Showing posts with label Charles Sanders Peirce. Show all posts
Showing posts with label Charles Sanders Peirce. Show all posts

Monday, May 12, 2008

Axiomatic Set Theory (AST)


I would like to pay homage to Charles Sanders Peirce (1839-1914), the very find logician and creator of Axiomatic Set Theory (herein AST). AST completes the deductive work of Aristotle, clarifies and generalizes the category notions of Emanuel Kant, and has become the basis of most modern mathematical methods. In short, AST has emerged as the essence of reason. That makes it an important thought for Ourkind.

Clarity of thinking, which grew bold with Socrates’ commitment to defining terms, found ready pupils in Plato and Aristotle. The work Aristotle did with deductive thinking (that is, think about things in context) is world class. Deduction set the stage for Kant’s categories and Peirce’s recursive axiomatic sets. It also allowed Euclid to define a geometric point of view that stood for 2,000 years. Even Einstein used deductive reasoning and AST methods to articulate and mathematically define relativity.

Peirce was a symbologist (all symbols must relate to real things) and a logician (all things fit hierarchically and recursively into sets: parts make wholes: sets sit), whom linked mind with matter. As such, he was a forerunner of boutonics (the study of bouton behavior) and an early Mind Scientist.

Peirce’s work foreshadowed the “hard problem” found in the study of consciousness. In creating a direct isomorphic link between the real and the ideal, between physical and metaphysical, Peirce set the stage for the modern boutonologist. We can now ideate using physical laws, and know that the real affects the ideal and vice versa. Finding the integrative force of life, which overcomes entropy, is just a short step away (artropy??).

To understand the power of AST, start with the Universe as the largest real thing, and then recursively place all other contained things in that Universal set. As you order these things, go from the largest things and down into the very smallest real thing known (a photon). Place these into named sets, categories, like Venn diagrams. In short, sit the sets to define your symbolic domain.

Now go smaller than the photon and move into the metaphysical area of Platonic ideas and their ideals. Your stepping-stone down is Quantum Mechanics and it’s known anomalies.

How can a particle be also a wave, at one and the same time? How does Uncertainty manifest itself into a predictable probability of material becoming? Why do all things have a life cycle and no-thing permanence?

The answers to these questions help we mindscientists know the nature of human consciousness. We see how boutons want to live and how they consume the traveling magnetic waves of energy (those formative forms). We see how this repetitive selection process ingrains a mind, of habitual behaviors, via bouton-populated neuronal pathways. In so knowing how the human mind works, we can help people make it work better.

Charles Sanders Peirce took a key step into this understanding. AST symbolism and logic best maps the mind. Sets sit for life.