A brief comparison with other approaches

The approach proposed in this thesis is not the only endeavor that is motivated, in a sense, by discontent with classical approaches to language and logic. Although the motivation of this thesis cannot be wholly attributed to such discontent, it may be helpful to briefly compare the merits/shortcomings of other ``revolting'' theories.

For one thing, classical approaches are symbolic and top-down, and use the classical Turing machine (computer) as a metaphor of human mind. More importantly, these accounts, explicitly or implicitly, assume a Cartesian dualist stance. In this case one is obliged to take an anti-naturalist philosophical position regarding mind. Partially driven by the need for a descriptive and naturalist account, the alternatives (the so-called soft-computing models) address the shortcomings of the classical approaches and try to build theories which are more or less bottom-up.

For instance, observing that human thinking is very often ``fuzzy,'' fuzzy logic [70] replaces the set theory underlying classical logic with a ``fuzzy set theory.'' In this regard, fuzzy logic offers certain insights into the fundamental characteristic of human reasoning. However, in fuzzy logic theory, while the fuzziness of human reasoning is correctly identified, it lacks a theoretic framework explaining why the member function is a monotonic real mapping with the range of $[0,1]$. Furthermore, the continuity of the real-numbered member function is obviously at odds with sophisticated human reasoning -- at least when a verbal or mathematical argument is expressed. In this sense, fuzzy logic can be at best regarded as an extension of (classical) physiological reflection (as in the example of arms, which can be treated as an automatic control system with feedbacks) to some mental tasks. A more severe problem lies perhaps in its implicit dualist stance, in which the ``member-of'' and other symbolic concepts are given from without. In fact, even if one can think of a thing being ``$0.51$ big'' (call it big) the thing cannot be ``less than $0.51$ big'' (call it medium) anymore. So being ``$0.51$ big" and being ``less than $0.51$ big'' is a crisp distribution. For students of fuzzy logic, it seems that symbols, as particular categories to which an entity (or a state of affairs) belongs, must be something innate to the human mind. In this sense, fuzzy logic remains a top-down theory and does not offer a bottom-up account of why the brain functions the way it does.

In a sense, artificial neural network (ANN) or connectionist models, based on simplified neurological findings, may come to the rescue. In ANN models, the fuzziness is attributed to the continuity of neuronal activations. In fact, connectionist approaches seem to be the only class of soft-computing models that may have a deep root in physics (of biology) and deserve the name bottom-up. However, the models used in most artificial neural networks are highly simplified. They are hardly similar to real neurons in the brain. Moreover, at least at the present time, connectionist models cannot accommodate symbols in a satisfactory way [71], although it remains an open question whether a connectionist model may one day achieve this implementation account. Most severely, the physical objects on which the current neural network models are based are classical. Thus a connectionist model must carry with it all the weakness of classical physics. It is hardly convincing that out of passive, mechanistic classical physics something we call intention can emerge without resorting to mysterious (therefore non-naturalist) accounts. Nevertheless, there are interesting studies in neurology that may one day reveal how some perceptions can be accounted for classically (as long as classical physics is regarded as a limiting case of quantum physics). Perhaps the most interesting of recent studies is that on the neurological basis of consciousness [72]. Not surprisingly, quantum mechanics is promising in some of these studies [73,74,75].

Acknowledging the complexity of the physical neuronal substrate, there are simplistic connectionist approaches to language [76,77,78,79,18] which, with some success, have demonstrated how symbols and other symbolic structures may emerge from or be implemented with so-called ``sub-symbolic features.'' Strictly speaking, these approaches have to be called hybrid because they still start with an abstraction of characteristic sub-symbols. Enumeration is a common technique of implementing these sub-symbolic features. These sub-symbols have at least the most important symbolic features, that is, coordinates. They are nevertheless given from without and remain symbols in disguise (for example, Wickelfeatures employed in [76]). In fact, a ``neuron'' in these approaches has a coordinate as its label and an activation as its content, which render it a classical variable (a classical slot-filler). These endeavors may prove successful as far as engineering applications are concerned, but their theoretic implications, aside from being a limiting case of underlying quantum computation, is rather problematic. As far as the artifact design of sub-symbols is concerned, these approaches are top-down.

Statistical approaches are perhaps the most engineering-oriented among these models for language and logic. In language research, in particular, there are a growing number of projects [80,81,82,83] that employ large natural language corpora as the source of bottom-up knowledge. In reasoning, a similar motivation has spurred statistical modeling of decision making (Bayesian/Markov approach, etc.). The main merit of these approaches is that they emphasize quantitative aspects and are able to ``learn.'' Nevertheless, the constitutions of these models are more or less arbitrarily postulated. It is more a matter of engineering. For most statistical approaches, an intelligible explanation that can be traced to the brain is rather an unimportant issue. In fact, while a statistical approach can accommodate many intuitive stochastic processes, parameters of the model and the model itself (how many hidden states, for example), it is still far from the genuine physical implementation in the brain. At best, such approaches can be regarded as an engineering-oriented abstraction of mental tasks. Moreover, since the parameters involved are real numbers (therefore additive), they cannot account for wave-like interferences.

In general, all these soft-computing models suffer an explanatory gap between primitive behaviors and the highly sophisticated structural and logical reasoning of a human being. It is like trying to explain how an earthworm might comprehend the Pythagorean Theorem and articulate a proof. (A postulate of mechanistic evolution does not help, since all arguments against classical physics apply to it as well^8.1.) I believe this difficulty lies in the heterogeneity within the theory -- that discrete classical computation has to be reconciled with continuous classical physics. This is impossible without resorting to Cartesian/Newtonian dualism, which may render the theories incoherent. In fact, this may oblige many researchers to take an obscure and radical ``unscientific'' step in that, as Jack Copeland (who claims to be a physicalist himself) [84] put it, ``the physicalism is supported by nothing but faith.''