This got me to thinking about one of my favourite mathematical proofs from back in my school days - the proof by contradiction aka Reductio ad absurdum; the principal is that you take a definition and then prove that the definition is self contradictory. The first time that I encountered this technique was for proving that the square root of two is not a rational number. This is done by assuming that the square root of two

**is**rational and then showing that the assumption is self contradictory:

**CAUTION:**The following contains maths and will probably only be enjoyed by geeks. If you want to skip down to "So what does all this have to do with god(s)?" then no-one will mind, but you are missing out.

If √2 is rational, then √2 =

*m*/

*n*

where

*m*and

*n*are integers with no common factors.

So our definition consists of four things:

**1)**√2 =

*m*/

*n*

**2)**

*m*is an integer

**3)**

*n*is an integer

**4)**

*m*and

*n*have no common factors

If we can show that these four things cannot all be simultaneously true then we have a contradiction and √2 must therefore be irrational.

If √2 =

*m*/

*n*

Then 2 =

*m*²/

*n*²

and 2

*n*² =

*m*²

therefore

*m*² is an even number (since it is divisible by two) and since the square of a odd number is odd and vice versa,

*m*itself must be an even number.

Since

*m*is an even number it can be represented by 2

*a*, where

*a*is an integer,

thus 2

*n*² =

*m*²

=> 2

*n*² = (2

*a*)²

=> 2

*n*² = 4

*a*²

=>

*n*² = 2

*a*²

So now we can see that (for the same reasons as above)

*n*must also be an even number, thus we have contradicted

**4)**as both

*m*and

*n*have a common factor of two. Therefore, since all numbers are either rational or irrational, √2

**must**be irrational.

**So what does all this have to do with god(s)?**

Well, one of the favourite little nuggets of stupid pulled out by apologists is, "to know that [insert name of deity(s) here] doesn't exist would require you to know everything about the entire universe and, since you don't, you cannot state that [whatever] doesn't exist." Leaving aside the obvious fallacy of proving the negative, it isn't necessary to know the entire universe inside out to prove that it doesn't contain square circles, for example, since the definition of such an entity is self contradictory and thus no entity can possibly fulfill the definition. Likewise with most deities; their definitions are self contradictory, such as being omnipotent which is a contradiction all in itself, and so they

**cannot**exist and the questions as to where you would look and "what evidence would convince you" (another favourite) become nonsensical.

That then is my mission for this blog; I will (at least attempt to) disprove by definition the existence of any gods that I come across. Initially I will use the common definitions of gods as they are understood by most people, but to avoid the whole, "that's not my god - his beard is too long," phenomenon, I will also be accepting definitions from commenters of a theistic persuasion. Assuming that anyone is still reading, that is...