Saturday, December 10, 2005

Pegasus Exists

I apologize for the length of the following brain dump. Writing is my way of forcing myself to think these things through.

Unlike The Golden Age of Balloning, there no fees or penalties imposed for not reading this post.

Radical Empiricism
I have really taken an interest in Radical Empiricism. I'm not buying into the philosophy of William James wholesale. Instead, I merely claim that thought and emotion are experienced, and should be accorded a more equal footing with the physical experiences of taste, touch, sight, sound and smell.

Suppose we redefine the term empirical to refer to any pattern which is experienced, i.e., not just patterns among the five senses. This radical empiricism asserts that all the things we think and feel are also empirical because we experience them. So, the very idea of, say, "Pegasus", commits us to its existence, at least among mental sensations.

Of course, in common use, we don't normally say that purely mental things "exist." So what is the connection between existence in this radical empiricism and existence in the everyday sense? It is clear that the more familiar use of the verb "to exist" signifies a correlation between a mental pattern and a physical one. Thus, in common use, claiming that "Pegasus exists" is the same as asserting that one can experience patterns in the five physical senses that correlate with the mental pattern of Pegasus.

The correlations between patterns of mental sensation and patterns of physical sensation need not be direct. Finding feathers with equine DNA would qualify as an indirect correlation between the mental and physical patterns that would be Pegasus.

Philosophical Existence
Philosophically, the question of existence gets more complex. The world of sensation appears to us "as if" there is an external world that impresses upon our senses.

In the scientific world, existence still retains the same meaning as it does in everyday use, namely, as a correlation between mental sensations and physical ones. This is why it is perfectly valid under radical empiricism to formulate a theory of quarks that explains the experimental data, even though quarks are not observable. Quarks themselves exist as mental patterns that correlate indirectly with physical observations.

Though we are permitted to ask whether mental patterns have corresponding physical patterns, we cannot ask whether there is a correlation between mental patterns and things that, even in principle, cannot imprint upon our senses. The question is simply malformed because there is nothing to correlate the thoughts with. Neither the verb "to exist" nor the noun "thing" has any meaning beyond experience or potential experience.

From this perspective, a multitude of metaphysical problems are just a result of misclassifying thought as something beyond experience, a classification which seems, at best, an artificial distinction among experienced things.

Consider platonism. Here's how the Stanford Encyclopedia of Philosophy briefly defines it:
Platonism is the view that there exist such things as abstract objects - where an abstract object is an object that is wholly non-spatial and non-temporal (i.e., that doesn't exist in space or time) and, hence, is entirely non-physical and non-mental.
Are platonists claiming the existence of things not experienced? If so, they would be taking language far beyond its realm of applicability.

Philosophical Inferences
How precisely can we state the limitations of knowledge given that our only window on the world is an empirical one? Historically, we have been very successful in identifying patterns in the world of physical sensation that are well-explained by structures that exist only in mental models (e.g., the aforementioned quarks). We have also been able to do the reverse. We have correlated physical observations with patterns of mental sensation using lie detectors or functional Magnetic Resonance Imaging.

What is not so obvious is whether it is possible to infer information from sensation that is wholly non-empirical. I claim that such inferences are impossible.

If I have a set of propositions P = {P1, P2, P3, ...}, I can only make an inference, N, from these propositions if N has some implications for the truth of my set of propositions P. That is, knowing N and some subset of P, I can derive the remainder of P.

Therefore, any inference I make from a set of sensations must have implications for that set of sensations. This rules out any possibility of inferring anything non-empirical from empirical facts.

Furthermore, when we say that a mental conception is "about something," we're saying that the conception correlates with some other sensation, mental or physical. This raises doubt about whether non-empirical propositions are really about anything at all.

What Doesn't Exist
The non-existence of a thing is the absence of a sensation that correlates with a mental conception. There are mental and physical things that don't exist. Prime numbers between 7 and 11 would be an example of a mental sensation that does not appear to exist. However, we can only say that we have searched for a thing and found nothing, not that there is no possibility that such a thing will be found. We can have very high confidence that certain patterns (especially some mathematical ones) will not be found to exist, but I have proposed no mechanism to guarantee certainty of non-existence.

