As analyzed in various parts of this thesis, there are fundamental disadvantages and failures in the classical approaches to language and logic. While very effective, one of their most grievous difficulties, for many perhaps the most fundamental one, is that they cannot provide a satisfactory explanation for why the brain, following the law of physics, can display activeness and creativity. The fact that the brain is a physical object is difficult to refute if we acknowledge the discovery of modern neurology and biochemistry. A reduction of mind down to simple physical phenomena, on the other hand, will eliminate even the most fundamental belief in individual responsibility. Ironically, this denies the responsibility of the advocators of the theories as well. These are taken as the main difficulties of anti-physicalist and physicalists, respectively.
The fatal fallacy of these arguments is, of course, that the law of physics is incorrectly conceived as to how classical physical objects mechanistically follow classical physics. It is also all but impossible to escape from Cartesian dualism in classical physics, and this renders the whole enterprise incoherent. On the other hand, once we are freed from a clockwork world view, a serious monistic approach to mind in general and language/logic in particular becomes conceivable again.
Specifically, the strategy of monism is an analogy -- whatever the case is in 
, that is the case in 
; and indeed that is the case in everything. But the paradoxical coexistence of classical objects (as measuring instruments) and quantum objects forbids a naive analogy free of (classic) logical inconsistency. In this regard, one has to trace the paradox all the way to an account of meaning (especially that of inconsistency) and ponder the genuine roles of symbol and language. In fact, one can arrive at this account of meaning by arguing along the line of Cartesian Meditations and, additionally, by taking language-like memory into consideration. Thus, it is symbol that has brought us to the idea of reality and it is the invariance of symbol brought us to the idea of objectiveness. One can see not only that there is a niche for a quantum mechanical account of language, but that in addition it must be a linguistic account of quantum mechanics. In this account, the invariance of symbols is equivalent to the invariance of eigenstates under the operation of an observable. This is the language formulation or representationing operator mentioned in Chapter 4.
Classical qualities such as truth and grammaticality have to give way to quantities8.2. Specifically, a state of affairs is to be regarded as a superposition of eigenstates. In this sense, the apparent well-definedness of macroscopic classical properties is a limiting case of quantum properties. It can only be addressed in aggregate. On the other hand, qualities per se have to be regarded as eigenstates (symbols) corresponding to a particular quantum experimental arrangement (associated with a formulation or representationing operator). As discussed in Chapter 4, these eigenstates are references without referent -- or symbols per se. In this sense, folk psychological terms such as freedom, intention, consciousness, emotion, etc. must have their own merits and can be consequently retained. The discreteness and abruptness of symbols can be satisfactorily accommodated. In fact, even classical consistency can be saved. This is because all eigenstates are orthogonal to each other. A symbol is either the case or not the case. Based on these observations, non-monotonic reasoning, counterfactual conditionals, and causal arguments (as counterfactual reasoning in disguise) can also be accommodated in this framework. In a sense, these approaches are a quantum computational simulation of others' subjective mind. It is therefore a framework for intersubjectivity.
In technical terms, the strength of quantum mechanics lies in its sophisticated mathematical formalism. Although the formalism is, mathematically speaking, well-formed and well-defined, one should not be lured to the idea that language and/or logic -- both classical and common sense, can be treated as well-defined at a higher level. It is the case only if we choose to represent them at the higher level. In fact, one should be careful here that well-definedness all too often goes hand-in-hand with conventional understanding of objective reality. Taking this position of ``higher level,'' one is apt to assert that at least the formalism of quantum mechanics is ``real'' (in its conventional sense). But this cannot be the case, for a coherent monistic theory cannot afford the traditional Cartesian hierarchic thinking. Rather, a quantum mechanical approach to language and logic has to be an epistemological instead of an ontological account. That is to say, the conventional way of separating res extensa and res cogitans must be put away.
Specifically, the Uncertainty Principle of language wards off the collapse of the approach as a whole. Furthermore, it also advocates the need for narrative as a complement of proof8.3. In fact, a narrative is holistic and content-rich; but a proof (or a classical logical argument) is local and content-free. So the complementarity of narrative and proof is implied in the symbol-concept duality which is associated with the Uncertainty Principle (technically speaking, it is based on the non-commuteness of formulation or representationing operators). In fact, the Uncertainty Principle sets the horizon of the intelligible discourse. A horizon not only indicates the limits, but also implies that there must be something beyond, but what is beyond the horizon is not describable (literally unspeakable).
Nevertheless, if the account proposed in this thesis is correct, there are a wide range of phenomena to be taken into account in a quantum mechanical theory of mind. In the future, a very important issue of quantum mechanical approaches to language/logic will be to re-apply the new theory to old linguistic/logical problems. For instance, it remains to be shown how conventional linguistic syntax (grammar, for example) and conventional semantics can be explained as an aggregate phenomenon in a language community. Also of interest is the acquisition of first and second (verbal) languages. In the case of syntax and semantics, we have to show how quantum computation can build a bridge between bottom-up non-verbal memory of the environment and structured verbal expression. In the case of language acquisition, we have to show how verbal expressions in a foreign language can first be simulated in the native language (through translation) and then become automatic (achieving fluency). Equally interesting is how situations and/or objects that are found in only one community can be expressed in another community -- using the same or a different language. Of course, it still remains to be shown how a verbal expression corresponds to its logical form.
In logic study, for example, it is interesting to see how expertise can be stored as a ``database'' of quantum states of affairs. There are many arguments -- legal, moral, and aesthetic, to name a few -- which are very difficult, if not impossible to be accounted for in a classical framework. These are interesting as well as practical scientific issues.
The second part of this thesis, it is hoped, has engendered a little optimism for the practical applications of a quantum computational approach. It is a matter of turning a theory into engineering. Indeed, quantum mechanics may have profound influence on natural language understanding/processing -- both in scientific and engineering terms. For one thing, classical symbolic as well as bottom-up statistical, template, or connectionist approaches to NLP do not offer any adequate account for subjectivity and intention. At best, the ``intention'' of a computer program (such as in a dialog system of diagnosis) is only a programmed function, created so that the user can make believe that the computer program is willing to help or is user-friendly.8.4 Indeed, it is hardly imaginable that a program without free will or emotion can in any way be called ``friendly.'' Moreover, it is as unlikely that an NLP system can help us in sophisticated works without understanding what utterances or texts actually mean. All these difficulties, it seems to me, have to be traced back to the absence of an adequate account for intention in both the classical symbolic and the classical physicalist theories of language.
The implication due to intention can be profound. For example, we come to an anticipated application of quantum mechanical NLP/AI in automatic agents, to which the intention of the host (a human user in this case) is to be understood. Without intention, it is hardly possible to talk about understanding. This is a crucial difference between a handy tool and a competent agent. For example, in an application consisting of an internet agent who is supposed to recommend to users which web pages may be relevant or of interest, the application has to have adequate access to the states of affairs of the web pages as well as that of the users adequately. In fact, for us as humans, a state of affairs is seldom a fixed and mechanistic ``representation.'' It is rather a dynamic and living whole that makes sense, most of the time, only to us. Evidently, the most suitable implementation of states of affairs of an agent are those that are genuinely similar to that of a human.