After a recent discussion in which I was challenged to distinguish between sophistry and philosophic dialectic, I found myself compelled to reread Plato's Phaedrus. The following are some reflections that I had upon reading the dialogue.
The fundamental Socratic distinction between what seems to be and what is is mirrored in the difference between sophistry and dialectic. What is immediately suggestive of their relation is that sophistry and dialectic seem almost identical to the untrained ear. Lysias' lying speech that one ought to favour the one who does not love you reaches what appears to be precisely the sort of bizarre conclusion that philosophers are popularly thought to reach. Both proceed through linguistic inquiry that appears to start from basic and generally accepted principles. But sophistry is not dialectic--it is its diabolical double. Dialectic attempts to clarify the principle under discussion, moving upward like the freed prisoner in the allegory towards an apprehension of the beautiful. As such, the purpose of philosophy is to bring us into a loving relationship with the "transcendental" ideals.
The sophist also feels drawn to the beautiful, but instead of undertaking the purifying process of dialectic, he seeks to master the beautiful. Language for the philosopher is not a tool to be used to catch the elusive creature wisdom; language, rather, is the gift in which the revelation of the beautiful takes place. The sophist tries to use language (which is of course ultimately impossible, though often temporarily quite successful) for the purposes of acquiring power. Of course, the sophist must understand in his heart that this whole enterprise is as useless as it is self-destructive; Socrates observes the deception inherent in sophistry when he states that the "cunning" sophistical rhetor is attempting to persuade the youth that he does not love him, though "he really loved him all the same." The philosopher also often seems dishonest, but this dishonesty is always resulting from the dishonesty of the situation in which he has been placed and undertaken expressly to dispel the underlying lie. Socrates (masked) imitates Lysias' speech precisely precisely to show how flawed it is...
30 November 2010
16 July 2010
new aphorisms
1. Rather than thinking that the Ideas are questionable, perhaps we should instead learn to understand how the Ideas call us into question.
2. What is most hidden away is one's own face.
3. Dialectic is the mirror of the soul.
4. We think in images, but the ideas are not images--not exactly. But when we come face-to-face with the ideal, we can only speak of it in images. This is the origin of all poetry.
5. The essential defect of philosophy is that it has often failed to be poetry. The essential defect of poetry is that poets often confuse art and narcissism.
6. Very few things should be taken seriously, and those things that should most often turn out to be what no one any longer takes seriously.
7. Nothing lasts forever.
2. What is most hidden away is one's own face.
3. Dialectic is the mirror of the soul.
4. We think in images, but the ideas are not images--not exactly. But when we come face-to-face with the ideal, we can only speak of it in images. This is the origin of all poetry.
5. The essential defect of philosophy is that it has often failed to be poetry. The essential defect of poetry is that poets often confuse art and narcissism.
6. Very few things should be taken seriously, and those things that should most often turn out to be what no one any longer takes seriously.
7. Nothing lasts forever.
13 July 2010
Marginalia
Idea means—what something looks like. Appearances are never deceiving, insofar as an appearance is an appearance of and not an appearance to. But this is out of balance. If the difference between appearance and essence is a function of perception, then we end up with Hegel and Nietzsche and oblivion. The difference that appears between appearance and reality must belong in some way both to perception and appearance.
05 July 2010
America is rhetoric
Political documents from the ancient and medieval world generally seem to be articulations of a certain set of political decisions and, in a broader sense, of the political order that created the document. The Declaration of Independence is the first document to imply a political order that did not yet exist. Though many of the liberties the Declaration sought to establish were existing liberties that had been abridged by the tyranny of the British crown, these liberties were asserted in the name of citizens of a state that had not yet come into being. The essence of this state was created by the Declaration itself: a true city in speech. At its foundation American political existence was rooted in rhetoric. Instead of political symbols arising from a long process of national self-identification, people identified themselves as Americans in virtue of the symbols established by the Declaration.
What makes a society created by rhetoric great is that its essential existence is ideal. The great danger of a society created by rhetoric is that people will lose touch with language, and thereby lose touch with everything that makes them who they are. The mystery of a society created by rhetoric, which can be its salvation and its destruction, is the distance that usually seems to exist between what is ideal and what is "actual."
What makes a society created by rhetoric great is that its essential existence is ideal. The great danger of a society created by rhetoric is that people will lose touch with language, and thereby lose touch with everything that makes them who they are. The mystery of a society created by rhetoric, which can be its salvation and its destruction, is the distance that usually seems to exist between what is ideal and what is "actual."
01 July 2010
Why space does not exist [1]
It is a great (and highly practical) illusion that something called space exists. This is not a mystical utterance (at least not in the typical sense of mystical); it is meant quite literally. For context, I would recommend the series of posts beginning here and continuing with the next two in December of 2009. In those posts I attempted to show that the concept of space demands to be thought as a field (sort of a cubic Cartesian plane) composed of discrete units. This point was proved more or less to my satisfaction and to the satisfaction of some others (who, I suspect, were privy to the secret we are about to discuss).
We begin by considering the manifold meanings of the word space. In common parlance we might ask someone to give us space. We might ask how much space is in a room, or how much space a certain object takes up. We speak of outer space and space travel. Things are spaced, words on the page no less than the pickets of a fence. Americans (we are told) like their space.
