Logic and Epistemology

You were born with a brain, but you were not born with an owner's manual for that brain. Science tells us that feral children who reach puberty without learning any language never really learn how to think. Thinking is a skill that we have to learn. It is not an inherent ability. More particularly, assessing the truth value of a declarative statement is something that is learned, not something we pick up via osmosis in the course of learning how to talk. How do you know that you know what you claim to know? Seriously, how do you make your case that you actually know to be true what you assert to be true? If you are not asking yourself this question at least once in a while, you might some day have to entertain the notion that you have no idea whether there is any truth to anything you claim to be true. The branch of philosophy which deals with this question is called epistemology. One way to handle epistemological questions is through logic (another is ideology, which will not be discussed in this post, except obliquely).

For the purposes of this post, I am going to make a distinction between symbolic logic and rhetorical logic. Symbolic (or mathematical) logic is a field in mathematics that explores the expressive and deductive power of formal systems. While a fascinating topic, it is highly abstract and not immediately related to the way that people express themselves and make deductions through spoken or written language. For that, we need rhetorical (or informal) logic.

Rhetorical Logic

Rhetorical logic is the analysis of how truth is conveyed through language. Truth is hard to define, but falsehood (especially demonstrable falsehood) is easier to define, so rhetorical logic is usually introduced by teaching the concept of logical fallacies. These are statements that use an argument that is flawed. There are lots of different ways in which an argument can be flawed, but fallacies are usually categorized into two major groups: formal fallacies, or flaws in the form of the argument (regardless of the subject matter of the argument); and informal fallacies, or other kinds of flaws in the argument (usually, but not always, in the content of the argument).

Formal Fallacies

A formal fallacy is a structural non sequitur (Latin for "it does not follow"), or an argument where the conclusion does not follow from its premises. This can happen for a variety of reasons. I'll go over many of the more prevalent:

Appeal to probability: just because something is likely to happen, does not mean that it will happen. "My small child wandered into the street. He must have been killed." Streets have cars, and cars drive fast. Sometimes cars hit people or animals that wander into the street. However, just because it is possible that a child in the street could be hit by a car, that does not mean that it is inevitable that the child was killed.

The Masked Man Fallacy: "I know who my father is. I don't know who the thief is. Therefore, my father cannot be the thief." The problem is that both premises can be simultaneously true even when they refer to the same person. You do not know who the thief is, and even though you know who your father is, your father might be the thief anyway and you might not know that your father and the thief are the same person.

Some specific types of formal fallacies are propositional fallacies, quantification fallacies and formal syllogistic fallacies.

Propositional Fallacies

Affirming a disjunct: "The car is red or the car is large. The car is red. Therefore the car is not large." The problem is that the or in the sentence is not an exclusive or (or xor), but an inclusive or (A or B means one of  a) A, b) B, or c) A-and-B is the case). The car can be large and red, and still have the premise be true.

Affirming the consequent: "Hostile people make Jane feel apprehensive. Alex makes Jane feel apprehensive. Therefore Alex is a hostile person." Alex could make Jane feel apprehensive for reasons that have nothing to do with any hostility on his part.

Denying the antecedent: "If my cat were a person, she would drink water. My cat is not a person. Therefore she cannot drink water." Even though the first premise is false, that does not make the conclusion necessarily false.

Quantification Fallacies

Existential Fallacy: "All unicorns are animals. Therefore some animals are unicorns." Unicorns are an empty subset of animals. An empty subset is still a subset. The quality of being a subset does not infer that the subset is non-empty.

Formal Syllogistic Fallacies

A syllogism is an argument in three parts: a major premise, a minor premise, and a conclusion. A simple example is: "All men are mortal. Aristotle is a man. Therefore, Aristotle is mortal." "All men are mortal" is the major premise, "Aristotle is a man" is the minor premise, and "Aristotle is mortal" is the conclusion. There are a bunch of different types of syllogism:

• A is a B; B is a C; therefore A is a C.
• B is not a C; A is a B; therefore A is not a C.
• B is a C; A is sometimes a B; therefore A is sometimes a C.
• B is not a C; A is sometimes a B; therefore A is sometimes not a C.

I could keep going here, but I'll stop. There are 24 valid syllogisms in total. If you mess with the structure of a syllogism, you get a syllogistic fallacy.

Affirmative conclusion from a negative premise: "We don't read that kind of trash. People who read that kind of trash cannot appreciate good literature. Therefore, we appreciate good literature." The conclusion does not follow from the premises.

Fallacy of four terms: "Nothing is better than enlightenment. A tuna salad sandwich is better than nothing. Therefore a tuna salad sandwich is better than enlightenment." The word nothing is being used in two different meanings here, creating a fourth term.

