The most formidable weapon against errors of every kind is reason.

Thomas Paine, The Age of Reason.

Given the central role of language in our thinking, it is well past time to resurrect a Classical Liberal curriculum known as The Trivium. In the Classical Liberal education, there are seven branches of knowledge upon which our knowledge of the world is built. The first three, also known as the trivium, are made up of the three Rs—not of reading, ’riting, and ’rithmetic, but of ‘riting (grammar), reckoning (logic), and rhetoric. The trivium was preparatory for the quadrivium, the remaining four branches that dealt with matter—arithmetic, music, geometry, and astronomy (with the first two dealing with discrete quantities and the latter pair dealing with continuous quantity).

Made up of the three arts of language, the trivium lays the basis for understanding and building models of the world and is important to our quest to understand better the role of anomaly in our lives.

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.

Joseph, Sister Miriam. The Trivium: The Liberal Arts of Logic, Grammar, and Rhetoric. Philidelphia: Paul Dry Books, Inc., 2002

(I highly recommend Sister Miriam Joseph’s book for its straightforward presentation. Much of what follows here owes greatly to her explanations)

Grammar: The Thing-As-It-Is-Symbolized

Grammar is the most basic of the Liberal Arts. It’s the craft of inventing and combining symbols (words or terms) to form correct sentences that convey ideas clearly. The foundation upon which all of this rests is made up of ‘terms’—words that carry concepts. Terms are analogies that stand for some aspect of reality. When you ‘come to terms’ with someone or something, it means that you are in agreement or acceptance of the reality represented through your terms.

Terms exhibit qualities known as extension and intension. They are inversely related—the more extension a term has, the less intension it has (and vice versa). The extension of a term is the total set of objects it can refer to. For instance, the extension of the term ‘swan’ is all swans—white or black. Extension is a measure of abstractness and ambiguity while intension is the definition or the meaning of a term. For example, the intension of the term ‘swan’ would comprise all qualities that distinguish it from other birds, or in fact, everything else.

The more discrete and specific a term, the fewer the things it can possibly refer to. While disciplines, such as science and law, require terms with more intension (i.e., less extension) for precision and clarity in communication, religious prophecy and psychic readings (not genuine psi phenomena in Radin’s sense, but the ‘cold readings’ of pseudo-psychics) often use terms with large amounts of extension leaving room for ambiguity. However, if terms do not have adequate extension, the result could be cognitive dissonance and anomalies, such as with the case of the UFO cult (who noticed an anomaly when the world didn’t end according to the schedule set by their model of the world) or the proponents of the pre-heliocentric model of the solar system (as when Copernicus, and later Galileo, presented strong evidence that proved the geocentric model to be very wrong).

In this way, the concepts of intension and extension are parallel to Frege’s concepts of sense and reference (for example, the names Borat, Ali G, Brüno and Sasha Baron Cohen all refer to the same person, but they present that person in meaningfully different ways. In other words, the four names or references (extension or denotation) each have different senses (intension or connotation).  

Grammar categorizes words/terms into lexical categories that behave in a particular way when put in a sentence. Grammar also describes how these combine to form correct sentences carrying meaningful propositions. Correct propositions then allow us to communicate in a logical, non-contradictory fashion. Grammar enables accurate expression of thoughts, models, and analogies through correct, unambiguous sentences and is, therefore, the most basic of liberal arts.

Logic: The Thing-As-It-Is-Known

Logic offers the mechanics of reasoning or “good thinking”. Once we are adept at the craft of inventing and combining terms to convey ideas clearly, we need to be able to build our argument or model. The influence of Aristotelian logic on the history of Western thought is unparalleled. Now days, there are several systems of logic—sentential logic, predicate logic, and mathematical logic to name a few. While they are outside the scope of this presentation, we’ll only try to get a feel of how logic works by discussing deductive and inductive logic.

Aristotle’s famous syllogisms are a form of argument (a formal relationship of propositions) where two propositions (aka ‘premises’) share a common term, which leads to a third proposition called a ‘conclusion.’ The ‘conclusion’ is argued to be true because of the way the ‘premises’ are related. Here is an example:

All swans are white. The Australian bird is a swan. Therefore, the Australian bird is white.

The term ‘swan’ has a greater extension than ‘the Australian bird’ because the second proposition includes ‘the Australian bird’ in the extension of the term ‘swan,’ and therefore, what is true of a ‘swan’ is true of ‘the Australian bird.’ The way this argument is built is called deductive logic. But what happens to this deductively valid argument when an anomalous black swan comes along? While the original syllogism may still be ‘valid’ logically speaking, ignoring the black swan will result in a poor decision in reality. As software engineers are fond of saying, “garbage in, garbage out”.

