##### volume **II:** Synopsis

#### page 3:

### Naming

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]