In this article, I discuss the relation between methodology and advantage(expanding speed) for fixed mathematical expression of pursued quantity(purpose).

Axiom 1: A methodology is a one-one mapping between a set of methods and a set of applicable conditions.

A methodology must be both complete and consistent.

Axiom 2: For a methodology, in order to be complete, there must exist a method to be used under any condition; in order to be consistent, there is no more than one method under any condition.

For the following axioms, there is a common condition "when mathematical expression of pursued quantity is the same".

Axiom 3: For any two quantities in a close PS, when both are pursued well enough, in order to pursue one better, the other must be pursued worse.

For any methodology, there is at most one quantity that is actually the best pursued among all possible methodologies. From axiom 3, a pursuit system can not pursue equality and developing velocity the best together; can not have the largest satisfaction at each moment; can not pursue the largest satisfaction for each particle. This is called the incompatibility property of pursuit.

Axiom 4: Advantage of all methodologies forms an order, the order is invariant with dimension and unit of pursued quantity. Larger advantage leads to higher expanding velocity.

In science of pursuit, truth or fallacy is only decided by which makes system expanding faster. One ultimate truth(the best methodology) will triumph over infinite bad methodologies just because of its advantage. From axiom 4, if we could find advantage order in one pursuit system, it will be valid in all pursuit systems with the same mathematical expression.

If advantage is not influenced by unit of pursued quantity, large(more developed) and small(less developed) systems have the same expanding velocity when following the same methodology.

Axiom 5: A(M) is continuous function of methodology.

Continuity of A(M) means: For any M, if dM is enough small,

|dA|=|A(M+dM)-A(M)|

can be smaller than any degree. So any methodology that is similar to a good methodology is good too.

Number of methodologies in unit advantage is called methodology density in advantage order, marked as N(A).

Axiom 6: N(A) decreases with advantage. There is only one methodology at the maximum value of advantage: the best methodology. The best methodology consists of natural laws only.

dN(A)/d(A)<0

From axiom 6, methodologies can not be infinitely improved, so there is ultimate truth in science of pursuit. This is the reason why natural laws are time-invariant¡ªbecause they are always the best.

One fact foundation for axiom 6 is that truth is scarce compared with fallacies. The larger advantage is, the fewer methodologies there are.

In social history, people of different countries and races made many decisions in choosing methodologies. Statistically, these decisions are toward the same direction--basic natural laws, including more exchange, free market, better desire equality and pursuer independence. This should not be explained as coincident, because its possibility is too small. So "there are many perfect methodologies" is not true, and I propose "the best methodology is unique". This also shows a new way to discover truth in science of pursuit. The methodology improvement process in history provides us materials to establish causal relation from methodology to advantage.

In a perfect pursuit system, pursuing quantity A the best also means pursuing quantity -A the worst. In the universe, pursuing action the worst is equivalent with pursuing negative action the best. In society, pursuing happiness the best also means pursuing negative happiness the worst.

Axiom 7: A(M) becomes -A(M) when the purused quantity becomes negative pursued quantity.

So there is symmetry between good and bad. Number of methodology with advantage A equals to number of methodology with advantage -A. So there are both best and worst methodology(WM), and they are identical!

So methodologies that are neither too good nor too bad for any pursuit are called "wicked".

Axiom 8: Around any M except BM and WM, there exists an infinitesimal substitution dM at least, satisfying:

A(M+dM)>A(M)

there is also dm satisfying:

A(M+dm)<A(M)

Apart from BM and WM, any methodology can be both improved and worsen a little. So BM and WM are the only extreme value for A(M).

If there is a behavior Y brings more pursued quantity than behavior X, X can not happen in a perfect pursuit system. This is sufficient condition to prevent X from happening in a perfect pursuit system. On the other hand, if X happens, there is no behavior better than it.

Axiom 9:

A(M) is measured to be larger when average expanding velocity in whole system is larger.

¡°Average¡± refers to average value of expanding velocity for all time and all places. Exploiting the rest can make part of pursuit system expanding faster, but it can not make whole system expanding faster, so advantage is not evaluated by expanding velocity in part of a pursuit system.

From axiom 9, there is truth decision theorem:

In a pursuit system, truth or fallacy is decided by which makes whole system expanding faster.

One ultimate truth, best methodology, will triumph over infinite bad methodologies because of its advantage in expanding velocity.