Welcome one and all to Logic 101. Today we will be discussing Modus Ponens, Modus Tollens, affirming the consequent, denying the antecedent, and begging the question (also sometimes called circular reasoning, though they are not entirely the same thing).
The form of Modus Ponens is as follows:
1. If P, then Q
2. P
-----------------
3. Therefore Q
The form of Modus Tollens is as follows:
1. If P, then Q
2. NOT Q
-----------------
3. Therefore NOT P
Affirming the consequent is an INVALID utilization of logic and its form is as follows:
1. If P, then Q
2. Q
-----------------
3. Therefore P
Another similar fallacy is called Denying the Antecedent, whose form is as follows:
1. If P, then Q
2. NOT P
-----------------
3. Therefore NOT Q
And really the most important one for this discussion is the fallacy known as begging the question, whose form is as follows:
"Any form of argument in which the conclusion occurs as one of the premises, or a chain of arguments in which the final conclusion is a premise of one of the earlier arguments in the chain." (Not an exact form because there isn't one cookie cutter form, but either way this definition I think explains it well) -
SOURCE
Just wanted to add that to the discussion. But let's look at Dre's scenario again, and try to break it down to basics:
Question 1.
A and B are on a sea-saw.
X: Why is A in the air?
Y: Because B is on the ground.
X: Well then why is B on the ground?
Y: Because A is in the air.
First, "A and B are on a sea-saw." Let's assume for arguments sake, that what Dre meant is that "A and B are on the
same see-saw" (I know I'm being nitpicky, but logic is always nitpicky) and we'll call that premise P.
Next, we'll replace the former X ("Why is A in the air?") with the conclusion it's implying, "A is in the air", and call that conclusion Con1.
Now, instead of "Because B is on the ground" we'll write the premise implied: "B is on the ground" and call that premise Q.
Onto the next Y statement, we'll replace "Well then why is B on the ground?" with "B is on the ground", which we will call Con2.
Finally, we will replace "Because A is in the air" with the premise "A is in the air" and call it premise R.
So, to recap, here is the argument written out in reduced form:
First the definitions:
P: A and B are on a sea-saw
Q: B is on the ground
R: A is in the air
Con1: A is in the air
Con2: B is on the ground
I will also assume that our sea-saw isn't physical, and follows the following rule:
1. When A is on the ground, B is in the air, and vice versa.
Finally, let's write out the form of Dre's argument:
1. P
2. Q
-------
3. Therefore Con1
4. R.
-------
5, Therefore Con2
When written like this it actually looks alright, but what happens when we replace Q and R with their appropriate conclusions? Let's take a look:
1. P
2. Con2
-------
3. Therefore Con1
4. Con1
-------
5, Therefore Con2
Is it clear now, that we are in fact using a "chain of arguments in which the final conclusion is a premise of one of the earlier arguments in the chain"?
That is why this argument is logically fallacious.
Now, in order to keep the fun going, I'm adding another logical challenge, albeit one that is in my opinion easier to determine than Dre's. I must give credit to my philosophy professor, Dr. Jacques N. Catudal for this, but here goes:
1. If there are some free actions, we are responsible for some of our actions.
2. We are not responsible for some of our actions.
Therefore,
3. If we are not responsible for some of our actions, it's not the case that there are some free actions.
Is the argument above valid or invalid?
-blazed
