Friday the thirteenth surprised by bringing something brand new to be skeptical at.

And from a most unlikely source too! First period, and we were in class learning all about Logical connectives. From what I could gather, Logic is used by mathematicians to prove stuff, and also in more mundane applications such as electronics and programming (or is it

*coding* these days?) The lecturer kicked off by explaining that a statement has to be either true or false. One can then join two or more statements in a way such that the combination of the statements must also be true or false. The truth values of these combinations can be written concisely in a

*truth table*. In the case of a conjuction (two statements joined by "and") the truth table will look like this:

A B A and BT T T

T F F

F T F

F F F

This means, for example, that if statement A is true, and statement B is also true, and you join the two statements by "and", you will find that the result is also true. But whenever a false statement is included the conjuction will be false. For instance, if I were to say that "6 is a prime number

**and** Colorado is in the USA", one of the statements is false, and therefore the conjuction is also false. This makes perfect sense.

The truth table for the disjunction (two statements joined by "or") seems similarly intuitive:

A B A or BT T T

T F T

F T T

F F F

So you need only a minimum of one of the statements to be true in order for the disjunction to be true. "6 is a prime number

**or** Colorado is in the USA" is therefore perfectly acceptable as true. No problems so far.

But the part that made me take issue was the table describing the truth values for the implication (two statements joined up by "implies" or "If ... then ...":

A B If A then BT T T

T F F

F T T

F F T

Here is why I'm not convinced by this particular table. If two true statements always result in the implication being true, I could link up any two true statements, each of which has nothing to do with the other, and suddenly "

**If** Six is an even number

**then** Colorado is in the USA" is true! Yet, I somehow doubt that the early frontiersmen had any concerns about the divisibility of integers when they named the state.

In short, the table says that: ANY TRUE STATEMENT IMPLIES ANY OTHER TRUE STATEMENT.

I queried this, and was told that Logic focuses on the

*structure* of the arguments, and not the

*content* of the statements.

Hmmm.

I'm not sure if I'm letting too much philosophy seep into my rudimentary understanding of mathematics, but still : if no consideration is paid to the content, then an implication is inherently meaningless. And of what use will a meaningless implication be in proofs?

Rigil