CHAPTER 4: THE STORY OF 'NOT'
 

Before I proceed, I must digress so you can hear the story of ‘not’. The story of ’not’ is also the story of ’may’ and ‘shall’.  The word ‘not’ frequently appears in our laws. It is common to see it escorted by the words, ‘shall’ or ‘may’, as in the sentences, ‘Thou shall not kill’ or ‘Thou may not kill’.  But what does it mean?  Or better, what ought it mean? How ought it be used?

In A Unified Theory of a Law, ‘not’ has a well defined job.  A flow of conduct has the property of polarity:  it is either positive (on) or negative (off).  The job of ‘not’ is simply to turn off conduct that is flowing. ‘Not’, by affecting the polarity of a flow of conduct is, therefore, a word that belongs to the ‘factual’ not to the ‘legal’.  In colloquial use, however, ‘not’ sometimes escapes from the ‘factual’ into the ‘legal’.  ‘Thou may not kill’ is often intended to mean the same as ‘Thou shall not kill'.  The ‘not’ in ‘Thou may not kill’ indicates the absence of permission.  It is like saying, ‘Thou hath not permission to kill’. 
The on and off state of a flow of conduct tends to make us think that both the legal aspect of a law and its factual aspect are binary. However, the legal aspect of a law is not binary.  It is tertiary.  Although the factual aspect of a law can assume either of two polarities: on or off, the legal aspect of a law can assume any of three permutations.  That which is not ‘on’ conduct is ‘off’ conduct. That which is not ‘off’ conduct is ‘on’ conduct.  However, that which is not one permutation of a law is either of two others.  For instance,  that which is not a command for ‘on’ or ‘positive ‘conduct is either a permission for either on or off conduct or a command for ‘off’ or ‘negative conduct and so on.

Therefore, to keep our thinking straight it is helpful to be mindful of the existence of the two factual polarities - off and on – and the three legal a permutations – a command for  positive  conduct, a permission for negative or  positive conduct, and a command for  negative conduct. 

Furthermore, both factual polarities of a flow of conduct either expressly or by implication exist in each of the three permutations of a law.
  1. A lawmaker desires one polarity of conduct not its opposite (command),
  2. A lawmaker is devoid of a desire for either polarity (permission), or
  3. A lawmaker desires the opposite polarity not the one polarity (command).
Although both polarities of a flow of conduct exist, both are seldom explicit.  Our language has evolved so that, usually, only one polarity is expressed.  In commands, the polarity expressed is the polarity that is desired not the undesirable polarity.  In permissions, the polarity that is expressed often depends upon the command against which it is compared.  One example will suffice to illustrate what goes on.  Assume that advocates of life promote the command, ‘thou shall not kill’.  Their opponents can advocate either of the two remaining permutations of a law: ‘thou may kill or not kill’ or ‘thou shall kill’.  Assuming further that their opponents are promoting the permission, the tendency is for the opponents to use the polarity that is the opposite of the one used in the command.  In the command, ‘thou shall not kill’, the negative polarity was used.  Therefore, the opponents would use the positive polarity and say, “thou may kill’.  Yet, using both polarities in the expression of a permission reinforces the central characteristic of a permission that a lawmaker does not object to either polarity of conduct. That is why we often see the word ‘or’ as a companion to “may”. After ‘may’, one polarity of conduct is expressed  and after ‘or’ the other.