A Quick and Dirty Guide to Formal Logic: Part I of IV

Preface:

To the detriment of our collective education the ability to form logical statements and draw logical conclusions has nearly disappeared in the US. Those who have braved the halls of higher education realize that the modern curriculum vitaea for most professors is exceedingly narrow. A doctorate in any particular field means extensive study within the confines of that field, as does most Bachelor degrees. Few institutions adhere to the tradition of the Greek and Roman Trivium or Quadrivium anymore and thus the education of a great many people has an excruciatingly shallow foundation. Obviously logic should be taught as soon as a child enters school, but it would require the public schools teach children to read prior to graduation, which is far too much to ask. As such, I and a few others thought it a profitable use of my time to develop a series devoted to helping those who have never been introduced to formal logic. We concern ourselves much with politics and abstract political ideas on the right, yet few have taken the time to sufficiently study the framework within which me attempt to make these arguments. By no means is this an exhaustive study of the subject, but it may help you frame and organize your thoughts and arguments in a more sound manner, as well as helping in the deconstruction of positions, particularly any works on philosophy, law, political theory, metaphysics and theology.

 

The foundations of how we understand logic in the West began with Aristotle’s Organon. I recommend a significant amount of caffeine before wading into it. The most relevant of the six I would say is Prior Analytics, however the scope and depth of the book is far, far beyond what I am trying to achieve here and better left to the reader to slowly comb through. Some familiar with the field may protest that Aristotelian logic (also known as term logic or formal logic) has been replaced by the more modern predicate logic. My primary objection to this is the inadequacy of the field in philosophical applications without resorting to abstract algebra and it’s reliance on calculus to be understood. At a formal level it appears to be able to go further than term logic may, but for application by laymen it is unwieldy and needlessly complicated. As such, my references in this and preceding posts in this series to logic are a reference to term logic.

 

PART I: Terms and Syllogisms

 

The nature of term logic relies on precise definitions of certain terms, some of which have little to do with the colloquial definition of the word.

Deduction: the end goal of formal logic is to draw deductions from other, known facts.. Aristotle defined it as such: “certain things having been supposed, something different from those supposed results of necessity because of their being so.” Admittedly it is a clunky definition, better illustrated.

All Greeks are human.  [ G = H ]

Aristotle is a Greek. [ A = G ]

Aristotle is a human. [ A = H ]

For sake of the illustration assume we did not know if Aristotle was human, but we did know that all Greeks are humans. We also know that Aristotle is a Greek. By knowing these two things, we may deduce that Aristotle is human because if the prior statements are correct then Aristotle must be human. No other options exist. Deduction at its core is that leap we allow the mind to make by eliminating all other options on the table to arrive at a conclusion we have not verified by our own experiential knowledge. One caveat made by Aristotle is that a proper deduction must contain a  different fact than those in the premises. One may not conclude that all Greeks are human because…all Greeks are human.

 

Syllogisms: A syllogism is a form of argument that allows us to deduce something. The primary focus of differentiating syllogism is one of form and function. If logic were a car to get us from point A to B, deduction is focusing on the fact we can get from A to B using the car, the syllogism would be the roads the car takes to get to the destination. Formal logic consists of 24 valid types of syllogisms, none of which you need to memorize for a test.

  •      The structure of a logical syllogism is extremely important. Every term must contain a subject and a predicate. In my previous example the subject in the first sentence is Greek. The predicate is human. Likewise in the second sentence.
  •      Contained within the syllogism are a major and minor premise. The major premise is the sentence that contains the predicate of the conclusion. Going back to our well-worn example, human is the major term, making ‘All Greeks are human.’ the major premise. Similarly, the minor premise is the subject of the conclusion. In our example, ‘Aristotle is a Greek.’ would be the minor premise. This matters because it allows us to take a sentence and construct it in standard form.
  • The standard form of a syllogism is major premise, minor premise, conclusion. Once again referring to my example, you will see it is in standard form. One does this to orient the argument in the same way every time to avoid confusion and provide a consistent basis for comparison.

Proposition: Propositions are the building block of syllogisms. A proposition consists of a subject and predicate (verb). The major and minor premises are each a proposition, as is the conclusion. It may be helpful to think of it like this: 1 syllogism = 3 propositions, and one proposition = 2 terms.

 

Square of Opposition (also known as you definitely need to understand this): Propositions are split into four categories: A, E, I, O. Allegedly the categories were named as such during the Middle ages for nEgO (I deny) and AffIrmo (I affirm). What helped me remember these is 1) keeping them in the same order as we say vowels (A,E,I,O,U) and 2) the mnemonic or whatever you wish to call it, AbsolutE. The A and E categories are universal statements (more on that later), and the other two can be worked out by…logic. The two sets of factors each of these represent are universal and particular statements, and positive and negative statements. Textbooks and academic material will refer to it as the quantity, and quality of the proposition, respectively.

