diamond geezer

 Friday, April 05, 2019

This is a syllogism.

All kittens are cats.
Some kittens are monsters.
∴ Some monsters are cats.

The first statement is the major premise.
The second statement is the minor premise.
Both premises are assumed to be true.

The final statement is the conclusion.
∴ stands for 'therefore'

The conclusion is a logical deduction from the two premises.
If the first two statements are true, then the third must be too.

There are 24 distinct valid syllogisms.
Here's an example of each.

All/All	All kittens are cats. All cats are monsters. ∴ All kittens are monsters.	All kittens are cats. All cats are monsters. ∴ Some kittens are monsters.
	All kittens are cats. All kittens are monsters. ∴ Some monsters are cats.	All kittens are cats. All cats are monsters. ∴ Some monsters are kittens.
All/No	All kittens are cats. No monsters are cats. ∴ No monsters are kittens.	All kittens are cats. No cats are monsters. ∴ No monsters are kittens.
	All kittens are cats. No monsters are cats. ∴ Some monsters are not kittens.	All kittens are cats. No cats are monsters. ∴ Some monsters are not kittens.
	All kittens are cats. No cats are monsters. ∴ No kittens are monsters.	All kittens are cats. No monsters are cats. ∴ No kittens are monsters.
	All kittens are cats. No monsters are cats. ∴ Some kittens are not monsters.	All kittens are cats. No cats are monsters. ∴ Some kittens are not monsters.
	All kittens are cats. No monsters are kittens. ∴ Some cats are not monsters.	All kittens are cats. No kittens are monsters. ∴ Some cats are not monsters.
All/Some	All kittens are cats. Some monsters are kittens. ∴ Some monsters are cats.	All kittens are cats. Some kittens are monsters. ∴ Some monsters are cats.
	All kittens are cats. Some monsters are kittens. ∴ Some cats are monsters.	All kittens are cats. Some kittens are monsters. ∴ Some cats are monsters.
	All kittens are cats. Some monsters are not cats. ∴ Some monsters are not kittens.	All kittens are cats. Some kittens are not monsters. ∴ Some cats are not monsters.
Some/No	Some cats are kittens. No kittens are monsters. ∴ Some cats are not monsters.	Some cats are kittens. No monsters are kittens. ∴ Some cats are not monsters.
	Some cats are kittens. No cats are monsters. ∴ Some kittens are not monsters.	Some cats are kittens. No monsters are cats. ∴ Some kittens are not monsters.

The Greeks had all this sorted.
They did not use kittens in their examples.

n.b. Technically 9 of the 24 rely on an additional assumption, which is that the category in question is not empty. If the category is empty, this triggers the existential fallacy. For example...

All kittens are cats.
All kittens are monsters.
∴ Some monsters are cats.

...is not true if there are no kittens. But let's not worry about that.

Other fallacies exist. Here are six of them.

Undistributed middle	All kittens are cats. All monsters are cats. ∴ All monsters are kittens.
Illicit major	All kittens are cats. No monsters are kittens. ∴ No monsters are cats.
Illicit minor	All kittens are cats. All kittens are monsters. ∴ All cats are monsters..
Exclusive premises	No monsters are cats. Some cats are not kittens. ∴ Some kittens are not monsters.
Affirmative conclusion from negative premises	No kittens are monsters. No monsters are cats. ∴ All kittens are cats.
Negative conclusion from affirmative premises	All kittens are cats. All cats are monsters. ∴ Some monsters are not kittens.

None of these are valid arguments.
None of the conclusions follow logically, even if it looks like they do.

And I mention all of this syllogism stuff because we live at a time when false arguments are rife.

Sometimes the argument doesn't follow from the evidence given.
Sometimes the premise isn't true, however convincing the conclusion looks.
∴ Be careful out there.

posted 07:00 :

<< click for Newer posts

click for Older Posts >>

click to return to the main page

...or read more in my monthly archives
Jan24  Feb24  Mar24  Apr24  May24  Jun24  Jul24  Aug24  Sep24  Oct24  Nov24
Jan23  Feb23  Mar23  Apr23  May23  Jun23  Jul23  Aug23  Sep23  Oct23  Nov23  Dec23
Jan22  Feb22  Mar22  Apr22  May22  Jun22  Jul22  Aug22  Sep22  Oct22  Nov22  Dec22
Jan21  Feb21  Mar21  Apr21  May21  Jun21  Jul21  Aug21  Sep21  Oct21  Nov21  Dec21
Jan20  Feb20  Mar20  Apr20  May20  Jun20  Jul20  Aug20  Sep20  Oct20  Nov20  Dec20
Jan19  Feb19  Mar19  Apr19  May19  Jun19  Jul19  Aug19  Sep19  Oct19  Nov19  Dec19
Jan18  Feb18  Mar18  Apr18  May18  Jun18  Jul18  Aug18  Sep18  Oct18  Nov18  Dec18
Jan17  Feb17  Mar17  Apr17  May17  Jun17  Jul17  Aug17  Sep17  Oct17  Nov17  Dec17
Jan16  Feb16  Mar16  Apr16  May16  Jun16  Jul16  Aug16  Sep16  Oct16  Nov16  Dec16
Jan15  Feb15  Mar15  Apr15  May15  Jun15  Jul15  Aug15  Sep15  Oct15  Nov15  Dec15
Jan14  Feb14  Mar14  Apr14  May14  Jun14  Jul14  Aug14  Sep14  Oct14  Nov14  Dec14
Jan13  Feb13  Mar13  Apr13  May13  Jun13  Jul13  Aug13  Sep13  Oct13  Nov13  Dec13
Jan12  Feb12  Mar12  Apr12  May12  Jun12  Jul12  Aug12  Sep12  Oct12  Nov12  Dec12
Jan11  Feb11  Mar11  Apr11  May11  Jun11  Jul11  Aug11  Sep11  Oct11  Nov11  Dec11
Jan10  Feb10  Mar10  Apr10  May10  Jun10  Jul10  Aug10  Sep10  Oct10  Nov10  Dec10 
Jan09  Feb09  Mar09  Apr09  May09  Jun09  Jul09  Aug09  Sep09  Oct09  Nov09  Dec09
Jan08  Feb08  Mar08  Apr08  May08  Jun08  Jul08  Aug08  Sep08  Oct08  Nov08  Dec08
Jan07  Feb07  Mar07  Apr07  May07  Jun07  Jul07  Aug07  Sep07  Oct07  Nov07  Dec07
Jan06  Feb06  Mar06  Apr06  May06  Jun06  Jul06  Aug06  Sep06  Oct06  Nov06  Dec06
Jan05  Feb05  Mar05  Apr05  May05  Jun05  Jul05  Aug05  Sep05  Oct05  Nov05  Dec05
Jan04  Feb04  Mar04  Apr04  May04  Jun04  Jul04  Aug04  Sep04  Oct04  Nov04  Dec04
Jan03  Feb03  Mar03  Apr03  May03  Jun03  Jul03  Aug03  Sep03  Oct03  Nov03  Dec03
 Jan02  Feb02  Mar02  Apr02  May02  Jun02  Jul02 Aug02  Sep02  Oct02  Nov02  Dec02