Solo Furthering Education (Part 1)

[Kaizer Dragos]

Winter, 12, 515

The library in Lhavit was a place of great interest to Kaizer and one where he could often be found. On this day in particular the man was seeking to expand his into a new area of knowledge, philosophy. There were so many fields to study on such a number of interesting subjects that it was hard to pick just one. Never the less Kaizer narrowed his focus to something that suited his specific mindset, logic. Seated at a table with a book to the right and a quill in his left hand, the man was about to do what he was becoming notably better at, writing. The fresh piece of parchment in front of him and the nearby inkwell were calling his name.

To start with Kaizer began by reading through the book about the topic of philosophy and logic. He already knew that logic is the study of the principles of correct reasoning, however a deeper understanding of the specifics would be needed. Kaizer continued to read through the book about the basics and found them to be quite interesting. Much of what he had been doing for a number of years in regards to trying to understand the world around him had specific names. There was deductive reasoning which was quite simple, but then there was inductive reasoning where the conclusion, based on the presented evidence, wasn't absolute, instead it was probable.

Kaizer stopped to think about that for a moment and nodded to himself, it made sense. Deductive reasoning, with sufficient information, always ended with absolute proof of the conclusion. Inductive reasoning on the other hand pointed to the conclusion was that most probable. That was something Kaizer had done in the past as well, arriving at a conclusion that made the most sense based on the information at hand. Letting that sink in Kaizer thought about the two branches of logical philosophy, and appreciated how both helped people to pursue knowledge. One lead person to an incontrovertible conclusion while another lead to that which was most likely.

With a smile Kaizer realized how often he used both skills without even knowing it. Heinrik had always taught him to use logic and reason to understand the world around him, rather than falling prey to superstition and fear. He also explained that there was a logic to everything, including the gods themselves, even if the human mind wasn't able to comprehend certain matters. More than once Kaizer had seen people shrink away from something exclaiming it a curse from the gods, then upon closer inspection he found a logical cause that could be explained. On the other hand he'd also seen a few real divine curses that logic fell short of being able to provide an answer for. Bringing his thoughts back to the present Kaizer put quill to paper finally.

I find the study of logic to be quite interesting because it provides a lot of details about the processes that I've relied on most of my life. Through deductive and inductive reasoning I have come to a far greater understanding of the world around me than I would normally be able to. Now by starting to understand these processes I believe that I will be able to better analyze information that I come across, and help me in my endless pursuit of knowledge. I plan to study this in considerable detail as I feel it will also help me to categorize information more effectively as well.
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[Kaizer Dragos]

The next thing that Kaizer read about was the most popular method of logical reasoning known as modus ponens. The words seemed rather odd and he wasn't sure which language they originated from, however it was the definition that he was interested in. According to the book modus ponens was a form of elimination implication that is a valid argument form and rule of inference. Not sure exactly what part of that meant he turned a few pages to look up rule of inference. Those pages explained that rule of inference was a logic form which consisted of taking a premise, analyzing the syntax, and finally returning a conclusion. With a nod he returning to studying modus ponens.

A implies B, A is asserted to be true, therefore B must be true as well. The example given by the book was simple and easy for Kaizer to understand. This was a form of logical reasoning he'd used since childhood, however until now he didn't know it was called modus ponens. This was also where he learned something interesting about logic itself. An argument is considered valid if it follows the premise, regardless of the premise being true or not. If the premise was true then the argument was considered sound. Again lapsing into thought about that Kaizer understood the value of both.

Even if the premise of an argument isn't true, following the process helps to train a person's mind. Also arguments were one of the best ways for people to find out if something was valid or sound. Other people could often offer more information or details that someone else originally missed. The very act of arguing a premise was often how people discerned theory from fact. That was something that brought a smile to his face as Kaizer thought about past family arguments. He would often bring something up to Heinrik and the two would have a spirited debate about the topic, every now and then his mother would even jump in. Nine out of ten times Heinrik was right, but that slowly changed as Kaizer got older and the two often bounced ideas off each other for another point of view.

Now intent to write something about modus ponens in his research of philosophy, he thought about the subject for a time. There were some interesting terms for processes that people used in everyday life. He was also interested by a mention in the book that modus ponens was a branch of logical philosophy that predated civilization itself. Scratching his chin a little Kaizer finally started to write.

The method of modus ponens is an interesting term for something that a lot of people do in everyday life. It surprises my how often people use logic to try to understand the world around them without even realizing it. Although at the same time it also doesn't surprise me, it's a natural part of sentient nature to try and make sense of things around them, to understand how the world works and why. It seems that most sentient being have an innate need to add structure to their lives and try to form order out of chaos.
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[Kaizer Dragos]

The next subject of research was something called propositional logic. That was a term that perked Kaizer's curiosity because he'd never heard of it before. This meant it was something completely new to learn. At this point he learned it was also called propositional calculus which was a form of logical mathematics. That was something of an annoyance for Kaizer as his math skills were considerably lacking. Basic addition and subtraction were the current sum of his skills derived from the daily use of money, beyond that he knew next to nothing. Never the less he could read and try to understand the concept presented in the book.

This involved the study of propositions, regardless if they were true or false, that formed other propositions based on logical connectives, and how their value depended on the truth value of their components. That actually caused Kaizer to stop and think for a moment as he wasn't entirely sure what that meant. While staring off into space the gears upstairs turned double time as he thought about the implications of what was written. After a few minutes Kaizer still wasn't sure, so he decided to read further to see if it would help clear things up.

When C is expressed as “It's snowing” and D as “it's windy” the above symbolic expressions can be seen to precisely correspond with the original expression in natural language. They will also correspond with any other inference of this form, which will be valid on the same basis that this inference is. After reading that Kaizer arched a brow slightly. “What the f...” Learning back he was now even more clueless than before. Further reading only muddied the situation further rather than clearing it up. It was obvious to Kaizer that his lack of understanding mathematics likely had a large part in him being unable to understand this process.

