School in a Book: Basic Logic and Rhetoric

Everyone loves winning an argument. Actually, everyone just loves an argument. It’s stimulating. Challenging. Energetic. If you want to argue better, or just be better able to discriminate between arguments, logic studies will help–a lot. Just keep in mind that once you learn this stuff, it’s hard not to get a bit snobbish about it; I recommend you flavor your powers of logic with tact.

Important note: Many logical fallacies are known by more than one name. I’ve attempted to use the most common in my list, but if you rely too much on memorization, you won’t always recognize other people’s terms. More important, you’ll miss the point.

Finally, a quote to consider: “One and one cannot become two, since neither becomes two.”– Gongsun Long, Chinese logician (c. 325–250 BCE)

I think that pretty much says it all.

Basic Logic and Rhetoric

Logic: The set of rules that guides the formation of valid arguments and tests argumentative conclusions for validity.
Rhetoric: The art of persuasion

Practical uses for logic: Ethics, politics, computer programming, writing and any situation in which arguments are posited, questioned and defended.

An argument: A defense of an opinion or position. Arguments can be logical or rhetorical. Logical arguments are those which determine whether a particular statement is true or false. Rhetorical arguments are those which attempt to persuade a person or audience that a particular statement is true or false, regardless of whether it actually is true or false.

Premise: An idea upon which other ideas in an argument rely.

Logical form: The formula that an argument uses to arise at its conclusion. Example: All A’s are B’s and all B’s are C’s; therefore, all A’s are C’s.

Valid: Logically correct. Example: All zebras are mammals and all mammals are ugly; therefore, all zebras are ugly.

True: Actually correct. Example: All zebras are mammals and all mammals drink their mothers’ milk; therefore, all zebras drink mothers’ milk.

Rational/sound: Logical, valid and true

How to analyze an argument for soundness: First, notice whether or not the form of the argument makes sense. Does the conclusion follow from the premises? If not, you likely have a formal fallacy on your hands. As a beginning logician, don’t spend too much time figuring out the name of the fallacy; instead, point out the problem and say something like, “The conclusion doesn’t follow the premises.” Step two is to notice whether or not the statements made in the argument are true; if not, there is an informal fallacy. You should be able to identify all ad hominem fallacies and name them as such. You should also be able to call out these fallacies by name: the fallacy of equivocation; the slippery slope fallacy; the poisoning the well fallacy; the straw man fallacy; the appeals to emotion, fear, pity, ridicule and the like; and the appeals to tradition, authority, and popularity. Other fallacies can simply be identified as such, and often, this is enough.

Semantics: The meanings of words. These can often be problematic and unstable, which contributes to illogic.

Inference: A true or false conclusion in the form of “A, therefore, B.”

Implication: A true or false conclusion in the form of “If A, then B.”

Deductive reasoning: Deducing a specific fact from a general principle

Inductive reasoning: Arriving at a general principle from a specific fact or case

Analysis: Deconstructing part-by-part to find deeper meaning

Synthesis: Putting parts together to find deeper meaning

A posteriori: Not known to be valid or true except through observation and experience

A priori: Known to be valid or true by reason alone

History of the study of logic: Logic comes from the Greek word logos, originally meaning “the word” or “what is spoken”, but later meaning “thought” or “reason”. Aristotle was the first known proponent of formal logic, and since then, it has been applied to many scientific areas, including computer programming. Logic studies, though, normally refers to rhetorical logic.

Logical fallacy/non sequitur: A weakness in an argument, often hidden, that causes the conclusion to be invalid or untrue. Informal fallacies have to do with the content of the argument, and formal fallacies have to do with the form of the argument. (Non sequitur means “it does not follow.”)

Formal logical fallacy: A fallacy in the structure of the argument that causes the argument to be invalid, regardless of the content of the argument. Remember, just because an argument contains a fallacy doesn’t mean the conclusion isn’t true. It simply means that particular argument doesn’t prove it to be so.

Informal logical fallacy: A fallacy in the content of the argument. Most often, informal logical fallacies are simple distractions from the actual argument. They point to external ideas or the opponent’s personality and the like. Literally any distraction from the validity of the argument itself can be an informal logical fallacy. Don’t memorize the names–just understand the problem with them in the collective. (For a ridiculously long list, see Wikipedia’s list of logical fallacies.)

