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Tag: Conversion

Reductio.

Published on January 28, 2026

I have learned and now know how to properly do the reductio ad absurdum to valid syllogisms. Even though, I think what I learned was perhaps too far outside the scope of this chapter. During my study, I saw there was a sharp distinction being drawn by Aristotle between ‘demonstrations’ and ‘demonstrating through the impossible’. For some reason, I sensed that I needed to fully understand what these actually meant, before proceeding any further. What ensued was a confusing week in figuring out what exactly I was looking at.

The principles seemed straight forward at first: assume the opposite conclusion, convert the premises if needed, and compare with original syllogism. It seemed easy enough to execute. So, with that in mind I began to write out, and chart different reductio examples from different valid syllogisms. The problem is that I did not realize that the reductio syllogism was structurally inverted. Meaning, that the opposite conclusion was now the new major premise, thus flipping the original order of the premises. I assumed that the premises of reductio syllogism kept the same sequence, but with the opposite conclusion being different. Also, my understanding of what direction the reductio would lead us was completely flawed. I mistakenly thought the reductio would lead us in the direction of imperfection, not back to the perfection of the 1st figure. Lastly, I was not aware that the lesser extreme in the valid syllogism becomes the middle term in the reductio.

All of these things were unbelievably dense, difficult, and confusing to sort out. However, I think I’ve learned a very valuable tool and intellectually grown from the labor I put into it.

EAR

Aristotle, Prior Analytics. Book 1, Chapter 7.

Conversions, & contingencies.

Published on December 19, 2025

I could not understand what the difference was between the fact that a necessary universal privative proposition is converted, and a contingent universal privative proposition is not converted. I thought that perhaps the answer would be revealed by asking figuring out why this was the case metaphysically. So, I went down the rabbit hole and tried to do an abstraction, and brought it to the tutor: “Why are universal privative propositions impossible? I reason that it is because even if A and B were not, the fact that they are, begins from somewhere, or some inductive universal predicate, or point of origin. E.g. every man is not every rock, and every rock is not every man, but both exist, and so therefore, they can’t mutually and indefinitely exclude the other into subversion.”

I overstepped myself, and the tutor tried to clarify and reel me back, while citing from Posterior Analytics, and later chapters in the Prior Analytics. I was not having any of that, so after a dialectical tennis match, I felt utterly lost, and that was not a good feeling. With a shattered brain the tutor finally brought me back to my original question, and demonstrated in a way in which clarity returned, and I could see again: “… the key difference between the conversion of necessary and contingent universal privative propositions lies in their logical necessity and how their conversion relates to syllogistic validity. First: “A is present with no B” being the necessary, and the second: “It happens that A is not present with any B” being the contingent.”

EAR

Aristotle, Prior Analytics, Book I. Chapter 3.

Asymmetry.

Published on December 17, 2025

Once I got passed the extremely subtle style of Aristotle’s demonstrations, the complex web of elements composing a proposition, and perceiving the entire treatise as being divided into four main parts, a question arose in my soul: “Why are there no universally converted affirmative universals?” I attempted to abstract the idea in my mind. It is difficult to explain what exactly I was seeing, for it wasn’t necessarily tied to any known natural dianoetic conception, but the image I got seemed to be a reduction to a single point, upon which there was simultaneous convergence, and divergence from which the entire fabric of reality flowed into, and out of.

In this painfully abstract image, I noticed something: it was not symmetrical, but asymmetrical. For it seemed that what is universal can only regress to something more universal, and likewise whatever is particular can only progress to something more particular. This seemed to be simply the way things are. I abstracted further, “Then what would symmetrical look like with this image?” I attempted to assert the condition in my mind, and whatever fabric of reality I was seeing, seemingly flatlined, immediately subverted, and then there was nothing. I didn’t know exactly what to interpret from this at first, but after pondering on it, the answer seemed to come up from the depths of my soul, I took it to the tutor: “Asymmetry allows for potency.” The tutor replied: “This asymmetry is important because it preserves the logical potency and prevents contradictions. If universal affirmatives converted universally, it would collapse distinctions between categories and make reasoning unreliable. In short, the lack of universal conversion of universal affirmatives allows for logical structure and potency by maintaining asymmetry in predication, which aligns with Aristotle’s syllogistic framework.”

So, I have learned that universal propositions seem to scale and model the logical deduction of predications that exist with what is, and the rational soul, with reasoning, through Aristotle, now has a way to coherently express these in proposition, with precision.

EAR

Aristotle, Prior Analytics, Book I, Chapter 2.