The Irreducible Remainder of Improper Reduction

If you reduce all x to nothing but y, then what you have left at the end of the process is no x at all: nothing to explain. To say that x is nothing but y is to say that there is really no such thing as x in the first place.

Eliminative reductionists generally prefer to overlook this difficulty. They try to explain explananda exhaustively as nothing but collisions of dead items, yet retain their reference to the explananda. They won’t take the last entailed step of asserting that there is in the first place simply no such thing as the explananda.

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Nature Never Sucks

When my kids were taking high school biology, their (brilliant) teacher’s jocular mantra was, “Nature never sucks.” It meant, first, that Nature is wonderful, beautiful, and so forth – worthy of admiration, study, awe. Second, it was a nod and a prod in the direction of Ockham’s Razor, urging his pupils to adduce no more factors of natural phenomena than are absolutely necessary. But third, and more salient to his honest reductive Ockhamist pedagogical purposes, and most of all, it meant that Nature is not teleological: it neither seeks nor is pulled toward goal states, but rather pushes itself toward certain equilibria, not intentionally, but on the contrary chaotically. The idea is that these equilibria are not themselves somehow attractive, but rather are simply the most stable way that things can be arranged, so that when things happen to blunder into those stable configurations completely by accident, they then tend to stay there until something disturbs them. Things are never falling into place, but are rather only, always, merely falling.

The notion is not new. It goes back to the first Greek atomists, Lucretius and Democritus.

It is Dawkins’ notion that what perdures is only what has not yet failed to perdure: “there are lots more ways to fall apart than to hang together.” It’s true, but as tautological is uninformative.

There are other problems with it.

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Sex in Church

In a wide-ranging and penetrating essay contra the ordination of women, Peter Leithart argues that because sex is inerasably graven in the logos of man, ipso facto is it graven in the nature of whatever man does, from liturgy to marriage; that worship, being the quintessentially human activity, in which we can reach the sublimity of all our special capacities (for thought, word, deed; for art, music, argument, prayer; and so forth), is the font and archetype of all subsidiary activities, to which it lends them form; so that when we upend or confuse the sexes in church, we must perforce do likewise in marriage, and everywhere else.

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The Science of Science

Theology encompasses metaphysics the way that the necessary concrete actuality of God encompasses and outpasses the mere abstract intellectual conception of God as that than which nothing greater may be conceived. Anselm’s Argument is where abstract metaphysical ratiocination entails the Act of a Being whose actuality makes metaphysics possible, ergo necessary.

Only if God exists actually can metaphysics be possible conceptually. Or, ergo, mathematics, or its application in physics.

The Moderns who insist that metaphysics is dead or impossible or obsolescent all argue from the basis of a metaphysical presupposition – a prejudice, and no more – that there is no God. If there is no God, then they are right. But if there is no God, nor therefore any metaphysics, then neither is there anything else, either; including materialist metaphysics, that boasts to abjure metaphysics altogether.

You can’t get any of the beings that are less than the most real being if you don’t first have the most real being. Take a set of beings; one of them is most real, the others all relatively less real. If the most real being is not real at all, then all the less real beings are even less real than “not real at all.” And the only way to be less real than what is not real at all, is to be in the first place inconceivable.

Theology, then, is the science of all science, the science in virtue of which any other science can know anything. If God is not actual, nothing else can be; if God is not intelligible, and knowable (at least in part, and in principle), then nor can anything else be either knowable or intelligible.

Wonder suffuses the practice of all science – drudgery, too, of course, but the drudgery is motivated by the wonder, which is the engine at the base of the whole project. Appropriately, it is at the far sublime edge of theology that science reaches the limit and culmination of wonder: worship.

The Proper Terminus of Any Science

Explanations, and the understandings they mediate, must all terminate (at least in principle) upon *some singularity or other* if they are to hang together – if they are to succeed as explanations by satisfying our urge to understand. This is as true for explanations of singular phenomena as it is for explanations of regularities. Science then, of any sort, has no alternative but to adduce some singularity or other as the original fact or truth at the basis of all others. The terminus ad quem of the scientific project must be an account of the terminus a quo of all things: a terminal singularity. This, whether the posited singularity be a historical event such as the Big Bang, or a fundamental equation that can work as a Theory of Everything, or what have you.

But only one sort of terminal singularity can ultimately succeed – not at completing inquiry, for (per Gödel) that completion is not possible to finite beings, but rather at satisfying them that things cohere intelligibly. Only one sort of terminal singularity can set the scientist’s mind finally and fully at ease.

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What is science?

The following are reflections based on my years teaching introductory astronomy for non-science majors.  Few of my students take the class out of personal interest.  It fulfills a natural sciences general education requirement and sounds less scary than geology or chemistry.  Thus, the ultimate purpose of the class is to expose students to the scientific enterprise, so I put a lot of thought into the impression of science I’m giving them.  When I speak of “science” below, I will be using the word in its modern rather than its classical sense, according to which biology and sociology are sciences while philosophy and history are not.

