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Welcome to Rich Theory. This is a work about the foundations of mathematics and logic with an eye on the effects that such foundational theory have on the world at large.
I confess that this work is ideological at heart. I favor the classical liberal view over the modern liberal view.
I feel that many of the problems of the day are a direct result of paradoxes and convolutions injected into the foundation of logic during the Modern Age. As such, I believe that we can dramatically improve our ability to engage in discourse and reason by de-emphasizing the paradoxes, and by making a concerted effort to re-affirm the foundations of Sound Rational Thinking.
I call the work "ideological" because I believe that society advances by defining ideals through rational discourse. The problems of this world are not the result of people having ideals. Problems generally result from low quality discourse or from poorly thought through ideals.
Stated simply: Rich Theory is the belief that we live in a rich, multidimensional universe. In order to thrive in this multidimensional universe, we need healthy systems of language, logic, mathematics and economics that allows us to develop and communicate our ideas.
Rich Theory stands in contrast to many modern theories that place conflicts or paradox into the foundations of reason. For reasons that will become clear as this work progresses, I've chosen to call the negative theories Foundational Dialectics.
The work will examine Transfinite Theory in detail. Transfinite Theory is the logical foundations for New Math.
I intend to write a parallel work called The Sense of Value which will address my thoughts on economics. This secondary work discusses how the free market differs from Capitalism and Communism.
Both Rich Theory and The Sense of Value are deeply interested in education. Rich Theory claims that the classical curriculum that emphasized grammar, logic and rhetoric did a better job preparing students for prosperity than the modern system which is dominated by a desire to affect social change.
The Sense of Value argues that the goal of a liberal arts education is to help people develop their values and to give the student the tools needed to develop and communicate their values to others.
Following this logic, education itself becomes the primary concern of a free society. Education itself is the ultimate product in a free market.
To make the argument for Rich Theory, this work takes a detailed look at Western History. The presentation is tilted toward the thesis that the classical liberal view provides a better path to prosperity than the modern progressive view.
This work will dive into essays on complex mathematical topics including Calculus, Transfinite Theory, Topology, Symbolic Logic and other fun advanced concepts.
One of the primary contentions of Rich Theory is that educators should present mathematics as a tool for developing and communicating ideas. I intend this work to be a sample of public discourse that boldly uses mathematics in a general setting.
In this work I take great strides to keep the language at an accessible level. In my opinion, anyone who studied math through precalculus should be able to keep up.
Keeping the language at an accessible level does not mean taht I've dumbed down the subject. I have far too much respect for my readers to give them a "dumbed down" version of my thoughts.
Many of the books I've read on mathematical history skip the important role that religion played in the history of ideas. Even worse, a growing number of intellectuals have become openly hostile to Christianity.
As there are deep ties between our intellectual and spiritual nature, it is impossible to impart an accurate view of the history of ideas which does not take into account the both the positive and negative effects of religion.
I believe that secularism has had a positive impact on history because secularism encourage people to assess the good and bad aspects of a society's core beliefs. Unfortunately, some modern secularists have forgotten that the negation of religion simply creates a new—paradox ridden—religion. Efforts to cast aside religion for science has the negative effect of transforming science into a religion, which effectively undermines science.
The challenge is for schools and academic writers to develop a curriculum that imparts ethics and is supportive of religion in the community while avoiding the impulse to use the school as a tool for indoctrination.
The tact I take is to emphasize that religion is multifaceted. It is possible to find good and bad things in all religions. We make our world better by encouraging positive things and discouraging negative things.
This work is not about religion. The primary thesis of this work is that there are some aspects of classical western reasoning that work better than modern reasoning. The result of this thesis is that religions of the western tradition and of the classical era get better press than those of the modern world.
There are good and reasonable people in all religious traditions. Conversely, all religious institutions can be infilitrated and controlled by rogues. Regardless, imparting a healthy respect for spirituality and religious traditions is necessary for developing a healthy society.
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