Showing posts with label Aristotle. Show all posts
Showing posts with label Aristotle. Show all posts

Friday, April 15, 2011

M is for... Mososaur

Loyal readers who are, like Funes, memorioso, may remember I said something in an earlier blog about returning to discussion of cryptids.

Not yet.

The mososaurs, for any non-paleontologists out there, were large marine lizards - probably snakes are their closest living relatives - that became the dominant marine predator in the late Cretaceous Period. Almost certainly, coelacanths would have formed part of its diet: pretty much everything else did. The mososaurs, as a family, were tremendously large: the smallest species identified grew to be over 3 meters in length, while the largest exceeded 15 meters. Their limbs adapted into flippers, mososaurs had some characteristics in common with fish, and some with crocodiles. There is an interesting story to be traced in the identification of mososaur species, involving one of paleontology's many storied rivalries, which would make a fantastic subject for a blog.

Not yet.

Mososaurs make an interesting subject for paleontological study, for a variety of reasons; it is not surprising that Marcus Ross, a graduate student at the University of Rhode Island, selected them as the subject for his doctoral thesis. As the holder of a Ph.D., it is not surprising that he is recognized as an authority on the evolution, diversity, and extinction of mososaurs some 60 million years ago. You may be suspecting at this point that there is some relatively surprising factoid lying in wait, and if so your suspicion is correct. The surprising aspect of Dr. Ross' career as a paleontologist is that he is also a Young Earth Creationist. As a function of his religious beliefs, Marcus Ross sincerely believes that the Earth, and indeed the entire Universe, is only a few thousand years old. As a function of his professional status, he is an expert on a species that existed millennia before that.

This apparent dichotomy - I say apparent, because that apparition arises only from the assumption of an excluded middle - attracted the attention of New York Times journalist Cornelia Dean, who published an article on Dr. Ross in 2007. As Ross explains it, he is simply "separating the paradigms" between the scientific and religious perspectives of the world. He has been accused of intellectual dishonesty; it has been suggested his "impeccable" doctoral dissertation should have been rejected, since he has used it to argue for creationism as a plausible explanation for the Cambrian Explosion, in defiance of conventional scientific wisdom. The notion that the Earth could simultaneously be only 6,000 years old, and yet host massive predators 60,000,000 years old, is unscientific; in fact, the assumptions supporting that notion are beyond the capacity of science to examine. They have to do with philosophical conceptions of Time; while the question "how long does a second take to pass" may seem alternatively pataphysical and asinine, its implications make it, for this chronicler at least, one meriting consideration.

Rejecting the Aristotelian assumptions underpinning materialist-mechanist empiricism opens one up to a vertiginously uncertain universe; Ross identifies a quintessentially American solution, in pragmatically behaving as if one paradigm or another is "true" in the Aristotelian sense, depending on the situation. Other resolutions to this irrealist situation exist...

Friday, April 1, 2011

A is for ... Axiom.

An axiom is a particular kind of sentence, that forms the basis of a logic. Logic describes any method for establishing true conclusions from true premises, and is broadly subdivided into deductive logic, which draws specific conclusions from specific premises, and inductive logic, which draws general conclusions from general premises. The truth of the conclusions in any logic is determined by the soundness and validity of the steps connecting them to the initial premises. The overall logical process by which conclusions are induced or deduced from premises is an argument; ultimately, every logical argument begins with one or more axioms.

The thing that makes an axiom so special is that it can't be proven by any sort of logical argument. You just have to accept an axiom is true, and go from there. For this reason, axioms are generally statements that seem self-evidently true; statements we find it hard to imagine could be false. The logic most people understand and recognize as logic was formalized by the Greek philosopher Aristotle. His logic rests on a small number of axioms that state seemingly uncontrovertible assertions: the Axiom of Identity states that a given A is the same as itself, so A = A; the Law of Excluded Middle, which is actually derived from the identity axiom and so not strictly axiomatic itself, asserts that a given A must either be the same as a given B, or different from it, so A = B or A = ~B (~B means 'not B' in formal logical notation). Most of Western philosophy accepts these axiomatic principles as Aristotle formed them; but it's worth remembering that there is no logical reason that we have to. We can, for example, emulate Oscar Wilde and assert "nothing is itself alone" (it should be clear that this denies the validity of the identity axiom); we can posit that there may be a class of things which can both be and not-be one another simultaneously. It may seem absurd, to modern people conditioned to accept the assumptions - the axioms - of empirical scientific method, but it is entirely valid; even, for some purposes, advantageous.

