| This particular grammar of English uses systematic paraphrase as the principal tool in linguistic analysis. What happens when a process is systematized is that it is made to conform to some set of principles. What this grammar seeks to do is apply mathematically sound principles and constraints to the concept of paraphrase. There are at least two meanings for the term paraphrase (Merriam-Webster 1987:854). For this study we want to concentrate on the first: a restatement of a text, passage, or work giving the meaning in another form. The idea is that the meaning must remain constant while the words and the structure that the words bring with them change. For the scientist the use of the very term “paraphrase” must be changed from that commonly found in the literature. Among many language arts teachers and literary critics “paraphrase” has become eviscerated of this literal meaning (David Mulroy, 2003:15-17). Mathematics is the language of science and its descriptive apparatus, especially that of mathematical logic, has become an integral part of the scientific method. Good sound linguistics is the science of language and this means that mathematics should be a major desideratum for the student of language who uses the scientific method. Wanting to proceed scientifically we will try to use sound linguistic principles to analyze carefully selected observations made of English. |
General state of linguistics.In most fields of science the investigator is guided by some sort of scientific framework as he embarks on the analysis of the phenomena observed. In linguistics we cannot say that there is a dearth of frameworks and infrastructures upon which to build a theory. Even the modern frameworks seem burdened with elements of an impressionistic nature and of an intuitive origin (Edmonson & Burquest, 1994). This is probably due to the many valuable contributions made by anthropologists, sociologists, psychologists, and others, who all work in different paradigms (Chapman & Routledge, 2005). At the risk of continuing the confusion further this work introduces its own paradigm and develops its own set of modeling tools. Since the 1970’s there has been a virtual cultural war between the scientific community and the philosophical postmodernists (Nadeau & Fafatos, 1999:174). The protagonists are from a large variety of backgrounds, training, and education. Until recently the scientific training associated with linguistics has rarely included much of foundational mathematics or the hard sciences (physics and chemistry). Without having a solid foundation in model design, the modern investigator is usually satisfied working with definitions and terms adapted from other studies. The result appears to be that a linguistic theory is fundamentally a model of linguistic description. Theories of language that may have arisen have failed to find anything close to universal acceptance (cf. Pinker, 1994, Pinker, 1997). To formulate a sound theory, the investigator needs to make as many assumptions explicit as practical and build on them using principles that can be shown to be mathematically rigorous and sound scientifically. |
Observation & analysis of English.The easiest strategy for me has been to ignore many of the previous attempts to build theoretical frameworks. However, my intent is not to supplant deeply entrenched paradigms. The reason they are so popular has generally been their utility and enlightening nature. My goal is to exercise linguistic analysis and in this way create an illuminating description of English syntax with sufficient detail to be applied in many frameworks. Any exposition of English syntax requires some sort of descriptive apparatus and if this one is truly enlightening, perhaps it will become more widely used. This apparatus grows out of some of the more familiar principles of modern mathematical logic and generative linguistics. The feeling commonly conceded in the scientific community is that knowledge is best captured by mathematics. For example, Isaac Newton, who was the founder of modern physics, found it necessary to develop a whole new branch of mathematics (the calculus) so that he could model the principles of his field. Science is committed to the language of mathematics when it comes to bridging the awsome gap between human experience and physical reality (cf. Nadeau & Fafatos, 1999:175). |
Uninformed formality of this work.Today the work of building a descriptive apparatus is being influenced increasingly by certain ground rules for building models. When mathematicians and computer scientists approach their understanding of a domain, they use principles and rigorous practices. Imposing such constraints on a grammar of English brings about both rigor and explicitness. When I first published this work on the web, I expressed an unrestrained hope that its formal approach could lead to new scientific theories of language. In the meantime the linguistic approach to syntax has moved on. In some ways my approach has anticipated what has been done since. For example, the work published by Richard Montague in 1973 had the same focus as my 1974 thesis. The effect of his incorporation of logic and mathematical rigor, which I hardly had even an inkling of, was pivotal to the formalizations to come. The most influential movements in linguistics today concentrate developing a universal grammar (UG)—one suitable to the description of any and all natural languages. The transformations of some are greatly simplified, e.g., “move-alpha”, whereas the generative rules neglect any special details needed for a comprehensive description of the structure of English. The current framework of Optimality Theory concentrates the descriptive detail in the nature and order of constraints to be placed on the generative component. |
