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volume II: Synopsis

page 3:


At the root of language is naming. '. . . from the soil Yahweh God fashioned all the wild beasts and all the birds of heaven. . . . The man gave names to all the cattle, all the birds of heaven and all the wild beasts.' Genesis 2.19-20. Naming yields immense power, since for many purposes we no longer have to move things, which may be heavy and dangerous, to express ourselves, merely their names. Genesis

Naming establishes a correspondence between a two entities. Often these entities are a word and a thing or action, but in the most general view, we may name anything with anything. This is possible in our Universe because every observable event is unique even though it may have elements in common with other events. Behind the events, the quantum no-cloning theorem tells, us every quantum state in the Universe is also unique. No cloning theorem - Wikipedia

All that naming requires is a fixed correspondence which enables one thing to stand for another. So my name means me and I mean my name, in the sense that when I walk into a room, someone prompted by my presence may say my name.

Usually we think of the name as the simpler of the two corresponding things. So while I am an unbelievably complex biological entity, my name may be embodied in a few micrograms of ink or a tiny quantity of sound energy.

Naming creates new world or spaces. Whereas once there was just the world of plants, now we have created a 'plant name space' which serves as a foundation for all our talk about plants. In the abstract way we understand it here, naming is the root of imagination. Council of Heads of Australiasian Herbaria

We save a considerable amount of time and energy (and thereby gain fitness) by using names rather than things in our imaginative manipulations of the world. Truly, talk is cheap, thought even cheaper.

In English grammar, we call the names of things nouns, and the names of actions verbs, and these two classes of words, together with all sorts of modifiers, go to make up our language. So 'the boy killed the cat' gives us a clear representation of a certain class of event. More specifically, 'John killed Tigger' narrows the field down to the interaction of a particular boy with a particular cat.

We call the correspondence between name and named meaning. Mathematics has a more general concept, mapping, to cover the same idea. The idea is intuitive. Each point in a geographic map corresponds to some point on the surface of the earth, and vice versa. We create a mapping between two mathematical structures when we establish correspondences between named points in the structures. Map (mathematics) - Wikipedia

A natural language is sufficient to describe everything that happens in a natural world. So we can say a mapping exists between the language and the world. Our minds embody this mapping, so that we can observe a situation and describe it in our language. We also embody the inverse mapping, whereby we observe a piece of natural language and act it out or imagine it acted out in the natural world.

The true complexity of the world very quickly exhausts natural language. To name the millions of species, chemical compounds, stars, minerals and all the other things that scientists encounter, special technical names must be introduced. To deal with the task of naming everything, we turn to mathematics. Chemical nomenclature - Wikipedia

Mathematical language feeds upon itself, so that it may grow large enough to describe everything that happens in any possible world. One version of this language is set theory invented by Georg Cantor. We can use set theory to develop transfinite numbers, an unbounded collection of names with which we can approach the immensity of God or the Universe. Transfinite numbers - Wikipedia, Set theory - Wikipedia, Jech

Science proceeds by modelling aspects of the world. We begin by naming all the elements of interest, and then try to create relationships between the names that match the relationships between the things named. One of the simplest approaches to modelling is arithmetic. We assign numbers to sets of objects like mobs of sheep and bags of beans. Then we can use arithmetic to determine the numbers which will result when we add, subtract, multiply or divide the sets. Provided we do not make mistakes in our counting, we find that this works perfectly, giving us a sound scientific basis for accountancy in all its forms. Arithmetic - Wikipedia

Arithmetic is a simple mathematical language and yet is leads to the the deep mathematical and logical theories developed by Gö and Turing. Naming is also the foundation of our much more complex natural and scientific languages, to which we turn next. Alan Turing - Wikipedia, Kurt Gödel - Wikipedia

[revised 26 March 2013]

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Further reading


Click on the "Amazon" link below each book entry to see details of a book (and possibly buy it!)

