Before journeying into a debate, however logically sound our position may be, we should attempt to maintain rational discourse by preparing ourselves to delineate both the axiomatic laws of thought and a set of logical errors known as informal fallacies. I have found that these errors in logic are constantly and continuously employed by a large percentage of people in debate. I will describe a few of the most relevant fallacies. However, I first wish to address the laws of thought.

“There is no greater evil one can suffer than to hate reasonable discourse.” — Socrates, Phaedo, Plato’s account of Socrates’ death.

The Laws of Thought

The three fundamental laws of logic are fundamental axiomatic rules upon which rational discourse itself is based. The three laws can be stated symbolically as follows:

  1. The law of contradiction (or non-contradiction)

    Essentially, Two truths cannot contradict one another. Aristotle stated it in this way, that “The most certain opinion of all” was “that opposed statements cannot be at the same time true.” On the other hand, for any pair of contradictory premises, one must be true and the other false. The Law of Non-Contradiction prevents both premises being true, while the Law of Excluded Middle points out that a pair of contradictory premises exhausts all possibilities.

    For all propositions p, it is impossible for both p and not p to be true, or: ∼(p · ∼p), in which ∼ means “not” and · means “and.” — Britannica

    The argument often arises, that all religions are right; however, this is not logically possible because it violates the the laws of thought, specifically the law of non-contradiction. To deny these laws, one would be using these laws in the process, thus self-refuting them. If one says “There’s no such thing as truth.” That’s a truth claim, to which you should respond “Except the truth that there is no truth?” ergo Self-Refutation.

    ‘Nothing can both be and not be.’ In other words: “two or more contradictory statements cannot both be true in the same sense at the same time”: ¬(A∧¬A). — Wikipedia

    Another way of putting it is: a proposition must be either true or false—not both true and false, nor in some limbo state in between truth and falsity. This can be useful in listing all possible alternatives and refuting all of them but the correct one.

  2. The law of excluded middle (or third)

    A principle in modern logic that means something is either true or it is false. There is no “middle” between true and false. In classical logic, this principle for a proposition A would be A∨¬A. Its opposite is dialetheism.

    Either p or ∼p must be true, there being no third or middle true proposition between them, or: p ∨ ∼p, in which ∨ means “or.” — Britannica

    ‘Everything must either be or not be.’ In accordance with the law of excluded middle or excluded third, for every proposition, either its positive or negative form is true: A∨¬A. — Wikipedia

  3. The principle (or law) of identity

    The law of identity states that if a statement has been determined to be true, then the statement is true. Here is an example, if I make a statement that ‘It is storming,’ and it is the truth, then the statement must be true. Imagine that! Applying this logically, lightning cannot be rain, a frog cannot be a dragon, each thing is something specific unto itself and has it’s own particular identity.

    If a propositional function F is true of an individual variable x, then F is true of x, or: F(x) ⊃ F(x), in which ⊃ means “formally implies.” — Britannica

    Another formulation of the principle of identity asserts that a thing is identical with itself, or (∀x) (x = x), in which ∀ means “for every”; or simply that x is x.

    ‘Whatever is, is.’ For all a: a = a. — Wikipedia

Informal Fallacies

Arguments that are logically unsound for lack of well-grounded premises.

In philosophy, reasoning that fails to establish its conclusion because of deficiencies in form or wording. Informal fallacies are types of inductive argument the premises of which fail to establish the conclusion because of their content. — Britannica

Informal fallacies are a type of incorrect argument in natural language. The source of the error is not just due to the form of the argument, as is the case for formal fallacies, but can also be due to their content and context. Fallacies, despite being incorrect, usually appear to be correct and thereby can seduce people into accepting and using them. — Wikipedia

Fallacies of Relevance (Relevance Fallacies)

A subtype of Informal fallacy (arguments that are logically unsound for lack of well-grounded premises).

  • Argumentum ad lapidem or an appeal to the stone, which is defined as, dismissing a claim as absurd without demonstrating proof for its absurdity. Not to be confused with reductio ad absurdum or an appeal to ridicule (see Red Herring Fallacies)

  • Argumentum ad ignorantiam or an appeal to ignorance: Assuming that a claim is false because it has not been or cannot be proven true, or vice versa, assuming that a claim is true because it has not been or cannot be proven false.

    • For example: Assuming there is no God, because it has not been or cannot be proven, is just as illogical as assuming there is a God, because it has not been or cannot be disproven.

      What lacks proof today may have proof tomorrow, which would mean, it was just as true the day it had no proof as the day in which the proof was found. We do not base our conclusions upon this form of faulty reasoning.

