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# Disproving The If-Then Statement - The Case of Global Warming

Introduction
A scientific theory, or any other type of theory, often takes the form of a logical "If-Then" statement.  For example, the theory concerning Global Warming basically states: If we continue to emit greenhouse gasses at the current rate, our planet will keep warming with catastrophic effects. See http://en.wikipedia.org/wiki/Global_warming.

The Logic Involved
Let
P = "We continue emitting CO2 and other greenhouse gasses at the present rate."
Q = "We will experience increased global warming with catastrophic effects."
The statement "If we continue to emit greenhouse gasses at the current rate, our planet will keep warming with catastrophic effects" becomes"

If P, Then Q

How Do We Show That If P, Then Q is False?
In mathematics,

If P, Then Q is False Only When Q is False when P is True.

In other words, the only way to disprove the Global Warming theory is to keep emitting greenhouse gasses at the current rate (P is True) and have one of the following occur:

The global warming discontinues and global temperature stabilize or decline. (Q is False)

The global warming continues but there are no catastrophic effects on mankind. (Q is False)

So If We Continue To Emit Greenhouse Gases With Global Warming and Catastrophic Results, Does this Prove the Global Warming Theory?

No.  It it simply provide a lot of support for the theory.  Like most scientific theories, we can only disprove the theory by satisfying the premise (if-part) and noting that the conclusion (then-part) does not always prove to be true. If the conclusion does prove to be true, we have support for our theory, but one must always be on the lookout for a false cause-effect relationship.  In the case of global warming, a possibility of natural causes for climate changes need to be considered.

Since the current Global Warming theory may only be disproved by a "wait and see" approach that could possibly result in catastrophic effects (if the theory is true), it is a theory that must be taken into serious consideration.

Mathematical If-Then Statements

In mathematics, we have the luxury of having no "grey" area in our theory.  A mathematical theory, often called a theorem, must hold true for all possible cases.

Example: If two numbers are even counting numbers, then their sum is an even counting number.

If we let x + y represent the sum of any two counting numbers, it is easy to show that the sum (x+y) will always be even.  Here is the proof:

 Statement Reason x + y is the sum of two even counting numbers x and y. Given There are counting numbers a and b such that x=2a and y=2b. Even numbers are divisible by 2 by definition of an even number. x+y = 2a + 2b Substitution of variables 2a + 2b = 2(a + b) Distributive Property of Multiplication over Addition a+b is also a counting number. Two counting numbers added results in another counting number. (Addition of counting numbers is a closed operation) 2(a+b) represents an even number Even numbers are divisible by 2 by definition of an even number. x+y is even Substitution of variables