Another form of logic Aristotle talks about is inductive logic; it’s where you build from the general to the particular. Induction lies at the nexus of reality and deductive reasoning. Human beings love to make sense out of chaos. We are always on the lookout for patterns. When we observe patterns of repeated experience, we build analogies.

For example, so long as we have observed only white swans, whiteness is one of the defining characteristics of the term ‘swan,’ and renders the proposition ‘all swans are white’ true. Induction allows us to reason in the face of uncertain outcomes, that is, having observed n number of white swans does not guarantee that the next swan you see will be white. Inductive reasoning also is where a lot of the slippage between our expectations and reality occur. Aristotle’s logic had remained largely unchallenged for millennia until the relatively recent arrival of Frege and Peirce.

…in Peirce’s phrase, inductions are ampliative. Induction can amplify and generalize our experience, broaden and deepen our empirical knowledge. Deduction on the other hand is explicative. Deduction orders and rearranges our knowledge without adding to its content.

Of course, the contingent power of induction brings with it the risk of error. Even the best inductive methods applied to all available evidence may get it wrong; good inductions may lead from true premises to false conclusions.

Vickers, John. The Problem of Induction. September 08, 2009

Both these types of logic have their value. While induction builds analogies by observing reality, deduction allows new insights to emerge by arranging and rearranging propositions already held true. However, both have their dangers. As said earlier, if any of the premises held true is not true, the conclusion drawn will not be true in the real world even though the argument may remain ‘valid.’ In other words, always maintain a healthy skepticism of authority and learn how to vet claims reliably yourself. With inductive thinking, it is important not to be seduced by statistics, especially with regards to prediction. As risk expert Dan Borge says:

Everyone knows that the past is, at best, an imperfect guide to the future. However, risk experts, like experts in other fields, are prone to fall in love with their tools and this love can lead to severe myopia. Experts can be tempted to define problems in ways that fit their tools rather than ways that fit the actual situation. Statistics is a favorite tool of the risk expert and the past is much more accessible to statistics than the future. Only the past has the data points that statistics craves. So the unwary risk expert may exaggerate the importance of the historical data that allow him to use his favorite tools and to arrive at a definite solution, even if it is the solution to the wrong problem.

Borge, Dan. The Book of Risk. New York: John Wiley & Sons, Inc., 2001., p. 55

A Note on Science, Falsification and Skepticism

British empiricist David Hume’s ‘problem of induction’—does inductive reasoning lead to truth?—has troubled thinkers for centuries. No amount of confirmatory observation can finally prove as true an inductively reached conclusion, such as a law of physics.

All the objects of human reason or enquiry may naturally be divided into two kinds, to wit, Relations of Ideas, and Matters of fact. Of the first kind are the sciences of Geometry, Algebra, and Arithmetic … [which are] discoverable by the mere operation of thought … Matters of fact, which are the second object of human reason, are not ascertained in the same manner; nor is our evidence of their truth, however great, of a like nature with the foregoing.

Hume, David. An Enquiry Concerning Human Understanding. 1748

Two centuries later, Sir Karl Raimund Popper promoted the revolutionary proposal that the goal of science is not to confirm theories, but rather to falsify them. No amount of verifying can establish a theory about reality as true. Science should, therefore, attempt to falsify—hunt for anomalies—theories that are not falsifiable are not scientific. In the words of Alan G Gross, “Falsifiability is prediction turned on its head.” (Gross, Alan G. The Rhetoric of Science. Cambridge, Massachusetts and London: Harvard University Press, 1990, p. 40).

To test a theory or model is to test the predictions it makes about how reality will function. Failed predictions reveal the bounds of the theory. Under this interpretation of scientific reasoning, the body of human knowledge grows by error-elimination much like evolution is driven by natural selection. In short, the scientific method is to hunt for anomalies and test, explain, and integrate them into our analogies making them fit our existing model of reality better, ad infinitum.

When we survey scientific literature, we observe the themes of predictability, control, falsifiability, and explanatory power recurring often. It is these variables, and the respective weight of each, that determine how scientific a statement is—the more scientific a statement, the higher its score on all variables. Newton’s equations for classical physics scored high across the board (at least, until the anomalies present at the sub-atomic level demanded changes). The models of the psychologist, astrologer, and economist often score high on explanatory power but low on predictability and control. Social scientist Hayek, as well as Popper, implicitly warns us against the tendency to grant excessive weight to explanatory power (for example, as in scientism), without seeking high scores for other equally important variables.

