Well most know I am a layman looking at the methods of your arguments and understanding the Traditional versus the Modern, is a understanding of the move from Aristotelian to Boole, as a historical sense of use of mechanics.
I had come to know about Plato's recognition of the pyramids in Egypt, as a pattern used in the Aristotelian Square of Opposition......Aristotle had to have learn this method, as an opposition too, Plato's point of views about God in Heaven, without suggesting that the way in which things flow downward.
|The Inductive-Deductive Method of Aristotelian Science|
Aristotelian intuition supplies the first principles (archai) of human knowledge: concepts, universal propositions, definitions, the laws of logic, the primary principles of the specialized science, and even moral concepts such as the various virtues. This is why, according to Aristotle, intuition must be viewed as infallible. We cannot claim that the first principles of human intelligence are dubious and then turn around and use those principles to make authoritative claims about the possibility (or impossibility) of knowledge. If we begin to doubt intuition, that is, human intelligence at its most fundamental level of operation, we will have to doubt everything else that is built upon this universal foundation: science, philosophy, knowledge, logic, inference, and so forth. Aristotle never tries to prove first principles. He acknowledges that when it comes to the origins of human thought, there is a point when one must simply stop asking questions. As he points out, any attempt at absolute proof would lead to an infinite regress. In his own words: “It is impossible that there should be demonstration of absolutely everything; there would be an infinite regress, so that there would still be no demonstration.” (Metaphysics, 1006a6ff, Ross.) Aristotle does make arguments, for example, that meaningful speech presupposes a logical axiom like the principle of non-contradiction, but that is not, strictly speaking, a proof of the principle. See: Aristotle: Logic
I will assign image symbology, as logica, grammatical, and rhetorica, to a triangle, the Square represents Earth. It is thoughts which fill my head that the liberal arts is defined when you look at the pattern, as the square of opposition, and that the peak is man's pinnacle and reach for God, and as modeled in the pyramid under this ancient schooling method.
The pyramid was a scheme for which those things which will become self evident, that after seeing infinite regress, allows views of Gods heaven to descend into the mind of man.
The Quadrivium is made up of the four triangles together with the trivium, seeks man as to perfecting. Each of the four triangles, represents aspects of perfecting when it comes to the understanding of the proponents of the Quadrivium.
The Quadrivium is made up of the four triangles together with the trivium, seeks man as to perfecting. The Quadrivium speak to a cyclical process as well as the developing the student toward logic, grammatical, and rhetoric.
This all belongs to Plato's Academy, but Aristotle took that pattern to the logic application, as the square of opposition, this, when Aristotle formed his own school.
|Parsons, Terence, "The Traditional Square of Opposition", The Stanford
Encyclopedia of Philosophy (Spring 2014 Edition), Edward N. Zalta (ed.),
All S are P, No S is P
All s is P is contrary to the claim NO S is P.
A contrary can be true as well as false.
Contraries can both be false. Contraries can't both be true.
The A and E forms entail each other's negations
Some S are P, Some S are not P
Sub contraries can't both be false. Sub contraries can both be true.
The negation of the I form entails the (unnegated) E form, and vice versa.
All S are P, Some S are not P,
Some S are P, No S are P
For contradictions -Two propositions are contradictory if they cannot both be true and they cannot both be false.
Contradictory means there is exactly one truth value and if one proposition is true the other MUST be false. If one is false the other MUST be true. The propositions can't both be true and the propositions can't both be false.
The A and O forms entail each other's negations, as do the E and I forms. The negation of the A form entails the (unnegated) O form, and vice versa; likewise for the E and I forms.
Every S is P, implies Some S are P
No S is P, implies Some S are not P
The two propositions can be true.
All S are P, Some S are P
No S are P, Some S are not P
A proposition is a subaltern of another if it must be true
The A form entails the I form, and the E form entails the O form.
Yes....I tried to get some clarity here regard such a start, and as a Universal. I have come to recognize, that such an association as may be given as to the statement of I am, of God, as something "inside the square of opposition" as it arose from the early understandings in relation to Aristotle and Plato. This, I have come to know of them, as expressions of the School run by Plato, and Raphael's setting of Aristotle and Plato together under the arch in that painting called Plato's Academy.
My distinction of intuition may be at odds with the classical description of the Aristotelian view, as to being infallible, while my own views were an assumption under the idea that such regressive moments, were when we had come to a point where infinite regress can no longer be applied, that such a step was necessary as to receiving the idea.
With regard to the advancement of science then, and under boole, the square of opposition changed as to being the undermined logic, as a product of the Aristotelian school. Mathematics then underwent a change in the modern sense as to giving up, the Platonism understanding of the Academy of the times.
While setting up for the idea, here I was seeking to have an idea as to descend into mind, was to me like inserting into an open space between the neurological function, as a gap. I was pushing discreteness to find that place in consciousness. Consciousness as a Derivative of Reductionism?
Can animals reason, yes they can, but do "ideas" settle into the neurological gaps as they do in humans? One would have to say yes as to the expressive state of animals as being part of God's creatures? Then, only to the degrees with which reason can be applied to animals, that such an idea may or may not be, evidential in the evolution of that animal? One may then understand "the idea of a stick being used" by a monkey in the termite hill, as to arriving from somewhere?