Tuesday, August 29, 2006

The Two Faces of Intuition

My recent discussion with Colin Caret led to this comment from Colin about intuition:
It seems to me that the difference between your view and mine is a difference of intuition about truth. So I think you might want to be cautious about throwing out intuition.
This prompted me to think about the role of intuition more carefully.

I think intuition falls into two categories.

In the first category, we intuit truth and objectivity in the sense that we are aware that there appear to be distinct meanings (between true and false, or between objective and subjective) for these terms in certain language games. We may not initially understand what we are intuiting, but this forms the jumping off point for philosophical investigation. We're bootstrapped with these intuitive distinctions, and philosophy asks whether our intuition for a distinction in a particular language game has any broader applicability.

Intuition of the second kind seems to be trying to answer questions raised by the first form of intuition. I'm not fond of this second kind of intuition which is not so much about the presence of distinction but about specific facts invoking the distinction. This is the kind of intuition that is subject to optical illusions like the Ehrenstein illusion. It's not that there's no such thing as straight versus curved lines - that intuitive distinction (of the first kind) is clear enough to inspire formal investigation. However, it is clear that intuition of the second kind is inadequate to accurately categorize lines as straight or curved without formal methods.

I'll focus on one example. We know intuitively that the verb "to exist" has meaning in certain contexts. Suppose I say that a chair exists in the next room. You look in the next room and find no chair. You must say that no chair exists in the next room. That's the standard language game for the verb "to exist." The test for the non-existence of a thing is in not finding that thing. This is a distinction revealed to us by intuition. So, when I logically extend this game using a formal executable rule, we are compelled to find that "in-principle undetectability" is identical with "non-existence."

Here, intuition of the first kind has inspired us to devise a rigorous definition for existence.

Of course, this formal conclusion rules out all sorts of nonsense that people are nevertheless rather fond of. They reject my formal definition of existence because their intuition (of the second kind) tells them that, say, undetectable unicorns can exist. For these dissenters, existence in one game (e.g., chairs) is not the same thing as existence in another game (e.g., invisible unicorns). It's as if the edges of squares within concentric circles (as in the Ehrenstein illusion) are not really straight anymore. Well, this dissent, frankly, makes a mockery of meaning. I submit that no philosophical progress is possible if we're not going to take the time and effort to formally fix our terminology and meaning. We might as well stick to intuition of the second kind because our choice of formalities is subservient to it.

Now, as a moral relativist, I can't say people are objectively wrong to play such silly games with meaning (like leaving definitions floating). However, I think that if people really saw what they were doing, most would subjectively agree with my moral position that philosophy should be formal, and that there's no point in calling something philosophy if it's actually just intuition of the second kind. I don't need philosophy to tell me that I want unicorns to exist. I need philosophy to tell me when my intuition leads me astray.

Sunday, August 27, 2006

Moral Argument vs. Moral Persuasion

Bucky Katt demonstrates how ethical debates can be resolved when the debating parties don't share the same moral axioms.

Thursday, August 24, 2006

Values and Validity

I've been enjoying a conversation with Alex Gregory over at atopian.org. We've been discussing moral relativism, and Alex has been asking whether I'm saying one can rationally deny demonstrated truths within axiomatic systems. Here is my answer to his question, with a little elaboration.

The truths (theorems) within each axiomatic domain exist whether we value them or not. The theorems of Euclidean geometry are true, even if we prefer non-Euclidean geometry.

In many cases, comparable theorems in different axiomatic systems contradict each other. The question is, on what basis should we value each set of axioms and theorems?

My point is that, at best, what we ought to do is subjective. What I ought to do involves a value judgment. Whether I ought to hold an axiom as true depends on how I value it (or its resultant theorems).

This happens in physics. Each scientific theory consists of a set of axioms for modeling the world, and each observation counts as an axiom. A theory is invalidated when it becomes inconsistent, and the predictions of a theory are those axioms that can be added to the system without contradiction.

If we have two scientific theories that are presently indistinguishable (say, because the distinguishing experiments are as yet out of reach), then we might still prefer one theory over another. Sometimes, this selection of axioms is based on aesthetics or taste, and one theory is valued over the other for accidental or historical reasons. For example, if one theory will benefit me, my past works and my department, I have reason to value that theory more than its competitor.

