Monday, June 09, 2008

Knowledge of Concepts (Language) and Knowledge of the World

In philosophy there has been a debate about whether connections between events in the world involve causes or whether such connections only amount to associations. There has been a related (but different) debate whether knowledge of the world requires knowledge of causes or whether knowledge can rest only on associations. A third position or question is possible: even if causes are at work in the world and even if the most perfect knowledge of the world requires knowledge of (all) causal mechanisms in the world, can human beings have knowledge of the world without (fully) knowing the causes of events in the world?

The third position or question just mentioned is slightly ambiguous. However, if the question is taken to be whether human beings can have some knowledge of the world without fully understanding the causes of events in the world, the answer is "yes" (unless, that is, "knowledge" is assigned a narrow, or "constipated," meaning).

But if causes are at work in the world, how is it possible for human beings to have knowledge of the world without having full knowledge of the causes of events? Various answers to this question are possible. One possible answer is that the human brain or neural system is so configured (as a result of evolution or whatnot) that human beings have effective knowledge of the world even though or even when human beings do not have express, self-conscious, knowledge of causes of events in the world. (Of course, until we human beings have perfect knowledge of causes, we cannot explain [perfectly] how human knowledge of the world without perfect knowledge of causes is possible.)

Human beings communicate in part through language (and explicitly-stated concepts, which are also part of a language). Furthermore, human language often or sometimes communicates knowledge of the world. But how is this possible? Ordinary human language is usually mushy and imprecise. (The same may be true to some degree of all non-ordinary human language -- e.g., the language of the hard sciences such as physics.)

In 1965 Lotfi Zadeh burst upon the scene with a theory of fuzzy logic. See Lotfi Zadeh, Fuzzy Sets, 8 Information & Control 338 (1965) This was a theory that took the mushiness and fuzziness of language and concepts seriously. It was possible, Zadeh said, to reason precisely about imprecise and vague propositions. But this insight, though in itself profound (in his hands), was perhaps not Zadeh's most profound insight or discovery. Perhaps Zadeh's most profound discovery was that the "crude" language of ordinary human beings -- such as the language and words used by the operators of a kiln -- conveys genuine knowledge of (part of) the world (such as the workings of a kiln). By using a meta-logic that arguably accurately mimics ordinary language, Zadeh and his many followers were able to accomplish the astonishing task of devising artificial procedures that run kilns, trains, and other such things without incorporating into the meta-procedures accounts of the mechanisms that cause kilns, trains, or whatnot to work the way they do under various circumstances.

In the last 10-15 years Zadeh has emphasized that natural language is language that captures or expresses perceptions. Although I am not a mathematician or a logician and although I do not know Zadeh's work well enough to say so with confidence, my strong sense is that part of Zadeh's motivation for stressing that his theories are about perceptions and are not purely "semantic" theories is to emphasize that his theories about the workings of vague and imprecise language and concepts are or can be theories that help human beings understand the workings of the world. (Professor Zadeh really is a genuine scientist -- as well as, e.g., an abstract logician or philosopher.) If this is an important part of what Zadeh is about, a popularizer of his approach might reasonably proclaim -- if provocatively and somewhat misleadingly --, "Superficial knowledge is genuine knowledge!"

Some pertinent quotations follow.

In his relatively recent paper outlining a general theory of uncertainty (see Lotfi Zadeh, "Toward a Generalized Theory of Uncertainty (GTU) - An Outline" (2005)), Zadeh describes or characterizes "uncertainty" as a "constraint" on "information." In this paper's abstract Zadeh writes:

It is a deep-seated tradition in science to view uncertainty as a province of probability theory. The Generalized Theory of Uncertainty (GTU) which is outlined in this paper breaks with this tradition and views uncertainty in a broader perspective.

Uncertainty is an attribute of information. A fundamental premise of GTU is that information, whatever its form, may be represented as what is called a generalized constraint. The concept of a generalized constraint is the centerpiece of GTU. In GTU, a probabilistic constraint is viewed as a special—albeit important—instance of a generalized constraint.

