A problem for easy ontology arguments

Consider this "easy ontology" argument:

1. There are no unicorns.
2. So, there are zero unicorns.
3. So, there is a zero.

This seems fine. Now consider the parallel:

4. Every leprechaun is a fairy.
5. So, the set of leprechauns is a subset of the set of fairies.
6. So, there is a set of leprechauns.
7. If there is a set of leprechauns, it's empty. (There aren't any leprechauns!)
5. So, there is an empty set.

That seems fine as well. So far so good. But now:

6. Every non-self-membered set (set a that isn't one of its own members) is a set.
7. So, the set of non-self-membered sets is a subset of the set of all sets.
8. So, there is a set of non-self-membered sets (the Russell set).

But of course (8) yields a contradiction (just ask if the Russell set is a member of itself).

What to do? One move is to make the easy ontology arguments defeasible. This isn't in the spirit of the game. The other is to add to the premises of the easy ontology argument a coherence premise: that there is a coherent theory of zero, of the empty set and of the Russell and universal sets. The coherence premise will be false in the Russell case but will be true in the other cases. But the point is one that should make us take easy ontology less easily. (I wouldn't be surprised if this was in the easy ontology literature, with which I have little familiarity.)

Space, time, spacetime and difficulty of causally affecting

I have previously speculated that the concept of spatial distance might be closely to connected to the difficulty of causally affecting. Roughly speaking, the further apart two things are, the harder it is for one to affect the other. This morning I was thinking about what happens if you bring time into this. Consider events a and b in spacetime, with a earlier than b. Then, keeping spatial distance constant, the greater the temporal distance, intuitively the easier it is for a to affect b. The greater the temporal distance, the greater the number of slow-moving influences from x to y that are available.

So we can think of the difficulty of causally affecting (DCA) as increasing with spatial distance and decreasing with temporal distance. And it turns out that this is pretty much what the Minkowskian relativistic metric describes: ds²=dx²+dy²+dz²−dt² (in c=1 units).

So if we think of distance as closely connected to dca, then it is very natural to think of distance as not just a spatial but a spatiotemporal phenomenon. And without any deep considerations of physics, just using everyday observations about dca, a relativistic metric looks roughly right.

We might now have a rough functional characterization of distance: distance is the sufficiently natural relational quantity which roughly corresponds to dca. In our world it seems there is such a very natural quantity: geodesic distance in a four-dimensional spacetime. In other worlds there may not be such a quantity. Those worlds which have a distance have space or spacetime or time—which it is will depend on the mathematical structure of distance in those worlds and/or on the structure of dca.

This is, of course, vague (I said: "sufficiently natural ... which roughly corresponds"). And so it should be. Compare: Mammals have hair. That's clear. But we should not expect there to be a precise characterization of what kinds of flexible filaments in other species—especially species completely different from ours (think of aliens!)—count as hair. We can give a rough functional characterization of which biological characteristic is hair, but it's going to be very rough, and it may be vague whether some species swimming seas of liquid ammonia is hairy, and that's how it should be. Likewise, if I am right, whether there is time in a world may be quite vague and not a substantive question in Sider's sense.

Ex nihilo nihil

Nothing comes from nothing. Take that as a given. But a mountain's coming from molehill[note 1], while not literally a case of something from nothing, would be just as bad. There is a Polish proverb that even Solomon cannot pour a drink from an empty container. But, likewise, even Solomon cannot pour wine from a container of water (at least without help from something greater than Solomon). The more doesn't come from the less.

What doesn't have something cannot give it.

Now, obviously, this principle needs to be limited. You can get a headache from playing a videogame for too long, but the videogame doesn't have a headache. The principle applies to positive being, to perfections.

So our causes must have all the perfections we have. It is plain, then, that the cause of humanity must have all the perfections of thought and will that humanity has. The First Cause cannot simply be a bunch of energy or matter. This is obviously important for the second part of the Cosmological Argument, the move from a First Cause to God. And of course, this is a very familiar line of thought. It's very forcefully there in Samuel Clarke, and it was already there in the medievals (whom Clarke amusingly criticizes while recapitulating their arguments).

But I don't want to dwell on the consequences of the principle that nothing can give what it doesn't have. Rather, I want to say something about the line of thought, if one may call it that, that leads me to it this morning. There is nothing really new here. The line of thought is one I had been thinking about for years, partly under the influence of Richard Sisca. But suddenly this morning it becomes very plausible. One is told that on big things people aren't convinced by argument, but rather have something like a conversion. But one can also have something like a conversion with regard to an argument. Suddenly it becomes clear that the line of thought is just right, and that the objections to it are mere technicalities. Sometimes one even has the experience of thinking that one knew this all along—or at least that one should have. This is a very interesting experience.