  • A – Universal, affirmative statement. “All (subject) is (predicate).” You should be able to see it’s universal by the term ‘all’ or ‘every’ or some other quantity that denotes such.
  • E – Universal, negative statement. “No (subject) is (predicate).” E is merely the converse of A. It consists of the same quantity, but a different quality, it being negative and not positive.
  • I – Particular, affirmative statement. “Some (subject) is (predicate).” This is NOT a universal statement, but one made about a particular subject within a group. In a practical sense it is less than A but more than E.
  • O – Particular, negative statement. “Some (subject) is not (predicate).” This again, is simply the converse of I.

 

In conclusion, while probably not the most riveting thing you have ever read, the discussion of logic is highly dependent on working within the established definitions and structures that make it up. Much to the denigration of the field, many works and textbooks either do not define, or put minimal effort in cultivating the reader’s understanding of the language before the main body of the work. None of the concepts discussed here are particularly difficult to grasp, but grasp them you must if the rest of these posts are to make any sense. Practice also helps as well, go pull a news article off CNN and begin arranging the meat of it into syllogisms. See if you can put them into a standard form, parse them out and identify the propositions made by letter. Not all will fit, as you will see there are some caveats to the square of opposition, but it will help you immensely over the course of this series of posts. The most dangerous thing to the status quo you can start doing this week is to stop being entranced by the noise and faux controversy, and start developing your mind. Spectators didn’t build Western civilization, and they won’t rebuild it.

 

 

 

 

Spread the love
                

Share This Story, Choose Your Platform!

About the Author: admin

19 Comments

  1. phil May 7, 2018 at 10:04

    Times change over the years. My 10th grade geometry class was almost solely about formal logic; how to do formal proofs about the principles of geometry. 10th grade for me would have been in 1979? Even that long ago it was not a required class though – only those of us wanting to get to calculus in high school took it.

  2. Wise Owl May 7, 2018 at 11:17

    Excellent! Liberals are devoid of logic/reason. If a conservative wants a car, they realize that it takes money to buy the car, so they set about to acquire money buy earning/saving. A liberal sees them with a car, and thinks “I want a car. I deserve a car. Why should THEY have a car and not me? I demand a car. Gimme a car. it’s unfair that I don’t have a car”, and so on. Liberals think with their feelings, not their brains.

    • DWEEZIL THE WEASEL May 7, 2018 at 11:47

      Wise Owl: Very true. Sadly, that kind of thinking has polluted our “Public Education” system for generations. And here we are.

    • Fred May 7, 2018 at 12:15

      This is Envy, a sin.

      • DWEEZIL THE WEASEL May 7, 2018 at 19:11

        Fred: Liberals do not believe in sin. That is why they are so dangerous. This is why so many of them are in public office at all levels. We are very close to a fight for our very survival.

        • Fred May 8, 2018 at 12:13

          Exactly. Jesus came to save sinners. If you don’t have the introspection or an epiphany then you’re not going to realize your sin. Some folks are jerks or violent dangerous people and don’t think that’s bad, necessarily. They are not sinners, well, they are, but they’re not. You get my point.

  3. Fred May 7, 2018 at 12:11

    My brain seems to do this automatically. But, of course, I don’t know when it doesn’t. So, I suppose that I now need to look for where I may miss a minor premise – major premise connection. Sweet, I’ll try it. I’m not taking the CNN challenge though. There are simply too many opinions stated as fact to be effective for this exercise, or maybe that’s your greater point. I’ll look for it elsewhere as I go.

    “Similarly, the minor premise is the subject of the conclusion. In our example, ‘Aristotle is a Greek.’ would be the minor premise. This matters because it allows us to take a sentence and construct it in standard form.
    The standard form of a syllogism is major premise, minor premise, conclusion.”

    1. Can you give us an example beyond ‘If all Greeks are humans, and if Aristotle is a Greek, therefor Aristotle must be human’ please? (or is that to follow in subsequent installments?)

    2.How, if we call the minor – major connection, a second order conclusion, can we attempt to reach third order conclusions and beyond? I suppose attempting to supply a statement of fact beyond yet another “therefore” would be worth a try, no?

    (This is one reason I like the Bible. Lot’s of therefor and wherefor. Smile. Always read to beyond the ‘therefor’ when reading the bible.)

    • Sonya Choate May 7, 2018 at 16:52

      Great comment about the Bible. There is only truth written in those pages. Prairie God!!