Illicit major: "All dogs are mammals. No cats are dogs. Therefore no cats are mammals."

Illicit minor: "All cats are felines. All cats are mammals. Therefore all mammals are felines."

Negative conclusion from affirmative premises: "All dogs are animals. Some pets are dogs. Therefore some pets are not animals."

Fallacy of the undistributed middle: "All students at Jefferson High wear uniforms. My grandfather wears a uniform. Therefore my grandfather is a student at Jefferson High."

Informal Fallacies

These are subtler, as they require an analysis of the content of the argument. They are also far more common. Let's tackle some common types:

Correlation does not imply causation (cum hoc ergo propter hoc): "Since the 1950s, global atmospheric carbon dioxide levels and rates of obesity have risen. Therefore, atmospheric carbon dioxide causes obesity." This fallacy is probably the most common, since it can be very persuasive.

Post hoc ergo propter hoc (Latin for "after this, therefore because of this"): "The rooster crows, and then the sun rises. Therefore the rooster's crow causes the sun to rise." This can often be more subtle. "I can't help but think that you are the cause of this problem; we never had any problems with the furnace before you moved into the apartment."

Begging the question: "Opium induces sleep because it has a soporific quality." Soporific means sleep-inducing. So it is assuming your conclusion in your premise.

False dichotomy: I deal with this one so often that it drives me nuts. "You are either with us or against us". Never mind the fact that most people are oblivious to the "us" in the previous statement. By reducing the myriad of possibilities by two, and observing that your opponent rejects one, you force them into the other possibility. "I hate how high my taxes are. You are less concerned about your taxes. Therefore you love paying high taxes."

Dicto simpliciter: "If you want to allow chemotherapy patients access to medical marijuana, then why not just legalize all illegal drugs?"

Hasty generalization: "Jane supports Proposition 1. Phil supports Proposition 1. Enrique supports Proposition 1. Trinh supports Proposition 1. Therefore everyone supports Proposition 1."

No True Scotsman: "No Scotsman would ever refuse a plate of haggis!"
"But Angus McClaren just refused a plate of haggis, and his family has been in Inverness for centuries."
"No true Scotsman would ever refuse a plate of haggis."

Cherry Picking: "Abraham is willing to sacrifice his son to God. Therefore, the Abrahamic faiths justify murdering your own child."

Ad hominem:  "Why should we listen to Bill's argument about the new budget? You know he cheats on his wife."

Appeal to fear: "A vote for candidate X is the same as voting for the terrorists."

Wishful thinking: "I dislike the incumbent. Therefore, if he is defeated in this election, our lives will be so much better."

Reducio ad Hitlerum: "You want to know who else invested heavily in infrastructure? Adolf Hitler. He built the Autobahn. Still think investing in infrastructure is a good idea?"

Straw Man: So called because one person builds a man of straw and demolishes it, instead of challenging the other person: "We should provide sex education in schools."
"Really? Telling them they can screw around with impunity? Don't you think that's irresponsible?"
The respondent is conflating sex education with an invitation to licentiousness, which is not the same thing as sex education, but easier to refute.

False analogy: using an analogy in your argument that does not sufficiently match the case you are arguing. "There should be a flat income tax. It's unfair to have a graduated income tax. That just punishes rich people for their success. After all, we don't penalize honor students for having good grades." Money exists in an economy. Grades exist in an evaluative educational setting. Grades are finite, whereas money is potentially infinite. The tools of economics cannot describe the fluctuation of grades, since money and grades are too dissimilar. There is an income tax, but there is no tax on grades, so it is comparing things that are qualitatively different.

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This should provide a start. Certainly you don't have to learn all these names, or be able to catalog these and other examples, but if you find yourself asserting that a fallacy is true, you are wrong. Basic intellectual hygiene depends on rooting out fallacies in one's reasoning and embracing a clear epistemology. Understand that a scientific epistemology will differ from a philosophical epistemology which will most certainly diverge from a religious epistemology. But when someone asks you: "How do you know that you know what you claim to know," you need to have an answer.

However, I do not assert that reason is the highest possible standard for dealing with the myriad of experiences, impressions and ideas that life has to offer, although it is very high. I can come up with reasoned arguments for and against why I should love my wife, but at the end of the day, I either love her, or I don't. Reason can persuade me to disengage or engage more deeply with her, which might augment or diminish my love for her, but at a given moment, I love her or I don't, regardless of what I think. [I'm not actually married].

Similarly, religious experiences probably cannot be reduced to reason. Certainly, gnosis is an extra-rational experience. Not necessarily beneath reason, but certainly beyond it.

