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.

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.

Where does this lead us?

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.

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.

An Argument Against Libertarian Free Will

Suppose I am deciding whether or not to buy ice cream. Suppose also that all things being equal, a past-omniscient agent would predict a 50/50 chance of my buying ice cream. How does my final decision get made? Is there a reason for it?

Before I go any further, I want to note that I'm not talking about probabilities that result from a lack of knowledge on our part. If I flip a coin, I typically estimate the odds of tails at 50%, but that's really due to my ignorance about the behavior of a coin when I flip it. However, an observer who is omniscient about the past will be able to predict the outcome of my coin flip by computing what the laws of physics have to say about forces on the coin. In other words, when I speak of probabilities below, I'm talking about probabilities as they appear to an observer who is omniscient about the past.

According to libertarians, I somehow choose to buy or not buy the ice cream without my decision being (1) fully determined by the past, (2) random, or (3) some combination of determined and random.

Let's suppose that the world is not fully deterministic. How can the outcome of an event be partially determined?

Well, in quantum mechanics, as an example, the probability distribution for the event outcomes is determined, but the actual outcome is the result of a random selection according to the distribution.

For example, suppose a quantum theory predicts a 67% chance of an experiment finding an electron spin-up versus a 33% chance of finding the electron spin down. The theory says that nature acts as if the experiment is equivalent to placing 67 red balls and 33 green balls in a barrel, and randomly drawing a ball from the barrel. If the ball comes up red, then the electron is spin up, otherwise it is spin down. The past-omniscient observer only knows how many of each type of ball there are in the barrel.

This way of looking at events is quite general. It's not general because the world is physical, material or made up of quantum elements. It's general in the theoretical sense. If the past is determining something, then the past is altering the probability that an outcome will occur. A fully deterministic world is one in which the probabilities of outcomes are either 0% or 100%.

When pushed, even libertarians will agree that the past makes certain outcomes more probable than others. Will I choose to step in front of a moving bus this afternoon? Being a happy, stable person who lives a charmed life, probably not. Indeed, very probably not. Even if the libertarian believes I have the "free choice" to step in front of a moving bus, they can still admit that that choice is highly improbably due to factors in my past.

However, when we factor out the probability, what is left for a decision to be based upon?

It's very frustrating trying to pin down incompatibilists on this issue. As far as I can tell, the incompatibilist's belief in libertarian free will is generated by moral considerations, and comes without any technical accounting. For most libertarians, there is not only no mechanism for free will, but there's no way of distinguishing free will from randomness.

To make my argument more airtight, I'm going to suppose there's a detailed accounting for deterministic factors. What we'll see is that there's no basis for an agent to make a choice except via fundamental randomness.

Suppose I enumerate all the reasons I have to buy ice cream, and all the reasons not to buy ice cream. Suppose there turn out to be 5 reasons to buy (B1, B2, ..., B5), and 5 reasons not to buy (N1, N2, ..., N5).

For example, perhaps

N2 = "Ice cream will make me fat, and I want to be slim."

and

B4 = "Ice cream is one of the great pleasures of life, and I don't want to miss out on life's pleasures."

Each reason has an associated importance or weight. Being vain, I assign 10 points to N2, and 5 points to B4.

Since my vanity is is a part of my character, and my character is part of the past state of things, it is predictable. That is, the weight assigned to each reason is mostly determined by the past.

Suppose that these reasons and their weights translate into a 50/50 chance that I will buy the ice cream. That is, we are assuming that, all things being equal, the weight I assign to the reasons is such that they happen to cancel each other out.

At this stage of the thought experiment, the libertarian would say that I choose to buy or not to buy using my free will. What does this mean?

Well, something has to change the weighting of the reasons. It must be that, as I make my decision, I reassign weights to my reasons, and this causes me to come down on one side of the decision or the other.

But on what basis can I reassign weights to my reasons?

Presumably, the libertarian does not mean I am whimsical in reassigning the weights. Whimsy is random. There's no reason for it. It is arbitrary. To see this, imagine that my brain incorporates a random number generator which randomly shifts the weights of all the reasons. If the random number generator happens to throw the balance to buying the ice cream, I can't rationalize the decision by saying that my decision occurred because of B1-B5.

Could I have an actual reason to change my weights?

No. If I did have a reason to change weights such that I buy the ice cream, this reason would constitute B6, and should have been accounted for in my set. That is, the existence of such a reason contradicts the premise that I already had a complete set of reasons in sets B and N.

Is it possible that I discovered a new reason at the moment of my decision?

No. Nothing in the analysis above is phrased in terms of my own perspective. Rather, it's phrased in the perspective of a past-omniscient observer. It doesn't matter whether I was aware of B5. If I was unaware of it, the past-omniscient agent would have assigned it a low weight.

Is my attention to a particular reason the missing factor?

Well, attention or memory or prominence to consciousness may be a factor, but it doesn't help. Either there is a reason for the reason to have prominence to my consciousness or not. If there is a reason, it is already accounted for. If there isn't a reason, it is random.

At this stage, we are forced to conclude that whatever is not determined to the past-omniscient observer is fundamentally random. That is, there can be no possible reason or cause for the selection from the determined probabilities.

I would not be surprised to see some libertarians try to escape this conclusion by trying to redefine the word random. However, there's really nothing special to my definition. Just because an event occurs in the mind of an agent doesn't make any difference to my definition. There remains no reason for the decision, whether you call it random or not. Any attempt to make such a distinction is like saying that when a random event occurs in the mind of an agent, it's called whimsy. What value such nomenclature might have is beyond me.

Shagging Disproves Design

Design is like painting. A painter has a palette of different colors to choose from, and a final painting is typically a combination of different paints from the palette.

