Thursday, January 15, 2009

103rd Skeptics Circle

The 103rd Skeptic's Circle is up at Bug Girl's Blog, along with some of the cutest pictures of insects. Enjoy!
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Monday, January 12, 2009

A Martin Cothran trilogy

Martin Cothran, spokesman for the Discovery Institute and Focus on the Family (at least, so I have heard), presented a trio of posts that I felt a need to correct over the past couple of weeks.

The first contains a very curious understanding of the Constitution.

Now whatever your view of Blagojevich or Burris, there is one thing that we know without a doubt: the Constitution leaves it up to the states. Reid has no business telling Illinois what to do. Blagojevich is still governor (even though most of the rest of us wish he weren't), and has perfect right to make the appointment.

Whether Burris serves as Senator from Illinois is a matter for the people of Illinois to decide, not the U. S. Senate.

However, the people who actually wrote the Constitution seem to have a different opinion on the matter. Quoting from Article 1, Section 5:

Each House shall be the Judge of the Elections, Returns and Qualifications of its own Members, and a Majority of each shall constitute a Quorum to do Business; but a smaller number may adjourn from day to day, and may be authorized to compel the Attendance of absent Members, in such Manner, and under such Penalties as each House may provide.

Each House may determine the Rules of its Proceedings, punish its Members for disorderly Behavior, and, with the Concurrence of two-thirds, expel a Member.

So, there is certainly an argument that the Senate does indeed reserve the right to decide if a particular appointee has been too tainted by virtue of the person doing the appointing, and is therefore unqualified. The Senate is not able to decide who gets nominated for membership, but it does seem to have the right to turn people away. Strike one for Cothran.

In the second post, we have a vague attempt to define a word that means nothing to people who accept the Theory of Evolution, and something different to each different type of creationist, "Darwinism" (typically, it means whatever parts of the Theory of Evolution the creationist in question does not accept). Cothran's take on the word:

As a prelude to some more posts on the issue of Intelligent Design, I thought I might address a question that has come up on this blog several times, which I have answered in bits and pieces, but never, I think, directly. It is the question of why I use the term 'Darwinism' rather than using the term many Darwinists prefer that I use: 'evolution.'

I use the term 'Darwinism' simply because it is more accurate. By Darwinism I mean the belief, not simply that the complex organic world as we know it evolved from simpler life forms (the definition of 'evolution'), but that that process can sufficiently be explained by completely natural processes--the two reigning explanations, as I understand it, being natural selection and modern genetic theory.

Darwinists themselves seem to use this term when they think the rest of us aren't looking, but they don't seem to want the term to be used publicly because it has acquired a somewhat pejorative sense. To that, all I can say is that that's not my problem.

The distinction is important because there are some of us who don't have any particular problem with evolution, but have their doubts about Darwinism.

Cothran manages to make several mischaracterizations in a very short post. The first is that there is no such thing as a Darwinist, because no one (that I have read, at least) treats the writings of Darwin as being the the final or ultimate authority on biological development and history. Darwin was the not the first to note the history of biological development, and certainly not the first to note that selection can cause morphological change even within a person's lifetime. He took these ideas and put them together, but his works, like many works at the beginning of a scientific revolution, contain their fair share of errors, incorrect hypotheses, and discarded notions. Scientists don't believe anything because Darwin wrote it, they believe what the evidence of the 120+ years since Darwin has confirmed.

Second, knowledge that the natural process involved in evolution are sufficient to have fueled the world's biodiversity is not a belief, it is a fact. We know from decades of experience that the mechanisms of evolution are capable of doing astounding things. Of course, a careless person might confuse being sufficient with being actual, a problem that Cothran seems to have (as will be shown below). If I see a pile of rocks at the face of a cliff, it is a sufficient explanation that they fell of the cliff face due to erosion. This does not rule out the possibility of a person rearranging the rocks after they fell, causing them to fall, etc. It is sufficient, not conclusive.

