2013-09-06

Certainty

I'm a bit short on time for blogging today, so I thought I would pull out a blog post that I wrote a long time ago, but never bothered to publish. The reason I didn't publish it before is because I wanted to respond to something Simon Grey and I were going back-and-forth about, but I didn't want to go back-and-forth so much that it created any animosity. So I thought I would let this post lie for a couple of months and make my point later, after some time had passed. Well, some time has passed, and I think it should be okay to publish this one now.

I don't at all have it out for Simon Grey, unless by "have it out," you mean "closet bromance." Part of what makes the "blogosphere" so interesting is that it enables ideas to not only exist, but also to interact. And since comments are not available on Grey's blog, I resort to continuing the dialog here.

In the end, though, I think this is a good thing. The "blog comment" is a very different medium of communication than the "blog post." The latter is more thorough, more organized, and requires more intellectual energy and patience. The blog comment is a knee-jerk. So while I sometimes feel disappointed that I cannot provide a one-line, knee-jerk reaction to Simon Grey in his own space, in the final analysis, I think it's better if I don't. I tend to think my blog posts are better than my comments, anyway.

Regarding the continuing dialog, Simon Grey responds to my post from a few days ago, with characteristic thoughtfulness. He makes a number of interesting points that I am finding difficulty excerpting. In your own best interest, read the whole thing. However, for standout passages, Grey starts strong:
The most interesting thing about philosophy in general, and epistemology in specific, is how it has a wonderful to tendency to simply go up its own ass.  Eventually, at some point, any logical application of an asserted truth, particularly about the nature of knowledge, leads to some hilarious, and often depressingly self-defeating conclusions.  Most conclusions are nihilistic, at least in the sense that, once you begin to think about knowledge you eventually conclude nothing is really certain, and even things that appear certain may not necessarily be certain, and we can’t ever really be sure of everything, so maybe let’s go home, put a gun to our respective heads, and pull the trigger.
Grey writes about a literal, albeit unintended, nihilism. The more one questions the universe, the fewer certainties exist, the more apparent it becomes that, perhaps, nothing exists. Understanding the world in which we live, with all its frustrating ambiguity and nuance, necessitates that we "let go of the reins," or in typical Stationary Waves lingo, "free ourselves of our illusions." Grey's key point in his post is to remark that there is a trade-off between knowledge and certainty.

He makes his case brilliantly. But is it true?

I Laughed At Love, It Was A Big Mistake / In The Absence Of, I Filled It With Hate
For a long time now, I have had a concept in mind that I like to call "practical nihilism" (see the Lexicon for a definition). Practical nihilism is what fills the void left by uncertainty. Grey describes the process perfectly in the passage excerpted above. You can find my take here.

One way to look at it, as Grey points out, is that certainty is some sort of opposite of knowledge, at least in so far as more knowledge gives rise to less certainty. It's not unlike viewing the world through a microscope, zooming in further and further, only to discover progressively more elementary particles that each behave in a manner quite differently from that of the larger particles they form; a quark behaving differently than a proton, which behaves differently than an atom, which behaves differently than a molecule, which behaves differently than a cell, which behaves differently than an organism, which behaves differently than a species, and so on. 

This is true, but does that mean that the rule generalizes? In other words, can we really say that the result of all additional knowledge is the discovery of more uncertainty?

In my previous post, I pointed out that mathematicians, for example, are certain of specific mathematical truths regardless of their ability to prove those truths. The more they know about mathematics, the more certain they become of basic principles like the value of a number's square root. These basic principles are logically irrefutable; logic is, in fact, one thing of which we are decidedly certain.

At the same time, the more we expand our mathematical knowledge, the more we struggle with the Peano Axioms, for example. For some mathematicians, the ability to call the very definition of numbers into question creates a mathematical world of profound nuance and great uncertainty. But for the likes of Steven Landsburg, it's not a big deal. Why not? Here is Landsburg in his own words:
The point [of the Peano Axioms] isn’t to “allow mathematicians to talk” about numbers; mathematicians from Pythagoras through Dedekind had absolutely no problem talking about numbers in the absence of the Peano axioms. Instead, the point of the Peano axioms was to model what mathematicians do when they’re talking about numbers. Like all good models, the Peano axioms are a simplification that captures important aspects of reality without attempting to reproduce reality in detail.
Or, in my words: when we set out to decipher the truth - particularly when the truth we are interested in is abstract, intangible, or predominantly derived from logic - the nature of the enterprise requires that we simplify some things, or hold them constant (ceteris paribus), or otherwise ignore them, in order to get at the central object of the analysis. Once having learned about the central object, we relax the constraints (hopefully progressively) so that we can learn new things that pertain to the new constraints. But the result of each analysis, if it's successful, is more knowledge and less ambiguity.

