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Calcimator

Syllogism Validator

Check the validity of categorical syllogisms by figure and mood. Identifies all 19 traditionally valid syllogistic forms.

About this calculator

This calculator checks a categorical syllogism's validity by looking up its figure and mood against a fixed set of 19 traditionally valid forms (the validForms Set, lines 12-36), counted directly from Aristotelian syllogistic logic. Figure (1-4) describes where the middle term sits in the two premises, and Major Premise, Minor Premise, and Conclusion are each one of four categorical proposition types — A ("All S are P"), E ("No S are P"), I ("Some S are P"), or O ("Some S are not P"). Every combination is a lookup, not a derivation: the engine builds a key like "1-1-1-1" from your four inputs and checks whether it's in the valid-forms Set (line 42) — there's no logical proof happening at run time, just membership testing against a table copied from classical logic.

Counting the Set literal directly: Figure 1 and Figure 2 each contain 4 valid forms, Figure 3 contains 6 (the most of any figure), and Figure 4 contains 5, for the 19 total. Total Possible Moods is a fixed 64 (4×4×4 combinations of major premise, minor premise, and conclusion types, line 73) and does not depend on figure at all — it's the same number no matter which figure you select.

Inputs

Results

Valid Syllogism (1=Yes)

1

Figure1
Valid Forms in Figure4
Total Valid Forms (All Figures)19
Total Possible Moods64
Mood NameAAA
How to Use This Calculator
  1. Enter the major premise (e.g., 'All men are mortal').
  2. Enter the minor premise (e.g., 'Socrates is a man').
  3. Input the proposed conclusion (e.g., 'Socrates is mortal').
  4. Review whether the syllogism is valid (the conclusion necessarily follows) and whether the premises are true.
  5. Identify the syllogism figure and mood to classify it in classical logic.

What each input means

Figure (1-4)
Syllogistic figure determining the position of the middle term in premises
Major Premise
Categorical proposition type for the major premise.
Minor Premise
Categorical proposition type for the minor premise.
Conclusion
Categorical proposition type for the conclusion.

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    Figure (1-4) = 1, Major Premise (1=A, 2=E, 3=I, 4=O) = 1, Minor Premise (1=A, 2=E, 3=I, 4=O) = 1, Conclusion (1=A, 2=E, 3=I, 4=O) = 1 = 4 input(s) provided
  2. Calculate Valid Syllogism
    Valid Syllogism
    1 = 1
  3. Calculate Figure
    Figure = 1
    1 = 1
  4. Calculate Valid Forms in Figure
    Valid Forms in Figure
    4 = 4

Engine last updated . Checked against 4 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.

Frequently Asked Questions

Why does nudging Figure slightly show no change in the result?

Figure defaults to 1, and the site's usual proportional sensitivity probe moves it to 1.1 and 0.9 — both of which round straight back to 1 (Math.round, line 4), so the probe reads zero effect there. Major Premise, Minor Premise, and Conclusion are dropdowns, not numbers, so that +/-10% nudge doesn't apply to them at all — the site instead tests each option directly. Picking a genuinely different figure or premise type (2, 3, or 4) in any of the four inputs changes the mood name and can flip the validity result entirely.

Does the calculator prove the syllogism is valid, or just look it up?

It looks it up. The engine builds a key from your Figure, Major Premise, Minor Premise, and Conclusion — for example "1-1-1-1" — and checks whether that exact combination is in a fixed set of 19 traditionally valid forms (line 42), rather than deriving validity from first-order logic at run time.

Which figure has the most valid syllogistic forms?

Figure 3 does, with 6 of the 19 total valid forms (Darapti, Disamis, Datisi, Felapton, Bocardo, and Ferison), one more than Figure 4's 5 and two more than Figure 1's or Figure 2's 4 each — all counted directly from the validForms Set defined in the engine (lines 12-36).

Does changing Figure affect Total Possible Moods?

No. Total Possible Moods is a constant 64, from 4 possible types each for the major premise, minor premise, and conclusion (4×4×4, line 73) — it counts every mood combination regardless of figure, so switching Figure only changes Valid Forms in Figure, never this total.

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