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AB DIALECTIC.
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ABA FOUNDATION RULE               1
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We have seen in AA that phenomena occur necessarily as components 
of polar structures, as poles of phenomenal dipoles. Within a dipole
one of the components may be considered as the referential, or 
the foundation of the other. In other words, knowledge of a phenomenon 
cannot be dissociated from that of the involved referential and any 
proposition expressing this knowledge must refer explicitly or 
implicitly to this referential. We shall say that the proposition is
founded in the referential, which we shall call its foundation.

We have proposed the following classification of referentials:

proper (of human class)    
   pertinent (to phenomenon)
   non-pertinent
improper

This classification may be used as the base for a corresponding
classification of the propositions which we propose to call
FOUNDATION RULE:

Foundation                       Proposition type              

existing                         meaningful
   proper                           rational
      pertinent                        rigorous
      non-pertinent                    non-rigorous
   improper                         irrational
non-existing                     meaningless

Only rigorous propositions may be associated with a logical value, i.e.
be true or false. Logical inference applies exclusively to rigorous
propositions. All propositions involved in any logical calculus must be 
rigorous.

In AAA we have introduced UH, the human universe of discourse. It has  
a particular importance as foundation of the overwhelming part of 
human knowledge. With respect to UH the fondation rule may be precised 
in several details.

ABA FOUNDATION RULE               2

We have seen that the element of UH, the situation divides time into 
past, domain of objectivity and future, domain of subjectivity. 
Past admits knowledge, future admits belief and volition. Propositions
founded in UH have to respect this structure. Consequently, objective 
propositions are rational IFF (if and only if) they refer to past 
phenomena. Propositions refering to future phenomena are rational 
IFF they concern subject's attitude with respect to these phenomena, but
not the phenomena themselves. The proposition "The plain from Paris 
landed yesterday at 11 h." is rational and may be true or false on 
further condition to be rigorous, i.e. supported for instance by a 
record of plain arrivals.

On the contrary, "The plain from Paris will land to morrow at 11 h." 
is irrational. It is therefore logically undetermined, neither true, 
nor false. The question about its truth may only be reasonably answered 
by "let's wait and see". However, this type of proposition usually 
implies subject's belief. If that is the case, the proposition really 
means: "I believe that the plain from Paris will land to morrow at 
11 h." Now it is rational and may have a logical value, however with 
respect to my belief, rather than to the landing itself. It is true 
if I really believe in what I utter, it is false if I am lying. 

With respect to UH the foundation rule restricts the domain of 
rationality of objective propositions to the past and of subjective 
propositions to the future.

We shall use the terms "foundation", "foundation rule", etc. as 
implicitly refering to UH. In other cases involved referentials will be 
explicitly specified.

In the the rest of the present chapter we shall discuss the impact of 
the foundation rule and more generally of the relativity on the 
domain of human reasoning.

Let us start by applying the foudation rule to some of the best known 
logical antinomies.