Material Implication and its implications...part 1

Since my life is utterly devoid of any excitement....alright alright I take it back, it has some excitement if you consider solving an equation that you have been staring at for the last fortnight and watch as its result unfold nice inferences, as exciting...well if you do, then you need to Get A Life(apparently gal for short in texting language... hmmm what will they think of next, and NO i did not find that out when some girl told me to do so... picked it up from one of the speakers at the world science festival which btw was awesome!! \m/ he told us he gets that particular msg from his daughter quite often...tch tch!!)
AS i was saying, since my life is utterly devoid of excitement (and plus since I like science thingys) I shall talk continue talking about mathematics and logic. (However I intend to change this soon for i believe you cannot do great things if you are not willing to look like an idiot now and then). Like the title indicates, I have decided  to ramble on about material implication. Material implication is a boolean function with some far reaching consequences. A boolean what you ask?? For those who havent done boolean algebra and logic functions, I will give you a very brief, need-to-know only tutorial. (if you know all these already, you might as well skip the next paras or so)
Consider a binary system with 1(true) and 0(false). A function by definition is something which takes inputs and produces outputs(crudely speaking ie). A logic function does the same, for eg: the AND function has output 0(false) unless both the inputs are 1(true), its a little like multiplication and hence symbolised by the '.' symbol. The OR function is always true(1) unless both the inputs are 0(false), indicated by the '+' symbol. The NOT function takes the input and inverts it. True gives false and false gives true.
A      B      A.B         A       B    A+B
0       0        0            0       0       0
0       1        0            0       1       1
1       0        0            1       0       1                <------This is the truth table!!
1       1        1            1       1       1
Now any other function in boolean logic can be constructed using what are called fundamental or basic gates. Examples of these include NAND( AND followed by a NOT) and NOR(OR followed by a NOT).
We can also describe any possible function using a platform consisting of two functions: the FALSE function (which gives output as 0 for any input) and another function called the 'IMPLICATION' function (also called material implication to distinguish from logical implication) and denoted as 'A IMP B' or more commonly     'A-->B'. (I came across the use of implication as a basis function in a footnote of a paper and not sure how exactly so, so if I am wrong kindly let me know).
Now this implication function A-->B is read "if A then B" ie as the name suggests it implies(though its not wise to literally do this in all cases as it leads to some paradoxes). Before I dive into its actual meaning and its paradoxes, objections,etc I shall quickly tell you what its equivalent to, if expressed using other functions. A IMP B comes out to (NOT A) OR B. Though the intuitive meaning of "if A then B" is not clear, in terms of functions, they are equivalent. The truth table looks like this
A   B    A-->B
T    T        T
T    F        F         ----> T-True   F-False
F    T        T
F    F        T
As we can see the implication function is false only when A is true and B is false. Now in A-->B, A is called the antecedent and B is called the consequent. Though this definition of material implication forms the foundation of advanced study is mathematics and logic, there are some paradoxes that comes along with it. Notice rows 3 and 4, we can see that whenever A is false, the implication is still true. Why is this a paradox you ask? Consider the statment "If the moon is made of yellow cheese, then life exists on earth". Now even though the antecedent("moon is made of cheese") is false, the whole statement is still true as per the definition of material implication. Again look at rows 1 and 3, whenever B is true, the whole statement is considered true. Keeping this in mind, check this statement "If life exists in other planets, then life exists on earth". This statement is true because the consequent("life exists on earth") is true. Well yeah they are not clear cut paradoxes but something about the whole sentence is counter intuitive right??
FINE!!! if its such a problematic definition then why do we stick to it?? Well I was gonna explain that part here but since this post is going on much longer than I expected it to, I am gonna quickly go upstairs and make this part 1 and see you all in part 2.

Cheers
Gnut
....going to do something really really stupid...