Category: Studies

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.

Quality.

Published on January 22, 2026

Quality also does not seem to be subject to bodily things. Rather, just like quantity, ‘what is’ seems to assume the quality that is apparent, or rather inherent in the thing that ‘is’. The question qualities answer does not seem to be a numeric one, but a kind of unique distinction, or similarity between the subjects being talked about. Assuming the same terms in the prior passage: e.g. 3 red blocks, 3 red sticks, 3 red stars, etc. Quality seems to address the accidental range of inherent shades, and hues, that can be seen by rational men.

Nicomachus, Introduction to Arithmetic. Book 1, Chapter 1.

Quantity.

Published on January 21, 2026

Quantity does not seem to be subject to any material body, rather, the material body must is assumed by the quantity itself, if there is an instantiation of the thing or things themselves. E.g. 3 balls, 3 sticks, 3 stars, etc. Quantity, being inherently true to rational men, seems to simply affirm how many there was, is, or could be, with anything that may be known.

EAR

Nicomachus, Introduction to Arithmetic. Book 1, Chapter 1.

3rd figure.

Published on January 20, 2026

This lesson went smoother than the other two figures. I was tracking all the distinctions just fine, so perhaps that is a sign that there has been a growth in perception for these syllogisms. One thing that became more evident to me as I began to notate, and chart the syllogisms, was the positioning of the middle term across all three figures. Viz. in the first syllogism the middle is both subject, and predicate, in the second figure the middle is only the predicate, and now in the third figure the middle is only the subject. Stumbling on this made the hierarchical flow of the first figure, the categorical order of the second figure, and the convergent induction of the third figure, more obvious to me.

Maybe this will all begin to tie together the more I internalize these valid syllogisms? When possible, I’ve been trying to just meditate on different ones in atomized form, the relationships of the terms, what they are implying, thinking of the middle, the flow predication, etc. I’m avoiding any attempt to do demonstrations on my own with any ideas I already know and sticking to ABC terms. I’m interested in finding out what is next from Aristotle now that these figures have been taught to me.

EAR

Aristotle, Prior Analytics. Book 1, Chapter 6.

Arithmetic.

Published on January 16, 2026

Tomorrow, I will begin studying Classical Arithmetic from Nicomachus’ treatise, Introduction to Arithmetic, simultaneously with Aristotle’s Prior Analytics. I don’t know where the idea came from, but I got the very strong sense that it was time to start Quadrivium with the Trivium. We’ll see how it goes, or rather – where it’s going.

EAR

M.

Published on January 14, 2026

I think just getting past the switching of naming conventions was a huge breakthrough for me. My confusion on the actual positioning, or rather the assumed signification of M, was a mess from the beginning. My assumption of its inherent alphabetic sequencing, as if it were univocal to the function of A, and then – with that flawed assumption – tracking the conversion of the major premise as if M is now posterior to N because it was originally prior pre-conversion. All these things were distorting my perception of the premises, their relationships, and their implications to the conclusive propositions. Nothing made any sense, and it only got worse during the subsequent reductions of invalid demonstrations.

Towards the end of my intense first line-by-line study on Chapter 5, all my notes were corrupted because of this error; but after getting into another dialectical tennis match with the tutor for clarification, and wrestling past my ignorant equivocation of M as if it were the subject, instead of the predicate, finally my error revealed itself, and then the light began to shine on everything I had previously stumbled through. There was an immense clarity as I re-wrote the notes, and with the proper terms defined for ‘NMO’, viz. M being properly understood as the middle term, I could then properly understand each line from Aristotle in a way that was not apparent before. I was able to ask the tutor more intelligent, and nuanced, questions and give more logical interpretations on sentences that were difficult to understand at first glance.

EAR

Aristotle, Prior Analytics. Book I, Chapter 5.

Mnemonics.

Published on January 4, 2026

Had I not stumbled upon the mnemonic chart of syllogisms, as used by the Renaissance masters for their students at that time, I would have been utterly lost in this chapter. I honestly could not figure out, why in the world Aristotle would provide all these different examples of invalid syllogisms, and not provide one demonstration of a valid one with predefined terms from natural philosophy. I was trying to understand the point and purpose of this. Every example he provided did not make any sense to me and felt very absurd to even reason with: “Some horse is no white, no crow is a horse, therefore no crow is white.” I kept asking myself, “So what? That, ‘no crow is a horse, while some horse is not white?’ What does that have to with a crow not being white? It has nothing to with it; these things are irrelevant and prove nothing about each other.”

Learning of Barbara, Celarent, Darii, and Ferio shed light on this question. It was such a huge breakthrough for me. Once I learned their propositional order, then it became a piece of cake to simply diagram out each syllogism in my notes and see why these were not working. In fact, I was able to quickly recognize what was universal, particular, privative, categoric, and the quick determination of the validity of each demonstration. I also noticed a commonality between the four perfect first figure syllogisms: viz. B A, C B, C A. Coming back to my original conundrum of not understanding why he demonstrates these as he did: it seems that he is showing us examples that are wrong, in order to make what is true more apparent to us.

Aristotle, Prior Analytics. Book I, Chapter 4.

EAR

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.