REVIEW - Glossary

Linguistic Consistency Objectives

In the mid Nineteenth Century P. M. Roget introduced his Thesaurus with the observation that “The most cursory glance over any Dictionary will show that a great number of words are used in various senses, sometimes distinguished by slight shades of difference, but often diverging widely from their primary signification, and even in some cases, bearing to it no perceptible relation. It may even happen that the very same word has two significations quite opposite to one another.” Whilst this situation may be of benefit to astute politicians, it is a serious problem that has to be addressed in attempting to define any logical theory.

This glossary is an integral part of the theory, and contains and defines the intended meanings of basic words used throughout the book. As Roget observed, Dictionary definitions of words usually offer a number of meanings that may be synonyms, differ subtly, or differ widely from one another. To avoid any misinterpretation of meaning that may arise from this, the definitions listed in the Glossary are the ones chosen from the selection of meanings offered for each reference in the dictionary.

The use of words with more than one distinct meaning has been avoided wherever possible. Words that are uncommon or abstruse, although they convey precisely a required meaning have been deliberately avoided. For example ‘incompossible’ is defined as "incapable of coexisting", and ideally and uniquely describes a situation of totally conflicting objectives. Somewhat reluctantly the more familiar word ‘irreconcilable’, which is less meaningfully appropriate has been used throughout the text.


REVIEW - Equations and Logic Diagrams

            The purpose of introducing mathematical equations in the text is to provide an alternative shorthand notation to narrative descriptions of concepts. The use of equations also implies a logical discipline that is being applied to the description of relationships. The equations are based on algebraic, Boolean, and Set conventions, each of which has its own peculiar limitations. Applying algebraic equations gratuitously can lead to illogicality and delusions of accuracy. For example the statement that management consists of 20% experience, 30% motivation, and 50% common sense could be expressed algebraically as:

                                                M = .2e + .3m + .5c

If true, this mathematical statement provides a convenient and concise shorthand notation of the previous sentence. Some people find such brief statements easy to remember. However, if the equation is manipulated using conventional algebra, the result it produces is bizarre. The equation can be rearranged to be expressed as:

                                                c = 2M - .4e - .6m

This suggests the absurd statement that common sense equals twice management minus 40% experience and minus 60% motivation. A more appropriate methodology is to specify Boolean logic, and avoid spurious numerical weightings. If the statement is changed to ‘management requires experience, and motivation, and common sense’ it can be expressed conveniently by using Boolean notation as:

                                                M  ^  e × m × c

In this notation the × represents the Boolean operator ‘AND’. Unlike an algebraic equation, weightings and values cannot be applied, and therefore a higher value of one element cannot be used to compensate for a low value (especially zero) of another element. The Boolean based equation means that for M to be True, e must be True, m must be True, and c must be true. Most importantly, the equation implies that all three of the elements (experience etc.) are necessary, and none may be omitted for this hypothetical equation of management to be true. In order to avoid ambiguity the narrative interpretation of all equations in the text is shown below them.


'You are old,' said the youth, 'one would hardly suppose
That your eye was as steady as ever;
Yet you balanced an eel on the end of your nose -
What made you so awfully clever?'

'I have answered three questions, and that is enough,'
Said his father, 'don't give yourself airs!
Do you think I can listen all day to such stuff?
Be off, or I'll kick you down stairs!'

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