Disproving The IfThen Statement  The Case of Global Warming
Introduction
A scientific theory, or any other type of theory, often takes the form
of a logical "IfThen" 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 (ifpart) and noting that the conclusion
(thenpart) 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 causeeffect 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 IfThen 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 