Allen, Richard Hinckley, Star Names: Their Lore and their Meaning, Dover 1963 Jacket: 'From his studies of the writings of scores of ancient astronomers, the author has come up with a fascinating history of the names various cultures have given the constellations, the literary and folkloristic uses that have been made of the stars through the centuries, and the often incredible associations that ancient people established with the stars. ... The book is the only complete coverage of its kind in English. It is completely non-technical, hence accessible to etymologists, anthropologists and amateur star-gazers. But it contains so much unique reading material on early astronomical theory, so many delightful accounts drawn from the pages of books almost impossible to find today, that even the practicing astronomer will finds its pages refreshingly new and instructive.' 
Bierce, Ambrose Gwinnett, and David E Schults, S T Joshi (Editors), The Unabridged Devil's Dictionary, University of Georgia Press 2001 Amazon customer review: 'Ambrose Bierce, in this hilarious book, satirizes all aspects of human behavior. This lexicon that he has created provides often true insight in to the tacit meanings of otherwise benign words. For example, PRAY, v. To ask that the laws of the universe be annulled in behalf of a single petitioner confessedly unworthy. This book is a must-get.' Doshi 
Borowski, Ephraim J, and Jonathan M Borwein, HarperCollins Dictionary of Mathematics, Harper Collins 1991 'It is the immodest hope of the authors that this dictionary will not only prove valuable as a reference book for students of mathematics at all levels from secondary schools to a master's degree, but also offer much to interest a more general readership.' 
Bronowski, Jacob, The Origins of Knowledge and Imagination (Silliman Lectures), Yale University Press 1978 The Silliman Foundation Lectures: 'On the foundation established in memory of Mrs. Hepsa Ely Silliman, the President and Fellows of Yale University present an annual course of lectures designed to illustrate the presence and providence of God as manifested in the natural and moral world.' Jacket: '[Bronowski] examines the mechanisms of our perception; the origin and nature of natural language; formal systems and scientific discourse; and how science, as a systematic attempt to establish closed systems one after another, progresses by exploring its own errors and new but unforseen connections.' Library Journal 
Dauben, Joseph Warren, Georg Cantor: His Mathematics and Philosophy of the Infinite, Princeton University Press 1990 Jacket: 'One of the greatest revolutions in mathematics occurred when Georg Cantor (1843-1918) promulgated his theory of transfinite sets. ... Set theory has been widely adopted in mathematics and philosophy, but the controversy surrounding it at the turn of the century remains of great interest. Cantor's own faith in his theory was partly theological. His religious beliefs led him to expect paradox in any concept of the infinite, and he always retained his belief in the utter veracity of transfinite set theory. Later in his life, he was troubled by attacks of severe depression. Dauben shows that these played an integral part in his understanding and defense of set theory.' 
Eco, Umberto, and William Weaver (translator), The Name of the Rose, Harcourt Brace 1983 Jacket review: 'No mere detective story, we are given absorbing insights into [the] age - its history, its predicaments, its intricate politics and religious wars, its philosophy, mythology, science, handcrafts, cuisine, medicine and sorcery.' The London Times Literary Supplement.  
Hofstadter, Douglas R, and The Fluid Analogies Research Group, Fluid Concepts & Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought, Basicx Books 1996 Jacket: 'Readers of earlier works of Douglas Hofstadter will find this book a natural extension of his style and his ideas about creativity and analogy; in addition psychologists, philosophers and artificial intelligence researchers will find in this elaborate web of ingenious ideas a deep anmd challenging new view of mind.' 
Jech, Thomas, Set Theory, Springer 1997 Jacket: 'This book covers major areas of modern set theory: cardinal arithmetic, constructible sets, forcing and Boolean-valued models, large cardinals and descriptive set theory. ... It can be used as a textbook for a graduate course in set theory and can serve as a reference book.' 
Man, John, Alpha Beta: How 26 Letters Shaped the Western World, John Wiley and Sons 2001 Jacket: ' The idea behind the alphabet - that language with all its wealth of meaning can be recorded with a few meaningless signs - is an extraordinary one. So extraordinary, in fact, that it occurrred only once in human history: in Egypt about 4000 years ago, newly discovered origins that this book is the first to detail. Apha Betas then follows the emergence of the western alphabet as it evolved into its present form, contributing vital elelemtns to our sense of identity along the way. The Israelites used it to define their God, the Greeks to capture their myths, the Romans to display their power. And today it seems on the verge of yet further expansion through the internet.' 
Winchester, Simon, The Surgeon of Crowthorne: A Tale of Murder, Madness and the Oxford English Dictionary, Penguin Books 1998 Review; 'Absolutely riveting ... a portrait of the emergence of the modern tongue; an insight into Victorian mental health policies; and an evocation of a remarkable intellectual friendship between two men who were radically divided ... a tour de force' Will Self, The Times 
Alan Turing - Wikipedia Alan Turing - Wikipedia, the free encyclopedia 'Alan Mathison Turing, OBE, FRS ( 23 June 1912 – 7 June 1954), was an English mathematician, logician, cryptanalyst, and computer scientist. He was highly influential in the development of computer science, providing a formalisation of the concepts of "algorithm" and "computation" with the Turing machine, which played a significant role in the creation of the modern computer. Turing is widely considered to be the father of computer science and artificial intelligence. . . . ' back
Arithmetic - Wikipedia Arithmetic - Wikipedia, the free encyclopedia 'Arithmetic or arithmetics (from the Greek word ἀριθμός, arithmos “number”) is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations.' back
Chemical nomenclature - Wikipedia Chemical nomenclature - Wikipedia, the free encyclopedia 'A chemical nomenclature is a set of rules to generate systematic names for chemical compounds. The nomenclature used most frequently worldwide is the one created and developed by the International Union of Pure and Applied Chemistry (IUPAC). . . . The primary function of chemical nomenclature is to ensure that a spoken or written chemical name leaves no ambiguity concerning to what chemical compound the name refers: each chemical name should refer to a single substance.' back
Council of Heads of Australiasian Herbaria Australia's Virtual Herbarium 'Welcome to Australia's Virtual Herbarium (AVH) AVH provides access to information obtained from the collections held in Australian herbaria. Australia’s major state and territory herbaria house over six million plant, algae and fungi specimens. The collecting data stored with these specimens provides the most complete picture of the distribution of Australia’s flora to date. From this site you can search, map, download and analyse records from the databases of the major herbaria in Australia.' back
Genesis The Book of Genesis 'Genesis is the first book of the Pentateuch (Genesis, Exodus, Leviticus, Numbers, Deuteronomy), the first section of the Jewish and the Christian Scriptures. Its title in English, “Genesis,” comes from the Greek of Gn 2:4, literally, “the book of the generation (genesis) of the heavens and earth.” Its title in the Jewish Scriptures is the opening Hebrew word, Bereshit, “in the beginning.”' back
Genesis Genesis 2 '19 So the LORD God formed out of the ground all the wild animals and all the birds of the air, and he brought them to the man to see what he would call them; whatever the man called each living creature was then its name.