Another EEG

Josh Rasmussen encouraged me to run the toy EEG while I was writing book chapter, presumably as a way to get me to make more progress on our joint book arguing for a necessary being.  So, here it is.

Looks to me slightly intermediate between the graphs for blogging and for feeding in the earlier EEGs.

The topic of the chapter is the same as that of the post I was doing in the earlier EEG.

In case anybody is curious, here's how raw data (not from the above, just from some software testing I was doing) looks like.

Amusingly, one can also touch the electrode to one's chest, put one's fingers in the ear clips, and get an ECG.  I think I got my $21 worth of fun. :-)

EEG of me blogging vs. feeding/cleaning

I recently acquired a MindFlex EEG-based toy (on ebay, for a total of $21 with shipping), which is based on a NeuroSky ThinkGear ASIC chip.  As a toy, it's not that great, but if you solder wires to the transmit and ground pins, and hook it up to a TTL-level serial port, you can read the data off it.  By default the data comes processed into a bunch of frequency domains (presumably by running an FFT on the raw potentials), though if you attach your serial port to the receive pin (I ended up shorting that pin to another and had to cut through the blog carefully afterwards; I'm not good at soldering), you can switch to raw data mode, though my bridge hardware isn't fast enough for that.  As a safety measure, it's a good idea to either have the computer be a laptop not plugged into mains or else to bridge from the ASIC to the laptop wirelessly.

I hooked up the mindflex to the BrainLink all-purpose-BlueTooth-interconnect device (coupon code SS72142 gives a 30% discount on everything at SurplusShed this week).  I had some initial technical difficulties.  For some reason, the BrainLink keeps on resetting when it gets a lot of incoming serial data, and so I had to write some custom communication code for it that un-reset when receiving data, instead of just using the standard BrainLink java library.  And I wrote some quick visualization code in java (it's a mess, as I've never written desktop java GUI code before).  If you want to play with the messy code, it's here (it's called brainflex).  (You probably don't have a BrainLink, but any serial-to-BlueTooth adapter should work, as long as you create a new implementation of DataLink, which should be quite easy.)

Anyway, while doing the preceding post, I had the BrainLink on, and recorded the processed EEG.  (The Attention and Meditation data is computed by the chip from the Fourier transform data.)  Here it is:

As control data, I then switched to feeding the toddler and cleaning her and after her:

There is discussion online on whether the BrainFlex toy actually works, or if it's just an illusion-of-control thing, though the NeuroSky folk have research data on their chip that suggests it does do something.

Note that all the regular frequency domains (not the Attention and Meditation, though) are normalized to sum to a constant total.

Beta and alpha seem much more active when blogging than when feeding/cleaning.  On the other hand, the chip's computed Attention value seems rather higher for the feeding/cleaning, which fits with how I felt: the blogging seemed fairly automatic, while the feeding/cleaning involved more conscious attention.

A confound for the experiment is that as I was blogging, I was on the computer, so there would have been electromagnetic interference from that.  I did make sure that the computer was not plugged into the mains, which may have reduced interference.  And another confound was that I knew I was recording myself.  This isn't real science!

From necessary abstracta to a necessary concrete being

Start with the Aristotelian thought that abstract entities are grounded in concrete ones. Add this principle:

1. If x is grounded only in the ys, then it is impossible for x exist without at least some of the ys existing.

Consider now a necessarily existing abstract entity, x, that is grounded only in concrete entities. (Some abstract entities may be grounded in other abstract entities, but we want to avoid circularity or regress.) Thus:

2. x is a necessarily existing abstract entity.

Add this premise:

3. There is a possible world in which none of the actual world's contingent concrete entities exist.

This isn't the more controversial assumption that there could be a world with no contingent concrete entities. Rather, it is the less controversial assumption that these particular concrete entities that we have in our world could all fail to exist, perhaps replaced by other contingent concrete entities.

If the concrete entities that ground x are all contingent, then we have a violation of the conjunction of (1)-(3), since then all the actual grounders of x could fail to exist and yet x is necessary. So:

4. There is at least one necessary contingent entity among the entities grounding x.

Presentism and referring to past individuals

It seems to me that the presentist can only de re refer to past (or future—but that's less of a problem) individuals if there are haecceities or the identity of indiscernibles is true.

Meaning

1. Every meaning derives from components to which intelligent beings have assigned a meaning.
2. Some things that have a meaning that does not derive from components to which earthly beings have assigned a meaning.
3. Therefore, there is a non-earthly intelligent being.

