In a recent post I defined cardinality and ordinality as having the property of being either exact or in-exact and induction starts from the context of the inexact. Consistent with Objectivist epistemology an analysis of the terms demonstrates 'exactness' as the conceptual common denominator. It is important to know that I am using ordinal and ( Read more... )

Building from my last post, I want to 'chew' the ideas relating reason to emotion. Starting with the fact that nature has not automatically given us reason in the same way that it makes us hungry and horny, it follows that there is some key difference. Volition would seem to be the obvious choice. There is a sense where we choose to reason while ( Read more... )

This is a quote from Philip E. B. Jourdain's "The Nature of Mathematics' as reprinted in Newman's "The World of Mathematics', "Thales introduced the ideal of establishing by exact reasoning the relations between the different parts of a figure, so that some of them could be found by means of others in a manner strictly rigorous." Also, "The ( Read more... )

Mathematics and logic are man's monuments to objective reason. Right now they may look a little abused. Most intellectuals today are Kantians in that they agree with Kant that the human mind is not acquainted with absolutes through perception. Absolutes according to Kant are dependent on 'pure reason' which means independent of perceptual ( Read more... )

This project of certifying reason has kept my nose in my philosophy dictionary. I just looked up paradox and found the information interesting. I had always thought of paradox as a clear sign of an error in logic, which is impossible to generate. My dictionaries first definition is softer, something like, appears to be either true or false, but ( Read more... )

Thales is the father of philosophy, science and mathematics circa 600 B.C. Because - he did something that changed the way we look at the world. We know that Egyptian mathematics had a pure, theoretical aspect about it that made their cardinal numbers impractical. We have their 'rope stretchers' as an example of them using ordinal numbers to ( Read more... )

In the history of philosophy an important question is the question of origins. If, objectivly, there was an origin to what we call 'western thinking', its objectivity makes it possible to find. Whatever the answer, it must be of a sort that anyone might notice. Philosophy starts with the obvious. Ordinal numbers are obvious. We usually think ( Read more... )

When a baby is born it has no ability to form abstractions. In the history of humans there was a time when humans did not think abstractly. So, obviously, there must have been a first time when someone made that first integration. Rand's theory of concepts describes how humans use abstract thought as a tool to enhance life. The first thing ( Read more... )

Continuing my attempts to bring some kind of certainty to philosophy, this is an argument that unites perception and irrational numbers in that they are both ordinal and can only be proved indirectly. This depends on Rand's correct identification that the concept 'unit' is the base of all numbers and concepts. A 'unit' is conceptual. To see ( Read more... )

Stated on my home page is a goal to teach the world the value of reason. The difference between objective and subjective in epistemology is that one can be verified and the other cannot. Integrity is a concept that refers to the integrations required for conceptualization. In general the concept furniture involves relations between tables, ( Read more... )