Showing posts with label induction. Show all posts
Showing posts with label induction. Show all posts

Tuesday, October 2, 2012

An article of faith

"Doubt is a pain too lonely
to know faith is his brother."
~
Khalil Gibran
 
 
 
 
 
The Fifth Key of the Tarot, known variously as the Pope or, more commonly, the Hierophant (the word literally means 'teacher of holy things'), is the sixth card along the journey of the Fool. The Law of Fives, that false teacher, suggests it should be significant (not only is it the fifth key, but the prime factors of six sum to... five).
 
We've intimated previously that knowledge is bound by unsurmountable limitations, and that transcendental truth cannot be gained through the application of reason alone. What is left is what necessarily underpins any edifice of reason: faith.
 
Faith is what the Hierophant offers - faith, the "substance of things hoped for, the evidence of things not seen," as the Book of Hebrews relates. Faith is often derided in our materialist culture; but the truth is revealed when we consider the foundation of that culture - for it rests on certain axioms of ontology, of epistemology, which in their nature are not and cannot be proven from earlier principles. Faith is the bedrock of rational consciousness: faith, which appears to admit none of the character of reason, turns out to be essential to reason; just as reason, appearing to ridicule faith, depends upon it. This is an intimate paradox, whose nature I shall leave it to the reader to decide.
 
It is tempting to assert that enlightenment, that cannot be accomplished through Reason alone, can be accomplished through Faith. There are even examples that seem to corroborate this assertion; but, in truth, Faith alone fails too. The reason for this is in fact rather subtle; it has to do with the relative plasticity of Reason.
 
Suppose you hold some view derived logically from certain agreed axioms - as a trivial example, suppose you are of the opinion that there are no black swans, based on the empirical observation that you have never seen anything but white swans and the meta-empirical observation that empirical observations are reliable arbiters of actual fact. Suppose you then encounter a black swan. This new datum contradicts a predicate of your hypothesis, and, as a rational thinker, you revise your hypothesis: you accept the existence of black swans (this possibility is why Hume had a Problem with Induction).
 
Now, suppose your belief that all swans were white stemmed from a pure faith, unsullied by Reason. Suppose you encountered a black swan: your faith would not admit its existence. You would rationalize that it was not a swan, or that it was a white swan painted black, or that you imagined it, or any of a hundred other counterfactuals to avoid having to assail your article of faith.
 
Faith in the transcendent is a precursor to enlightenment; faith in the merely subjective is a barrier to enlightenment. And neither Faith, nor Reason, will enable us to tell the difference...
 
This then, is both the power and the peril of the Heirophant: that he offers a reality more permanent than the one we can apprehend through Reason, yet less certainly true.

Wednesday, September 19, 2012

Time travel

"Change alone is eternal, perpetual, immortal."
~ Arthur Schopenhauer
 
 
We'd talked yesterday about identity, and how fractured a thing that is. We considered primarily the intersubjective entity - the word, the symbol, the representation of the objective in discourse. Today we're going to look more at the objective entity itself, the Dasein, as we move from a consideration of self-referentiality to infinite recursion.
 
What do we mean by Dasein? The term comes to us from Martin Heidegger, and it literally means "being there." As opposed to simply "being," it denotes being in a particular place - which, for a dynamic entity in a dynamic universe, entails being also at a particular time. A "being," particularly the abstract "being" that we draw upon in discourse, does not have a necessary relation to any other being; the Dasein exists in the context of other entities in time and space. It has coordinates. In an important sense, the Dasein gives meaning to Time and Space - we understand both indirectly by the changes entities undergo through dimensions of time and space. Our consciousness of space is perhaps more direct: our proprioceptive sense tells us how our physical body is oriented in space, and gives us some idea of its relative propinquity to other physical bodies. Our sense of time passing is not as direct, and in fact the naive view of Time as a river flowing from past through present into future can limit our worldview in important ways despite being the most straightforward way to interpret our impressions of the empirical world.
 
Borges, in Funes el memorioso, describes a remarkable character blessed (or cursed) with absolutely perfect recall. This individual's unique worldview creates for him a difficulty with identity - his recall is so perfect that he can recall every single instant of his subjective existence with crystal clarity. He does not need to reference an abstract intersubjective as a placeholder for the vague recollection that must suffice for most of us. He remembers every single instant of perception as its own unique set of entities - the bed or the book or the tree that he saw this morning is, for him, isolated from every other perception of what we would see as "the same" bed or book or tree. Number has no meaning for him; defying arithmetic, he invents his own number system in which each number has its own idiosyncratic name (the number five hundred in his system is known as nine, for example). It may seem that Borges invents Funes merely as a device to investigate the assumptions that underlie our perception of the world; in fact, the neuropsychologist Alexander Luria describes a real-life case with striking similarities, and there are perhaps a dozen such cases in the literature of brain science.
 
There are obviously good reasons to assume that Time does indeed flow in a linear fashion from Past to Future; that our naive impressions are accurate depictions of an empirically real world in which physical entities interact in predictable and measurable ways. Centuries of scientific experiment support this view; but it's worth remembering that the assumptions underpinning science, the axioms of science, predispose us to accept certain sorts of evidence. Inductive reasoning - the scientific habit of extrapolating from known patterns exhibited in the past to predicted patterns expected in the future - suffers from this problem, as David Hume noted: there is no good reason to believe that some relation which has been demonstrated between entities in the past will continue to be demonstrated in the future. One pithy formulation of this is the observation that we can't know that the Sun will rise tomorrow, just because it did today and yesterday and every day before. We can produce all sorts of scientific arguments why it should, but all of those arguments rest on inductive reasoning as well. We must accept axioms on faith, in science as in any system of thought. In fact, an axiom is necessarily not provable within the logic it supports (this isn't Godelian Incompleteness, however; this is a fundamental question of knowability, and one we'll look at later in the company of Fitch and Gettier, among others).
 
If Time is somehow other than linear; if it is, for example, a continuous dimension in which all events we perceive as consecutive are actually simultaneous - if, going one step further, it is a fractal dimension in which all possible events, perceived and unperceived, are simultaneous - then our assumptions about its passing and our motion through it are flawed. The limits of our experience of Time are revealed as precisely that: limits of our experience, and not of Time itself. Paradoxes of infinite recursion encourage us to visualize alternative models of Time that resolve or obviate the paradox - but that we are discussing in another metanow...