Unit 10: Applied Reasoning

Passage A — The main conclusion is that the professor's proposal should be rejected. The stated reason is that he will benefit financially — this is the ad hominem fallacy (specifically, a conflict-of-interest attack). The professor's argument (salary comparison with executives) may or may not be valid on its merits; his personal interest is irrelevant to whether the argument is sound. An evaluation should identify: conclusion = reject the proposal; premise = professor benefits financially; fallacy = ad hominem; evaluation = the conflict of interest is relevant to disclose, but insufficient to dismiss the argument without engaging with the actual salary comparison data.

Passage B — The structure is a disjunctive syllogism: either cause A or cause B; not A (no evidence of flammable materials); therefore B. However, ruling out one option on the basis of absence of evidence is the argument from ignorance fallacy. The conclusion that Researcher Y is responsible also relies on the hidden assumption that the listed options are exhaustive — which is precisely what was not established. Additionally, Researcher Y's unavailability for comment is not evidence of guilt.

Passage C — This is a false cause / cum hoc fallacy. The argument cherry-picks correlations (diet and heart attack rates across nationalities) and offers a deliberately absurd conclusion (speaking English) to highlight the pattern. While humorous, the structure is genuinely fallacious: correlation without a plausible mechanism and without controlling for confounding variables is not sufficient for a causal conclusion. The real purpose of this example is to illustrate how correlation-based arguments can "prove" almost anything.

A necessary cause must be present for the effect to occur — but its presence alone does not guarantee the effect. A sufficient cause guarantees the effect when present — but the effect can occur without it.

Oxygen is a necessary cause of fire (no fire without it) but not sufficient (you also need fuel and heat). A massive earthquake is sufficient to trigger a tsunami but not necessary — tsunamis have other causes.

A proximal cause is the most immediate cause in a causal chain. A distal cause is further back in the chain — a contributing background factor.

In a car crash: the proximal cause is the vehicle collision; the distal cause might be the driver's fatigue or poor road conditions.

A common cause (shared cause) produces two effects that appear correlated — but neither causes the other. A rival cause is an alternative explanation that could account for the same evidence.

Ice cream sales and drowning rates are both caused by hot weather (common cause). Whether a drug or placebo caused a patient's recovery are rival causes.

A causal chain is a linear sequence: A causes B, B causes C, and so on. A causal network involves multiple interacting causes and effects, with feedback loops and branching paths.

The spread of a disease is a causal network: infection rates affect behaviour; behaviour affects infection rates; policy affects both.

Loki had no money, but bet his own head in a wager with the dwarf Brok. He lost. When Brok came to collect, Loki argued that he had only bet his head, not his neck, and since it was impossible to determine where one ended and the other began, Brok could not take his prize.

This is a paradox of vagueness: the boundary between head and neck is not precisely defined in natural language. Loki exploits this to make a logically unanswerable claim. It illustrates that many everyday terms lack the precision required for rigorous logical argument.

If you have a heap of sand and remove one grain, do you still have a heap? Presumably yes. If you keep removing grains, one at a time, when does the heap cease to be a heap?

The paradox arises because heap is a vague predicate — there is no sharp boundary between a heap and a non-heap. The Sorites paradox applies to many everyday predicates: tall, bald, old, rich. It shows that classical two-valued logic (true/false) may be inadequate for vague language — motivating fuzzy logic and other multi-valued systems.