PIRIE, MADSEN (2006)(2015) How To Win Every Argument, Bloomsbury, London.
The undistributed middle
All horses have four legs and all dogs have four legs, so all horses are dogs. (205).
Neither horses or dogs occupy the entire class of four-legged creatures. (205). See archives for my Langer, symbolic logic articles on 'class'.
Pirie:
'The 'middle' which carelessly omitted to get itself distributed is the term which appears in the first two lines of a three-line argument, but which disappears in the conclusion. The classic three-liner requires that this middle term must cover the whole of its class at least once. If not, it is undistributed.
All men are mammals. Some mammals are rabbits, therefore some men are rabbits.
(Even though the first two lines are correct, the middle term 'mammals' never once refers to all mammals. The middle term is thus undistributed and the deduction invalid. . . .
The standard three-liner (called a 'syllogism') works by relating one thing to another by means of a relationship they both have with a third. Only if at least one of those relationships applies to all the third thing, do we know that it is certain to include the other relationship.' (205-206).
Logically fallacious
'Fallacy of (the) Undistributed Middle (also known as: maldistributed middle, undistributed middle term)
Description:
A formal fallacy in a categorical syllogism where the middle term, or the term that does not appear in the conclusion, is not distributed to the other two terms.
Logical Form:
All A's are C's.
All B's are C's.
Therefore, all A’s are B’s.
Example #1:
All lions are animals.
All cats are animals.
Therefore, all lions are cats.'
To avoid a fallacy, the first two premises must both relate to the third premise, the conclusion. (206).
The classic syllogism
All men are mortal.
Socrates is a man.
Therefore Socrates is mortal.
My recent example
What exists as necessary is good.
God exists as necessary.
Therefore, God is good.
