiation would have on them. If Alice went, she would permanently lose her eyesight. If Bob went, he would lose his eyesight and his mobility. In both cases, their life would be worth living, and both agree that the injuries would be better than dying. I assume (if not, ratchet up their prospective injuries) that it would be be praiseworthy but not obligatory for either Alice or Bob to go rescue Carl.

Alice then puts enormous effort into trying to persuade Bob to go and defuse the device, vividly describing to them the terror that Carl is feeling, the joy on the faces of Carl’s children if he are rescued, and gives an excellent account of how the exercise of heroic virtue is the most important thing in life, far more valuable than sight and mobility. All of this falls a little bit flat given that Alice has no inclination to go herself, which would be even better objectively speaking. When asked by Bob the natural question of why she doesn’t do it herself, she just says: “I am not obligated to, and while I could, I choose not to sacrifice my life for this guy I don’t know. But it would be really good if you did.”

What Alice is doing seems to be the second best of three options. The best thing would be to go defuse the device herself. The least good would be to do nothing. Persuading Bob to go is second best, since if Bob goes, instead of a person dying, a person loses sight and mobility.

Yet I feel that even though Alice isn’t doing anything wrong, her actions are a manifestation of a particularly bad character. While there is nothing immoral about trying to persuade someone else to make a greater sacrifice than one you are willing to make, there is some kind of a serious character flaw here, and that flaw is being exhibited in the action, even though the action is a good one.

Cases like this make me suspicious of virtue ethics. Manifesting character flaws is different from acting wrongly.

Types of reasons

There are two ways of drawing a distinction between moral and epistemic reasons:

1. What kind of value grounds the reasons (epistemic or moral).

2. What kind of thing are the reasons reasons for (e.g., beliefs vs. actions).

If we take option (1), then there will be epistemic reasons not merely for beliefs, but for actions. Thus, the scientist will have epistemic reasons for doing a particularly informative experiment and the teacher may have epistemic reasons for engaging the students in a certain didactically beneficial group activity—i.e., in both cases, epistemic goods (to self and/or others) justify the action.

I like option (2). Moral reasons are reasons for action, while epistemic reasons are reasons for having a belief or credence or the like.

Here are some reasons for not drawing a distinction between reasons for action in terms of the kind of value as in (1).

First, we would morally admire someone who sacrificed a well-paying and easy career option to become a science teacher at an inner city school in order to pass the gift of knowledge to students. In other words, our admiration for someone who at significant personal cost promotes an epistemic value (by otherwise morally upstanding means) is moral.

Second, if we distinguish moral and epistemic reasons for action, consider conflicts. We would have to say that a scientist may have moral reasons to come home on time to feed her hungry children, and epistemic reasons to complete an experiment that cannot be done at another time. But now whether it is right to come home on time or to complete the experiment depends on the details. If the information gained from the experiment is unimportant while the experiment will take hours, and the kids are very hungry, coming home on time is right. But if the children are only very slightly hungry, and the experiment would only protract this hunger by a few minutes, while being extremely illuminating, staying a few minutes may well be the right thing to do.

Right in what way? Well, I think once again the kind of praise that we would levy on the scientist who balances their epistemic goals and their children’s needs well is moral praise. But then the moral praise does not always align with what I have been assuming are moral reasons for action. For we would not morally praise the scientist who neglects a short but extremely illuminating observation in order to make their children dinner a few minutes earlier. Such a scientist would have an insufficient love of epistemic goods. The scientist who hits the right balance is morally praiseworthy. Yet it is very odd to think that one is morally praiseworthy for subordinating moral reasons to non-moral ones!

If you’re not yet convinced by this case, consider one where the moral and non-moral goods are to the same person. A parent is explaining some very interesting matter of science to a child. The child would rather eat a few minutes earlier. If there really is a moral/epistemic reason distinction in actions, then the parent’s reasons for explaining are epistemic and the reasons for feeding are moral. But it could be morally praiseworthy to finish out the explanation.

Third, there are multiple kinds of non-epistemic good: health, virtue, appreciation, friendship, etc. The heterogeneity between them does not appear to be significantly less than that between all of them taken together and the epistemic goods. It seems that that if we are cutting nature at the joints, there is no reason to posit a particularly significant cut between the epistemic and non-epistemic goods. Instead, we should simply suppose that there is a variety of types of good, such as maybe health, virtue, beauty, friendship and understanding (and almost certainly others). All of these are alike in being goods, and different from each other as to the fundamental kind of good. To give the honorific “moral” to all of the ones on this list other than understanding seems quite arbitrary.

On the other hand, the distinction as to the type of thing that the reasons are reasons for does seem quite significant. Reasons for action and reasons for belief are quite different things because we respond, or fail to respond, to them quite differently: by willing and by believing, respectively.

It is interesting to ask this question. If the will has moral reasons, and the intellect has epistemic reasons, are there other faculties that have other reasons? Maybe. We can think of a reason R for ϕing in a faculty F as something that has a dual role:

1. it tends to causally contributes to ϕing within F

2. its presence (and causal contribution?) partially grounds ϕing counting as an instance of proper activity of F.

(Thus, reasons are causes-cum-justifiers.)

Are there things like that for other faculties F than will and intellect? Yes! The presence of a certain bacterium or virus may be a reason for the immune system to react in certain way. Humans thus have moral, epistemic and immune reasons, distinguished respectively by being reasons for the will, the intellect and the immune system. And there are doubtless many more (e.g., I expect there are reasons for all our sensory systems’ identifications of stimuli).

Some of these reasons are tied to specific types of goods. Thus, epistemic reasons are tied to epistemic goods, and immune reasons are tied to health goods. But moral reasons are different, in that action has a universality about it where any type of good—including epistemic and health ones—can ground a moral reason. And both epistemic and moral reasons tend to be different from immune reasons in that in the normal course of immune functioning we do not process them intellectually, while both epistemic and moral reasons are intellectually processed in normal use.

A slight tweak to the at-at theory of change

The at-at theory of change says:

1. Change is things being one way at one time and another way at another time.

McTaggart complained that this was like saying a poker changes because it’s hot at one and end cold at the other. It seems that (1) just fails to capture the “dynamism” in change.

A slight modification to (1) takes care of these, and some other, problems.

2. Change is things being one way at one time and another way at a later time.

You might think there is no real difference, because if there are two times, one must be later than the other. First, that’s not obvious, actually. In a Minkowski space-time, a time from one reference frame will be neither earlier nor later than a time from another reference frame.

But in any case, even if it were true that one time must be later than another, putting it in the definition makes a difference. First, McTaggart’s poker: one end isn’t earlier than the other! Second, dynamism: you can put all the dynamism you like in the “later”. You can say that t₂ is later than t₁ just in case at t₁, t₂ is future, is impending, is approaching, is a time of the actualization of a potential found at t₁, etc. The dynamism all goes into the “later”.

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.