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Tag: Demonstration

Privation ≠ Demonstration.

Published on February 7, 2026

In my studies this week, I was stuck on the following passage from Aristotle: “In other things, therefore, it is demonstrated after the same manner through conversion, that the conclusion is necessary, just as in existing or being present with a thing.” I wrestled with its meaning, or rather what its point was. After re-reading the chapter, and after many dialectical sessions with the tutor, a workable interpretation came to the surface of my mind.

I noticed that in the prior passage Aristotle is speaking of privations: “For a privative assertion is in a similar manner converted, and we similarly assign to be in the whole of a thing, and to be predicated of every.” The more I thought about it, the more I came to the conclusion that a confirmation of what something is not, could not be a certain demonstration of what that very same thing is. E.g. the propositions ‘no B is A’, and ‘no A is B’, co-witness a universal privation that both A and B are not each other. However, we have not ascertained what A and B are. On the other hand, the first figure syllogism Barbara demonstrates what A and B are: viz. ‘every B is A’, and ‘some A is B’ post-conversion. 

Therefore, in my notes, I wrote the following to summarize this passage: “What is affirmatively necessary, conclusively, is demonstrated by conversions.”

EAR

Aristotle, Prior Analytics. Book 1, Chapter 8.

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.

Ex nihilo.

Published on December 16, 2025

At first, the main ideas of this chapter were not immediately apparent to me on my first two introductory light reads. I was trying to organize it into parts but was not understanding how to divide the chapter. I think my field of view was too deductive, or narrow, having just come out of On Interpretation. It wasn’t until I began the process of taking careful notes and working through each line, that the main ideas revealed themselves: proposition, term, syllogism. It seemed as if Aristotle just picked me up by the collar from the ground, while I was in the middle of looking at the individual grains of sand, and showed me the bigger picture of the beach we were standing on, or at least to be aware of it. The terms form the proposition, the proposition forms the syllogism, and the syllogism signifies the reasoning, and perhaps the deeper meaning beyond it.

Everything after that, as far as comprehension were concerned, was locked into place, and it was not difficult to organize my notes. My question to the tutor then became: “Is this structural framework (proposition, term, syllogism) necessary to penetrate the truth of reality?” The simple answer was “Yes… this framework is fundamental to Aristotle’s theory of knowledge and demonstration, as it enables the penetration of truth by logically deriving conclusions from primary truths.” My reply was: “Then it seems to me that rational minds are incapable of omniscience, and creating anything from nothing, but rather coming to know what is, and what was; also, coming to fabricate, or form new things from what is, and what was, created prior to Man’s existence, am I correct? It seems as if Man was put into a reality, which he can come to know, and interact with, but could not create himself. In fact, it seems as if nothing tangible, or intangible, whether physical, or intellectual, would be something outside of, or in addition to, the given and designed capacity, or potency, of what could be.

So, i.e. rational minds must have been designed to employ this framework: to be aware of the truth, to investigate the truth, the know the truth, to be protected by the truth, and to teach the truth. The truth is, what is, as God has it to be. In His omniscience, it seems that he gave us the power to be able to come to know the energy of His will, which is what is. So, therefore, logic seems to be an invitation to walk with Him, to penetrate the truth, be transformed by the truth, and perfected by the truth.”

The tutor replied and introduced me to a new term: “The intellect does not bring into being new essences or realities from nothing but discovers and works with what is. Therefore, your understanding that man is placed in a reality where he can know, interact with, and form new things from what is pre-existing, but cannot create himself or reality ex nihilo (from nothing), aligns well with Aristotle’s philosophy as presented in these classical texts.”

EAR

Aristotle, Prior Analytics, Book I, Chapter 1.