Word and Object

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Typecasting Bertrand Russell

September 9th, 2006 by David Kronemyer · No Comments

I always have been a huge fan of Bertrand Russell. I never met him personally; in fact, he died the year I entered college at Berkeley. I was, however, taught by people who were his students, and thus have what might be called a “second generation” connection.

One of the things that always has slightly confused me about Russell, is exactly why he was bewildered over what came to be known as “Russell’s Paradox.” The basic idea, as set forth in The Principles of Mathematics (1903), is simple. You start by imagining something utterly fictitious, which is, the “class” of “all classes” – in other words, what results, if you took classes of various things, elements or objects, in the world, or elsewhere, and then in turn comprised them into a class.

Keep in mind that this fictitious “class of all classes” does not comprise a collection of the objects, themselves; rather, it is a class “of the classes” of those objects. You can define the members of the constituent classes, however you want. For example, there is the class comprised of the objects on my desk, let’s call it d. And then, there is the class comprised of the objects on my bookshelf, let’s call that b. All of the members of class d share a single, unambiguous, defining characteristic or property, which is that they reside on top of my desk. This also is true for all of the members of class b, only in this case, it is that they reside on my bookshelf. If we let cbc stand for the “class of both classes,” it in turn comprises cbc = {d, b}.

So what got Russell worked up, was this. Assuming you have a certain number of underlying elements, the number of resulting classes necessarily must be greater than the number of elements. The reason why is that the “class of all of the classes,” as defined above, itself comprises two different kinds of classes. First, there are classes that are not members of themselves. An example of this type of class is {d, b} – because the class {d, b} neither is a d, nor a b. But, second, you also have a very peculiar class of classes, that are members of themselves – the most noteworthy example being the class of all classes. Thus, it is possible to define a class that has more subsets or sub-classes, than there are members, or elements, of that class; which means that the class of all classes cannot be considered, itself, to be a class.

So my problem is that I really don’t think this is that complicated. It is a simple truism that no system can be evaluated on its own terms, because you need a kind of “meta”-language or “meta”-view of the system, that is outside of the system, itself. For example, for whatever reason, you might call somebody’s action either “good,” or “bad.” But, everybody knows that neither “good” nor “bad” are actions, themselves – rather, they’re ways of evaluating actions.

Put slightly differently, you don’t ascribe a predicate, to itself – because, if you do so, you’re creating another level. To think in terms of a visual metaphor, it’s like those nested Russian dolls that you sometimes see around the holidays.

Here’s another example: a current slang expression is, “my bad” – intended for use when, say, one errs in connection with some trivial matter, and wants to offer a quick apology. A bystander might say, “that was a bad ‘my bad’” – meaning, that the use of “my bad” in that particular context for some reason was inappropriate, infelicitous, or otherwise inefficacious. Perhaps, for whatever reason, the bystander may have thought that the apologizer’s addressee actually was the person “at fault” in connection with the event, and, if anybody was going to be doing any apologizing, it should be that person. The bystander certainly isn’t proposing to interject this evaluation into the action, itself. Rather, the bystander’s observation is more of a commentary on it (just like me writing this, and you reading it, is yet another level of commentary on the bystander).

All of this to-ing and fro-ing later resulted in a discovery by the great mathematician Kurt Gödel, of something that has come to be called the “incompleteness theorem.” The incompleteness theorem is a slightly more complex mathematical formulation of what we’ve just been talking about – that is, no internally consistent system or theory can, within that system, and using the system’s language and concepts, determine whether every single proposition that potentially could be formulated within that system, is “decidable.”

“Decidable” means either that the original propositions, or axioms (or propositions derivable from them) are provable, or their negations are provable, by using the language and concepts of the system, and first-order logic. If it were possible to prove both a proposition and its contradiction, then the system would not be consistent. And the reason why the system is not complete, is because you need a system-extraneous theorem, or criterion, in order to conduct this exercise.