Mathematician Kurt Gödel asserts that all logical systems are incomplete; so too is science incomplete. Every logical system has a set of axioms that it assumes to be true, that has not been proved, and that may be unverifiable given the extent of our current knowledge. This isn’t to suggest, however, that we throw the baby out with the bathwater; instead, we need to approach science critically, albeit with an open-mind.

This brings us to scientism: a “pejorative term for the belief that the methods of natural science, or the categories and things recognized in natural science, form the only proper elements in any philosophical or other inquiry” (Oxford English Dictionary). It looks like science but turns science and accepted methods of science into faith by taking them beyond the purview of falsification. For science to remain science it must be falsifiable, and it must have adequate intension.

Famed Type I Error skeptic Michael Shermer has used the term scientism in an article to describe “a scientific worldview that encompasses natural explanations for all phenomena, eschews supernatural and paranormal speculations, and embraces empiricism and reason as the twin pillars of a philosophy of life appropriate for an Age of Science” (Shermer 2002).  In Shermer’s sense, scientism is no different from naturalism or simply science, this is trope. Scientism, as Hayek and Popper use the term and as it was originally used, gives unwarranted veracity to potentially unscientific claims, which then ultimately undermines what science stands for. Since scientific claims are the result of human endeavors they are subject to error, ambiguity, and/or deception, i.e., they warrant scrutiny. To his credit, however, Shermer ends his article with words that do capture the essence of scientism:

Because of language we are also storytelling, mythmaking primates, with scientism as the foundational stratum of our story and scientists as the premier mythmakers of our time.

Shermer, Michael. “The Shamans of Scientism.” Scientific American, June 2002

At the other extreme of scientism waits skepticism that accounts for both Type I and Type II Errors. A skeptic (in the tradition of Phyrro, at least) does not take a position. It’s like agnosticism, which makes no claims either ways about the existence of God. An anomalist, like the agnostic, claims that there is not enough evidence to prove the existence of God since the absence of proof isn’t the same as proof of absence. 

Both critics and proponents need to learn to think of adjudication in science as more like that found in the law courts, imperfect and with varying degrees of proof and evidence. Absolute truth, like absolute justice, is seldom obtainable. We can only do our best to approximate them.

Truzzi, Marcelo. On Pseudo-Skepticism.” Zetetic Scholar, 1987: 12-13

Errors, Cognitive Illusions, and Informal Fallacies

To its believers, the UFO cult’s theory about the world could seem high on explanatory power and predictability as it predicted doomsday and was able to explain why the prediction did not materialize. But rather obviously, their theory or model is far from reality. When building models, it is not uncommon for errors and fallacies to creep into our reasoning, which take us away from reality. Before moving away from the branch of logic, we’ll take a quick peek at some of these errors and fallacies. (As with logical systems, it is beyond the scope of this presentation to deal comprehensively with the potential errors, fallacies, and illusions in reasoning.)

Pattern Finding

Our ancestors attributed random lightning and thunder to the anger of the gods (Zeus for Greeks, Indra for Hindus, Thor in Norse mythology, etc.). As children, many of us looked at the moon and saw a man’s face. Finding a pattern where none exists is common. It’s the projection of meaning upon meaningless noise. Though misleading, apophenia (also called a false positive or Type I error) could be less fatal than periphenia (the belief that no pattern exists when in reality it does, also known as a false negative or Type II error).

Harvard University biologist Kevin R. Foster and University of Helsinki biologist Hanna Kokko …demonstrate that whenever the cost of believing a false pattern is real is less than the cost of not believing a real pattern, natural selection will favor patternicity. …For example, believing that the rustle in the grass is a dangerous predator when it is only the wind doesn’t cost much, but believing that a dangerous predator is the wind may cost an animal its life.”

Shermer, Michael. “Patternicity.” Scientific American, December 2008

This also may explain why American culture breeds conspiracy theories. It doesn’t cost much to hear them out. If they’re wrong, it is no big deal. But what if they are right? The cost of enduring Chicken Little is microscopic compared to the cost of ignoring Cassandra (ironically, Shermer provides the above example in an article that argues against such risk-averse thinking). If chaos theory is correct and there is a sensitive dependence upon initial conditions, then given our country’s roots in conspiratorial groups, such as the Sons of Liberty, the modern American love of conspiratorial thinking makes even more sense.