Science, Physical and Mental
If there are well-defined patterns in sensation, what are the properties of such patterns, and how can we find them?

We perceive correlations in sensation. We can see a man on horseback, water under a bridge, water flowing downstream, and apples falling from trees. We can see the patterns of arithmetic in collections of objects, and the simultaneous presence of two sensations.

We can also correlate the correlations themselves. We can correlate the man on horseback riding across a bridge under which water flows downstream. What we don't see is a correlation of correlations that denies one of the correlated sensations. We don't simultaneously correlate the pattern of the man on horseback riding across a bridge under which water flows downstream with the pettern of the same horse with no rider.

There is a name for this latter kind of correlation: an inconsistent correlation. Not only do we perceive the world to be largely consistent, we have little use for inconsistent information. Any action that is inconsistently correlated with the experience of something desirable, might just as frequently produce the experience of something unpleasant. It would be fair to say that an action that has an inconsistent correlation with a particular outcome is not truly correlated with that outcome at all.

Logic is the procedure used for detecting inconsistencies in correlations. By correlating sensations with symbols, we can implement the rules of logic more formally as symbolic logic.

If there are useful correlations to be found in sensation, they must obey the rules of logic. The search for useful correlations is a search through all of the logically consistent mental patterns that can be correlated with observations. That is we are looking for a mental pattern that acts as a model of the world, so that our observations appear as if the world fits the model. This is why mathematics is important. Not only are mathematical structures empirical themselves, they also represent an enumeration of logically consistent models that can be correlated with a logically consistent physical world.

From here, it is easy to see why the scientific method works. We locate a logically consistent mathematical structure that can be correlated with our observations of the world, then we use that same structure to predict future observations and correlations. If the prediction turns out to be wrong, we modify the mathematical model and try again.

There is a very important empirical fact about mathematics that has implications for this analysis. Given a finite number of experiences and correlations, there are an infinite number of mathematical models that can be correlated with those experiences. If I provide you with some points on a graph, you can fit a curve to those points, but you cannot be certain that you have correctly fitted your curve to all the points that might appear on the graph in the future.

Meaning
What implications does radical empiricism have for meaning in language? Given the experience of a language proposition, we can only interpret it by correlating it with other experiences. This means that meaning in language is a scientific endeavor. No language proposition has infinite precision in its meaning because no correlation confers infinite precision. Instead, we form a scientific theory about the meaning of the proposition that has implications for how we expect to see the proposition used (correlated) in the future. That is, to have meaning, a proposition must be correlated reliably with something other than the symbolic sense data in which it is written. The meaningful proposition must claim definite implications, if it is true versus if it is false.

The extent of the implications of a proposition map out the domain of its meaning. If a proposition has implications only within a related set of propositions about mental sensations, then the proposition's meaning does not extend to physical patterns. The propositions of algebra do not, by themselves, have meaning that extends to the physical world. All propositions are evaluated within a specified context. This allows a proposition and its negation to be true in two different contexts without contradiction. The separation of contexts is what eliminates the simultaneous truth of the propositions from rendering the system inconsistent. Note that context boundaries may not be on sense boundaries. Two purely mental contexts may be totally independent, e.g., two algebra problems can exist without contradiction in their respective contexts, despite having axioms that would conflict if they were in the same context.

A scientific theory combines the propositions of mathematics with the empirical propositions of physical experience. The theory creates a new context in which the mathematical propositions have implications for the physical ones. This merged context is created by rules of correspondence between mental and physical sensations. In such a system, physical sensations are added to the system as new axioms. If the new empirical axioms render the system inconsistent, then the theory is disproved. If the new empirical axioms are consistent, then the theory is confirmed.

In contrast, a metaphysical system is one in which propositions about mental sensations are declared to have no implication for physical sensation. This is a denial that the metaphysical propositions share context with the physical world. However, creating this kind of separation is no different from the establishment of a mathematical context. Thus, at best, metaphysics is no different from mathematics, save for the evocative symbols it uses.

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