    • Jesse James May 8, 2018 at 00:07

      Fred,

      There will be other examples, but I approached this from the standpoint of someone having exactly no experience in any way with term logic. One can construct subsequent valid logical statements based on valid deductions. Most logicians are exceptionally touchy that validity is a reference to the argument and not the truth of what is said. The construction of the argument may be valid, but if you reduce it back to a certain point you cannot simply deduce, you need to provide experiential, existential or self-evident fact. For example, logic cannot tell us what a human is. Truth is a metaphysical and theological concept, which is related to logic, but not necessarily the actual PRACTICE of it. It is part of the reason I am so obsessive about the underlying beliefs arguments are based on. Incorrect beliefs result in wrong deductions, even if they are LOGICALLY VALID.

      1) No communists deserve citizenship. Some Americans are communists.. Some Americans do not deserve citizenship. Notice the same interplay of the subject and predicate.

      2) Take the Aristotle example. We can now create another valid syllogism using our previous conclusion. All humans have ten fingers (stipulated as true for the sake of example). Aristotle is a human. Aristotle has ten fingers. On and on we can go, either constructing or deconstructing these things into more complex arguments. Think of it as Legos, each syllogism is a small brick on its own, but you can amass them into enormous orderly collections.

      Most people’s brains do this automatically, but we also have a tendency to ignore this cause and effect or logical deduction in favor of emotional appeals. Part of limiting/eliminating that is to be able to sit back and deconstruct your own beliefs or what you are being told and test it for logical consistency.

      • Fred May 8, 2018 at 12:02

        Thanks. Awesome answers.

        “Most logicians are exceptionally touchy that validity is a reference to the argument and not the truth of what is said.”

        From a (modern) scientific standpoint this makes sense to me because how could one investigate a theory using logical deduction if only current fact were allowed. So, we would not have, say, discovered that microorganisms were what was the biggest killer, if somebody didn’t posit that, perhaps, there is something smaller than we can see entering our bodies. And even then that attained knowledge that they existed and are alive and therefor potentially dangerous was still insufficient to finding a method to kill them with antibiotics/antimicrobials. It’s several investigative steps based on a hunch later proven by the ‘mere’ validity of the argument itself and not what was then a set of facts. Interesting, got it.

  4. John May 7, 2018 at 12:12

    A newsie on the street in Baltimore was interviewing a black man who was an admitted thief. One of the questions asked was “why do you steal from people”?
    The thief pointed across the street to a man who was wearing a thick gold chain
    and said “do you see that gold he’s wearing? That’s mine.”
    And there is the logic of the socialist.

    • Sonya Choate May 7, 2018 at 16:53

      Good analogy.

  5. Sonya Choate May 7, 2018 at 16:11

    As a high school student in the 1970s we touched on this s subject matter in English Lit. It was far too involved for 1 semester, but the classics should begin early and in depth. Thank you for taking on this series. I will be sharing far and wide.

  6. Neil M. Dunn May 7, 2018 at 18:23

    ” Reluctant monarchist because…” and “Recovering libertarian and….”
    Would you consider using the above as examples in this 5 part introduction to logic short course?

    • Jesse James May 7, 2018 at 20:52

      I’m not sure I follow, Mr. Dunn.

  7. Anonymous May 7, 2018 at 18:35

    4.5

  8. Sean May 10, 2018 at 12:45

    I don’t think I could reach to the end of part four about logic. I say that because I also dropped out of college, because things like this are a bit to difficult for me to study, let alone, understand. I’m a pretty simple man, and my logical frame of reference is to question every thing, even things that are supposedly bedrock that I know. The power of a question often exceeds the power that people try to wield in order to lord it over you. Using logic gives me power, on a limited scale, and mostly it gives rise to discernment, which also becomes an exercise in logic. For me, things, places, and time is what I deal in. I don’t cloud my own mind with things that can’t possibly be of use, like the things Aristotle said more than two thousand years ago, and took him many volumes to say. A basic understanding is all I need. Because a thing is lengthy, and difficult to grasp, doesn’t mean it is useful, or pertinent. You’d have better luck trying to convince me that all those Latin lessons taken by all those students in the 20th Century were useful to them, and pertinent to their lives. I believe that the downfall of the colleges in the US was not only the planned execution of dedicated communists, but an ossification brought on by neglect of the world changing around them. Look at them now, charging many thousands of dollars, and churning out illiterate communists and sexually confused idiots, with a “degree”. I’d give Aristotle his due, were he alive today, but too much is too much.

  9. RCW August 6, 2018 at 11:33

    Thanks for this enlightening post which; I’ve been eager to see the remaining three parts.

Comments are closed.

GUNS N GEAR

Categories

Archives

Spread the love