03-Aug-03
I am working on this right now. I have a lot more material to bring in and the grammer/syntax/spelling has not been checked. (There's a joke in there somewhere...) Consider it an alpha product right now.

Logic

I do not consider myself an expert on 'logic.' On the other hand, I have been using logic structures in my work and play for over 8 years. My studies in college focused on Asian Philosophies. This subject required a very good understanding of the contrasts between the notions of Western thought and reason versus the Eastern thought and reason. In short I know 'more than a little' about 'nothing in particular.'

Let's start with a definition provided by WordNet:

A branch of philosophy and mathematics that deals with the formal principles, methods and criteria of validity of inference, reasoning and knowledge.

Logic is concerned with what is true and how we can know whether something is true. This involves the formalization of logical arguments and proofs in terms of symbols representing propositions and logical connectives. The meanings of these logical connectives are expressed by a set of rules which are assumed to be self-evident.

Boolean algebra deals with the basic operations of truth values: AND, OR, NOT and combinations thereof. Predicate logic extends this with existential and universal quantifiers and symbols standing for predicates which may depend on variables. The rules of natural deduction describe how we may proceed from valid premises to valid conclusions, where the premises and conclusions are expressions in predicate logic.

Symbolic logic uses a meta-language concerned with truth, which may or may not have a corresponding expression in the world of objects called existence. In symbolic logic, arguments and proofs are made in terms of symbols representing propositions and logical connectives. The meanings of these begin with a set of rules or primitives which are assumed to be self-evident. Fortunately, even from vague primitives, functions can be defined with precise meaning.

Boolean logic deals with the basic operations of truth values: AND, OR, NOT and combinations thereof. Predicate logic extends this with existential quantifiers and universal quantifiers which introduce bound variables ranging over finite sets; the predicate itself takes on only the values true and false. Deduction describes how we may proceed from valid premises to valid conclusions, where these are expressions in predicate logic.

That was big and heavy.

The first paragraph defines the central goal of logic: 'Logic is concerned with what is true and how we can know whether something is true.' 

Western thought focused on the crispness of a topic or subject. He is tall. He is short. These are binary expressions. If A then not B. Let's pause here and look at Boolean Logic.

Boolean Logic

This leads me to truth tables.  George Boole codified a matrix of True / False results for any set of arguments.  This type of logic is called Boolean logic.  Below is a very simple truth table.  The actual content of each statement is not important at the moment.

Still working on this...  (Need to explain the table with real sentences.)

So, Aristotle taught that objects had a given nature about them.  An object was of set 'A,' therefore it could not be of set 'B' at the same time/moment.  But does this perspective always work? 

How many grains of sand does it take to make a mound?  Now remove one grain.  Is it still a mound of sand?  Remove another grain.  Is it still a mound of sand?  Continue this until you have but a few grains left in the mound.  Would you still call it a mound of sand?  Now, can you define at what point or grain count did the mound cease to be a mound? 

Time for a bit of Fuzzy logic.

Fuzzy Logic

Fuzzy logic is neither fuzzy nor logic in a formal sense. Fuzzy logic is about the gradience of things.  'A' is bigger the 'B' but smaller than 'C.'  To refer to the mound of sand example, fuzzy logic would allow us to say the sand is 100% mound at the beginning state.  With the removal of a grain, then the sand pile would be a little less of a mound.  Say 98% of a mound after 300 grains have been removed.  On the other end of the spectrum five grains of sand would be about 2% of a mound, while one grain would be 0.5% of a mound.

Fuzzy logic helps us to qualify and quantify the variations in the real world.  The concept of fuzzy logic was developed in the United States, but American companies refused to accept the idea.  Western thought did not allow for these in-between distinctions.  So it was exported to Japan, a place where such ideas were considered 'normal.' 

Today, fuzzy logic is used to control trains, concrete mixers and air conditioning systems.  Trains in Japan stop at just the right place in front of the platform, by using fuzzy logic controls.  You probably have never given it any thought, but it takes many hours (over 8) to process the raw materials used in concrete.  The ingredients are blended in a blast furnace, which rotates on its side.  Since this process takes longer than one regular work shift, different operators control the process.  Add to that an environment where temperatures are very high.  (pull book for more/better examples.)  Any place where the situation is extremely complicated or requires very subtle adjustments, fuzzy logic can be used in the control protocols.