Third is the common Creationist tactic of taking the 17+ mechanisms of evolution and ignoring at least 11 of them, referring only to natural selection and modern genetic theory

Fourth, the term Darwinism only comes up when discussing ID/Creationism. The reason it has any pejorative sense at all is because it was created to be a pejorative term.

It was nice of Cothran to confirm for us, in the last paragraph, that "Darwinism" is defined by what is rejected. Strike two for Cothran.

Finally, I will quote from the third piece of dreck put out in a four-day span.

This has been said before in different ways, but, put very simply, if you say that the assertion that the universe as a whole or any particular part of it are intelligently designed is by necessity a non-scientific assertion, then have you not also committed yourself to saying that the opposite assertion--that the world or the things in it are not intelligently designed--is equally non-scientific?

If so, then what are the ramifications for Darwinism, since Darwinism necessarily involves the denial of the assertion of Intelligent Design?

Cothran's rhetorical question in the first paragraph is absolutely correct: it is as equally non-scientific to make a positive denial of design (as opposed to an affirmation of the lack of evidence for design) as it is to make an affirmation of design. Going back to my pile of rocks under the cliff: to claim it is a design, all a person has to do is move one rock by any measurable amount, he has then a proper claim to design in the final result. If I come by six hours later, how am I supposed to make a positive claim that no one has designed the rock positions? They could have been designed on one side of the road,not designed on the other side, and there is no way for me to distinguish the two.

Cothran's second paragraph reveals the confusion to which I referred earlier. His very own definition of "Darwinism"refers to the notion that natural mechanisms are are sufficient, but again there is a difference between sufficiency and conclusiveness. The denial of ID has absolutely no ramifications at all for Darwinism under the very definition he provides!

And if so, then what does that say, not only about the anti-Intelligent Design proclamations of some in the scientific community, but about the scientific status of Darwinism insofar as it is a denial of the Intelligent Design assertion?

In his haste, Cothran seems to have forgotten to mention which of the many ID assertions that he's referring to. However, there is a blanket answer: any particular ID assertion that says merely that the mechanisms of the Theory of Evolution are insufficient to explain a particular biological phenomenon has made a scientific statement. It just happens to be a false one. Strike three for Cothran, he is again out of touch with reality.
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Sunday, January 4, 2009

The reality of sets

I checked the blog of the Maverick Philosopher, aka Dr. William Vallicella, over the course of the last week, and once again find he has provided material to which I would respond. In fact, in writing two posts about the existence of sets, he has touched on a subject near to my heart. In fact, I discuss this very topic, in a much less formal manner, in every single Geometry class. There is a very real distinction between a formal system, a construct of the mind that we use to generalize reality and draw deductive conclusions, and the underlying reality itself. Mathematics is first and foremost a formal system. I think Vallicella provides an excellent example of how the eagerness that believers have to create these non-materials things of real existence spills over into assigning reality to all sorts of fanciful concoctions, much as we see supporters of one type of woo are often more likely to pickup or support other sorts of woo. Vallicella's comments are italicized.

Set theory can be done either naively or axiomatically. In the standard axiomatic approach to the subject, that of Zermelo-Fraenkel, the existence of the null set is posited in a special axiom.

Two errors in two sentences. One of the primary reasons that set theory was put into an axiomatic format is that, when doing set theory naively, you come across both logical and semantic contradictions that are avoided by the axiomatic process. Also, while Zermelo's original approach had a special axiom for the empty, the standard approach to the Zermelo-Fraenkel axiom schema contains no such axiom. Rather, the empty set is the derived result of the axiom schema of replacement, which in the short form says that functions defined on classes will map sets into sets.

Intuitively, the existence of a set depends on the existence of its members. The set consisting of me and my cat cannot exist unless both man and cat exist: if either of us should cease to exist, the set would cease to exist. It exists because we exist, not vice versa. (This is of course not a causal use of 'because.') In the case of the null set, however, there is nothing on which the null set can depend for its existence.

