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 :

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