Of course, a painter could use just one color. But if the canvas was large and the products diverse, it's pretty unlikely that a painter would use one color exclusively.

It's even more unlikely that the painter would use one specific color, like burnt sienna. However, if we knew of a painter who had no choice but to use burnt sienna, then a painting in burnt sienna would be far more likely to be by this restricted artist than by any other painter.

The above is an analogy to the argument I have given for why evolution disproves design. Neo-Darwinian evolution places a lot of constraints on the way things have to be. There has to be descent (breeding) and common descent (any two individuals have a common ancestor). Experiment tells us that common descent is true. In other words, something like neo-Darwinian evolution has been used consistently throughout the history of life on this planet.

Evolution is just one method of design. In general, a designer doesn't need to try every possible design. A designer can simulate and use complex rules to create a single design, then just implement that design by manufacturing, with no need for breeding. In general, a designer can also create designs that have little in common with past designs, and which are constructed from completely new materials.

Since the number of ways of designing things without evolution is far greater than the number of ways of designing things with evolution, the fact we see evolution and only evolution means that a designer is ruled out.

This is my standard probability argument against design.

One response I get back from intelligent design sympathizers is that evolution is a design technique that even we humans use. Clearly, anyone who responds this way is missing the point entirely. I say from the very beginning that evolution is a form of design. The point is that it is just one form of design, and there's no reason to use just one technique exclusively. If there was a reason for exclusive use of evolution, and if there were any rational reason to grant that scenario a privileged share of the probability, then there would be predictions stemming from that reason.

However, it occurred to me that there's yet another good reason to dismiss the ID rebuttal. Suppose I'm designing an airliner. I don't want my airliners to breed for survival. Airliners are supposed to be useful to me, not to themselves. However, suppose I want to use evolutionary methods to design the wing of the airliner. That's aplausible scenario. So I create simulations of wings, test them in virtual environments, and preferentially carry forward effective designs in the simulation, and cull ineffective designs from the population. This is a straightforward application of genetic algorithms to the problem of wing design.

However, at no time in my simulation to I create a detailed mechanism for the wings to breed or have sex. There is, of course, a mechanism for simulating the outcome of "breeding" wings, i.e., of passing on design elements or altering population sizes. However, none of the wings have genitals, and they don't shag.

So, even if a designer chose to develop life on this planet using evolutionary techniques, there's no need for breeding. Thus, the fact that we have genitals is yet another reason why we're not designed. If we were designed (or if we're the evolutionary simulation), we wouldn't need genitals.

Living in a Box

Imagine a crystal cube. Suppose this crystal is purely a static 3D entity in a 3D universe. There is no time dimension.

Like all crystals, it is a lattice of points connected by bonds (line segments) to nearest neighbors. But let's suppose, also, that these bonds are directional. The bonds aren't merely line segments, but are arrows that always point away from a particular corner of the cube. We'll call this special corner, the "origin". The opposite corner of the cube we'll call "the terminus".

If we were somehow living in this cube, we would notice that EVERY point in the lattice "attracts" arrows (bonds) from the origin side, and "radiates" arrows out towards the terminus side. Invariably.

Naturally, we would conclude that it is an absolute law of the crystal in which we live that there are always arrows going in to a point, and always arrows going out of it.

However, would we also conclude that, if the crystal is finite, there MUST be arrows entering the origin corner point of the crystal?

Would we also conclude that, in a finite crystal, at the opposite corner of the cube, there MUST be arrows exiting the terminus point?

We obviously would not.

I hope you can see the analogy. The cube is like our universe. Every point in the crystal is an event or interaction. The arrows flowing into the points are causes from the past. The arrows flowing out from a point are effects radiating into the future. The law of cause and effect is the observed law that events have causes and effects.

You should be able to see that the concept of causation is only defined INSIDE of our universe. It applies only to points within it. It has no leverage at the origin corner or the terminus corner of the cube/universe.

The Problem With Detroit

The U.S. auto mobile industry in an a shambles. Why?

Well, there are several contributing factors, such as higher labor costs, but there is one big reason. U.S. automakers don't make fuel-efficient vehicles that can compete.

Chronically, the automakers have planned on a short time horizon. They didn't invest over the long term, and they're unwilling to change the status quo. Ford, GM and Chrysler have too many inefficient trucks and SUV's, and their manufacturing processes take too long to retool. That's why cars like the Pontiac Grand Prix don't change body styles for 5 years or more, whle Toyota Camry gets a facelift every year or two.

Though the automakers developed hybrids, electric and fuel cell vehicles, they did so primarily as a PR move, with no intention of shipping green machines to the public unless they were absolutely forced to do so. Toyota forced their hand, and now American cars are playing a sad game of catch-up.

This myopic strategy has been ongoing for the last decade. Everyone knew the U.S. car industry was doing it.

What could have changed this? CAFE! Increasing average fleet fuel efficiency standards. The government could have forced the U.S. auto industry to build more fuel-efficent vehicles.

This would not only have made our carmakers greener, it would have made them more competitive over the long term.

Why didn't it happen? Because the Republicans insisted that it was better to let business play their game instead of having government get involved. Oh, and political contributions from the automakers might have had something to do with it, also.

It's really very simple. When you look at an industry, there are limitations in how the marketplace works. Most U.S. corporations don't have a long-term strategy. They're obsessed with short term profits and stock prices. Meanwhile, other governments write articles of legislation that force their industries to plan for the future. Consequently, their corporations are safer, greener, and more citizen friendly, and more competitive.

I'm all for free trade, but if we're going to take down trade barriers, why should the U.S. compete with one hand behind its back?