§2 Fallacies of Irrelevant and Inadequate Support

In the framework of informal logic, a “good” argument must satisfy the ARS Criteria: its premises must be Acceptable, Relevant to the conclusion, and Sufficient to support the conclusion. Section 2 focuses on arguments that fail the tests of Relevance and Sufficiency.

2.1 Failures of Relevance (Irrelevant Support)

A failure of relevance, classically known as Ignoratio Elenchi (Irrelevant Conclusion), occurs when the premises offered have no logical bearing on the truth of the conclusion, regardless of whether those premises are true.

A. The Argumentum ad Hominem (Against the Person)

The systematic study of this fallacy traces back to John Locke’s An Essay Concerning Human Understanding (1690). Locke identified the ad hominem as a maneuver to “press a man with consequences drawn from his own principles or concessions.”

• The Philosophical Error: In epistemology, the truth of a claim is independent of the person making it. To dismiss a claim because of the speaker’s character is to commit a “category mistake”—confusing the context of discovery (who said it and why) with the context of justification (the evidence supporting it).

• Modern Dialectical View: Douglas Walton notes that ad hominem is not always fallacious in legal testimony where “character” is relevant to “credibility.” It becomes a fallacy in a critical discussion when it is used to silence a proponent rather than address their argument.

B. Argumentum ad Populum (Appeal to the Masses)

This fallacy relies on the “social force” of a belief rather than its evidential merit.

• The Scholarly Critique: Philosophers such as Søren Kierkegaard argued that “the crowd is untruth.” Logically, the popularity of a belief is a psychological fact about humans, not a metaphysical fact about the world. For example, the historical consensus that the Earth was flat did not make the Earth flat; the popularity of the belief was irrelevant to the planetary shape.

C. The Genetic Fallacy

This error involves evaluating a claim based solely on its historical or biological origins.

• Origin vs. Justification: A classic example in philosophy is dismissing chemistry because it evolved from alchemy. While alchemy’s origins are based on flawed assumptions, the current justifications for chemistry are based on the scientific method. To conflate the two is to ignore the evolution of evidence.

2.2 Failures of Sufficiency (Inadequate Support)

Even when premises are relevant, they may fail to be sufficient. These arguments provide some evidence, but the “inductive leap” to the conclusion is too great to be rational.

A. Hasty Generalization (Secundum Quid)

This is the failure of the “sample to population” relationship.

• The Inductive Risk: As John Stuart Mill detailed in A System of Logic (1843), the primary danger in induction is “generalizing from a few particulars.” A single unrepresentative instance (a “small sample”) cannot support a universal law.

• The Philosophical Correction: A reasonable person requires a sample that is both large enough and sufficiently diverse to minimize the risk of “atypicality.”

B. False Cause (Post Hoc Ergo Propter Hoc)

This fallacy, meaning “after this, therefore because of this,” occurs when one mistakes correlation for causation.

• Hume’s Challenge: David Hume famously argued in An Enquiry Concerning Human Understanding that we never actually “see” causation; we only see “constant conjunction” (one thing following another).

• Mill’s Methods: To avoid this fallacy, philosophers use “Mill’s Methods” (Agreement, Difference, and Concomitant Variation) to test if A actually causes B or if they are simply occurring together by chance or because of a third, hidden factor.

C. Appeal to Ignorance (Argumentum ad Ignorantiam)

This fallacy assumes that a lack of evidence for a claim is evidence against it (or vice versa).

• The Burden of Proof (Onus Probandi): In logic, the burden of proof always rests on the person making the positive assertion. To say “God exists because you can’t prove He doesn’t” is to shift the burden of proof inappropriately. As the “Skeptical Standard” suggests: Absence of evidence is not evidence of absence.

§2 Summary Table: Relevance vs. Sufficiency