It would be wrong to call the relaxing of constraints a new form of confusion, nuance, or uncertainty. At every step in the process, we are more certain of what we set out to know. But each new fact brings with it a hunger for more facts, a curiosity for that which is yet to be explained, a thirst for a greater depth of knowledge.

I contend that it is really this new curiosity that Simon Grey calls "uncertainty." The real challenge is neither knowledge nor certainty, both of which come in due course. The real challenge is building a meaningful understanding of the universe using what you've learned. The real challenge is Authenticity.

Meaning
Simon Grey himself may have been the one who first made me aware of the inadequacies of language with respect to human knowledge. Just as a human being may express individualist and collectivist tendencies, depending on the context, without becoming any less of an individual or member of the collective, so too knowledge can increase our certainty while providing a higher tolerance for nuance. We need not choose.

Left to our own devices, I'm fairly sure that both Grey and I could blather on and on about the particulars of knowledge, belief, and certainty. The fact that we have the ability to explore the nuances of the matter by no means implies that the nuances we discover make the truth of any situation less certain. It feels less certain, but remember: Newtonian physics is no less true than quantum physics. The physicist's task is to explore the details; for the rest of us, we limit the scope of the analysis to that which provides the best results.

Grey suggests that this means that the value of knowledge is in its ability to predict the future; that we come to believe in the best estimator of reality thanks to its proven value as an estimator. He might even be right about that - but even if so, what does that have to do with truth or knowledge? Something isn't true because it serves as the best estimator, but the exact reverse: because something is true, it therefore serves as the best estimator.

Grey writes about knowledge as it relates to belief. I don't disagree with his analysis, but I would open the matter up to a third variable: meaning.

To work this into Grey's view, recall that Grey wrote:
Before I disappear down a rabbit hole of my own digging, let me simply say that we know what we know, and we know what we believe, but what we believe may not necessarily be true. Therefore it wise to hold fast to our experiences while also considering our beliefs as things to be challenged from time to time.
This is true, but also hinges on the vital assumption that the questions we ask have meaning. Now we're coming full circle, because if you recall, this issue arose out of what I wrote regarding Lubos Motl's assertion that there is such a thing as a stupid question. I'll illustrate this by example:

You find yourself lost in the woods with nothing but a map. There are many meaningful questions you might ask about your predicament. Considering that you possess a map, I submit that one of the most important questions you can ask at this point is: Which way is North? A less useful question would be How did I get here? A somewhat unhelpful question would be: How do I know that this map is even a map of my present location? A very unhelpful question is: What is the meaning of words like 'North' or 'South' considering the fact that I exist in an M-dimensional universe? Or even worse: Does modern physics tell me more about my existence than The Qu'ran?

I'm not suggesting that none of these questions are ever worth asking. Instead, I'm suggesting that some of them are more meaningful than others. I'm also suggesting that the meaning is context-dependent.

So, one can meaningfully question Peano axioms if one knows that the context of the question is the improvement of a conceptual model for Real Arithmetic. One can meaningfully question the scope and relevance of physics if the context of the question is the struggle to find one's place in the universe. One can question even the meaning of the words "North" and "South" if the context is astronomical cartography.

What matters to these questions is the context in which they are being asked, because the context gives these questions meaning in exactly the same way that the context of a physical analysis will determine whether one chooses Newtonian or quantum physics to conduct the analysis. A more casual view of the situation would suggest that "we don't even know which kind of physics is certain," but within the context of our situation and considering the full scope of human knowledge on the subject, the truth is clear. And certain.

Some days I am a bigger fan of Ayn Rand than others. One of her more important contributions to philosophy was her relentless focus on the context in which discussions occur. Without the all-important context of the analysis, we risk slipping into meaninglessness. This meaninglessness eradicates our ability to relate to those facts in the universe that really are certain.

Conclusion
All that having been said, let me end by focusing on the context of this post: I hope that readers will see this post as being a contribution to line of thought originating from Simon Grey, rather than any kind of rebuttal to it. Another way of saying this is that his thoughts on my thoughts spawned additional thoughts, and we seem to have entered an oscillatory cycle of some kind.

Take it all for what it's worth. It's in the universe now, and exists apart from either he or myself, part of an ongoing dialogue that has existed for millennia as is not likely to end any time soon. Such is the nature of the big questions, I suppose.

And to think that you made it all the way down to the bottom of the page.