Wednesday, April 28, 2010

"Anger always leads to hate" counterexample

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

(You are angry at the table because you hit your shin on it by accident, which hurt. You do not hate your table for this, though, since it was your fault for being clumsy.)

Both of these arguments prove that "anger always leads to hate" is false. As shown by the two arguments, anger does not always lead to hate.

Time for logical symbols and whatnot:

M= I am angry at mom
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

P1: M H
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

T = true
F = False.

There are four scenarios that can occur: M and H can both be true, M could be true and H could be false, M could be false and F could be true, or both could be false.

Adding on “~H”:

M-- H-- ~H

T---T-----F
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.

Adding on “M H”:

M--H---~H---M H

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

This would take too much to explain (at least for me it would, since brevity is not my forte). Take a logic class if you wanna figure it out.

Last we have the final 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

The 2 represents P2 and is placed over the M, because M was our second premise. The C represents conclusion, and is over the ~H, because ~H was our conclusion. The 1 represents P1 and is over the M H, because M H represents our second premise.

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.

***

There you have it folks: anger does not always lead to hate. You have an example right there proving that anger toward your mom will not lead you to hate. If you are thoroughly confused, just take my word for it. I tell no lies (that was a lie).

2 comments:

  1. Oh Hollie. I don't think I understood half of this blog, but I agree :P

    ReplyDelete
  2. heh, I got a little carried away.

    ReplyDelete