At the risk of venturing farther out on the gang-plank than I already have, I would like to suggest that there is a profound analogy between the type-theory solution to Russell’s Paradox, and an historical notion in the philosophy of mind, which is that of “epoché.”

As framed initially by Aristotle, “epoché” means suspension of judgment – what happens when you stop doing what you’re doing, and engage in an act of critical reflection. Without picking on him unduly, this is the same process that René Descartes engaged in when he “suspended belief” in the real world, and all of its constituents, and tried methodically to doubt everything that there was. But the person who moved this football furthest down the field is the great German philosopher Edmund Husserl.

Husserl wanted to “get to the essence” of things. In this respect, it would not be out of line to suggest that, in some respects, at least, he may have been a latent neo-Platonist. He thought, however, that this wasn’t an abstract intellectual exercise, but rather, something we actually could do. And, the way to do it was by “bracketing” all of our (essentially, naïve) assumptions about the external world, and entering into a special modality, or orientation, with the objects that populate that world, outside of our consciousness.

Let’s take a spoon, for example, or a hammer. Forget for a moment about the object’s utility, what it’s used for in practical, day-to-day life. This might be characterized as our “natural point of view” vis-à-vis the object. We believe it exists, we know how to use it, and we can describe its physical properties. These, however, simply are clues as to the essential nature of the object, itself.

Rather, what we have to do is to start examining the object, “qua” object – that is, as a thing in-and-of-itself, with its own essential traits and characteristics. One stops regarding the object simply as a thing situated in the world, its existence deriving from that fact. Rather, it becomes a collection or collage of perceptual relationships – the ways in which we examine, assess and regard it. The spoon is shiny and reflects the light when you twist it, the hammer has a hard head for banging in nails. That light in turn causes irradiations on our retinal walls, the sound of the hammer, vibrations in our auditory canals. These (and many other attributes, of course) are the raw materials, or ingredients, of which the object is comprised. In a way, we want to strip the object down to these “essential” elements.

But that’s only half of the process, because the key then is being able to get into a special frame of mind, in order to abstract these ingredients, and discern the nature of the classes (or types, or groups) into which they belong, and their relationship to how we perceive them. For example, one might ask, “exactly what is it about the shiny-ness of the spoon, when I twist it into the light, that draws it to my attention?” In this way, one focuses upon, or calls to mind, the question of what it is for something to be shiny and bright, to begin with. One might imagine a full moon in a clear sky, or a bird picking up a piece of glass, and putting it into its nest, all as extrapolations from, or variations of, the notions of “shiny” and “bright.”

Another aspect of this, which Husserl doesn’t really bring up, but which to me is integral to the whole process, is then being able to recombine or reconstruct the elements in new and different ways; to juxtapose them against their original iterations, and the accidental environments in which they are found. Latter-period paintings by Pablo Picasso are a marvelous illustration of how I’ve always imagined this process working – because the reconstruction phase never is perfect (that is, you never end up exactly where you started). Rather, invariably it’s affected by a host of factors such as environment, temperament, and personality. Various aspects of the original object, which may even be insignificant, such as a reflection of light, achieve heightened prominence and visibility. Conversely, critical features, such as size and shape, may become completely mangled, as it is reassembled.

The most compelling literary example I can think of is the novels of Alain Robbe-Grillet. Rather than focusing on plot, or character development, his stories primarily are concerned with the surface appearance of things. He will go on for pages, for example, describing the interior of a room, or the way in which a road winds across the landscape. Better still, these descriptions appear in no apparent order, or sequence; the “beginning” of the novel, conventionally understood as a linear rendition of activity, is just as likely to be at its end, as the end is, at the beginning. He will focus in on odd details, such as the way a character is walking, or what they are wearing – details that a Tolstoy or a Dickens, just to pick a couple of names out of the hat, never would notice. The reason why they don’t notice them, is because they don’t care about them, they’re not integral to either plot or character development.