Cognitive Illusions and Other Fallacies

The formative work of psychologists Tversky and Kahneman has inspired extensive study of the phenomena known as cognitive illusions, or epistemological anomalies. Cognitive illusions fall into three basic categories—illusions in thinking, in judgment, and in memory. Illusions in thinking are typically due to the misapplication of a particular heuristic or rule-of-thumb; illusions in judgment are usually due to non-logical, unconscious biases that affect the choices we make; and illusions in memory are due to problems with either the encoding or retrieval of remembered information.

For example, attributing a false cause, or believing that you’ve control over or can influence random outcomes, or even looking for or seeing only those pieces of evidence that confirm a theory are all thinking illusions. The illusion that guns are more dangerous than medical malpractice when, in fact, more people die of medical malpractice than of gunshot wounds is an example of a judgment illusion. When an incorrect use of a term is not noticed or when external information is remembered incorrectly because of its association with internal representations, it’s a memory illusion. For example, when asked “how many animals of each kind did Moses take to the ark?”, people usually answer “two” instead of noting that it was ‘Noah’ and not ‘Moses’ who took animals to the ark (For more information on cognitive illusions and the criteria to judge something as a cognitive illusion, please refer to Pohl, Rudiger. Cognitive Illusions: A Handbook on Fallacies and Biases in Thinking, Judgment, and Memory. Hove and New York: Psychology Press, 2004).

Some of the many fallacies and illusions that riddle our reasoning and deserve your attention include:

undistributed middle

illicit major and minor

composition (that which is true of parts must be true of whole)

division (that which is true of whole must be true of parts)

affirming consequent

denying the antecedent

false alternative

ignoratio elenchi

tu quoque

ad hominem

ad baculum

ad populum, ad verecundiam, ad misericordium, ad ignorantium, petitio principia, and plurimum interrogationum.) There are great free resources on the internet for learning all about these fallacies.

Enthymemes

Another cause for faulty reasoning is unstated assumptions—conditions taken for granted to be true but not stated explicitly. In an Aristotelian syllogism, explicitly stated premises lead to a conclusion. If the explicitly stated premises are true, the conclusion will follow, there is nothing implicit except for the veracity of the premises. Arguments with implicit assumptions influencing the conclusion are called enthymemes. Aristotle categorizes it as a rhetorical syllogism—its aim being persuasion rather than demonstration. If a premise is left unstated because it is obvious, there is no cause for concern. However, persuasion sometimes depends on suppressing dubious premises. Advertisements are good examples of enthymemes. The bright images and large print tell you one story. The small print or fine print that follows is the suppressed premises, which if you take the trouble to go through, will change the story, maybe, completely. Enthymemes lead to misinterpretation because of possible ambiguities. The defense against enthymemes and the resulting model slippage is awareness and avoidance of them.

Rhetoric: The Thing-As-It-Is-Communicated

There grew up in Athens a body of knowledge about how to get people on your side voluntarily. This body of knowledge speedily became, and remained for more than 2,000 years, the core of Western education. It was called ‘rhetoric.’ (Rhetor was the usual term in Greek for ‘politician.’) It taught you how to get people’s attention and how to argue your case once you had it.

Lanham, Richard A. The Economics of Attention. Chicago and London: University of Chicago Press, 2006, p. 25

Rhetoric is considered the senior art of the trivium with the mastery of both grammar and logic as prerequisites. While grammar is ultimately concerned with correctness and logic with truth, rhetoric is measured by its effectiveness. Rhetoric is the art of persuasion based upon correctness and truth. Mastery of this art and its tools will not only enable you to see anomalies in many of the epistemic hand-me-downs you encounter daily but also free your own arguments of fallacies that arise from a misuse of rhetorical tools.

Polysemes

Since a word is a symbol, an arbitrary sign whose meaning is imposed on it, not by nature, not by resemblance, but by convention, it is by its very nature subject to ambiguity; for, obviously, more than one meaning may be imposed on a given symbol. In a living language, the common people from time to time under changing conditions impose new meanings on the same word….“

Joseph, Sister Miriam. The Trivium: The Liberal Arts of Logic, Grammar, and Rhetoric. Philidelphia: Paul Dry Books, Inc., 2002, p. 34

One of the biggest sources of trouble in reasoning is ambiguities caused by the use of polysemes—terms that have many related meanings. Logical fallacies that specifically arise from ambiguity and the use of polysemes include equivocation, amphiboly, and the fallacy of accent. Equivocation is the fallacy that arises when a polyseme is used in its multiple meanings to develop an argument causing confusion. Amphiboly occurs when a sentence is constructed in a way that creates double meanings. And finally, the fallacy of accent happens when the wrong word in a sentence is emphasized creating a false impression.