20 The man gave names to all the tame animals, all the birds of the air, and all the wild animals; but none proved to be a helper suited to the man.' back

Kurt Gödel - Wikipedia Kurt Gödel - Wikipedia, the free encyclopedia 'Kurt Friedrich Gödel (April 28, 1906 – January 14, 1978) was an Austrian American logician, mathematician, and philosopher. After World War II, he emigrated to the United States. Considered among the most significant logicians in human history—at the level of Aristotle and Frege—Gödel made an immense impact upon scientific and philosophical thinking in the 20th century, a time when others such as Bertrand Russell, A. N. Whitehead, and David Hilbert were pioneering the use of logic and set theory to understand the foundations of mathematics.' back
Map (mathematics) - Wikipedia Map (mathematics) - Wikipedia, the free encyclopedia 'In most of mathematics and in some related technical fields, the term mapping, usually shortened to map, is either a synonym for function, or denotes a particular kind of function which is important in that branch, or denotes something conceptually similar to a function.' back
No cloning theorem - Wikipedia No cloning theorem - Wikipedia, the free encyclopedia 'The no cloning theorem is a result of quantum mechanics which forbids the creation of identical copies of an arbitrary unknown quantum state. It was stated by Wootters, Zurek, and Dieks in 1982, and has profound implications in quantum computing and related fields.' back
Set theory - Wikipedia Set theory - Wikipedia, the free encyclopedia 'Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. The language of set theory can be used in the definitions of nearly all mathematical objects. The modern study of set theory was initiated by Georg Cantor and Richard Dedekind in the 1870s. After the discovery of paradoxes in naive set theory, numerous axiom systems were proposed in the early twentieth century, of which the Zermelo–Fraenkel axioms, with the axiom of choice, are the best-known.' back
Transfinite numbers - Wikipedia Transfinite numbers - Wikipedia, the free encyclopedia 'Transfinite numbers are cardinal numbers or ordinal numbers that are larger than all finite numbers, yet not necessarily absolutely infinite. The term transfinite was coined by Georg Cantor, who wished to avoid some of the implications of the word infinite in connection with these objects, which were nevertheless not finite. Few contemporary workers share these qualms; it is now accepted usage to refer to transfinite cardinals and ordinals as "infinite". However, the term "transfinite" also remains in use.' back is maintained by The Theology Company Proprietary Limited ACN 097 887 075 ABN 74 097 887 075 Copyright 2000-2018 © Jeffrey Nicholls