## Tuesday, October 19, 2010

### The Logician Who Wouldn't Check His Work

In mathematics, it is common to start from some foundational assumptions, and see what you can prove. The assumptions are called axioms, and the notable generalities you can prove are called theorems.

The classic example is the Pythagorean Theorem. You learned this theorem in high school because it's extremely useful in everyday life. You may even have proved it in class. If you start from the axioms of (Euclidean) geometry, you can prove that the square of the length of the long side of a right triangle is equal to the sum of the squares of the lengths of the other two sides.

Yes, for a lot of people, mathematical proofs put them right to sleep. However, I think they understand the point of the exercise. There are important truths that you can't easily work out in your head. It's important to check the steps, even if you're not the one doing it.

There are some ideas in mathematics we think might be true, but which we have yet to be able to prove. One of the most famous is the Goldbach Conjecture:

Every even integer greater than 2 is a Goldbach number, a number that can be expressed as the sum of two primes.

Boffins have been trying to crack this nut since Goldbach came up with it in 1742. No one has yet succeeded, though several complex proofs have been proposed.

Imagine a mathematician, well call him Oiler, who claims that the Goldbach Conjecture is true. Oiler claims he has thought his way through the proof in his head, and he's confident the Conjecture is true.

Naturally, we are thrilled, and we ask Oiler to write down a detailed proof to support his conclusion. Oiler refuses. Oiler tells us that the Goldbach Theorem is special. It's a special class of theorem that's true, but which you can only see to be true if you DO NOT write down the proof and check your work carefully. After we pick our jaws up off the floor, we would quiz Mr. Oiler about his claim just to make sure we understand him correctly.

We would then proceed to cover Oiler in tar, and feather him. We would ridicule Oiler savagely.

Yes, this is an analogy for superstitious thinking. What is superstitious thinking?

Superstitious thinking is counting the hits but not the misses. It's about looking for ways to confirm your theories, but never looking for ways to prove them wrong. It's a matter of ignoring the possibility that an effect would exist even if the theory was false. It's a matter of succumbing to human cognitive biases.

Superstitious thinking can be overcome by using statistics, random sampling, blind testing, and an array of other techniques for checking our work. Basically, it's a matter of using science to suppress human bias and get to the truth.

There are a lot of people in the world who believe in the paranormal, and when you ask them to prove their case, their favorite answer is that God (or the aliens, or the fairies, or whatever) won't be tested. They tell us you can only see them when you don't use science to check your work. Now, how is this any different from Mr. Oiler in the above?

I'm not seeing a significant difference.

## Thursday, September 30, 2010

### Qualia and Reductionism

I have a couple of observations.

First, it seems impossible to imagine that the quale for red and the quale for green could ever be the same as long as we can distinguish red and green. So, we can never intuitively reduce red to green, or, indeed, reduce one quale to another. (This suggests to me that we should identify a quale for X with "a capacity to recognize X". However, I don't need to adhere to such a controversial statement.)

My second observation is that when things are said to "reduce" in the sciences, that reduction never reduces one quale to another. I'll describe what I mean with a specific example.
NOTE: As a preface to my example about reduction, let no one persist in the faulty belief that reductionism is eliminative. Reduction of water to H2O does not eliminate water, nor does it eliminate oceans, droplets or any other watery things. Reduction identifies, but does not eliminate. Reduction identifies a droplet of water with a configuration of H2O molecules. At the end of the reduction process, droplets of water still exist.
Suppose we reduce a droplet of water to the presence and motions of H2O molecules. What does this mean in terms of qualia?

Well, the reduction relies on experiments. Things like electrolysis which breaks water into oxygen and hydrogen gases, spectroscopic experiments the can identify the gases by the light they absorb, and the way hydrogen burning in oxygen creates water vapor.

However, at no time can we say that the qualia we experience while performing the experiments are equivalent to the experience of, say, dipping our hands in a pond. If they were equivalent, then we would be unable to distinguish the experience of performing the experiments (and perhaps the experience of making the relevant inferences) from the experience of dipping our hands into a pond. That would be absurd.

Yet I doubt that any of us is uncertain that water reduces to H2O. We don't think that water is anything more than H2O. We don't argue that there is some non-physical stuff which bridges the gap between the qualia of our experiments and the qualia of water itself.