This is why an understanding of classical rhetoric is so important, and it is here that we complete our revolution, back where we began, back to the slippage between models and reality (as if in a circuit.) This circular, or rather spiral, path is what I call the rhetorical revolution.

I hope that my speculative portrayal of analogy as the lifeblood, so to speak, of human thinking, despite being highly ambitious and perhaps somewhat overreaching, strikes a resonant chord in those who study cognition. My most optimistic vision would be that the whole field of cognitive science suddenly woke up to the centrality of analogy, that all sides suddenly saw eye to eye on topics that had formerly divided them most bitterly, and naturally — indeed, it goes without saying — that they lived happily ever after.

Hofstadter, Douglas R. “Analogy as the Core of Cognition.” In The Analogical Mind: Perspectives from Cognitive Science, edited by Dedre Gentner, Keith J Holyoak and Boicho N. Kokinov, 499-538. Cambridge MA: The MIT Press/Bradford Book, 2001

Tropes or Figures of Speech

Trope is a rhetorical device that creates a shift in the meaning of a term or terms. It is meaning that we must vet carefully since the entire structure of our knowledge rests upon a foundation of analogy and metaphor. As Lakoff and Johnson say, “Metaphor is pervasive in everyday life, not just in language but in thought and action… the way we think, what we experience, and what we do every day is very much a matter of metaphor” (Lakoff, George, and Mark Johnson. Metaphors We Live By. Chicago: University of Chicago Press, 1980, p. 3). The important thing to note, for purposes of mental self-defense, is that trope changes the intension of a term for the purpose of persuasion or manipulation.

Categorically, there are four master tropes—metaphor, metonym, synecdoche, and irony. Metaphor is the equation of two terms to provide meaning to one or both of them. When Pat Benatar tells us “Love is a battlefield,” she is using the term ‘battlefield’ to describe ‘love,’ thereby extending the intension of the latter term to the former.

Included in the master trope of metaphor are simile, onomatopoeia, personification, and antonomasia. Metonymy is the act of substituting a term or phrase for another closely related one. For example, the classic quotation “The pen is mightier than the sword” actually means that persuasion is more powerful than coercion. The pen is substituted for persuasion and the sword for coercion.

Synecdoche is the substitution of a part for the whole, the whole for a part, a species for the genus, and vice versa. For example, when I ask for a Kleenex, I am not asking for a particular kind of tissue; I am simply asking for any similar sort of tissue. Similarly, the media often uses ‘The White House’ to mean the Executive Branch of the United States Government. Both the concepts of branding in advertising and sound bites in the media thrive on synecdoche.

Lastly, irony is simply saying one thing while meaning the opposite. In irony, there is an incongruity between the expression and the intention. For example, when you say that something was “as clear as mud”, you are being ironic.

All of these tropes can leave our hard-earned knowledge and important communications vulnerable. The rhetoric of science is crucial to our understanding of the world as is the philosophy of science. As analogy and metaphor are central to all of our mental processes, the study of rhetoric will help us understand our world and ourselves better.

What, then, is truth? A mobile army of metaphors, metonyms, and anthropomorphisms—in short, a sum of human relations which have been enhanced, transposed, and embellished poetically and rhetorically, and which after long use seem firm, canonical, and obligatory to a people: truths are illusions about which one has forgotten that this is what they are; metaphors which are worn out and without sensuous power…”

Nietzsche, Friedrich. “On Truth and Lies in a Nonmoral Sense.” 1873

As mentioned earlier, knowing reality is an ongoing process. Here’s how it works: something in reality (an anomaly, maybe) warrants our attention. In order to process this thing, a representation, symbol, model, or metaphor is established in our mind (as first-hand or ‘tacit’ knowledge). We reason out this model or symbol integrating it into our knowledge (for example, via the trivium). This knowledge is then transmitted in the form of explicit knowledge (that is, second-hand knowledge expressed using symbols and rhetoric).

“As the base rhetorician uses language to increase his own power, to produce converts to his own cause, and to create loyal followers of his own person, so the noble rhetorician uses language to wean men from their inclination to depend on authority, to encourage them to think and speak clearly, and to teach them to be their own masters.“

Szasz, Thomas. The Myth of Psychotherapy 1988, p. 20.