In my blog "Vague" I stated “‘Anger always leads to hate.' That is an amazingly vague generalization that numerous people could interpret to mean a plethora of different things. I won’t go into the logic of how that statement is very unsound... I'll leave that for another blog." This is that blog (+1 for stating the obvious?).

So the argument is: Anger always leads to hate

… Or…

If you are angry, then you hate.

…Or…

Premise 1(P1): if you are angry, then you hate

Premise 2(P2): you are angry

Conclusion (C): you hate

Counterexample:

P1: If you are angry at your mom, then you hate your mom

P2: You are angry at your mom

C: You do not hate your mom

(For whatever reason your mom has momentarily angered you, but all else being equal, mentally sound humans do not hate their mothers after being angered by their moms once, thus proving the original argument wrong)

Counterexample:

P1: If you are angry at the table, then you hate your table

P2: You are angry at the table

C: You do not hate the table

Time for logical symbols and whatnot:

H= I hate mom

If/then = ⊃

Not = ~

P1: If I am angry at mom, then I hate mom.

P2: I am angry at mom

C: I do not hate mom

P2: M

C: ~H

Table:

2---------C------1__M-- H---~H---M ____⊃____ H__

T---T-----F------T-----counterexample

T---F-----T------F

F---T-----F------T

F---F-----T------T

And with a counterexample we prove that

"P1: M ⊃ H

P2: M

C: ~H"

is an invalid argument.

***

confusing explanation of the tables:

__M--H__

T---T

T---F

F---T

F---F

F = False.

__M-- H-- ~H __

T---F-----T

F---T-----F

F---F-----T

~H is the opposite of H, so you switch around the Ts and Fs. In English, “I hate you” is the opposite of “I do not hate you,” so if “I hate you” is true then “I do not hate you” must be false, and vice versa.

__M--H---~H---M ____⊃____ H__

T---T-----F------T

T---F-----T------F

F---T-----F------T

F---F-----T------T

2---------C------1__M-- H---~H---M ____⊃____ H__

T---T-----F------T-----counterexample

T---F-----T------F

F---T-----F------T

F---F-----T------T

The first line is a counter example because we have all true premises and a false conclusion. A counterexample means the argument is not valid. Thus the argument that anger toward your mom leads to hate is invalid.

***