The truth is that sets don't exist, at all. The set of Vallicella and his cat is a mental shortcut that we use, but it has no reality unto itself. When I talk about the red books on my bookshelf, they are a set of books for only as long as any person considers them to be a set of books. There is no ontological status the property of their being a collection. After all, how is the nature of the books changed if I say that I have carefully designed them to be a set, or if I say they are just a bunch of book I have in that place? I can tell Person A the one and Person B the other, they can't compare notes, examine the books, and thereby discern which account is more truthful. So, it seems the nature of being a set has no reality behind it. In particular, why should the empty set have any more reality?

No working mathematician is likely to lose any sleep over this, however. He will tell us that the null set is convenient, computationally useful and ought to be judged by its practical fruits.

Working mathematicians generally seem aware that almost everything they do is based upon assumption that are help arbitrarily, because we have found them useful. The very grammar of mathematics, predicate logic, is based upon the highly arbitrary notion notion that every statement is true or false. The arbitrariness of this decision is shown by the success of the intuitionists and the various alternate logical evaluation schemata in creating perfectly functional mathematical systems. They know that sets exists only to the degree that we think of the collection of various objects as a set, and so one more useful, non-real entity is not going to cause consternation.

From the first post:

So on the one hand, the null set is useful and well-motivated from within the circle of set-theoretical ideas, but on the other hand, it appears philosophically to be a creature of darkness. Is there a way to get rid of the darkness?

By my lights, the philosopher aims at a degree and a type of clarity that the mathematician qua mathematician -- not to mention other nonphilosophers -- does not care about. Of course, I am not saying that he should care about it. He is within his rights in simply dismissing concerns like the one raised in this post as irrelevant to his concerns or unimportant given his goals and priorities. What is intolerable, though, is the mathematician who gives a lousy philosophical answer to a philosophical question, especially if he is only half-aware that it is a philosophical question.

Of course, philosophy itself is also a formal system. When the mathematician chooses to ignore the needs and desires of one formal system in favor of another, they do so 2with the understanding that all formal systems are arbitrarily chosen based upon their perceived usefulness.

He is then like the neuroscientist who, refusing to stick to his subject-matter, says silly things about mind and consciousness, all the while oblivious to the philosophical problems to which he gives silly answers.

Naturally, we see one sort of woo dissolving into another.

From the second post:

A set in the mathematical (as opposed to commonsense) sense is a single item 'over and above' its members. If the six shoes in my closet form a mathematical set, and it is not obvious that they do, then that set is a one-over-many: it is one single item despite its having six distinct members each of which is distinct from the set, and all of which, taken collectively, are distinct from the set.

Or, since the very notion of set is in and of itself a mental construct, and not a reality, it is certainly different from the shoes themselves, which presumably are real enough that Vallicella puts them on his feet once in a while.

Vallicella goes on for quite a while being very clear that sets are created as a product of thinking. Yet, somehow he does not seem to understand this means they are just as unreal as Romeo or a modern-day Casanova. Just as we can use the conventions and shortcuts of our understanding of Shakespeare's play or a historical personage to create mental constructs of what it means to be Romeo of a moder-day Casanova, we use conventions and shortcuts to understand what a set of size six means, and assign contents to sets at need.

Your objection does not show that sets cannot be mental constructions; it shows that sets cannot be mental constructions of a finite mind. If there were an infinite, necessarily existent mind, then sets could be the constructs of such a mind. If you maintain that there is no such mind, then you should also maintain that there are no sets. If, however, you hold that there are mathematical sets, and that nothing contradictory can exist, then you should hold that they are the mental constructs of an infinite mind. If you deny that there is an infinite mind, but hold that there are sets, then you owe us an alternative explanation of how a set can be both one and many.

Left unaddressed is the reason we should think sets exist at all.
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