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 Some familiar with the field may protest that Aristotelian logic (also known as term logic or formal logic) has been replaced by the more modern predicate logic.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.