In the USA, we are coming upon another Presidential election, and emotions are high, and much of what passes for reason is actually highly emotive and not very rational. If your argument is: "My proposition is true because I am very emotional about it," you have no argument. If your argument is: "My proposition is morally obvious," then if even one person fails to find it obvious, you need a backup argument that appeals to reason, which if it truly is obvious, should not be that hard to do. Political parties, and more especially political action committees are going to be trying to persuade you to vote for their candidate, and they are not usually going to bother with giving you valid arguments. Be vigilant.

In Hermetic philosophy, reason is symbolized by a sword. A logical argument is similar to a fencing match, with thrusts and parries, and the occasional kill shot. But reason can also be a heavy claymore, or a scalpel, or a poignard, or a bayonet, depending on how we use it. The four elements are earth, air, water and fire, symbolized by disks (or coins), swords, cups and wands in the Tarot. We master the element of earth, with coins, by harmonizing with our bodies, and with the environment, and by figuring out how to earn a living and support ourselves. We master the element of air, with swords, by mastering reason and understanding its role in our lives, and how it is able to overcome folly and error. We master the element of water, with cups, by being able to hold our emotions in suitable vessels, that do not stagnate or fester, but allow our emotions to flow through us, enriching us. We master the element of fire, with wands, by discovering our true wills, and empowering ourselves to exercise our true wills to take up the space we occupy in the universe, and to further our aims. All students of Hermeticism learn to use these tools to master the four elements, and thereby to transcend them and enter higher consciousness.

You should have been taught logic, and especially rhetorical logic, in high school (if not middle school). Chances are, unless you were on the debate team, none of your teachers shared any of this with you. That's tragic, but remediable. Start now. If you Google "fallacy", there are 12.8 million results, including lots of web pages explaining more about fallacies. Please do yourself a favor and spend a few minutes learning about them.

And if you are a Mason, than the study of logic is non-optional for you. From the night you became a Fellow of the Craft you have been beholden to study logic and follow reason. If you no longer feel that logic applies to you, and you no longer want to follow reason, you might want to sit down and seriously consider why you chose a fraternity that values reason so highly, and demands adherence to reason of its members.

The Necessity of Grammar, Rhetoric and Logic

No Masonic lodge would allow an Entered Apprentice to become a Master Mason without passing to the degree of Fellowcraft first. It would be unimaginable to proceed otherwise. One of the Working Tools of an Entered Apprentice is the Common Gavel, which we use to divest our hearts and consciences of the vices and superfluities of life; thereby fitting our minds, as living stones, for that spiritual building, that house not made with hands, eternal in the heavens. There is a suitable proficiency in the use of this tool which is required of us before we can be passed, and our conductor vouches for us that we have that suitable proficiency.

In the Fellowcraft degree, we are taught about the seven liberal arts and sciences, that we should engage with in constant study. There is a certain peril in making the transition from Operative Masonry to Speculative Masonry. Stones can be tried objectively by the square, but men cannot always be so tried, even though the candidate lecture of the Fellowcraft invites us to do so. In making the transition from Operative to Speculative Masonry, we still try each living stone, only with the Working Tools of a Fellowcraft in their speculative usages, rather than their operative usages. No mason should be offended at being tried, as he has been ever tried, never denied, and ready to be tried again.

An Operative Freemason works in stone. A Speculative Freemason works on himself. At the Entered Apprentice level, he works on the guttural, pectoral, manual, and pedal levels. At the Fellowcraft level, he works on the verbal and intellectual levels. At the Master Mason level, he works on the spiritual level. If he fails to work on the guttural, pectoral, manual and pedal levels, he cannot be a fit subject for the lessons of the Fellowcraft. Similarly, if he fails to work on the verbal and intellectual levels, he cannot be a fit subject for the lessons of the Master Mason. This science is progressive, and indeed must be so.

The seven liberal arts and sciences are divided into the Trivium and the Quadrivium. The Trivium is a prerequisite for the Quadrivium. A man who fails to master the Trivium cannot be a Fellowcraft, let alone a Master Mason.

Grammar is the study of the structure of language, and the way that language conveys meaning. Without a serious study of grammar, we cannot assume that we are capable of conveying meaning through language. Language is complicated, ambiguous, frustrating, challenging. That is why it takes a lifetime of study. Language is a powerful tool, and as Masons, we insist that our brethren master the use of their tools. Words have meaning, whether we want them to or not. Syntax conveys meaning, whether we want it to or not. Human beings have the option of vomiting out strings of words (or things they wish were words) artlessly without any care as to how they are received and understood. But Masons do not have that option, not if they want to remain fellows of the Craft.

