Finding relation and pattern--Influence of Mathematics: formal inferring with concepts

Finding relation and pattern

Influence of Mathematics: formal inferring with concepts

Consciousness and matter are both objects which are to be discovered. As a formal language, Mathematics brought much influence, at least, including the knowledge about formal system, formal language, also about a special style of thinking－deducting
to find the truth, absolutely certain and indisputable. The logical truth in Mathematics, even, makes human think(or develop the fundamental idea), at least imagine, that logical calculus and formal-style--model of mathematics, can help human find more truth,
and that applying this style of thinking to other fields--defining formal systems well which are full of concepts and mutual relationships. This also invokes more “what, how and why”s--what is truth and what can be the truth, and how human could judge a truth,
if, why. In short, “Mathematics makes the invisible visible”, specially, Mathematics captures the invisible abstract pattern formally.

A formal system need not be mathematical as such; for example, Spinoza's Ethics imitates the form of Euclid's Elements. Spinoza employed Euclidiean elements such as "axioms" or "primitive truths", rules of inferences etc. so that a calculus can be built using
these. Each formal system uses a set of primitive symbols (sometimes known as an alphabet) to finitely construct a formal language from a set of axioms through inferential rules of formation.

It is also said that the world is a space in which is full of paradox, or of those paradoxical concepts, things and objects, which create paradoxical relationship. Generality and special is one of the paradoxical relations. However, in real world, the general
concepts is “hided”. The interesting thing is that abstracting is one of the capabilities which the Great Human uses to create concepts to discover the world, to find the paradoxical aspect of the concrete and special.

Abstract and general concepts are stable “beings” (not the meaningless imagination)and reflections produced and induced from the real, special and concrete physical world which could be seen, touched and perceived by feelings. Some, like Platu, assert that
these concepts are existing in another world, the idea world. Whereas, these are reflections of the real world in human brain. Even, the idea coupled with these abstract general should be founded then be represented. However, facing the concrete and real,
abstract concepts are just aspects. Human needs full description of real and concrete things.

Symbolized formal language is created by human to note these abstract concepts and the mutual relationships described formally! Formal language “hided” the real meaning behind the symbols, using the concrete invented symbols to represent the abstract meaning!
What does matter is not the superficial symbols, the meaning of symbols does really matter. These symbols make the abstract more concrete and easy to understand. Whereas, to some extent, more effort is needed to decode the meaning again and again. Formal language
is the pure outcome of human about the meaning in the brain.

It is difficult for human to know or understand the real world which is concrete, special and changeable with known concepts. Facing the complicated, the strategy of human is analysis with abstract to produce compartmentalized parts! Then synthesizing these
different parts with relationship to create the entire object is natural! Making use of less to represent the more, that is the wisdom of West! For the East, by contrast, people take the adverse－the entire first other than the parts! This is the difference.

With the involution of human mind, abstracting(selective attention), inducting from the special to the general, makes human find and obtain more practical truth. This wisdom is more about abstracting and deducting. Even, Human realizes that these great methods
of renovating world could be performed by the machine. Human can develop an ideal “mind” which has less disadvantages than human without the influence of the emotional and the animal instinct. Logically, the perfect and most reasoning “mind” is one of conceivable
developments of human. Human needs this perfect mind to understand humanity and to choose a better future. Maybe AI is the another greatest experiment since The Greece era. The result can invoke human think more about the value, the will of humanity and life,
more cherishing these unique creature.

The complicated capability of abstracting had produced many concepts in nature and social sciences at the beginning of human civilization. And this wisdom could also be used as a tool to create new concepts from old concepts in time and space. However, the
important problem is how to describe or demonstrate this pattern(capability or intelligence of abstracting) in any language or symbols? Can mathematics do this? Modern mathematics makes invisible pattern visible. First, maybe, making the pattern visible formally
in an understood way, such as, described in symbolized sign-system.

Another confused problem is that human can uses this wisdom all the time subconsciously. For example, in writing and speaking, “generally” and “concretely” are employed normally.

Some of the features of Aristotle’s theory of abstraction developed include: abstraction is a relation; perception and knowledge are types of abstraction; the objects generated by abstractions are relata which can serve as subjects in their own right, whereupon
they can appear as items in other categories. Paradox is the relation described as the law of the unity of opposite. Relation is invisible.

Subject is occupied easily by knowledge of only one aspect of paired paradox, this proconceived knowledge may lead one-sided understanding from known to another aspect of paired paradox, so a better understanding of the relationship between aspects of paired
paradox is requirement to know this world. The relationship is described by the law of the unity of opposite. Unity is about the existence of paired paradox both depend on the existence of each other, opposite is about the two aspects of paired paradox negate
each other, destroy each other. This relationship is there always, but hard to find and understand. We must know it and use it. Universals, accidents, forms, causes, and potentialities have being only as abstract aspects of individual substances. An individual
substance is identical to its essence; the essence has universal features but it is the singularity making the individual substance what it is. According to the relation, singularity of individual substance is negated by universal features, if subject does
the same thing, knowing and rebuilding the world is impossible.

In short, human is easy to be controlled by one aspect of the paired paradox. The active will of observing, finding, understanding and using is the most important to any one who does not want to be occupied by the known, the one aspect of the paired paradox.