Arguments

Inductive Arguments (Induction)

Bring as much evidence to bear as possible

The more evidence you get, the more conclusive

Can be defeated with a counter-example

Deductive Arguments (Deduction)

If A then B

Therefore, B ( ∴ B ) ( ∴ means therefore )

The reasons are the premises (If A then B; A)

The belief is the conclusion ( ∴ B )

Example: If I water my lawn, the grass will grow. I have watered my lawn, therefore the grass will grow.

Bad example: If I water my lawn, the grass will grow. It is Wednesday, therefore the grass will grow. (Wednesday has nothing to do with the grass growing.)

If either premise is not true, the conclusion may fail to be true.

Good (valid) arguments require two things.

First, the premises of the argument must be true.

Second, you must have the correct premises.

A second arrangement of premises

If A then B

∴ A

NOT valid. You cannot necessarily conclude that because your grass has grown, watering the lawn was the cause.

If there are many reasons (If x then y) we still can't draw any conclusions about the actual cause of the conclusion, even if the result is positive.

In a good argument, if your premises are true, your conclusion is almost embedded in the premises. You have enough information to come to that one conclusion. If not, it is not a good argument.

The negative versions...

If A then B; not B; therefore, not A. This is valid. If your grass hasn't grown, you must not have watered the lawn.

If A then B; not A; therefore not B. This is not valid. Just because you didn't water the lawn doesn't necessarily mean the grass won't grow, but if you did it will.

Saying that premises are incorrect does not necessarily invalidate a conclusion - it simply invalidates the reasoning behind the conclusion.

Arguments are valid or invalid. Statements (including individual premises and conclusions) are true or false.

Digression: Modal logic ( Modal logic - Wikipedia, the free encyclopedia ) is a method of expanding context so that statements are true/false in one world, true/false in another world.

Generalizations:

All m's are n's; a is an m; therefore, a is an n. Valid. All students in this class are smart; Jeff is in this class; therefore, Jeff is smart.

All m's are n's; a is an n; therefore, a is an m. Invalid. All students in this class are smart; Jeff is smart; therefore, Jeff is in this class. Not necessarily true - he can be smart without being in this class.