A Note on Several Logical Systems - Part 1

I think it will be better if I begin this discussion explaining  two fold Aristotlean dialectic logic which is  in power  now , due to the (neo) imperialist's propaganda .

The term 'statement' is essential to explain any sort of logic . Statement means a complete idea with a precise and unambiguous meaning. Usually a statement is a single complete sentence.

For instances, Both "Five is greater than six" and " Six is greater than five. " are statements.

Incomplete ideas are not statements .For example "Five" , "is Greater than " are not statements. In a grammatical way, a statement should have a subject and a predicate.

Ambiguous ideas such as "He is a tall man." are not considered to be statements. ( As it emerges instantly the question what the minimum requirement of height to be a tall man is.)

Aristotle was the first to introduce a two fold dialectic logic to the world .That is why it is called as Aristotlean dialectic . According to his logic, any statement should get exact one value from the two , " true " and "false" , so a statement may be " true " or otherwise "false". Nothing is possible beyond that.

After several decades philosophers and mathematicians found some faults in this logic and introduced some reformations such as universal set.

The concept universal set was introduced by the philosopher and mathematician de Morgan.
He considered this statement "One is red.". Is it true, or is it false ?
Morgan said it is not prudent to consider this type of statement either true or false . We cannot say either "One is red." or "One is not red."
Morgan proposed that there are some sets called universal sets only in which the aristotlean logic can be applied.
According to him, being red or not is a question in the universal set of colours while one is in the universal set of numbers. Therefore it is meaningless to say " One is red " . Though the problem is solved the two fold logic has been more restricted than before.