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intermediate18 min

Statements, Assumptions, and Conclusions

Distinguish a stated fact from an unstated assumption an argument actually depends on.

What you'll learn

  • Distinguish a stated premise from an unstated assumption an argument depends on
  • Apply the negation test to check whether a candidate assumption is truly necessary
  • Identify which of several candidate assumptions an argument actually requires

Prerequisites

Explanation

Every argument rests on more than what's written down. A stated premise is explicit ("sales increased after the launch"). An assumption is a claim the argument needs to be true for its conclusion to follow, but never says out loud. A conclusion is the claim the argument is trying to establish.

Take: "Sales increased after we launched the new fitness program, so the program is working." The stated premise is the sales increase. The conclusion is "the program is working." The unstated assumption is that nothing else caused the increase -- no seasonal effect, no unrelated marketing push, no coincidence. If that assumption is false, the argument falls apart even though the premise is true.

The standard technique for testing whether a candidate assumption is genuinely necessary (not just plausible or related) is the negation test: assume the candidate assumption is false, and ask whether the argument still holds up. If negating the assumption destroys the argument's support for its conclusion, the assumption was necessary. If the argument still basically holds even when the candidate is false, that candidate wasn't actually required -- it might be a nice detail, but it's not load-bearing.

This is different from finding any true-sounding statement related to the topic. Placement tests often offer several plausible-sounding assumption choices, and only one survives the negation test. The discipline is mechanical: for each candidate, ask "if this were false, would the argument still make sense?" -- not "does this sound reasonable?"

Example

The negation test, encoded as a boolean check: does the argument hold with the assumption, but fail without it?

function isNecessaryAssumption(holdsWithAssumption, holdsWithoutAssumption) {
  return holdsWithAssumption === true && holdsWithoutAssumption === false;
}
// isNecessaryAssumption(true, false) -> true (passes the negation test)

Guided exercise

Guided exercise

Write isNecessaryAssumption(holdsWithAssumption, holdsWithoutAssumption), two booleans representing whether the argument holds under each scenario. Return true only if the argument holds with the assumption AND fails without it.

Checks: Confirms a genuinely necessary assumption · Rejects an assumption the argument doesn't actually need · plus 1 hidden check

Code editor. Press Escape then Tab to leave the editor if keyboard focus becomes trapped. Press Control+Shift+M inside the editor to toggle Tab-key focus trapping.

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Independent exercise

Independent exercise

Write findNecessaryAssumptions(candidates), where candidates is an array of { holdsWith, holdsWithout } booleans. Return an array of the indices of every candidate that passes the negation test.

Checks: Finds exactly the one passing candidate · Finds multiple passing candidates · plus 1 hidden check

Code editor. Press Escape then Tab to leave the editor if keyboard focus becomes trapped. Press Control+Shift+M inside the editor to toggle Tab-key focus trapping.

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Common mistakes

  • Picking an assumption because it sounds true in general, rather than testing whether the argument needs it specifically.
  • Confusing a stated premise with an unstated assumption.
  • Assuming a conclusion follows from a premise without checking what unstated claim actually bridges them.

Knowledge check

Knowledge check

1. An argument concludes a new fitness program works because sales increased after its launch. What is the unstated assumption necessary for this argument?
2. Which best distinguishes an assumption from a stated premise in an argument?
3. What does the negation test check for a candidate assumption?

Takeaway

Test a candidate assumption by imagining it's false -- if the argument survives anyway, it wasn't the necessary assumption.

Summary

Arguments rest on unstated assumptions in addition to their explicit premises. The negation test -- checking whether an argument holds with a candidate assumption but fails without it -- is the reliable way to identify which assumption is truly necessary.

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Next: Non-Verbal and Pattern Reasoning →