Glaucon (Greek: Γλαύκων) (born circa 445 BC) son of Ariston, was the philosopher Plato's older brother. He is primarily known as a major conversant with Socrates in the Republic (Plato), and the questioner during the Allegory of the Cave. He is also referenced briefly in the beginnings of the dialogues of Plato Parmenides (Plato) and the Symposium (Plato).
While I of course understood this conversation between Plato and Glaucon, there is a statement of reference that needs to be explained. So that it is not misunderstood that "the object" and "state of the one who questions and the one questioned," are shown to be like "God as the Geometer?" It is an "innate feature to the state of enquiry." That it follows alongside mapping, which advanced my own position of "methodology by intuition." An accumulated to a state called"Correlation of Cognition."
So by introducing "this brother"( a figure in mind to advance the developmental methodology,) to create this "state of being" within us, is much like an artistic endeavour of a plot, a writer, since one may not have had this conversation other then to move this story forward. How?:)
So I am glad there is a Glaucon who would move the conversation for advancement.
As Socratic method requires both a questioner and one questioned to move forward, Glaucon, who is the most honest about his ignorance amongst the friends, will help “build” the ideal philosophical city by engaging Socrates without fighting his ideas.
We hold (they say) these truths to be self-evident: That all men are created equal. In what are they created equal? Is it in size, understanding, figure, moral or civil accomplishments, or situation of life?Benjamin Franklin-The Gentleman's Magazine, vol. 46, pp. 403–404)
Our attempt to justify our beliefs logically by giving reasons results in the "regress of reasons." Since any reason can be further challenged, the regress of reasons threatens to be an infinite regress. However, since this is impossible, there must be reasons for which there do not need to be further reasons: reasons which do not need to be proven. By definition, these are "first principles." The "Problem of First Principles" arises when we ask Why such reasons would not need to be proven. Aristotle's answer was that first principles do not need to be proven because they are self-evident, i.e. they are known to be true simply by understanding them.
"Deduction" is an interesting thing left on it's own. While we think it only as one avenue to the methodology of approach, it is not without pointing out that the "inductive part" is part of this philosophical adventure too. That it should leave one to understand that the "infinite regression" leaves one on a precipice of change. That what is self evident, becomes the "new stepping stone for advancement."
A VIEW OF MATHEMATICS by Alain CONNES
Most mathematicians adopt a pragmatic attitude and see themselves as the explorers of this mathematical world" whose existence they don't have any wish to question, and whose structure they uncover by a mixture of intuition, not so foreign from poetical desire", and of a great deal of rationality requiring intense periods of concentration.
Each generation builds a mental picture" of their own understanding of this world and constructs more and more penetrating mental tools to explore previously hidden aspects of that reality.
Where a dictionary proceeds in a circular manner, defining a word by reference to another, the basic concepts of mathematics are infinitely closer to an indecomposable element", a kind of elementary particle" of thought with a minimal amount of ambiguity in their definition.