So, let's look at my personal position. I value staying alive, comfort, my ego, my loved ones, peace of mind, etc. Since I view science as vital to survival and peace of mind, I think its axioms are important, and I'm willing to live as if they are true. I accept mainstream ethical values because I see those as conducive to my comfort and my general happiness.

However, a person who has different values (or who is confused or inconsistent) will accept different axioms. For example, a person who thinks that this world is less important than some fictitious afterlife, does not fear death or discomfort. Science does little for these people, and the fact that electronics and pharma science save millions of lives each year is unimpressive to them. Their values allow them to disregard the founding axioms of all scientific systems (logical consistency and regularity) if it delivers them the particular afterlife they seek.

That some primitive screwheads reject science does not imply that science is somehow untrue under its own axioms. It's just a question of whether a man thinks the objective power of science is important.

Now, let's get back to morality. Morality is supposed to guide values, but values are used to select axioms. So how can there be an objective morality? If a person thinks that following axiomatic moral systems is unimportant, on what basis can you logically demonstrate to that person that they are wrong? Their answer to any axiomatic system will be "so what?"

I'll add here that I feel that it is generally better to "game" axiomatic systems, and to do a comparative analysis of them. I think it is morally good to ask why each system is valued the way it is, and whether the method used for assigning value is a consistent one. Is my preferred system appealing to me for biological, social or psychological reasons? Do these values cause me to be blind to defects in my preferred system? Are these values themselves worthy?

I'm still working my way through these questions.

In comparing alternative systems, one will come across systems which actively discourage comparative analysis. Christianity is one such faith-demanding system. While it would be illogical for an outsider like me to pay any heed to such demands, it is significantly harder for Christians to do so, since they presumably value the axioms of their own system to a greater degree. It can be difficult to escape these Jedi mind tricks.

It's also true that social and family bonds act to suppress comparisons. There is an inherent negative value in abandoning the shared axioms of one's family or social group. This doesn't affect me much, and my mother wonders where she went wrong.

I also can't deny that I want to feel that I'm special, and that my formulation of philosophy is right and elite, rather than merely right and mundane. This, too, could potentially sway my judgment in a manner I find distasteful.

Anyway, I think I'm getting closer to understanding the dynamics of selecting axioms, and I plan to write more on this topic.

Tuesday, August 22, 2006

Moral Theories

Moral objectivists correctly argue that the apparent unreliability of our sense of right and wrong does not falsify the case for an objective morality. This can be seen by considering spatial orientation as an analogy. While flying an airplane, I can become disoriented, and not know which way is up or down. However, the fact that I can become disoriented, does not mean that there is no up or down, only that I am confused as to which way is which.

I don't think anyone attacks moral objectivity on these grounds, but I found it instructive to consider the differences between moral and physical sensation.

Our physical sense of orientation correlates feelings in our inner ear, our vision, and our sense of touch. Whether we are standing or ascending a rope, our sense of touch conveys a direction. It feels different to lie on an incline face up versus face down, or uphill versus downhill. Our visiion is somewhat less reliable, but, most of the time, the world looks different when we face up versus face down. Our inner ear primarily senses changes in orientation rather than orientation itself. Hence, it seems that up and down are primarily defined by our sense of pressure and touch, and that vision and balance provide additional guides to orientation. From this information we create models of the physical world that relate the positions of objects, and the forces we will experience given velocities and accelerations.

Our theory of spatial orientation is more than just physical sensation of directional pressure. The formal model of which way is up relies on a deeper model of the shape of the world, whether it be mostly flat, or like an M.C. Escher painting. Which way is up is based on the model, not just the sensation, because the model is a more accurate guide to future sensation. That is, the model is predictive.

Now, let's consider moral theories. Our physical senses serve to tell us what situation we're in. We can see a pocket watch lying on the sidewalk. Our physical theories tell us what will happen if we take the watch for ourselves and hold it or trade it for personal gain. Our theories also tell us what will happen if we try to return the watch to its owner. In each case, we also get a moral sensation. The former act feels wrong, and the latter act feels right. The question is, what do our moral feelings predict? What do they add to our physical model?