The conclusion is that reduction does not equate qualia. Reduction is about ontology.

What is ontology? Ontology looks at all of our experiences and asks what is the minimum number of substances and relationships that explain those experiences. When we see an apple, we don't assume that every property of every apple, and every possible conjunction of properties, at every moment in time is ontologically basic. There is something it is like to gaze at the same apple for 10 minutes, and there is something it is like to glance at the apple, and these two qualia are distinct. But we don't think that gazed-at apples are ontologically different from glanced-at apples. We think there is just one apple, whether we gaze at it, glance at it, look at its silhouette, or take a bite of it.

Ontology seeks to reduce the vast multitude of our experiences down to the fewest number of causes. In this case, a single apple, seen from different perspectives.

So, let's return to qualia in the mind-body problem. The goal of the Knowledge Argument, for example, is to show that the quale for red does not reduce to a scientific, ontological model. This seems to me to be a doomed project. Reduction never equates one quale with another. The fact that reduction doesn't do this (ever) is not a mark against reductionism. I now think that these sorts of arguments confuse epistemological basics with ontology.

Qualia are the most basic of epistemological inputs, and these inputs are unique. Ontologies are epistemological outputs. Epistemological outputs are never equivalent to basic epistemological inputs (because epistemological outputs are distinguishable from the things they model). Ontologies can, at best, explain or predict relationships between epistemological inputs.

There's an implicit assumption in dualist arguments that, if minds were physical, they ought to be able to do what we cannot. This is an implicit assumption because, if we believed that physical machines could not reduce one quale into another (i.e., that they would be in the same position that we are in), then we could not conclude that we are non-physical from the position we are in! Every mind would be in that position, whether physical or not!

So, would physical minds be in the same position?

Assume that a physical mind can exist and be conscious. This mind is going to have some raw experiences, some raw recognitions, some distinguishable inputs. When this mind works out an ontological model of its world, the best it will be able to do is to correlate the epistemological basics of its experience (its inputs), and build a model. That model may predict its inputs perfectly, but the model is not the same thing as the input it is predicting. If it were the same thing as the input it were predicting, then the model would be indistinguishable from what it was modeling.

I conclude that a physical mind will find itself in exactly the position in which we humans find ourselves. The only way the machine won't be that way is if it is incapable of distinguishing simulations of its model from the real thing. Again, this seems absurd.

Having shown that physical minds will be in the same position in which we find ourselves, I can argue that we can't infer ontological dualism from the position in which we find ourselves. The inability to reduce one quale into another is not a feature of dualist minds but of all minds, including purely physical ones.

## Thursday, September 16, 2010

### The "Free" in Free Will

A few nights ago, I was having a chat with some of my atheist/agnostic friends about free will. While we seem to agree on the way things actually are, there was some disagreement as to whether we have free will. After some discussion, I think I discovered that for most of my friends, free means "not deterministic" or "not deterministic and not random". And, since my friends think the universe is pretty much deterministic, they don't believe free will exists.

If this was just a dispute about terminology, there wouldn't be much more to say. However, I could tell that for one or two of my colleagues, this lack of free will was the source of some angst. Why should that be? Why should anyone care about a rather mathematical abstraction like determinism?

This got me thinking more about value. Daniel Dennett says that determinism gives us all the free will that's worth having. So, what is it that we value?

In my opinion, what people value is the product of the work they do when making decisions. They want to have made good decisions for good reasons. What I intend to argue here is that throwing non-deterministic factors into decision-making will not increase what we value about our decision-making.

The short version of the argument is simply this: a good reasoner is determined to get to a good conclusion from initial premises.

Consider the classic Socrates syllogism:

Premise 1: All men are mortal.
Premise 2: Socrates is a man.

____

Conclusion: Socrates is mortal.

If we assume the premises, then the conclusion follows. Any person who assumes the premises, but determines that Socrates is not mortal is a bad reasoner. Injecting non-deterministic factors into the reasoning process will only make a good reasoner worse!

What's more, this syllogism is constant and time-independent. It's as true today as it was a billion years ago, or as it will be billion years in the future. The validity of the syllogism is a timeless fact. The thing that is time-dependent, the thing that happens in time, is the way our mind parses and traverses this timeless logical fact. And here, non-determinism in the conclusion one reaches will only make a good reasoner worse.

