Their exist many forms of formal logics. 

One of the several concepts important to logic is an ancient concept:

If antecedents, then consequences.

In recent decades, the concept of para-consistent logic has emerged.
It has found many applications, particularly in the cybernetics of control 

Para-consistent logics are tolerant of apparent or so-called "inconsistencies" 
among several premisses.

Para-consistent logics are worth studying as they motivate consequences from 
antecedents.  One key author is Graham Priest.

One of the principle questions that para-consistent logics raise is "How does 
one compose premisses?"  not necessary dependent on the geometric metrics rules 
of a  line.



On Oct 20, 2014, at 6:44 AM, Karl Javorszky wrote:

> Workshop on the Combinatorics of Genetics, Fundamentals
> In order to prepare for a fruitful, satisfying and rewarding workshop in 
> Vienna, let me offer to potential participants the following main innovations 
> in the field of formal logic and arithmetic:
> 1)      Consolidating contradictions:
> The idea of contradicting logical statements is traditionally alien to the 
> system of thoughts that is mathematics. Therefore, no methodology has evolved 
> of appeasing, soothing, compromise-building among equally valid logical 
> statements that contradict each other. In this regard, mathematical logic is 
> far less advanced than diplomacy, psychology, commercial claims regulation or 
> military science, in which fields the existence of conflicts is a given. The 
> workshop centers around the methodology of fulfilling contradicting logical 
> requirements that co- exist.
> 2)      Concept of Order
> We show that the pointed opposition between readings of a set once as a 
> sequenced one and once as a commutative one is similar to the discussion, 
> whether a Table of the Rorschach test depicts a still-life under water or 
> rather fireworks in Paris. The incompatibility between sequenced and 
> commutative (contemporaneous) is provided by our sensory apparatus: in fact, 
> a set is readable both as a sequenced collection and as a collection of 
> commutative symbols. We abstract from the two sentences “Set A is in a 
> sequential order” and “Set A is a commutatively ordered one” into the 
> sentence “Set A is in order”.
> The workshop introduces the idea and the technique of sequential enumeration 
> (aka “sorting”) of elements of a set, calling the result “order”, and shows 
> that different sorting orders may bring forth contradicting assignments of 
> places to one and the same element, resp. contradicting assignments of 
> elements to one and the same place.
> 3)      The duration of the transient state
> We put forward the motion, that it is reasonable to assume that a set is 
> normally in a state of permanent change – as opposed to the traditional view, 
> wherein a set, once well defined, stays put and idle, remaining such as 
> defined. The idea is that there are always alternatives to whichever order 
> one looks into a set, therefore it is reasonable to assume that the set is in 
> a state of permanent adjustment.
> We look in great detail into the mechanics of transition between Order αβ and 
> Order γδ, and show that the number of tics until the transition is achieved 
> is only in the rarest of cases uniform, therefore partial transformations and 
> half-baked results are the ordre du jour.
> 4)      Standard transitions and spatial structures
> The rare cases where a translation from Order αβ into Order γδ happens in 
> lock-step are quite well suited to serve as units of dis-allocation, being of 
> uniform properties with respect to a numeric quality which could well be 
> called an extent for “mass”.
> These cases allow assembling two 3-dimensional spatial structures with 
> well-defined axes. The twice 3 axes can even be merged into one, consolidated 
> space with 3 common axes, the price of the consolidation being that every 
> 1-dimensional statement has in this case 4 variants. The findings allow 
> supporting Minkowski’s ideas and also some contemplation about 3 
> sub-statements consisting of 1-of-4 variants, as used by Nature while 
> registering genetic information in a purely sequenced fashion.
> 5)      Size optimization and asynchronicity questions
> The set is the same, whether we read it consecutively or transversally. The 
> readings differ. We show that the functions of logical relations’ density per 
> unit resp. unit fragment size per logical relation are intertwined, making a 
> change between the representations of order as unit and as logical relation a 
> matter of accounting artistry. (“If I want more matter, I say that I see 66 
> commutative units; if I want more information, I say that I see 11 sequences 
> of 6 units.”)
> The phlogiston (or divine will) fueling the mechanism appears to be the 
> synchronicity of steps of order consolidation happening. Using the concept of 
> a-synchronicity we can understand that we can, for reasons of epistemology, 
> perceive only that what is asynchronous, and as a corollary to this, perceive 
> not that what is synchron, which we have reason to call dark matter or dark 
> energy.
> These are the main ideas to be presented at the FIS meeting 2015. Hopefully, 
> the main event, dealing with Society’s answer to change in fundamental 
> concepts of information, will find the proceedings revolutionary enough to 
> merit observation from close quarters.
> Karl
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