I suggest two examples for premise (2).

Life: Life has a meaning. But a meaning of life that derives from our assignments is not a meaning that matters to us. What we have assigned meaning to, we could reassign meaning to. If the meaning of life were merely a matter of human assignment, then humanity's search for meaning would be a mere matter of curiosity, of figuring out how our ancestors have assigned meaning and how those meanings combine. It would be either like searching for the meaning of an ancient inscription (a case where we don't know the meanings of the components) or like parsing a complex sentence in first order logic (a case where we know the meanings of the components but don't know how they go together). There would be no deep existential relevance in such a meaning, since we could just as well assign a meaning ourselves. It would be just a meaning assigned by peers.

This example shows that the meaning of life needs not just to be a meaning assigned by a non-earthly intelligent being, but by a being whose meaning-assignments have deep existential relevance to us. A being with a deep kind of authority. So not just some space alien that seeded life on earth, say.

The sublime: Any case of the sublime—say, the Orion Nebula or Beethoven's 9th—has a meaning that escapes us, all of us. Cases of the sublime can be natural or human-made, but in both cases they have a meaning beyond us. And that meaning-beyond-us isn't just a matter of being better at figuring out how components combine, in the way that the meaning of a sentence of First Order Logic is. In a piece of the sublime we don't know very well, but can only vaguely sense, what the meaningful components are, and we are not responsible for the mysterious meaningfulness of these components. Even in the human-made cases, the creator is a servant to that mysterious meaning of the components.

Moreover, the meaning of the sublime piece is one that we resonate with, one we have a kind of grasp of—or maybe that has a grasp on us—that ever eludes us. We have a resonance to the meaning of the sublime. So whatever story we give about that meaning, we also need to give a story about how it's a meaning we resonate to. There could be aliens that have assigned deep mythological interpretations to various components of the Orion Nebula. But that isn't the meaning we resonate to. So, once again, the argument not only yields a non-earthly intelligence, but one who can make us resonate to his designs.

What is a material object?

I've found the notion of a material object very puzzling. Here is something that would render it less puzzling to me:

• x is a material object if and only if x has limited location.

There would then be three ways for an object y to be immaterial:

1. There are locations and y has no location.
2. There are no locations.
3. There are locations and y is unlimited in location.

It would now be plausible that a perfect being would be necessarily immaterial. A perfect being doesn't need anything other than itself, so it could exist in worlds where there are no locations, in which worlds it would have type 2 immateriality. And in worlds where there are locations, a perfect being would be unlimited in location, and would have type 3 immateriality. Thus, in all worlds, a perfect being would have immateriality. But in no world would a perfect being have type 1 immateriality.

One might worry that there could be an animal that is as big as space itself, and then it would count as an immaterial object. But even though the animal would be everywhere, it wouldn't be everywhere in every part and respect. Its digestive system would be here but not there, and so on.

Alternately, one might stick to our definition of materiality as limited location, but modalize. Maybe "limited location" is a modal concept, so that a being that could be limited in location is thereby limited in location.

More on the Adams Thesis

The Adams Thesis for a conditional → says that P(A→B)=P(B|A). There are lots of theorems, most notably due to Lewis, that say that this can't be right, but they all make additional assumptions. On the other hand, van Fraassen has a paper arguing that any countable probability space can be embedded in a probability space that has a conditional → which satisfies the Adams Thesis and a whole bunch of axioms of conditional logic. The proof in the paper appears incomplete to me (it is not shown that all necessary conditions for the choice of [A,B] are met). Anyway, over the last couple of days I've been working on this, and I think I have a proof (written, but needing proofreading) of a generalization of van Fraassen's thesis that drops the countability assumptions (but uses the Axiom of Choice).

The conditional logic one can have along with the Adams Thesis is surprisingly strong. In my construction, for each A, the function C_A(B)=(A→B) is a boolean algebra homomorphism. Thus, we have Weakening, Conjunction of Consequents, Would=Might, and the Conditional Law of Excluded Middle. The main plausible axioms that we don't get are Weak Transitivity and Disjunction of Antecedents (can't get in the former case; don't know about the latter).

The proof isn't that hard once one sees just how to do it, but it ends up using the Maharam Classification Theorem, the von Neumann-Maharam Lifting Theorem and oodles of Choice, so it's not elementary.

Trust and the prisoner's dilemma

This is pretty obvious, but I never quite thought of it in those terms: The prisoners' dilemma shows the need for the virtue of trust (or faith, in a non-theological sense). In the absence of contrary evidence, we should assume others to act well, to cooperate.

