B is for ... Brevity.

Brevity is the soul of wit ~ William Shakespeare (allegedly...)

Erin, you can stop reading now. Just kidding.

Out, out, brief candle! ~ also William Shakespeare (allegedly...)

The author of the plays commonly ascribed to one William Shakespeare often reflected on Man's mortality. "All the world is but a stage," opines Jaques in As You Like It, "and all the men and women merely players; they have their exits and their entrances." It is, perhaps, telling that the exits are mentioned first; although Polonius finds something admirable in brevity, Macbeth's lament is much closer to "Shakespeare"'s message.

Dust thou art, and into dust thou shalt return ~ Genesis 3:19

Yet there may be something comforting in brevity, if we focus more on our time on that stage than the waiting in the wings afterwards - and, perhaps, something more still if we reflect that beyond one stage may lie another. The action in Tom Stoppard's play Rosencrantz and Guildenstern are Dead - a landmark in the theater of the absurd - takes place mostly in the wings of "Shakespeare"'s Hamlet; might we also take wings when our lines our spoken and the curtain falls?

* * *

A story I love, which comes originally from Persian folklore - although the version I heard was a Hebrew adaptation - concerns a very wealthy and powerful king.

This king had virtually everything he could possibly want, and it amused him to demand yet more of his loyal subjects. Upon a time, he summoned his vizier and said to him, "I have been thinking long and hard about what more I can ask of you, and I have realized there is still one thing I do not have. Legend tells of a ring of power, such that any happy man who wears it becomes sad, and any sad man who wears it becomes happy. I would own this ring." And the vizier, who was quick on the uptake, knew better than to disappoint his king; so he assured him in unctuous tones that the ring would be obtained, and departed, fretting and gnawing his beard at the impossibility of the task.

The vizier was no slouch in the wisdom stakes himself, and he consulted with all the wise men his wisdom could reveal; but none of them knew the location of this ring. He journeyed far and wide, and his beard grew longer, for he could not have it trimmed to his liking, and yet more sparse, for he rent it daily in agitation. At length, he despaired and determined he must return to the king's palace and admit his failure, and he halted for a night's meager rest at a tavern. While there, he fell into conversation, as one does at a low ebb with some strong drink inside one, with a stranger: a man who turned out to be a jeweler himself.

"... And I have searched for that accursed ring this past year, and tomorrow I shall return empty-handed, and the king shall have me torn apart by wild tapirs!" For this was the king's custom. Much to the vizier's surprise, as he concluded his tale of woe, his drinking companion laughed brightly and said the most astonishing words in the world: "I have the ring you seek." And he produced it, quite as if it were only a very ordinary ring of the sort jewellers carry with them everywhere they go.

The vizier accepted it in shaking hands, and observed that it was inscribed with these words: Gam zeh ya'avor, which is to say, This too shall pass. And as he read those words, it was as if all the year's long, despairing drudgery fell away; he laughed too, and he and the jeweller drank each other's health until the dawn.

Next day, the vizier, beard trimmed to even his satisfaction and a jaunty spring in his step, presented himself to the king. "Twelve months have passed since you dared enter my halls," intoned the king wrathfully. "I had given you up for a miserable servant." He snapped his fingers imperiously. "Bring forth the tapirs!"

But even this dire threat could not blight the vizier's mood. "Behold!" he cried in a voice that carried throughout the king's great hall. "I have found the ring you desired!" And he hurried forth and laid it in the king's hand.

The king examined it closely. His lips were observed to move as he deciphered the inscription. And he looked around him, at the sumptuous finery of his hall, at the gilded tableware, at the ornate draperies and peerless rugs, at the mighty edifice of his palace and the hushed throng of his subjects. And he looked at the ring - this too shall pass - and his countenance became grey with sorrow...

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...