Validity of argument

A concept of validity of an argument must be differentiated from a concept of a valid argument. Let me give you an example:

(I)

My sister will cook or my mom will cook.

My mom will not cook.

______________________________________________

My sister will cook.

We usually represent (I) like this:

(I')

A or B

Not A

-----------------

B

(I') is so-called argument schema or a valid argument schema, and (I) is called an argument. When we write an argument within considerable sentences,we usually also picture an actual argument as (I). Definitively (I) and (I') are valid arguments, but move on next example:

(I'')

A if B

Not B

-----------------

A

Not merely (I'') cannot be a valid argument, but also not be a valid argument schema.

Different argument schemata have different conjunctions. The conjunction in (I') is or, and in (I'') is if. In logic class, we learn how to deal those conjunctions with logical principles, and this is an aspect of syntactic construction aiming to persist the validity.

An argument schema can be represented from various expressions, as we point out, the meaning of expression plays an essential role in validity of an argument. So logicians concern both the argument schemata and the validity of an argument. If the conjunction or, for example, plays a part of validity of an argument then we are also investigating its meaning.

However, the validity of an argument will not be changed if we replace the argument to another expression. When we are talking about the validity of an arguments, we are talking about the argument schemata, valid arguments, and meaning of conjunctions. These three parts of logic can be separately discussed later on.