We can divide these meanings into the following definitions:
1) The area surrounding an object that is, in some sense, part of the object
2) The purported vacuum that composes most of the universe
3) Empty space between objects that place the objects into a certain order
4) Distance conceived in light of an abstract field composed of mathematically functional units
The fourth underlies all the other definitions, though it underlies the first the least. The existence of some sort of field (called space) in which objects exist at a certain space from each other (the 4th definition) is certainly necessary before we can begin to conceive of the universe as a series of planets with in space with space between them. Indeed, this concept seems self-evident and unquestionable.
But who among us has seen space? And do we ever actually mean space when we say space? If asked to say what we mean when we say space, we probably imagine a sort of map grid extended into all three dimensions. Is that actually how things are? For the reasons outlined in the previous post (linked to above), if such a field exists, it must be segmented in a discrete manner. This deduction was an analytic one from the very concept of space. But look around you.! The room I'm in now (messy again, unfortunately) is filled with all sorts of things all over the place. Now I imagine our cubic Cartesian plane extended around the room. Every object is located somewhere on this cubic plane. Is this actually my room? The fact that I can imagine it hardly means it is the case.
What we wish to show (and will hopefully continue to show) is that "space" is an abstraction. It is not real. There is no such thing as space anywhere. And yet science depends upon the concept of space: and this should tell us something about science...
We begin by considering the manifold meanings of the word space. In common parlance we might ask someone to give us space. We might ask how much space is in a room, or how much space a certain object takes up. We speak of outer space and space travel. Things are spaced, words on the page no less than the pickets of a fence. Americans (we are told) like their space.
We can divide these meanings into the following definitions:
1) The area surrounding an object that is, in some sense, part of the object
2) The purported vacuum that composes most of the universe
3) Empty space between objects that place the objects into a certain order
4) Distance conceived in light of an abstract field composed of mathematically functional units
The fourth underlies all the other definitions, though it underlies the first the least. The existence of some sort of field (called space) in which objects exist at a certain space from each other (the 4th definition) is certainly necessary before we can begin to conceive of the universe as a series of planets with in space with space between them. Indeed, this concept seems self-evident and unquestionable.
But who among us has seen space? And do we ever actually mean space when we say space? If asked to say what we mean when we say space, we probably imagine a sort of map grid extended into all three dimensions. Is that actually how things are? For the reasons outlined in the previous post (linked to above), if such a field exists, it must be segmented in a discrete manner. This deduction was an analytic one from the very concept of space. But look around you.! The room I'm in now (messy again, unfortunately) is filled with all sorts of things all over the place. Now I imagine our cubic Cartesian plane extended around the room. Every object is located somewhere on this cubic plane. Is this actually my room? The fact that I can imagine it hardly means it is the case.
What we wish to show (and will hopefully continue to show) is that "space" is an abstraction. It is not real. There is no such thing as space anywhere. And yet science depends upon the concept of space: and this should tell us something about science...
27 June 2010
15 June 2010
Option pricing
The Nobel prize-winning Black-Scholes option pricing formula is generally advanced by financial academics as the best possible way to value options. This may be true, but that doesn't mean it is any good.
It is further worth noting that the formula (often used for dynamic hedging) models security prices as follows:
dS = mSdt + sSdW
Where S is security price, mS is the average rate of change of the security (drift rate), t is time, sS is standard deviation of the security, and W is a geometric Brownian function.
The problem here is that stock prices generally can be modeled using geometric Brownian motion. However, there is (more or less) a hard stop to trading at market close. Despite this fact, orders can be placed after market close, to be executed immediately upon the opening of the market. For this reason, we will rarely find extreme jumps between the underlying security price at closing and opening. The possibility of what is effectively discrete motion should make us realize that using the geometric Brownian without at least including some fudge factor for the possibility of discontinuous motion (though approximating the Brownian with a discrete probability distribution such as the binomial would be preferable) will occasionally but decisively give us bad pricing information.
Against those who would suggest that the error in the formula will be relatively minor, we advance the anecdotal but highly compelling evidence that the year after Mr. Scholes won his Nobel prize, the hedge fund he was helping to run (Long Term Capital Management) imploded in a multibillion dollar disaster that left financial markets reeling.
It is further worth noting that the formula (often used for dynamic hedging) models security prices as follows:
dS = mSdt + sSdW
Where S is security price, mS is the average rate of change of the security (drift rate), t is time, sS is standard deviation of the security, and W is a geometric Brownian function.
The problem here is that stock prices generally can be modeled using geometric Brownian motion. However, there is (more or less) a hard stop to trading at market close. Despite this fact, orders can be placed after market close, to be executed immediately upon the opening of the market. For this reason, we will rarely find extreme jumps between the underlying security price at closing and opening. The possibility of what is effectively discrete motion should make us realize that using the geometric Brownian without at least including some fudge factor for the possibility of discontinuous motion (though approximating the Brownian with a discrete probability distribution such as the binomial would be preferable) will occasionally but decisively give us bad pricing information.
Against those who would suggest that the error in the formula will be relatively minor, we advance the anecdotal but highly compelling evidence that the year after Mr. Scholes won his Nobel prize, the hedge fund he was helping to run (Long Term Capital Management) imploded in a multibillion dollar disaster that left financial markets reeling.
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