Instead of getting annoyed he knew this is something that would likely have to be set aside for later. It was something that Kaizer would come back to later on when he had a better informational frame of reference by which to understand the process written in the book. It still intrigued him. Mathematics was something that he was interested in learning because he knew it was a tremendous source of knowledge used in highly advanced sciences. In the past he'd seen a few papers with very advanced equations written on them and had no clue what they were about, but he wanted to.

At this point in time propositional logic is something that I don't fully understand, but later on I would like to. Mathematics itself is, in my humble opinion, the true key to knowledge and a greater understanding of the world at large. More than once I've heard learned men speak of how mathematics is the language of the cosmos, and how it something we can't live without. Even without being able to perform advanced mathematics myself I know there is truth to these words. Without it our economy would collapse, there would be no way to count or number, honestly I can't imagine life without it.
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[Kaizer Dragos]

To help further his grounding in formal logical philosophy Kaizer returned to the front of the book to study the four basic principles. There was a lot of new information rattling around in his mind and it was important to keep everything in proper order. The first and foremost of four principles was consistency. This meant that a theory or argument had no contradictions contained within. For Kaizer that was something of a foregone conclusion as it was pointless to argue something that shot itself down. That was also one of the first things he did before presenting any reasonable arguments, checking them for consistency.

The next was validity which was a little more complicated. This meant that a logic system's rules of proof couldn't allow for false inference from a true premise. The system itself had to be sound, valid, and only use premises that are true. If the system of validity itself was flawed, then nothing that came of it could be trusted to be true or accurate. Kaizer knew that was the most important aspect of a system, before knowledge could be acquired through testing and reasoning, it couldn't allow for errors when the premise itself was true. In Kaizer's mind that was the foundation upon which all knowledge had to be built.

The third aspect was completeness. He thought about that for a moment realizing that while it may seem obvious on the surface, there was more to consider. The book definition was a formula that was true and could be proven. More than once in his life Kaizer had come across people who had good idea, but they couldn't maintain a proper train of thought and often rambled. It would be hard to understand what they were talking about or make sense out of anything. When he was younger Kaizer had problems with bouncing from subject to subject, although that worked itself out later on.

The fourth and final foundation of logical philosophy was soundness. This was a converse of completeness. It referred to logical systems and a formula that could be proven as true. This also held importance for arguments which could be proven as true in the real world. Nodding to himself Kaizer could see how these four principles were were so important for the study of logic in both the real world and the theoretical as well. Haven gone over these a second time Kaizer felt he had a better understanding of the formal aspects of logical philosophy.

Although I've pursued knowledge since childhood learning how to formalize this so that I can better present arguments and conduct logical reasoning will make the acquisition of future knowledge that much more satisfying. As I've written before there is a considerable difference between book learning and real world experience, but the two also play into one another. The more you know about something, the more you can learn through experience. Even in writing this I am doing both, learning from a book and trying to apply this knowledge to real life to improve other areas.
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[Kaizer Dragos]

The next section of the book really sparked Kaizer's interest as it discussed rival concepts in the philosophy of logic. While a lot of people considered symposiums to be boring, it was something Kaizer enjoyed more than just about anything else. Not only would a number of people often talk and even debate something, it was watching others pursue truth in knowledge that drove Kaizer to seek out the same thing as a child. Now he was quite interested to learn more about rival concepts in logic, seeing systems themselves compete against one another often gave rise to a greater understanding of knowledge itself.

According to the book this arose from a concern over the correctness of argumentation itself. Logicians desire to ensure that logic studies only arise from appropriate general forms of inference. Others have argued that logic does not cover good reasoning as a whole, that is instead the domain of the theory of rationality. Logic deals with inferences whose validity lead back to the formal features of representation involved in the inference, including linguistic, mental, or otherwise. Some rather serious consideration on the matter arose in Kaizer's mind from what he read. Some of the information made him think about the basis for logic itself.

There were others who argued that logic should be viewed as the science of judgment. One person quoted was concerned with both the laws of thought as well as the laws of truth, treating logic in the context of a theory of the mind, as well as a study of abstract formal structures. Now Kaizer was lost in deep thought over that matter as it dove much deeper into the meaning of knowledge itself. This also drew to the fore of his mind something else that had long been considered, but was itself an abstract concept. It was never something Kaizer had ever put to a test, even if he could, it was more a curiosity that remained with the man for a number of years.

This was something that bordered on metaphysical, but once again scratching his chin, Kaizer allowed his mind to drift. For a long time he had wondered if it was sentient thought that shaped reality, or perhaps it was reality that shaped sentient thought. The way people looked at and perceived reality around them was never the same between two individuals, not even identical twins, so what was it? Did the sentient beings of the world unknowingly belong to some mental gestalt that formed the basis of the reality they perceived. Perhaps it was the nature of existence and the world itself that shaped the very thoughts of those that lived within it.

So often I have wondered about the world we live in, and not just the aspect of exploring it, I've contemplated the very nature of existence itself. Though I have no means to prove this, in the argument about the mind shaping reality, or reality shaping the mind, I'm of the belief that both are true to a degree. I know there is great power in belief and the mind itself, power we have only just begun to understand. As an example I remember playing a team game as a child when I attended school. Many of the other kids attended as spectators.

When I did well the others would cheer me on, a few even yelling my name. When that happened I would feel myself getting stronger and more confident, now the question is, why? What was it about their cheering that gave me this new found strength? Was this strength always there and just needed a little help to be used, or was it perhaps something more?

Part 2
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