Survey course textbooks in the branches of science usually include some discussion of the general nature of science.  Anxious to emphasize science’s quality as a process rather than a fixed body of knowledge, they often hold up the “scientific method” as the essence of science.  This, however, has disadvantages.  For one, actual science rarely follows the model given in these books.  More importantly, the scientific method is itself given no real justification, and the limits of its usefulness are left unclear.  What makes this problem pressing is that students may believe, and textbooks may even state, that the scientific method involves assumptions about the world and excludes a priori certain kinds of explanation, as for instance when scientific explanations are contrasted with assertions of miraculous or animistic spiritual causality.  The impression is given that science is at least methodologically naturalist, that when thinking scientifically we must pretend to be atheists.  This, I emphasize, is not a problem for religion; it’s a problem for science.  To tie oneself from the beginning to very questionable metaphysical assumptions threatens the credibility of the whole enterprise.

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No Way Out But In

A proposition that cannot be carried into practice at all cannot be true. An act that cannot be implemented in actuality must be somehow incoherent: self-refuting – for example, you can’t mean it when you say, “this statement is a lie” – or a contradiction in terms either simple or implicit – e.g., there’s just no way to implement “2 + 3 = 4,” for it is a contradiction in terms. That such propositions can’t work logically means that they can’t work in practice.

But a proposition that can be carried into practice might be true. E.g., “It is best not to defer gratification.”

When we sin, we assert one or more of a number of propositions:

  1. God does not exist.
  2. God is not omniscient.
  3. God is amoral.
  4. The world is amoral.
  5. God does not care whether I behave well or not, nor does the world.
  6. Whether or not God cares about my behavior does not matter (to me, at least).

And so forth. When we misbehave, we effectually attest to our belief in at least one of these propositions, or else in one of a number of other propositions like them. And to attest belief in propositions is to testify to their truth, and so is to urge their truth: behavior is an effectual proposal for how it might be well to behave.

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Value is Conserved

I have long been intrigued by the conservation laws. Conservation of energy, momentum, charge, and so forth all seem to point to a more basic conservation, of which they are all instances. I was therefore interested to read in Bill Dembski’s latest book, Being as Communion: A Metaphysics of Information, his discussion of Conservation of Information in search routines. He has apparently demonstrated (I have not read the demonstrations, which appear in the technical literature he cites in the book) that increasing the likelihood of a successful search – i.e., a search that has an object and finds it – over and above the walk of a blind drunkard who is not looking for anything in particular may be accomplished only through additional investment of information in the search routine. This can be done in a number of ways: by a more comprehensive specification of the configuration of the object, or by adding a feedback circuit to the algorithm, or by adding strange attractors to the configuration space (so that the environment of the search itself embodies more information) or some other similar measure. But any such improvements of search efficiency – of the likelihood of success – come at a cost of their own: it takes information to inform the search. At best, then, informed search will cost just as much as blind search, and cannot cost less. But then also if the information added to the routine is not essentially perfect – free of noise and error – then the addition will cost more information than it saves: the overall cost of the search, plus the cost of the search for the improvements to that search, will exceed the cost of random wandering about the configuration space.

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Nominalism contra Everything

The modern crisis all goes back to nominalism. The modern muddlings of clear definitions, confusions of really and essentially different things, and denials of essences or definitions in the first place are all outworkings of the nominalist turn. Once suppose that categories are merely conventional, that universals are merely nominal, that life is never simply black or white, but rather only shades of grey, and you find yourself on a steep and slippery slope to chaos.

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An Eye for an Eye Makes the Whole World Cooperative

An eye for an eye makes the whole world circumspect. But, also, an eye for an eye makes the whole world cooperative, as Robert Axelrod showed with his study of tit for tat and competing strategies using iterated rounds of contests among genetic algorithms (described in his book The Evolution of Cooperation). Tit for tat beat all the alternative strategies, again and again; and as rounds of the contest were iterated, with winning strategies favored by the reproductive mechanism of the iteration, it more and more perfused the population of competing algorithms. As tit for tat increased in frequency, so did the total value generated by all competitors in each round: fewer and fewer defections occurred, and responses to defections were more and more often optimal.

That tit for tat wins the evolutionary game does not mean that its superiority is merely adventitious, an artifact of this or that sequence of random events that might have been quite different, and so generated quite a different sort of winner. On the contrary: provided the game goes on long enough, tit for tat wins every time, sooner or later, and no matter how the sequence of outcomes varies. The utile superiority of tit for tat is a truth of game theory, so that like any other mathematical truth it is from before any and all worlds, and holds true in every world. The metaphysical superiority of tit for tat, then, is the source and reason of its practical evolutionary success, and not vice versa (this is true of all perdurant evolutionary success). Tit for tat is the optimal strategy in evolutionary practice because it is the best in metaphysical fact. As metaphysically best it is the most moral policy of all (these are two ways to say the same thing).

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