In the body of the paper Zadeh states (endnotes omitted):
Uncertainty is an attribute of information. The path-breaking work of Shannon has led to a universal acceptance of the thesis that information is statistical in nature. A logical consequence of this thesis is that uncertainty, whatever its form, should be dealt with through the use of probability theory. To quote an eminent Bayesian, Professor Dennis Lindley, “The only satisfactory description of uncertainty is probability. By this I mean ... that the calculus of probabilities is adequate to handle all situations involving uncertainty…probability is the only sensible description of uncertainty and is adequate for all problems involving uncertainty. All other methods are inadequate…anything that can be done with fuzzy logic, belief functions, upper and lower probabilities, or any other alternative to probability can better be done with probability,” (Lindley, 1987).

The Generalized Theory of Uncertainty (GTU) is a challenge to the thesis and its logical consequence. Basically, GTU puts aside the thesis and its logical consequence, and adopts a much more general conceptual structure in which statistical information is just one—albeit an important one—of many forms of information. More specifically, the principal premise of GTU is that, fundamentally, information is a generalized constraint on the values which a variable is allowed to take. The centerpiece of GTU is the concept of a generalized constraint—a concept drawn from fuzzy logic.... The distinguishing feature of fuzzy logic is that in fuzzy logic everything is—or is allowed to be—a matter of degree. ...

Zadeh further states (endnotes omitted):
In GTU, uncertainty is linked to information through the concept of granular structure—a concept which plays a key role in human interaction with the real world, Zadeh [43, 52].


Granulation is pervasive in human cognition. For example, the granules of Age are fuzzy sets labeled young, middle-aged and old, Fig. 1. The granules of Height may be very short, short, medium, tall, and very tall. And the granules of Truth may be not true, quite true, not very true, very true, etc. The concept of granularity underlies the concept of a linguistic variable—a concept which was introduced in my 1973 paper “Outline of A New Approach to the Analysis of Complex Systems and Decision Processes,” Zadeh [41, 42]. The concept of a linguistic variable plays a pivotal role in almost all applications of fuzzy logic [12], [15], [18], [29], [31], [38].

There are four basic rationales which underlie granulation of attributes and the concomitant use of linguistic variables. First, the bounded ability of sensory organs, and ultimately the brain, to resolve detail and store information. For example, looking at Monika, I see that she is young but cannot pinpoint her age as a single number. Second, when numerical information may not be available. For example, I may not know exactly how many Spanish restaurants there are in San Francisco, but my perception may be “not many.” Third, when an attribute is not quantifiable. For example, we describe degrees of Honesty as: low, not high, high, very high, etc because we do not have a numerical scale. And fourth, when there is a tolerance for imprecision which can be exploited through granulation to achieve tractability, robustness and economy of communication. For example, it may be sufficient to know that Monika is young; her exact age may be unimportant. ...

Further, consider these statements by Zadeh (references omitted):
There is a demonstrable need for GTU because existing approaches to representation of uncertain information are inadequate for dealing with problems in which uncertain information is perception-based and is expressed in a natural language. ... More specifically, the existing approaches do not address the problem of semantics of natural languages....
Finally, consider the following points by Zadeh:
How can precise meaning be assigned to a proposition, p, drawn from a natural language?

The problem is that natural languages are intrinsically imprecise. Imprecision of natural languages is a consequence of the fact that (a) a natural language is, basically, a system for describing perceptions; and (b) perceptions are intrinsically imprecise as a consequence of (a) the bounded ability of sensory organs, and ultimately the brain, to resolve detail and store information; and (b) incompleteness of information.

Important Coda: The last quotation makes Zadeh sound a bit like some behavioral economists, many of whom emphasize the limitations of human knowledge and the irrationality of human behavior. But Zadeh's work runs in a different direction, it has a more optimistic thrust. Note: unlike some fans of "ordinary thought," Professor Zadeh does NOT embrace ALL of the following propositions: ordinary language is a form of tacit knowledge, human beings have tacit knowledge, tacit knowledge works, and nothing much more can be said about ordinary tacit knowledge. His project rests on the premise that ordinary language really and truly captures and expresses perceptions and that it is possible that a meta-logic can bring to light and describe the real-world implications of the perceptions that are captured by the imprecise language that human beings use.
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