That leads to rhetoric, or the art of fashioning language to convey meaning, of moving the hearts and minds of those who receive our language, and ultimately, persuading them that we have something valid to convey. Men, and especially Masons, have strong opinions because we are intelligent men brought in close proximity with other intelligent men of very diverse backgrounds, faiths, political opinions, and educations. It is natural that, as much as we use the trowel to best agree, we sometimes will not agree. Rhetoric teaches us how to make our cases as Masons, and not as bullies nor as petulant children.

Rhetoric is neutral. It can be used for good, or it can be used for evil, as any propagandist knows. But Masons are committed to truth, and logic is the study of how to test our ideas for their truth value. Rhetorical logic (I would consider mathematical logic to be a different subject, better covered under arithmetic in the scheme of the seven liberal arts and sciences) is the study of how to fail to convey the truth verbally, by studying logical fallacies. Because a Mason values the truth above all else, when confronted with a fallacy, he divests his heart and conscience of it, as the dross he needs to leave behind in order to be a living stone fit for the Master's use.

A Mason who eschews these lessons is as contemptible as one who eschews our other virtues, make no mistake. A bus driver who does not know whether or not he cannot safely operate his bus but drives it anyway is a menace. A Mason who does not know whether or not his words have meaning cannot be responsible for his words, and words have launched wars, shaped nations, saved or damned souls, and have erected new sciences. A Mason who cannot sway the hearts and minds of others through his words will forever be thought a fool, and we should not be at the making of a Mason of a fool. A Mason who does not know whether or not his ideas are true, and declines to test them for their truth value, and yet persists in those ideas is a man who cannot value truth. This puts him in spiritual peril, and demonstrates that he eschews our other virtues—virtues more immediately obviously moral in nature.

To try a Fellowcraft is not to insult him but to honor him. You will not be the first, nor the last, to do so. If he is also a Master Mason, then his brethren have vouched for his proficiency. It makes liars of us all if he claims honors in the Craft that he has not yet earned.

I am adamant about this. A Mason who makes simple grammatical errors shows his contempt towards Freemasonry by doing so. A Mason who does not rise above cliché and uttered banalities he repeats from others shows his contempt towards Freemasonry by doing so. A mason who persists in ideas and sentiments that are logically false shows his contempt towards Freemasonry for doing so. We are all rough ashlars striving to perfect ourselves. But a Mason who does not strive to perfect himself stops being a Mason, and this includes every part of the Masonic curriculum, including the seven liberal arts and sciences. Not every Mason has studied atonal counterpoint or gravitational redshift, even though we strive to learn music and astronomy. But a Mason who defends his ignorance shows his contempt for Masonry by doing so.

We can try a Fellowcraft by his attitude towards what he does not yet know. The necessity of a virtuous education is stressed throughout our ritual. This education did not end when we left our respective schools; it continues as long as we remain conscious.

Some of us were educated men before we ever became Masons. Some of us never received a basic education and are called upon to learn now what we never learned before. Masons meet on the level; but not because we insist on a baseline mediocrity in our members. We meet on the level because we each strive to be worthy of our brothers, with zeal and humility. William Preston was an orphan who taught himself, and yet he became the framer of our Craft Degrees. Benjamin Franklin came from similarly humble circumstances. Freemasonry demands daily improvement, no matter what our starting points are, and the results of daily improvement are notable, whereas the results of inertia discredit our Craft.

Each of us is a walking advertisement for the Craft. A Masonic communication riddled with spelling and grammatical errors embarrasses the Fraternity as a whole, not merely because it reveals us as ignorant men; but because it reveals us as men who profess to value the very arts we demonstrate that we do not value.

Masonic Trivia

The Ahiman Rezon instructs new Fellowcrafts:

Grammar is the science which teaches us to express our ideas in appropriate words, which we may afterward beautify and adorn by means of Rhetoric; while Logic instructs us how to think and reason with propriety, and to make language subordinate to thought.

These three arts are collectively known as the Trivium, the initiatory phase of a Classical education, to be followed by the Quadrivium: Arithmetic, Geometry, Music and Astronomy. As the latter four are more technical than the former three, and taught with these as their prerequisites, the Trivium was considered to be more basic than the Quadrivium, and is where we get the modern word trivial from.

It was assumed that an unlearned person would begin by mastering these three arts, Logic, Grammar, and Rhetoric, and from this basis would be able to handle more specific concepts explored in more detail in the Quadrivium. Thus the ability to think rationally, to order these thoughts coherently, and to express them persuasively were abilities that an educated person had mastered.