Axioms are enormously powerful, because when we choose an axiom we are creating a whole potential logic that rests upon that axiom. It is important to distinguish between an axiom, which is unprovable within a logic, and an assumption, which is a statement whose truth is tested by logical analysis. For example, "cats have antlers" doesn't work as an axiom, since we can inductively show that there exists no cat in particular which has antlers, and so conclude that cats in general share this lack. It is a false assumption. "Cats do not have antlers" is not axiomatic, either, although it is so obvious empirically to anybody who understands what cats and antlers are that it can be treated as such under most circumstances. The danger lies in treating what seem to be obviously true assumptions as axioms - this is a good way to close ourselves off from valid alternative hypotheses. Ironically, this sort of confusion is common among adherents of the scientific method - which properly adopts a spirit of open enquiry, continuously challenging its own assumptions.

In common parlance, an argument is a dispute, a difference of opinion; each side has a reason for believing its conclusions to be true, and each side believes the other's conclusions to be false (this can be seen to be a function of Aristotle's Excluded Middle - without that, each side could have an opinion that worked for them, and not invalidate the other's opinion thereby). Some of the most intractable arguments concern situations that resist logical analysis - theology is a fertile ground for these, beginning with the fundamental argument over whether God exists. The atheist position that there is no God is grounded in an empirical worldview, which asserts that everything we observe can be explained without recourse to a God. A rule called Occam's Razor advises us that if we don't need an extra element to account for something, we should properly discard it, so that our explanation is as simple and elegant as possible. This rule, suggesting the simplest possible explanation for a phenomenon is also the best, has disadvantages which may become clear on a little reflection; we can readily conceive of situations that arise from complicated interactions but are explicable by more simple ones, and this is for example one facet of the magician's art. These performers rely on the assumptions people make based on what they observe; they are skilled at manipulating those observations, misdirecting their audience, and producing apparently 'magical' results that are explicable only by recourse to hidden phenomena of the sort Occam disregards. It should be said that the simplest explanation - "it's magic!" - is, from an atheist's perspective, closely similar to the theistic explanation - "God makes it happen." Scientific atheists assert that what we cannot explain with our current level of knowledge about the universe will become explicable as that knowledge increases and we appreciate the greater complexities of time and space. There are reasons to doubt this, and certainly no logical reason why we must accept it, but it is as logically valid a position as its counter from the theistic perspective.

Even among theists, arguments are rife, precisely because the dogma of each religion is beyond the scope of logical refutation. Where logic derives its authority from its axioms, a religion derives its authority from the Divine - belief in its deities is therefore a necessary precursor to acceptance of the religion's claims, although in this religion functions exactly as logic does: for we will only find logical force to an argument if we first accept the axioms that underpin it. Major religions differ in their characterizations of the Divine - some are monotheistic, believing in just one God (for example, the Abrahamic God worshipped by Christians, Jews, and Muslims); others are polytheistic, believing in a whole pantheon of Gods (Norse Pagans, Hindus, and Buddhists are examples). Within a given religion, there may be differences on small points of dogma, which result in schisms or splits. These can be extremely violent. A schism within the Catholic Church of medieval Europe led to the establishment of a rival Papacy in Avignon - these Popes were known as Antipopes because they stood against the temporal authority of the Popes in the Vatican, who were officially the earthly representatives of Christ. Individuals who challenge the dogma of a religion, as Martin Luther did with his 95 Theses, or as Galileo did with his assertion "eppur si muove", can find themselves accused of heresy - under some theocratic jurisdictions, this can be a crime punishable by death. The Albigensian Heresy of the Cathars, knights who founded the first central bank in history, led to the destruction of that immensely powerful order (although several modern secret societies, like the Prieure de Sion, claim descent from them).

It comes down to this: everything any of us believe, no matter what authority we claim for it, is simply a matter of opinion. And we all know what opinions are like - something else that begins with A...