Dualist eliminativism

Eliminativism holds that our standard folk-psychological concepts of mental functioning—say, thoughts, desires, intentions and awareness—have no application or are nonsense. Usually, eliminativism goes hand in hand with physicalism and scientism: the justification for eliminativism is the idea that the truly applicable concepts of mental functioning are going to be the ones of a developed neuroscience, and it is unlikely that these will match up our current folk psychology.

But we can make a case for eliminativism on deeply humanistic grounds independent of neuroscience. We start with the intuition that the human being is very mysterious and complex. Our best ways of capturing the depths of human mental functioning are found neither in philosophy nor in science, but literature. This is very much what we would expect if our standard concepts did not correctly apply to the mind’s functioning, but were only rough approximations. Art flourishes in limitations of medium, and the novelist and poet uses the poor tool of these concepts to express the human heart. Similarly, the face expresses the soul (to tweak Wittgenstein’s famous dictum), and yet what we see in the face is more complex, more mysterious than what we express with our folk psychological vocabulary.

There is thus a shallowness to our folk-psychological vocabulary which simply does not match the wondrous mystery of the human being.

Finally, and here we have some intersection with the more usual arguments for eliminativism, our predictive ability with respect to human behavior is very poor. Just think how rarely we can predict what will be said next in conversation. And even our prediction of our own behavior, even our mental behavior, is quite poor.

The above considerations may be compatible with physicalism, but I think it is reasonable to think that they actually support dualism better. For on physicalism, ultimately human mental function would be explicable in the mechanistic terminology of physics, and my considerations suggest an ineffability to the human being that may be reasonably thought to outpace mechanistic expressions.

But whether or not these considerations in fact support dualism over physicalism, they are clearly compatible with dualism. And so we have a corner of logical space not much explored by (at least Western) philosophers: dualist eliminativism. I do not endorse this view, but in some moods I find it attractive. Though I would like it to come along with some kind of a story about the approximate truth of our ordinary claims about the mind.

A pedagogical universe

Our science developed over milennia, progressing from false theory to less false theory. Why did we not give up long ago? I take it this is because the false theories, nonetheless, had rewards associated with them: although false, they allowed for prediction and technological control in ways that were useful (in a broad sense) to us.

Thus, the success of our science depends not just on a “uniformity of nature” on which the correct fundamental scientific theories are elegant and uniform. Most of our historical progress in physics has not involved correct scientific theories—and quite possibly, we do not have any correct fundamental theories in physics yet. The success of our science required low-hanging fruit for us to pick along the way, fruit that would guide us in the direction of truth.

We can imagine worlds where the ultimate physics requires an enormous degree of sophistication (much as we expect to be the case in our world) and there is little in the way of low-hanging fruit (except maybe for the lowest level of low-hanging fruit, involving the regularities needed to enable evolution of intelligence in the first place) in the form of approximately true theories that rewards us with prediction and control so that beings like us would just give up on science. Our world is better than that.

Indeed, our world seems to be pedagogically arranged for us, arranged to gradually teach us science (and other things), much as we teach our children, with intellectual and practical rewards. There is a design argument for the existence of God from this (closely related to this one).

Approximatable laws

Some people, most notably Robin Collins, have run teleological arguments from the discoverability of the laws of nature.

But I doubt that we know that the laws of nature are discoverable. After all, it seems we haven’t discovered the laws of physics yet.

But the laws of nature are, surely, approximatable: it is within our power to come up with approximations that work pretty well in limited, but often useful, domains. This feature of the laws of nature is hard to deny. At the same time, it seems to be a very anthropocentric feature, since the both the ability to approximate and the usefulness are anthropocentric features. The approximatability of the laws of nature thus suggests a universe whose laws are designed by someone who cares about us.

Objection: Only given approximatable laws is intelligence an advantage, so intelligent beings will only evolve in universes with approximatable laws. Hence, the approximatable laws can be explained in a multiverse by an anthropic principle.

Response: Approximatability is not a zero-one feature. It comes in degrees. I grant that approximatable laws are needed for intelligence to be an advantage. But they only need to be approximatable to the degree that was discovered by our prehistoric ancestors. There is no need for the further approximatability that was central to the scientific revolution. Thus an anthropic principle explanation only explains a part of the extent of approximatability.

Approximate truth and the very recent past

Suppose I say that Jim yelled in delight at 12:31. But in fact he did so at 12:32. Then I said something false but approximately true.

