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Categorical Syllogisms
Categorical syllogisms have 256 varieties; only 24 are valid. Any one of these 256 can occur in scientific arguments or everyday life, and we should be able to recognize whether it is valid or invalid. Simply but brutally put, we cannot always avoid false assumptions, false inductions, or misleading data, but we must avoid invalid deductions. A scientist who incorrectly judges the validity of a syllogism may design and undertake an entire experiment based on a fallacious expectation of its potential meaning.
Table 9: Valid categorical syllogisms [Hurley, 1985].
Unconditionally valid:
| All M are P. | All S are M. | ∴ All S are P. |
| No M are P. | All S are M. | ∴ No S are P. |
| All M are P. | Some S are M. | ∴ Some S are P. |
| No M are P. | Some S are M. | ∴ Some S are not P. |
| No P are M. | All S are M. | ∴ No S are P. |
| All P are M. | No S are M. | ∴ No S are P. |
| No P are M. | Some S are M. | ∴ Some S are not P. |
| All P are M. | Some S are not M. | ∴ Some S are not P. |
| Some M are P. | All M are S. | ∴ Some S are P. |
| All M are P. | Some M are S. | ∴ Some S are P. |
| Some M are not P. | All M are S. | ∴ Some S are not P. |
| No M are P. | Some M are S. | ∴ Some S are not P. |
| All P are M. | No M are S. | ∴ No S are P. |
| Some P are M. | All M are S. | ∴ Some S are P. |
| No P are M. | Some M are S. | ∴ Some S are not P. |
Conditionally valid:
| All M are P. | All S are M. | ∴ Some S are P. | (S must exist) |
| No M are P. | All S are M. | ∴ Some S are not P. | (S must exist) |
| All P are M. | No S are M. | ∴ Some S are not P. | (S must exist) |
| No P are M. | All S are M. | ∴ Some S are not P. | (S must exist) |
| All P are M. | No M are S. | ∴ Some S are not P. | (S must exist) |
| All M are P. | All M are S. | ∴ Some S are P. | (M must exist) |
| No M are P. | All M are S. | ∴ Some S are not P. | (M must exist) |
| No P are M. | All M are S. | ∴ Some S are not P. | (M must exist) |
| All P are M. | All M are S. | ∴ Some S are P. | (P must exist) |