That brilliant educator, Sister Miriam Joseph, wrote a book about the Trivium and what it means to education. She wrote:

Logic is the art of thinking; grammar, the art of inventing symbols and combining them to express thought; and rhetoric, the art of communicating thought from one mind to another, the adaptation of language to circumstance.

This quote is worth exploring in more detail. Humans think. Animals probably are able to cobble a few impulses together into something more profound. My dog hears my footsteps in the stairwell, and can distinguish mine from my roommates and neighbors, and has an emotional response: his tail begins wagging vigorously with enthusiasm. He likes to sleep by the front door, and my footsteps alert him so that, without getting up, he wags his tail, slamming it into the floor with a resounding thump that I can hear as I ascend the stairs. When I take his leash off of the hook on the wall, he dances with enthusiasm, because he can deduce that we are about to go for a walk. Is this a thought he is entertaining? I'm not really sure.

But humans think, and most of it do it without any explicit training. Why, then, is there an art to thinking? Because we can think things that are false. And those false thoughts can get us into trouble. Without training, we can make leaps of thought that are unsound. In the study of logic, we learn about fallacies, common errors in deduction that humans are prone to making. There is hubris in learning about logic, because one cannot learn about logic without learning how often one has failed to apply logic. Learning logic requires self-examination, and this threatens the ego. It takes an evolved human to examine errors one has committed, and by implication, their consequences. Therefore it takes humility to learn logic, and logic teaches humility to some degree, but it can also instill arrogance as well. Logical failures are ubiquitous, and the student of logic, in spotting these errors in the field, can conclude that most people are stupid, or worse, duplicitous, and feel superior as a result. People who hold logic above all other arts can become misanthropic and disdainful of those who order their values differently. So the student who learns logic first and will learn other arts learns a two-fold humility: one humility upon learning that one is frequently erroneous, and another from sitting in fellowship with others who are frequently erroneous. Logic is Wisdom.

Grammar is the art of infusing words with meaning. Sister Miriam Joseph tells us that grammar consists of "inventing symbols and combining them to express thought". We may think that inventing symbols is something our ancestors did, a finished task, but that would be short-sighted. Each new learner recreates the world anew. A word becomes ours when we own it as if we had invented it ourselves. Any student may put a string of words together that have never been put together before, and in this, there is invention. But the crucial concept in this phrase is the expression of thought. What we think is trapped in our brains, and others can only infer what thoughts we think. This is the basis of human liberty. Our thoughts are our own, and only ours unless we choose to share them with others. That transfer may be orderly, but it rarely is. Too often we fail to convey what we really think, and each word we utter is recontextualized by our hearers, to the detriment of what we intend to mean. Because thoughts are impulses cobbled together, it could be that we don't really understand our own thoughts until we can trap them into structures that have meaning in them, like rounding up wild mustangs, and taming them one by one.

We can observe that there are different types of words. Some words convey objects, some actions, some relationships between other objects or actions, and some color the actions or objects we mean to describe. By knowing how these different kinds of words fit together, we can ensure that our words convey the meaning we intend for them as suitably as possible. Without a mastery of grammar, we do not know if our utterances actually convey what we intend them to convey, but our confusion is even worse that that: until we concretize our thoughts through writing or deliberate speech, our thoughts have no form, no transferability, no existence outside of our own minds. Grammar is Strength. It takes logic and grammar for us to become effective thinkers.

No matter how polished our thoughts may become through the arts of logic and grammar, they will not be accepted by others until we make an effective study of rhetoric. We have to train how to shape our thoughts into a form that others will receive with meaning intact. It is useless to formulate ideas that cannot be shared, and useless to have thoughts that do not fit into the circumstances one finds oneself in. Circumstances change. The people we find among us will vary. We need to be able to tailor our ideas to each and every new situation we are in, in order for them to be effective. Rhetoric is Beauty.

Mastery of the Trivium is essential for any mason. It is not only an intellectual imperative, but a moral imperative. Masons are distinguished by the self-discipline that our obligations put upon us. A mason should be a man of his word, and it takes study to master thought enough to organize thought, to shape thought into words, and to shape words so that they are appropriate for the occasion. A mason cannot fulfill his obligations without a commitment to a life-long study of the Trivium.

We do not assume that an Entered Apprentice has these skills when he is challenged to learn them upon taking his Fellowcraft degree. But we do assume that a Master Mason has, by virtue of being found worthy to take that degree. The responsibility to ensure that these skills have been mastered is balanced between a Lodge that finds a Fellowcraft worthy to take another degree and that Fellowcraft who stands before his lodge and takes the Oath of a Master Mason for the first time.