Our moral feelings are predictive of just two things. First, our moral feelings may predict how we will feel in similar situations. Second, they may predict how other people might feel in similar situations, assuming they are like ourselves. That is, our moral feelings build a model of ourselves, not of anything else. All other prediction is part of our physical model.

This is much like art and gastronomic taste. All nutritional value being equal, we may feel differently about cherry-flavored candies than lemon-flavored ones. Such differences in taste inform us of nothing but our own gastronomic wiring. We might know that we prefer lemon to cherry, but that's not a statement about lemons and cherries per se, only about our subjective tastes for them. Likewise, two paintings with equal informational content, and equal material content may stimulate us in different ways. This reaction is about our own aesthetic tastes, not about something external to physics. It's predictive of nothing except how our subjective aesthetic tastes might react to other paintings.

Back in moral terms, knowing that we prefer not to take someone else's dropped pocket watch leads us to the model that we prefer not to take what doesn't belong to us. That is, moral theories are generalizations about our individual, subjective feelings on moral issues. While I assert that I feel that theft is wrong, I wouldn't call such an assertion an objective truth about anything but my own feelings.

Like other theories, moral theories can be wrong. Suppose my initial moral theory is "finders, keepers," and I take the dropped pocket watch. Later, I learn of the tragic effect the loss had on its former owner. This effect is a physical one, and I update my physical model accordingly. Given my new knowledge of the scenario, I might then regret my decision not to return the watch. In retrospect, my moral decision was wrong, as perhaps was my "finders, keepers" theory. However, the result of my moral theoretical revision is not deeper knowledge of something external, but a more accurate account of my own moral sensitivities. I have changed the scenario, and my feelings about that scenario change accordingly.

Thus, when examined carefully, we find that morality fails to be objective in the same way that physical sensation is objective. Our moral feelings can be used to construct a model of our personal tastes, and nothing more. Such models are not about anything external to ourselves, but only about our patterns of individual, subjective reaction to external situations.

Wednesday, August 16, 2006

You will obey me!

You scored as the Master. Sly, lonely, powerful, cunning, horrid.

Which doctor who villain are you?
created with QuizFarm.com

Yeah, these quizzes don't make any sense.

Doctor Who?

You scored as 3rd doctor. A man of science, a Gadget king, you can put up a good fight. You are just what the doctor ordered

What Doctor Who character are You?
created with QuizFarm.com

Monday, August 07, 2006

Should We Have Been Able To Predict Quantum Effects In The 19th Century?

In numerous blog commentaries, I have argued that while parts of the world are causal and consistent, there's no guarantee that the universe is globally so, or will always be so. There might be distant galaxies in which there are uncaused events, or future times when the consistency we see in the world comes to an end.

However, until recently, I harbored a suspicion that our cosmological neighborhood was causal and consistent. If anything can and does happen at any time, it's hard to imagine the universe being intelligible at all. I was prompted to re-evaluate my thinking by my realization that quantum mechanics is effectively acausal. Since not everything about the final state is fixed by the initial state, that which is not fixed is random and acausal. The fact that quantum mechanics is compatible with Newtonian mechanics shows that acausality can be ever-present without disturbing the results of classical physics. The randomness of nuclear decay doesn't make the whole world of planes, trains and automobiles utterly unpredictable.

Thus, I was led back to the question of whether logical inconsistency might also be able to exist in our universe without rendering the whole universe unintelligible.

Interpretations of Quantum Physics
I am no expert on the history of quantum mechanics, but my sense is that quantum inventions such as the Schrödinger Equation were constructed in a holistic or organic fashion. Quantum pioneers looked at the strange results from quantum systems, and built a framework for predicting experimental results while at the same time ensuring that the boundary conditions matched classical physics. Quantum mechanics was not derived from any deep principle, but was thrown together ad hoc.