  • Argumentum ad nauseam or argumentum ad infinitum otherwise known as an Argument from repetition: Repeating an argument until nobody cares to discuss it any more and referencing that lack of objection as evidence of support for the truth of the conclusion.

Red Herring Fallacies

“A red herring fallacy, one of the main subtypes of fallacies of relevance, is an error in logic where a proposition is, or is intended to be, misleading in order to make irrelevant or false inferences. This includes any logical inference based on fake arguments, intended to replace the lack of real arguments or to replace implicitly the subject of the discussion.” — Red Herring Fallacies (Wikipedia)

  • Argumentum ad hominem: An Ad hominem attack is an error in logic, which leads the loser of said argument, to attack the arguer instead of the argument. A very true statement (verified by the logic above) often attributed to (Irrelevant) the Greek philosopher Socrates, states “When the debate is lost, slander becomes the tool of the losers.” Subtypes of ad hominem include: circumstantial, poisoning the well, appeal to motive, tone policing & traitorous critic fallacy.

    Simply, if anyone starts name calling or attacking the debater instead of maturely debating the topic, it is looked at as an immediate loss.

    • Another closely related red herring fallacy called Tu quoque which is an appeal to hypocrisy also known as an whataboutism, states that a position is false, wrong, or should be disregarded because its proponent fails to act consistently in accordance with it.

      Simply, if someone avoids the debate at hand by showcasing supposed hypocrisy in your life, this is also an error in their logic and an immediate fail on their part.

  • Argumentum ad passiones: Also known as an appeal to emotion, an error in logic which attempts to manipulate the emotions of the listener rather than using valid reasoning to obtain a common agreement. Subtypes of ad passiones include: fear, flattery, pity (argumentum ad misericordiam), ridicule (reductio ad ridiculum, reductio ad absurdum, ad absurdum), spite, judgmental language, Pooh-pooh & Wishful thinking.

    • Reductio ad absurdum or an Appeal to ridicule would be a very good example – mocking or stating that the opponent’s position is laughable to deflect from the merits of the opponent’s argument. I think we’ve all, at some point in our lives, experienced this type of juvenile response. This is unsurprisingly a failure in logic.

      “Do not correct a scoffer, lest he hate you; Rebuke a wise man, and he will love you. Give instruction to a wise man, and he will be still wiser; Teach a just man, and he will increase in learning.” — Proverbs 9:8-9; 29:9

      Not to be confused with: Argumentum ad lapidem or an appeal to the stone which is defined as, dismissing a claim as absurd without demonstrating proof for its absurdity. Ad lapidem is only a relevance fallacy and not of the red herring subtype. Notice the difference between ad absurdum and ad lapidem, one is ridiculing and irrelevant while the other is simply irrelevant.

    • Another good example of ad passiones would be ad misericordiam or an appeal to pity, a fallacy in which someone tries to win support for an argument or idea by exploiting his opponent’s feelings of pity or guilt. This is an error in logic and an immediate loss.

      “All men suffer, but not all men pity themselves” — Emperor Marcus Aurelius

  • Argumentum ad verecundiam: An appeal to authority is where an assertion is deemed true because of the position or authority of the person asserting it. Subtypes of ad verecundiam include: Appeal to accomplishment & Courtier’s reply.

    • I think the best example of this is the Courtier's reply (a criticism is dismissed by claiming that the critic lacks sufficient knowledge, credentials, or training to credibly comment on the subject matter.

      Simply, if someone attacks your “lack of credentials” or credibility instead of focusing on the argument, they have lost the debate. You could also apply ad verecundiam to people who assert that they are right because they are older and “know better”. To whom it may concern, I did not use this on you, I was referring to my older age as having given me memories of a time since past, but I think it was misconstrued. Apologies for lack of clarification.

  • Argumentum ad crumenam: An appeal to wealth also known as an argument to the purse, is the informal fallacy of concluding that a statement is incorrect because the speaker is poor, or that a statement is correct because the speaker is rich.

    • An example might be: “If you’re so smart, why aren’t you rich?”

      This type of conclusion is an error in logic. Essentially, nothing is “above your pay-grade”. No matter your tax bracket, the merits of your argument should be taken seriously.

      But Jesus replied, “Foxes have dens to live in, and birds have nests, but the Son of Man has no place even to lay his head.” — Matthew 8:20

  • Argumentum ad populum: An appeal to the majority, is a proposition that is claimed to be true or good solely because a majority or many people believe it to be so. This is also known as: the bandwagon argument.

    • I think Einstein said it best when he said:

      “What is right is not always popular and what is popular is not always right.” — Albert Einstein

  • Straw man fallacy: Last but not least, misrepresenting an opponent’s argument by broadening or narrowing the scope of a premise and/or refuting a weaker version of their argument.