Now, suppose that I hear Jim giving a loud yell of delight about 300 meters away. While I am listening to that yell, I think that Jim is yelling. But in the last second of my hearing, Jim is no longer yelling, but the sound waves are still traveling to me. No big deal. My belief that Jim is yelling is false, but approximately true. Or so I want to say.

And it’s important to say something like this, for it allows us to preserve the idea that our sense give us approximate truth. The case of sound from 300 meters away is particularly strong, but the point goes through in all our sensation, as none of it travels faster than the speed of light. Now, granted, often when we become aware of a stimulus, our sensory organs are still undergoing it. But nonetheless it is strictly speaking false to say that this very part of the stimulus that we are now aware of is in fact going on. So our senses seem to lead us slightly astray. But at most very slightly. It is approximately true that this part of the stimulus is going on now, because it is in fact going on a fraction of a second earlier. Or, perhaps, it is a part of our common sense knowledge of the world that the data of the senses is only meant as an approximation to the truth, and so there is no straying at all.

Now imagine that I say that Jim actually yelled in delight at 12:31, but he was actually completely silent all day, although in a very nearby possible world he did yell in delight at 12:31. Then what I said is not approximately true. In ordinary contexts, the modal difference between the actual and the merely possible vitiates approximate truth, no matter how nearby the merely possible world is.

So now on to one of my hobby horses: presentism. If presentism is true, then the difference between what is happening now and what happened earlier is relevantly like the difference between the actual and the possible. In both cases, it is a difference between a neat and clean predication and a predication in the scope of a modal operator, pastly or possibly, respectively. If this is right, then if presentism is true, I cannot say what I said about its being approximately true that Jim is yelling if Jim has actually stopped. That difference is a very deep modal difference. That the time when Jim is yelling is in a nearby past no more suffices for the approximate truth of “Jim is yelling now” than that Jim is yelling in a nearby possible world is enough for the approximate truth of “Jim is actually yelling”. The ontological gulf between the actual and the possible is vast; so would be the ontological gulf between the present and the past if presentism were true.

Thus, the presentist cannot say that the senses tend to deliver approximate truth.

Objection: We know to correct the data of the senses for the delay.

Response: We know. But that's a recent development.

A modal approximative ontological argument

Here is an ontological argument that I haven’t seen:

1. Possibly, it is approximately true that God exists.

2. Necessarily, if it is approximately true that God exists, then it true that God exists.

3. If possibly God exists, then God exists.

4. So, possibly, it is true that God exists. (1 and 2)

5. So, God exists. (3 and 4)

Premise 1 is an interesting weakening of the familiar possibility premise from modal ontological arguments.

Premise 3 is also familiar, going back at least to Mersenne. We can say that God is the sort of being that couldn’t exist merely contingently: he either exists necessarily or he can’t exist at all—there is no room for mere possibilities in the case of God’s existence.

The thought behind 2 is rather similar to that behind 3: God is a kind of infinity that cannot be approximated. It is not possible for there to be a state of affairs merely approximating the existence of God.

Approximation in mathematics

The New York Times has an interesting article arguing that imprecise approximational intuitions--the ability to quickly and roughly reckon things--are crucial to success at abstract mathematics.

To someone whose mathematical work was in real-number based areas--analysis and probability theory--this is very plausible on introspective grounds. But I wonder how true it is in more algebraic fields. I've never been very good at higher algebra--things like the Sylow theorems were very difficult for me (I still passed the algebra comp, but it came noticeably less naturally to me than the analysis comp), perhaps in part because my approximational intuitions were close to useless.

Anecdotal data suggests to me that there are two distinct kinds of mathematical skills. There are the skills involved in analysis, skills tied to problems that are real-number based (complex numbers are real-number based, of course, since C is just the cross product of R with itself), often visualizable, and where approximation and limiting procedures may be relevant. And then there are the skills involved in more algebraic fields, where (as far as I can) approximation gets you nowhere, and while visualization is helpful, the visualization is much more symbolic (visualizing a path of a brownian particle is pretty straightforward, one visualizes quotient groups either explicitly in symbols like "A/H" or perhaps in some strange and highly abstract diagrams). I don't know where to put the combinatorial--it may somewhat straddle the divide (a lot of visualization is involved), but I think is very algebraic in nature.

It is quite possible for a person to be really good at one of these, without being very good at the other. There are fields of mathematics that call upon both sets of skills. And there is an asymmetry: I think the analysis-type skills may be of very little use to mathematicians working in very algebraic areas, but just about every mathematician working in an analysis-type area needs to be able to do algebraic manipulation (though I have a strong preference for proofs in analysis-type fields where the algebraic manipulation is just a way of making precise what is intuitively obvious).