Now, acausality at quantum scales has made many physicists uncomfortable over the years (Einstein included), but we can wash away our discomfort with the knowledge that our funky trip through the quantum looking glass ends when we make a macroscopic measurement. For example, creepy faster than light effects like the EPR experiment turn out to be mere parlor tricks that don't result in non-local effects in measured systems. In other words, we can put the bizarre nature of quantum physics out of our minds while we go an compute something we will actually see. As Paul Dirac once said, "Shut up and calculate!"

This is not to say that we don't try to interpret philosophically what quantum physics actually means. Over the last century, there have been many attempts to reconcile quantum mechanics with intuition. These interpretations aren't physical theories, and they generally make no experimental predictions. They're just ways to try and make intuitive sense out of the mathematics. The interesting point about these interpretations is that they seek to find a picture of the world in which causality and consistency are either restored or irrelevant. Let's look at the two poster children for this tendency.
  • In the Many Worlds Interpretation, every quantum event that can happen does happen, but the universe replicates itself into multiple, otherwise-identical universes. For some theorists, having an almost countless number of universes come into existence every second is a small price to pay for causality and consistency.
  • In the Bohm Interpretation, the universe is actually causal and consistent underneath, but limitations of the measurement process result in apparent quantum behavior. The tradeoff here is that we have to accept non-local (faster than light) effects that render the classical nature of the universe invisible to us.
Though there is no consensus on a best interpretation, there's a definite tendency to either make quantum mechanics causal and consistent, or else brush the problem under the rug. I don't want to disparage the rug brushing, as it really is quite pointless to assert propositions that will never have any experiential test.

Nonetheless, my perception of this issue has changed in the last few days. Quantum mechanics is a consistent formalism, but it can be seen as modeling a world that is acausal and inconsistent at a quantum level. In broad terms, quantum mechanics explains how to have a world be acausal and illogical at one level while preserving causality and logical consistency at classical scales. In short, it may be time to embrace acausality and logical inconsistency.

For economy, I want to refer to the combination of acausality and logical inconsistency using a single term. The most natural terms to choose are "anarchy" and "chaos." Chaos is a bit confusing because this chaos isn't the same as physical chaos. However, if I use the term anarchy, I will be accused of endorsing political anarchy (by the same idiots who think evolutionary biology endorses social Darwinism). I'll go with chaos.

Two Ideas
What we have is a convergence of two ideas. First, the there is the philosophical possibility that the world is consistent and causal only at classical scales, but chaotic at some deeper level. Second, there is the fact that quantum mechanics as a formalism shows us a way to account for small scale acausality and logical contradiction while maintaining compatibility with classical physics.

The interesting question is whether partial acausality and partial consistency actually predict quantum mechanics. Should the pioneers of quantum theory (and 19th century scientists and philosophers) have been able to derive quantum mechanics from classical physics and philosophical first principles? They might not have known what systems would exhibit quantum effects, nor at what energies the effects would appear, but they might have suspected that quantum systems would exist.

I want to note the non-obvious nature of this connection, if it exists. To begin with, the connection is non-obvious for cultural reasons. For physicists, causality and logical consistency are taken for granted. Using acausality and inconsistency to good advantage doesn't come naturally.

It's also non-obvious mathematically because quantum mechanics seems to give us more than just a way to deal with statistically random effects. Quantum mechanics makes uniquely strange predictions about energy levels and interference patterns. If electrons behave acausally, why should that lead to spaced atomic energy levels instead of a continuum? Why should fundamental logical inconsistency lead to interference patterns in electron beams?

Modeling Partial Acausality and Inconsistency
Partial acausality means that, given prior state, not all paths of the system are determined. Effectively, of all possible paths that can be taken by a system, a random one is actually taken. Therefore, a partially acausal physics can only speak of the probability that a particular path is taken.

Partial inconsistency means that, where there is acausality, multiple mutually exclusive and contradictory paths are taken simultaneously. Classical measurement of the final state will reveal a unique end point of the system, but cannot meaningfully speak of which path the system took to get there.

A mathematical representation of such a system will involve orthogonal state vectors representing mutually exclusive paths the system can take to a particular endpoint. These vectors must be combined using some sort of scalar product so as to produce a scalar probability density. This leads us to an Inner Product Space, or something similar. Such spaces incorporate the possibility of interference between different paths the system might take.