To be a bit more precise, getting to a non-deterministic conclusion would only make things better if we were really bad at reasoning. If our reasoning ability was worse than random guessing (e.g., if we pathologically got to wrong conclusions), then a non-deterministic element might improve our score, but I don't think we would value random guessing a whole lot more than we would value being absolutely awful at reasoning. Guessing just isn't the kind of reasoning we value.

The other reason why we might devalue deterministic reasoning is that the kind of deterministic reasoning that's on the table is physical determinism. If reasoning is the result of chemical interactions, then people worry that they didn't act for good reasons, but just because some electrons and nuclei buzzed around in their heads and created a new configuration. They worry that physical reasons are mutually exclusive of conceptual reasons.

This worry is the source of an anti-naturalistic argument called the Argument from Reason. The basic idea is that, if matter is not fundamentally mental at its lowest level, then thoughts are the results of non-mental physics (like chemistry). And if thoughts are non-mental underneath, then thoughts aren't really about things, and decisions are not for the reasons we think they are. And if reasons aren't reasons, then the reasons we gave for concluding that the world is based on non-mental physics are worthless, and naturalism is self-refuting.

I think the Argument from Reason is simultaneously under-appreciated and wrong. It's difficult to fault most naturalists when they follow scientific inferences and conclude that the mind is a biochemical mechanism, but I also think that it's important for naturalists to understand why the Argument from Reason is wrong.

The Argument from Reason assumes that things that occur for physical or chemical reasons cannot also occur for reasons in the world of ideas. This assumption seems reasonable at first. If we know that X is necessary and sufficient cause for Y, then we generally discount other, independent causes. In this case, if physics is a necessary and sufficient cause for what we think and do, then reasons from the world of ideas should be discounted as reasons for our thinking.

Greedy Reductionism
The problem with the assumption underneath the Argument from Reason is that it relies on something called greedy reductionism. Greedy reductionism is another expression we owe to Daniel Dennett. Reductionism is something that comes from the physical sciences. Historically, we have found that wide variety of objects and phenomena are actually the result of just a few kinds of objects and a few kinds of phenomena. For example, the periodic table of elements contains over a hundred chemical elements, and the number of chemical interaction phenomena is vast. However, we have discovered that chemistry is just the result of protons, neutrons and electrons interacting electromagnetically. The vast science of chemistry reduces to the physics of a few kinds of things that interact in one simple way. The complexity arises from the vast number of configurations that can arise from some simple physics. Carbon has unique chemical properties, but carbon is actually the result of electromagnetism plus protons, neutrons and electrons.

The greedy reductionist is the philosopher who takes this information and claims that chemical elements don't exist anymore. This is not an idea from the sciences. It is a confusion.

Reductionism identifies the thing being reduced with a configuration of something more fundamental. Reductionism doesn't replace the thing being reduced, but merely explains it. Our description of an interaction might be replaced by reductionism (e.g., a chemical reaction might better be described as an electromagnetic interaction between electrons), but the original thing is never eliminated by reductionism.

Minds have thoughts, and make decisions for reasons. If minds, thoughts and reasons reduce to physical mechanisms, then we eliminate neither minds, thoughts nor reasons. Those who champion physicalism are not saying that minds, thoughts and reasons do not exist. They are saying that minds, thoughts and reasons are physics. They are physical processes, states or configurations. Physics is not an alternative to thoughts and reasons as an explanation for thinking, but one and the same. Thinking is a physical process in humans.

This means that the physics of minds is not an explanation for thoughts that is independent of the conceptual reasons. And since physical mechanisms are not independent explanations, physical mechanisms are not mutually exclusive of conceptual mechanisms.

Explaining precisely how I thinking is a physical process is beyond the scope of this post, and, besides, I don't think such and explanation is necessary to refute the Argument from Reason. The Argument from Reason is really a gaps argument which says "I don't see how thinking can be a physical process, therefore it cannot be a physical process."

Summary
In summary, while the meaning of the word free is a matter of convention, I think that defining the word free to mean non-deterministic is confusing and counterproductive. What we care about is whether we have the kind of will that is valuable, and non-determinism doesn't help us get what we value.