Common Formal Logical Fallacies

The affirming the consequent fallacy: An argument that states “If A, then B; B, therefore A.” Example: “If Fred killed Todd, Fred is angry. Fred is angry, therefore, Fred killed Todd.”

The denying the antecedent fallacy: An argument that states, “If A, then B; not A, therefore not B.” Example: “If Fred killed Todd, then he hated him. Fred didn’t kill Todd. Therefore, he didn’t hate him.

The affirming a disjunct fallacy: An argument that states, “A is true or B is true. B is true. Therefore, A is not true.” In fact, both could be true.

The denying a conjunct fallacy: An argument that states that “It is not the case that both A is true and B is true. B is not true. Therefore, A is true.” In fact, both could be false.

Fallacy of the undistributed middle: An argument that states that “All Zs are Bs. Y is a B. Therefore, Y is a Z.” One must first prove that all Bs are Zs.

Common Informal Logical Fallacies

Ad hominem (“to the man”) fallacy: An argument that relies on attacking the arguer instead of the argument. This is really a category of fallacies which includes the appeal to authority/expert fallacy and the opposite of this, the courtier fallacy (which attacks the opposition’s knowledge, credentials or training).

The equivocation fallacy: An argument that relies onthe misleading use of a term with more than one meaning (by glossing over which meaning is intended at a particular time).

The straw man fallacy: An argument that relies onan argument based on misrepresentation of an opponent’s position.

The slippery slope fallacy: A slippery slope argument (SSA), in logic, critical thinking, political rhetoric, and caselaw, is a logical fallacy in which a party asserts that a relatively small first step leads to a chain of related events culminating in some significant (usually negative) effect.

The poisoning the well fallacy: A subtype of ad hominem presenting adverse information about a target person with the intention of discrediting everything that the target person says.

The appeal to emotion fallacy: An argument that relies on the manipulation of emotions. This is a general category that includes the appeal to threat fallacy, the appeal to fear fallacy, the appeal to flattery fallacy, the appeal to pity fallacy, the appeal to ridicule fallacy and more.

The false dilemma: An argument that relies ontwo alternative statements are held to be the only possible options when in reality there are more.

The circular reasoning/begging the question fallacy: An argument that relies on the presence of the conclusion within the premise in order to appear logical

The ad nauseam/ad infinitum fallacy: An argument that relies on mere repetition

The appeal to tradition fallacy: An argument that relies on a conclusion supported solely because it has long been held to be true.

The appeal to the people/bandwagon fallacy: An argument that relies on a proposition is claimed to be true or good solely because a majority or many people believe it to be so.

The guilt by association and honor by association fallacies: Arguments that rely on the idea that because two things share some property, they are the same.

The red herring fallacy: A speaker attempts to distract an audience by deviating from the topic at hand by introducing a separate argument the speaker believes is easier to speak to. Argument given in response to another argument, which is irrelevant and draws attention away from the subject of argument.

The cherry picking fallacy: An argument that relies onact of pointing at individual cases or data that seem to confirm a particular position, while ignoring a significant portion of related cases or data that may contradict that position.

The appeal to consequences fallacy: An argument that relies on describing the terrible things that would happen if the opponent’s position were true.

The appeal to motive fallacy: An argument that relies on attacking the motive of the opponent.

The tu quoque (“you too”) fallacy: An argument that relies on pointing out the hypocrisy of the opponent.

The etymological fallacy: reasoning that the original or historical meaning of a word or phrase is necessarily similar to its actual present-day usage.

The moving the goal posts/raising the bar fallacy: An argument that relies onargument in which evidence presented in response to a specific claim is dismissed and some other (often greater) evidence is demanded.

The survivorship bias fallacy: An argument that points to a small number of successes of a given process are actively promoted while completely ignoring a large number of failures

The false analogy fallacy: An argument that relies on an argument by analogy in which the analogy is poorly suited.

The hasty generalization: An argument that bases a broad conclusion on a small sample or the making of a determination without all of the information required to do so.

The oversimplification fallacy: An argument that relies on it is assumed that there is one, simple cause of an outcome when in reality it may have been caused by a number of only jointly sufficient causes.

The appeal to ignorance: An argument that relies on assuming that a claim is true because it has not been or cannot be proven false, or vice versa.

The pooh-pooh fallacy: An argument that relies on dismissing an argument perceived unworthy of serious consideration.

The moralistic fallacy: An argument that relies on assuming what ought to be true, is in fact true

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