This mathematical structure resembles the Feynman path integral approach to quantum mechanics. Not only does it lead to quantum interference, but to discrete energy levels in bound states.

Still, does partial causality and consistency predict quantum mechanics?

Well, quantum mechanics is normally second degree in the state vectors. That is, the inner product is normally the simplest possible inner product, the scalar product of two vectors. In principle, there might be all sorts of inner products we could define involving, say, determinants of tensor products. Some such generalizations of quantum mechanics have been explored, but only as toy models (as far as I know).

I suppose the key point is that partial acausality and partial inconsistency do generally predict quantum effects such as interfering realities represented by interfering wavefunctions. That is, to avoid quantum effects, one has to fine-tune a chaotic theory. In contrast, a classical theory must be somewhat tuned in order to get quantum effects. Of course, this analysis gets nowhere near a probability assessment for chaos. Science is open-ended, so the task of "integrating over all possible theories" is almost inconceivable.

When I started writing this post, I had hoped to obtain a more startling result. I had hoped to show that our actual quantum theory is necessitated by chaos (and the constraints of classical physics). However, in light of my recent thinking on metatheories, I think that chaos is better regarded as a metatheory than as a scientific theory.

I am left with further confirmation that an invisible cause is indistinguishable from a non-existent one.

I am also left to ponder a new interpretation of quantum mechanics that embraces acausality and inconsistency.

Junk DNA

ID proponents claim that ID predicts that so-called Junk DNA will turn out to have some useful function. Not being a biologist, I found it reasonable to assume that a lot of (but not all) junk DNA would indeed have some utility. However, this was just a naive assumption on my part. Andrea Bottaro at Panda's Thumb explains that there really is a lot of apparently useless junk in human DNA. It appears that I may have overestimated the utility of junk DNA. Not that it matters to the argument. ID does not predict that junk DNA will be useful. Not unless you make some specific assumptions about the designer, and ID proponents hate to say anything at all about the designer.

Sunday, August 06, 2006

Metatheories

Suppose we have a theory, T, that predicts our current observations. T has some property, P, that might also be possessed by alternative theories. Can we say that P is inferred by our observations?

Not necessarily. For P to be scientifically inferred from observation, we would have to be assured that P is scientifically testable. That is, we should be able to design an experiment that tests P independent of theoretic context because P itself predicts the experiment's result. If we cannot do this, then P may simply be a notational artifact. Rather than being a property of the observed world, P would be nothing but an artifact of how we describe it.

This is a problem that applies to both evolution and intelligent design (ID). Evolution is a category of theories that explains the evolution of living systems from physical principles. There are many theories, some of them mutually exclusive and competitive. What we can say is that predictive evolutionary theories have been confirmed by experiment.

ID is also a metatheory. Any scientific theory that accounts for features of living systems as the results of design and manufacturing by an intelligent agent would belong to the ID metatheory. To date, no scientific theories of ID have even been proposed, let alone confirmed by experiment.

The subject of metatheories will be relevant to my next post.

The Arrows of Inference and Causality

Sorry for the dearth of recent posts. I've been working on a big one, and it's been "almost done" for more than a week now.

In the meantime, my big post has forced me to consider another concept.

Question: Does our understanding of triangles come from the axioms of geometry, or is it the other way around?

Answer: It depends on the meaning of the expression "come from."

The axioms of geometry were not invented before we knew anything about geometry. Our observation of geometric figures led us to the understanding that the axioms of geometry predicted the theorems we already knew.

It works the same way in physics as it does in mathematics. Our knowledge of experimental regularities is used to infer the axioms of physical theories.

Thus, there is an arrow of inference that reasons from a collection of phenomena to a handful of axioms that predict those same phenomena.

This implies that there is an arrow pointing in the reverse direction, an arrow of causation. For the axioms to predict the phenomena, the axioms must define laws of causation that do the predicting. We follow the arrow of inference with induction, and follow the arrow of causality with deduction.

So, when we say "A comes from B" we need to be clear about the arrow to which "come from" refers.