Universal grammar vs. descriptive apparatus.The noble goal of universal applicability motivated linguists to develop principles with certain parameters, which are set to define particular language sets. The idea is that where languages differ is in their precise application of universal laws (Carnie, 2006). Then there is the idea that the laws are universal, but that the differences in languages can be explained in the variant priorities placed on them. Sometimes there are attempts to go deeper into the details of particular languages, but often the result is that new models are developed. One such model is the Head-driven Phrase Structure Grammar (Sag, Wasow & Bender, 2003). What comes across to me as missing in all these approaches, and is particularly clear with HPSG, is the presence of a clear divide between theory and model. Linguists generally develop an apparatus and this they take to be their theory—somehow the mathematical constructs represent the theory of language. For example, in the literature the apparatus that I came to call “situational calculus” is called “model theory.” Perhaps this unfortunate nomenclature creates a blurring between scientific theory and the descriptive apparatus. It seems that some linguists side with mathematical constructionists (Pullum & Scholz, 2004). Constructionists are the mathematicians who are unable to accept as proof theorems involving constructions or algorithms of infinite scope. I have taken a cue from engineers, in one sense: “if there is a useful tool, use it.” It is my hope eventually to incorporate some of the ideas of modern linguistics, such as X-Bar Theory and Optimality Theory, for the syntactic base. Perhaps even some of Starosta’s Lexicase dependency grammar (Starosta, 2000) will prove relevant. I believe the general nature of these theories makes them fully appropriate to the more functional parts of the semantic component. |
Expanding understanding.The philosopher Ludwig Wittgenstein (1889-1951) said, “The limits of my language mean the limits of my world.” He might have been speaking of human language, but the same might be said of metalanguages, the apparatus developed to describe language. When these are no more powerful than human language, they can do little more than skirt around the real issues that need resolution to bring us to a deeper understanding. The recent work of the linguistic philosopher, Wolfram Hinzen has demonstrated the importance of syntax in the structure of the semantics of a language (Hinzen, 2007). Yet even this man seems to ignore the fact that the allegories and metaphors built into human language cannot but be augmented by such devices as are made available by mathematics. On the other side is the work of Hermann Helbig and the engineers building MultiNet, meant to represent knowledge in a semantic net (Hellbig, 2006). This effort seems often to ignore syntax in favor of the mathematical structures of formal logic. Hopefully a synergistic combination will increase our discriptive power and bring about a better understanding. |
Primitive nature of work.The major thrust that has come to characterize this work is the concept of paraphrase. This bears a very strong resemblance to the canonicalization of sentence forms found in the work of Rodney Huddleston and Geoffrey K. Pullum (Huddleston & Pullum, 2001) They restrict the application of their term to just half a dozen grammatical relationships. This contrasts to the scores of paraphrastic principles developed in the present work. The expressed hope, that my approach will be enlightening, has been encouraged by the work of such linguists. Perhaps the present work will contribute to the scientific and mathematical grounding of future linguistic theories. For example, it is possible the the generative rule I propose can serve as the base required by Optimality Theory, and these principles express the constraints. |
Evolution of work.This work has grown from a conglomeration of several smaller works. The present attempt is to bring all the pieces together into a single coherent whole. One major revision was to remove peripheral studies in logic keeping them as excursus for the interested reader. I have been only partly successful in this. As time has passed and the work has grown, these excursus have become more integral to the whole. This is especially true of the one for chapter 4. As mentioned above, there is a great need to revise these chapters. Ideally these excursus will reformulate what I call “situation calculus” as model theory and the lambda calculus. I have attempted to state formal rules for most phrase and segment structures, and been able to state many of the clausal transformations formally. This has come to make this work much more comprehensive than I had originally planned. It has also suggested a more thorough treatment of infinitives, participles and gerunds, which may take longer than I anticipated it would. |
| Studies on foundations and models, 1995–6 | Chapters 1–3 | 1996, 2006 |
| Studies on formal grammar and logic, 1979–85 | Chapters 4, 5 | 1997, 2006 |
| Studies on language use, 1993 | Chapter 6 | 1997, 2006 |
| Analysis of determiners, 1993 | Chapter 14 | 1994 |
| Studies on graph theory, 1998 | Section 5-6 | 1998 |
| Sentence diagrams as trees, 1974 | Chapters 7–… | 2003 |
| Development of PS-rules, 1993–2005 | Chapters 7–17 | 2003–2006 |
| Development of SS-rules, 1993–2002 | Chapters 7, 11–15 | incomplete 2003 |
| Principles of Paraphrase, 1989–2000 | Chapters 7, 9, 12, 16, 19–30 | 2000 |
| Development of Transformations, 1989–2002 | Chapters 7–15 | incomplete 2003 |
| Analysis of quantifiers, 1974 (MA Thesis) | Chapter 15 | July 2000 |
| Analysis of predicate structures, 1989–… | Chapters 17, 18 | incomplete 2003 |
| Analysis in terms of parts of speech | Section 2-6 | 2003, 2005 |
| Production rules (BNF) as object & class diagrams (UML) | Chapters 4–17, Appendix C §4 | 2004 |
| Lett’s rules for critical thinking | Paragraphs 1-6.1–5 | Jan 2005 |
| Syntactic analysis of case | Chapters 8 & 14 | Feb 2005 |
| Revised structural diagrams | Excursus & Chapters 7–11 | 2006 |
| Semantics of Pronouns | Section 11-1 | 2007 |
| Details of Venn vs. Euler diagrams | Paragraph 5-5.2 | 2007 |
| Complete revision of PS-rules | Chapters 7–20, Appendix C | Mar 2007 |
| Addition of categorization and classification rules | Chapters 7–11 | Apr 2007 |
| Introduction to MultiNet | Sections 6-5–6, Chapter 8 | 2007, Jan 2008 |
| Addition of PS-rules 33, 34 | Chapter 14, Appendix C | Feb 2008 |