BREAKING NEWS DEVELOPMENT: Dr. James Weller has shown that fractal geometry can account for both the concepts: integrity and refinement.

If we say that 'an individual has integrity' what is implied by that?

Here is a good definition of 'integrity' : a self-similar value pattern that is morally stable; one that replicates itself at all levels, in all settings, and across time -- throughout one's life.

Such a pattern is a fractal. And this is explicated best by the mathematics of fractal geometry.

Here is a link to learn more about fractals:
Fractal - Wikipedia, the free encyclopedia

Dr. Weller has shown that fractals can also explain personal refinement. Here is a brief quote from the latesst issue of The Journal of Formal Axiology:Theory and Practice, (Volume 2, 2009), p. 142.

"The fractal model" he writes, points to "an endless road of personal refinement. An individual may quickly sense that it is wrong to kill, but applying that principle at a new level, he sees that threatening a person's social life is similar to threatening their physical life, so he chooses not to slander."

"Later he may become even more refined and acknowledge the harm that he does to himself by harboring angry fantasies about another. He is step-by-step turning away from contention and abuse, and towards attitudes of peace at progressively deeper levels within himself."

"By moving the conscious effort away from resisting grossly violent acts and towards adopting smaller, more peaceful impulses, he builds a broader barrier between himself and unethical behavior."

"As he effects these tiny changes near the core of who he is, the resulting pattern of being expands its way back up into his behavioral life to make largely visible differences."

Continuing on page 143 of that Journal he expands upon the implications of all this in a fascinating exposition which ends with these words:
"....In other words, while refining a just lifestyle she is also developing a merciful one." [formatting mine]

I, for one, believe this research is highly-relevant to Ethics and commend it to everyone's attention. There is no reason why you, the reader, cannot build upon this and carry the research forward. Merely study the geometry and see where it takes you, now that you have a feel for what ethics involves, and have an acquaintance with its major terms and relations. Apply the math by interpreting what it says in the terms of ethics, just as Dr. Weller has done. Extend it further.

This is how we are going to make real progress in Ethics.

The testable hypotheses will then follow; the measurements will be made; and the world will know that Ethics is a body of knowledge essential to the development of moral health on a massive scale. What the Science of Medicine does (albeit gradually) for physical health, Ethics does for self-improvement