This puts the reader in a peculiar position. In a “conventional” novel, it’s more-or-less easy to derive a composite picture of a character, or a scenario. The author has given us a certain list of ingredients, and really it’s just a matter of combining them, into a consistent and harmonious whole. With Robbe-Grillet, however, there are none of these clues. One is left with pieces of a jigsaw puzzle, and, no real illustration, or template, as to how they’re supposed to be assembled. This, of course, leaves it up to the perceiver’s own initiative, as to exactly how it’s all supposed to look, at the end of the story.

In the course of undertaking this exercise, the reader comes to accept these various pieces for what they are – as splinters, or slivers, of a composite world inhabited by flawed and under-described characters, moving uncertainly, towards less of a “destiny,” than simply a winding-up, or a winding-down, of the story’s action. The reader also becomes sensitive to what is involved in the process of deconstructing, then reconstituting, all of these elements, and the reader’s role in deriving an eventual outcome.

If you want to experience more of what I’m trying to describe, please view (repeatedly) the 1961 Alain Resnais film, Last Year at Marienbad.

Anyway, back to Husserl. By engaging in the form of analysis he describes, one becomes far more alert to the various qualities and features of the object, in context; including aspects we previously might have overlooked, such as how the object is used, and what it is for. One also becomes incredibly more aware of the dynamics of the relationship between the perceiver, and the perceived; our “intentionality” towards the object, as Husserl would say, which simply is a way of expressing our modes of orientation vis-à-vis the object, and how its essential nature thereby is revealed. However, almost as an added bonus, we also come to understand the essential features of what it is to “experience” something, to begin with.

Husserl calls this a “transcendental” experience, because we have managed to get beyond the mundane cares and concerns of the real world, the object “in isolation,” as something that merely exists in the world, like the subject of a still-life painting. We have stripped away everything that doesn’t matter about the object; its location in space and time, and extrinsic factors, such as light, or heat, that may impinge upon it. Instead, we have engaged with the object, and fully embraced it, in a syncretistic act of understanding and comprehension. The object becomes a correlate, or function, of pure consciousness, itself. In the process, we also have come to learn more about the nature of consciousness – consciousness detached from ego – and the complex, myriad, and multi-faceted relationships between object, and mind.

The process that I have been describing, of course, only can be undertaken by what Husserl refers to as a “transcendental” ego – that is, an ego elevated from the action down there in the subjective arena of life. By analogy to a football or basketball game, for example, the transcendental ego is a commentator on the action – not a participant in the action. The transcendental ego is completely transparent to the world; there are no barriers, or opacities, between it and the objects within its field of vision. It is alert and perceptive; without presuppositions, hypotheses, or unifying theories. It is ready to go forth, to confront reality, to paraphrase the end of Portrait of an Artist.

But it never can glimpse itself, because the only entity capable of doing so would be a transcendental-transcendental ego, and so forth. In this respect, it is, or so I would like to suggest, the epistemological equivalent of Russell’s Paradox – how we can experience something, yet be aware of that experience (that is, the fact we are experiencing it), at the same time. Obviously we all undertake these types of reflections, but we do so, seriatim – never at the moment of experience, itself.

An interesting subject, as to which I have a theory (what a surprise!) is how this process occurs; that is, how, and why we flit about from one object of consciousness to another, like a bumblebee gathering pollen from flowers. Clearly, in the final analysis, it’s about neuro-chemicals; but what I’m interested in is the higher-order abstraction, or patina, that we imprint upon this process. I think it’s somewhat akin to being on top of a mountain peak. A broad valley traverses at your feet. Yet, there in the distance, another peak looms. And then, in a single, bounding, leap – you’re there! The magnetism of the thought it represents is so strong, that it has overcome the background noise invariably adhering to any form of conscious activity. It looms in a position of prominence that is so compelling, our thoughts gravitate towards it, immediately. But, more on this later.