8.2 Logic — Assumptions, Conclusions & Syllogisms

Assumptions: the Unstated Premise

An assumption is a premise the author never states out loud but the argument silently depends on. Consider: "We should hold the training online to save on venue costs." The stated claim is that going online saves money on a venue. The hidden assumption is that holding the training online actually costs less than renting a venue. If that were false, the whole recommendation falls apart.

The most reliable tool is the negation test. Take a candidate assumption, negate it, and reinsert it into the argument. If the negation destroys the argument, the statement was a required assumption; if the argument still stands, it was not needed. Negating "online costs less than a venue" gives "online costs the same or more" — which kills the reason to go online, so the assumption is required.

Watch for advertising-style items: "Buy our vitamins for a healthier life" assumes the vitamins actually contribute to better health. The claim is meaningless without that bridge belief.

Conclusions: What MUST Be True

A valid conclusion is one that is true in every situation the premises permit — not merely one that could be true or seems likely. This distinction decides most conclusion items.

Worked example: "An office requires every new hire to attend orientation. Maria is a new hire." Because the rule covers every new hire and Maria is one, the conclusion "Maria must attend the orientation" is forced. Compare a weaker stem: "Some employees are union members" does not let you conclude anything about a specific named employee.

Categorical Syllogisms: All, Some, No

A syllogism joins two premises to force a conclusion. The quantifiers all, some, and no behave by fixed rules. Validity depends on form, not on whether the sentences are factually true.

Key rules to memorize:

• Two universal affirmatives (all...all) chain cleanly.
• A some premise yields at most a some conclusion — never an all.
• Two some premises together prove nothing.
• A no (negative) premise carries the negative into the conclusion.

Worked example: All birds have feathers. A penguin is a bird. This is All-A-are-B plus "penguin is an A," so "a penguin has feathers" is valid. Another: Some teachers are writers. All writers are creative. The bridge term is "writers": some teachers fall inside "writers," and all writers are creative, so some teachers are creative — a some conclusion, never "all teachers are creative."

Negative example: No heroes are cowards. All soldiers in the unit are heroes. Since every soldier is a hero, and no hero is a coward, no soldier in the unit is a coward.

A classic trap: If all managers are employees, and some employees are union members, you cannot conclude that any manager is a union member. The correct statement is the cautious one: "some managers may or may not be union members" — the overlap is undetermined.

If-Then Logic

An if-then (conditional) statement "If P then Q" supports two valid moves and two fallacies:

• Modus ponens (valid): P is true, therefore Q. ("If it rains, class is cancelled. It rained. So class is cancelled.")
• Modus tollens (valid): Q is false, therefore P is false. ("Class was not cancelled, so it did not rain.")
• Affirming the consequent (fallacy): Q is true, therefore P — invalid.
• Denying the antecedent (fallacy): P is false, therefore Q is false — invalid.
• The contrapositive "If not Q then not P" is always logically equivalent to the original.

Logical Fallacies (High-Yield)

The CSE most often tests post hoc, ergo propter hoc — the false-cause fallacy: assuming that because B came after A, A caused B. When a manager says, "Attendance improved after we offered free coffee, so the coffee caused it," the flaw is treating sequence as causation; a co-occurring change (a new bonus, seasonal effect) could be the real cause. Likewise, "Crime fell after streetlights were installed, therefore streetlights reduce crime" is weakened most by revealing a new police patrol started at the same time. Other tested fallacies: hasty generalization (a broad claim from too few cases), false dilemma (only two options when more exist), and circular reasoning (the conclusion restates a premise).

Converse and Inverse Errors

From "If a worker is tardy three times, then he is suspended," you may not conclude "if he is suspended, he was tardy three times" (the converse) — he could be suspended for a different reason. Nor may you conclude "if he is not tardy three times, he is not suspended" (the inverse). Only the contrapositive — "if he is not suspended, he was not tardy three times" — is guaranteed true. On the exam, a distractor that swaps the if and the then, or negates both parts without flipping them, is testing exactly this error, so read conditional conclusions letter by letter before choosing.