Tag: Aristotle

Simply.

Published on April 18, 2026

I think the thing that brought clarity to this lesson, and indeed to all the prior lessons was learning that what is asserted universally is necessarily, and simply necessary – unless stated otherwise. This makes complete sense now, and my intellect, having happily accepted this teaching from the Philosopher, now automatically makes that assumption of necessity upon the hearing or reading a universal premise. At the same time however, I can sense myself now actively looking for any qualifying indication of particularities that communicate any sense or mood actuality in the syllogism.

Also, I think I now better understand what reductio ad absurdum is doing, and how there are two kinds simulating two different scenarios. The first being via contradiction, where an objection is made to a perfect or true syllogism. To which then that objection is assumed as true and tested against the original premises. The absurdities of that false objection becoming quite obvious. The second being via conversions or figures, where a false syllogism is asserted first. To which then the false syllogism, assumed as true in the reductio, is offered a perfect syllogism in a contrasting response, with the same premises to demonstrate which syllogism makes the most sense side by side. I attempted my first reductio ad absurdum mentally today concerning the issue of baptism in the Eastern Orthodox Church and found that it actually powerfully served to show the truth in the Catholic Church on this issue. I can see now the benefit of running through argumentation in order to put all these things into practice. It’s not to inflate the ego, but to seek the truth.

EAR

Aristotle, Prior Analytics. Book 1, Chapter 15.

Fluidity.

Published on April 2, 2026

One thing I was not prepared for was coming into contact with the fluidity of contingent syllogisms. Up until now, everything has been very straightforward and rigid. Syllogisms of necessity and actuality, while the rules were difficult to understand at first, now seem like child’s play compared to the two recent chapters on contingency. The idea of conceptual conversions, how what is initially asserted as contingent could theoretically be converted to its opposing contrary, almost seems to demand that the intellect keep a bird’s eye level view of the syllogism, and does not permit one to go ‘down the rabbit hole’ as it were with these premises. To me, it almost seems to beg that one does not grant any assertion made, but to pay closer attention the key words shaping the premises: e.g. ‘it happens’, ‘it may’, it could be’, ‘contingently’, ‘perhaps it is’, etc. It is all incredibly abstract, so I hope that it will lock in with more examples for the mind to sink in and latch on to. However, I think I am beginning to notice the general pattern going on here. The prior intense studies of being extremely sensitive of the middle, practicing the mental formation of valid syllogisms in different figures, and subdividing these chapters into main ideas is paying off in a big way. I would have given up at this chapter if I had not done the necessary work prior to this. Also, the conclusion at the end, really brings all of this home. Necessary conclusions require necessary premises, and contingent premises do not warrant necessary conclusions. That is a very profound idea to ponder on. A lot of claims are made in our times, and I need to get in the habit more of challenging an asserter to provide evidence for any great assertion made; rather than just taking him for his word and now being subject to whatever rhetoric is to follow, whether it be true or false.

EAR

Aristotle, Prior Analytics. Book 1, Chapter 14.

Indefinite contingency.

Published on March 26, 2026

This was again, a very difficult lesson to sift through. As I took notes, I was tracking and laying out what Aristotle was saying, but I was not comprehending the substance of the message at all. The key that seemed to unlock the fog over the text was coming to understand the distinction between definite and indefinite contingencies. I meditated and prayed on these two terms as I drove home from work yesterday. My mind focused on indefinite and trying to understand why Aristotle would using walking and an earthquake to demonstrate his point. I began to ask myself the questions like: “Is walking indefinite? How can it be indefinite if what walks, must walk, before walking to be known and apparent? Would that not be a definite act? Indefinite seems to imply perpetuity in action. Yet the earthquake does not happen without a prior cause and not indefinitely? Is it the earthquake itself that which is contingent here or something else?” Then I locked in on the term ‘for’ which was used in both examples. It was walking to the animal, and the time and place to the earthquake which was indefinitely contingent. So, then what is indefinite must be related to the predicate, if that were true, then that meant what is definite is concerning the subject. I took this interpretation to the tutor and received affirmation that this aligns with what Aristotle is teaching.

EAR

Aristotle, Prior Analytics. Book 1, Chapter 13.

Minor.

Published on March 6, 2026

There is a distinction that has remained with me from the past three lessons. It is that the minor premise alone being necessary, with the exception of Darapti, seems to never yield a necessary conclusive proposition. The tutor confirms my interpretation of why this is the case. I reason that it is because the lesser extreme is posterior to the greater extreme in a priori, therefore what is necessary of a lesser in any figure, necessarily has no bearing on its syllogistic relationship with a greater. As I think about this, it seems to me that if we forget the hierarchical flow of terms in the different figures of syllogisms, then we are certainly tempted into thinking of everything being autonomous to itself and having prior causes to it. I don’t know why, but I can’t help but wonder if this line of thinking is a rotten fruit of the post-modern intellectual movement. If so, then it would explain why everything for a rational mind seems arbitrary, disconnected, and chaotic. There is essentially no flow, no connection, no relationship, and frankly an abyss of pointlessness without a mind that is perceptive in Prior Analytics. This seems to be a recipe for a possible existential crisis.

EAR

Aristotle, Prior Analytics. Book 1, Chapter 11.

Necessarily.

Published on February 24, 2026

I wondered at why a conclusion must be necessary if a necessary universal premise is present in a particular syllogism. It seems that the answer, according to my investigation with the tutor, is because the universal seems to fix what is true, and the particular draws from it. I found this to be very interesting to meditate on. I.e. if we can affirm what is true of things universally, then there must be something that is, or is not apparent with one of the extremes. So, assuming the term logic is coherent, and the figure of the syllogism is sound, it seems that we have the key to investigate the relationships of the middle to the extreme, or the extremes to each other. To be honest, I hope we do more exercises of this to make this sink in. I’m now seeing that we must track: the predication logic of the terms, the structure of the syllogism, the positioning of the middle, the ontological mode being asserted, and the type of opposition being used in the premises.

EAR

Aristotle, Prior Analytics. Book 1, Chapter 9.

Substitution.

Published on February 24, 2026

I spent two weeks on this chapter. I think it was the most difficult I’ve encountered thus far, but my perseverance, and struggle has yielded some very illuminating fruits from the labor. First of all, I was not expecting Aristotle to switch the middle from B to A in the first part of this chapter. That caught me completely off guard, and I could not understand what in the world was going on, what we were talking about, why we were talking about it, and the purpose of these demonstrations.

Nothing made any sense at all. My mind, having become accustomed to B being the automatic middle, struggled to disassociate it from being anything else other than the middle term. This caused many problems in my comprehension and tracking of necessity with the 2nd figure. My mind incorrectly assumed that: B was still the middle, the examples given were still in first figure, C A was the original conclusion now being temporarily tested as the minor premise, and somehow that was supposed to tell me whether this reconfigured 2nd figure syllogism could be necessary or not. Only after much wrangling with the tutor did I then realize that A was the new middle, and everything suddenly become clear and simple. The only thing I could ask is: “Why would he not tell me when the middle was about to change?”. Whatever the reason, as I go into this next chapter, I’m going to be far more sensitive to term positions, and ontological nuance. It’s as if every word in the syllogism is now significant to me and drastically affects the meaning of what is being asserted.

EAR

Aristotle, Prior Analytics. Book 1, Chapter 10.

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.

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