Traditional LogicCategorical Syllogisms

Standard-Form Syllogisms

In standard form the major premise (with the major term) comes first, then the minor premise, then the conclusion.

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Once you can name the three terms, you can put any syllogism in a fixed order. That order is what the names mood and figure describe, so it comes first.

Key idea

Standard form: the major premise (the premise with the major term) first, then the minor premise (the premise with the minor term), then the conclusion.

Why it works

A fixed order turns every syllogism into the same pattern, so two arguments with the same pattern can be recognized at once, even when their words differ. People speak arguments in any order ("We will be late, since the bus is slow and…"). Putting the conclusion last and the major premise first is like writing a fraction in lowest terms: a standard way to write the same thing, so that comparing is easy.
  • Find the conclusion (look for so, therefore, since, because).
  • Its predicate is the major term: the premise containing it is the major premise.
  • The other premise, which contains the minor term, is the minor premise.
  • Write: major premise, minor premise, conclusion.
Given in either order, the premises are shown in standard form: the major premise (with "cyclists") on top.

Worked examples

Worked example: Conclusion first

Put in standard form: "Some volunteers are not cyclists, because no cyclists are coders and some coders are volunteers."
  1. "Because" marks the premises, so the conclusion is "Some volunteers are not cyclists".
  2. Major term: cyclists. The major premise is "No cyclists are coders".
  3. Minor premise: "Some coders are volunteers".

Answer: No cyclists are coders / Some coders are volunteers / ∴ Some volunteers are not cyclists

Worked example: Premises in the wrong order

Which is the major premise? "All squares are rectangles. All rectangles are polygons. Therefore all squares are polygons."
  1. Conclusion: "All squares are polygons". Its predicate, polygons, is the major term.
  2. The premise containing "polygons" is "All rectangles are polygons", although it was spoken second.

Answer: All rectangles are polygons

Common mistake

Keeping the order in which the premises were spoken. Find the conclusion first, then put the premise with its predicate on top. Check: the first line of your standard form must contain the last word-group of the conclusion.

Practice

Pass with 3 right answers, the last 2 in a row. Each right answer earns 2 XP.

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Sources and further reading

  • Patrick J. Hurley, A Concise Introduction to Logic, 5.1 Standard Form, Mood, and Figure
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