Showing posts with label axiom. Show all posts
Showing posts with label axiom. Show all posts

Thursday, April 7, 2011

F is for ... Freedom.


Freedom - liberty - is a fundamental ideal of the United States, and indeed of most modern democracies. Philosophically, this reflects the considerable influence of the 17th Century English political philosopher John Locke, whose natural law arguments stemmed from the axiomatic assertion that Man in Nature is free. The preamble of the U.S. Constitution explicitly references this “self-evident” truth, and many of us today would accept it readily enough. We know, of course, that people don’t enjoy perfect freedom in the real world; but - and this is important - most of us consider this to be the result of unfair practices: discrimination, oppression, and so forth. Most of us can also readily identify persons whose liberties we feel properly ought to be infringed upon; the concept of social justice spares us the burden of hypocrisy in doing so. Locke and later social contract theorists defined social justice variously, but in each case the function of social justice is to delineate the circumstances under which freedoms can be compromised and the nature of that compromise.

One of the major philosophical divisions regarding the proper limits of the social contract hinges on the definition of liberty. One camp focuses primarily on positive liberty - that is, the “freedom to” perform some action. Another emphasizes negative liberty - the “freedom from” restrictive influences. Both aspects were represented in the famous “Four Freedoms” enunciated by Franklin D. Roosevelt: “freedom of speech, freedom of worship, freedom from fear, freedom from want.” It can be seen that the positive liberties thus identified are far more modest than the negative liberties. The positive freedoms are limited to what people can say and believe, liberties that prove in practice very difficult to infringe upon in any case - easier, perhaps, to criminalize and punish after the fact, although in practice such an approach generally only draws attention to its own inadequacy, as with the fatwa declared against Salman Rushdie for his authorship of The Satanic Verses. By contrast, the negative freedoms outstrip the scope of those freedoms guaranteed U.S. citizens under the Bill of Rights, and purport to promise the supply of every human need - an aim that could fairly be described “ambitious,” and one which led to the drafting of a far more sweeping assertion of rights: the Universal Declaration on Human Rights (UDHR) that was Eleanor Roosevelt’s lasting contribution to global society. Whether the existence of UDHR makes the negative liberties invoked as rights more achievable or reasonable is, perhaps, a valid question. Regardless, the emphasis on negative liberty is a hallmark of modern liberal political philosophy - the focus on positive liberty, by contrast, is the cornerstone of libertarianism and associated with the minarchist tendencies of the political Right.

My own approach to the question is along libertarian lines, and takes a lead from Locke’s own emphasis on property rights - the Preamble to the U.S. Constitution slightly bowdlerizes Locke’s original triad of “life, liberty, and property,” perhaps unsurprisingly given the sensitivity of the slavery issue as evidenced by the abhorrent “three-fifths compromise.” I’m also much influenced, here as elsewhere, by the pragmaticism of Charles Peirce: in the context of personal freedom, this manifests as a requirement that any freedom I claim be a freedom I can actually meaningfully enjoy in the context of my everyday life. Along these lines, I define freedom to be, specifically, the freedom to dispose of property according to my own will. The implication of free will is another nod to Peirce: if everything I do is predetermined, then I have no freedom in practice; I can only do what I am ordained to do, and whatever property I have is an accident and no more mine than I am mine own. I find this a miserable as well as an unnecessary philosophy, and have besides several reasons for believing that I, as a rational actor, make praxeological choices with my life.

Freedom should not be something that is given to me by somebody else: if I am free on sufferance only, then I am not free at all. Therefore, freedom must start within me - within my own willed actions. The first thing I am able to influence by my own will is my own body: thus, the beginning of property is the physical self, and all other property is obtained and secured through that self. Everybody who has a physical self that they can subject to their will is thereby made free to that extent; insofar as there are variations in the amount and security of property in each individual’s possession, there are also degrees of freedom individuals can enjoy. The person who controls most property - by which I mean, a person whose willed interactions with the world influence the most material entities in that world - is, by this measure, the most free. I’ll explore the implications of that argument, particularly in the context of the conflicting views of property expressed by Pierre-Joseph Proudhon and Karl Marx, in a future blog.

This conception of positive liberty sets the stage for a vision of society compatible with the one laid out by Thomas Hobbes in Leviathan - bella omnium contra omnes, a “war of all against all,” in which each individual strives against his fellows for a greater share of finite resources in the pursuit of greater personal liberty. Hobbes’ gloomier perspective on the natural state of Man, compared with that of Locke, provides a different rationale for the social contract: rather than being a natural expression of freedoms that Man enjoys with or without that contract, for Hobbes the social contract is an essential tool for protecting the individual from his society. In this way, it can be seen how unchecked positive liberty creates a need for negative liberty; there is, in fact, a dynamic between the two. At one extreme, positive liberty is unfettered by any structural constraint: de facto anarchy obtains, and the strongest thrive - a scenario Darwinians should find familiar. At the other extreme, the totalitarian state protects the citizen so thoroughly from the expression of their neighbor’s willed desire to curtail her freedom that she is left with no freedom to curtail. Neither extreme is stable - the powerful establish order out of anarchy, and the totalitarian state destroys its own legitimacy as it disempowers its citizenry. Each state of affairs - each thesis - creates an opposing condition - an antithesis. The tension between positive and negative liberty thus constitutes a Hegelian dialectic, in which the embrace of one idea cultivates a contrarian embrace of the other.

Equilibria can be envisaged, and indeed examples of such can be found in the real world, wherein either positive or negative liberty has the ascendancy. It is in the nature of a Hegelian dialectic that no equilibrium remains in perpetuity; the balance is constantly, if gradually, shifting. Giambattista Vico proposed a view of history as cyclical that is consistent with Hegel’s dialectical materialism, and consistent with a view of liberty as the product of competition between evenly-matched actors for finite resources.

Where exactly the equilibrium is now; where it is trending, and how fast; and what this might mean for us as citizens, are all questions worth considering.

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...