This assumption perhaps cannot be justified epistemically non-circularly, at least not without adverting to theism, since too much of our knowledge rests on the testimony of others, and hence is justified by trust. Our own observations simply are not sufficient to tell us that others are trustworthy. There is too much of a chance that people are betraying us behind our backs, and it is only by relying on theism, the testimony of others, or directly on trust, that we can conclude that this is not so.

It seems to me that the only way out of the circle of trust would be an argument for the existence of a perfect being (or for some similar thesis, like axiarchism) that does not depend on trust, so that I can then conclude that people created by a perfect being are likely to be trustworthy. But perhaps every argument rests on trust, if only a trust in our own faculties?

Responsibility and randomness

Consider this anti-randomness thesis that some compatibilists use to argument against libertarianism:

1. If given your mental state you're at most approximately equally likely to choose A as to choose B, you are not responsible for choosing A over B.

Note that being in such a state of mind is compatible with determinism, since even given determinism one can correctly say things like "The coin is equally likely to come up tails as heads."

Thesis (1) is false. Here's a counterexample. Consider the following family of situations, where your character is fixed between them: You choose whether to undergo x hours of torture in order to save me from an hour of torture. If x=0.000001, then I assume you will be likely to choose to save me from the torture—the cost is really low. If x=10, then I would expect you to be very unlikely to save me from the torture—the cost is disproportionate. Presumably as x changes between 0.000001 and 10, the probability of your saving me changes from close to 1 to close to 0. Somewhere in between, at x=x₁ (I suppose x₁=1, if you're a utilitarian), the probability will be around 1/2. By (1), you wouldn't be responsible for choosing to undergo x₁ hours of torture to save me from an hour of torture. But that's absurd.

Thus, anybody who believes in free will, compatibilist or incompatibilist, should deny (1).

Now, let's add two other common theses that get used to attack libertarianism:

2. If a choice can be explained with antecedent mental conditions that yield at most approximately probability 1/2 of that choice, a contrastive explanation of that choice cannot be given in terms of antecedent mental conditions.
3. One is only responsible for a choice if one can give a contrastive explanation of it in terms of antecedent mental conditions.

Since (2) and (3) imply (1), and (1) is false, it follows that at least one of (2) and (3) must be rejected as well.

There is an independent argument against (1). The intuition behind (1) is that responsibility requires that a choice be more likely than its alternative. But necessarily God is responsible for all his choices. And surely it was possible in at least one of his choices for him to have chosen otherwise (otherwise, how can he be omnipotent?). If the choice he actually made was not more likely than the alternative, then he was not responsible by the intuition. But God is always responsible. Suppose then the choice he actually made was more likely than the alternative. Nonetheless, he could have made the alternative choice, and had he done so, he would have done something less likely than the alternative, and by the intuition he wouldn't have been responsible, which again is impossible. Thus, the theist must reject the intuition.

Kant and Lewis on our freedom

Kant (on one reading) holds that the initial conditions of the universe and the laws of nature depend on us (noumenally speaking). This reconciles determinism with freedom: sure, our actions are determined by the laws and initial conditions, but the laws and initial conditions are up to us. Kant also thinks that a further merit of this view is that one can blame people whose misdeeds come from a bad upbringing, because noumenally speaking they were responsible for their own upbringing.

Lewis holds that freedom is compatible with determinism, and in a deterministic world had one acted otherwise, the laws would have been different.

Everybody agrees that the view I ascribe to Kant is crazy (though not everybody agrees that the ascription is correct). But Lewis's view is supposed to be much saner than Kant's.

How? The obvious suggestion is that Lewis only makes the laws depend counterfactually on our actions (assuming determinism) while Kant makes the laws depend explanatorily on our actions. But that suggestion doesn't work, since Lewis's best-systems account of laws makes the laws depend on the law-governed events, and so it makes the laws depend not just counterfactually on our actions but also explanatorily: the laws' being as they are is grounded in part in our actions. So both accounts make the laws explanatorily depend on us.

Admittedly, Kant also makes the past, not just the laws, depend on our actions. But that's also true for Lewis, albeit to a smaller degree, because of his doctrine of small miracles...

A quick Thomistic argument for alternate possibilities

1. I freely choose between A and B only if I am deciding in the light of a non-dominated reason for A and a non-dominated reason for B.
2. A non-dominated reason for C is a causal power for deciding in favor of C.
3. If x has a causal power for φing, then x can φ.
4. So, if I freely choose between A and B, then I can decide in favor of A and I can decide in favor of B.

Widerker on Pruss on incompatibilism

David Widerker has a very nice post explaining my version of the consequence argument.