LESSONS IN LOGIC: The Importance of the ‘Definition’

Regular readers will note that I often start a post by focusing on the definition of a word or term that is going to be discussed.  This is because the meaning assigned to a word is usually the foundation to whatever argument is being made.  However, that meaning can often be the strongest defense or weakest link in an argument.  This is why the ‘definition’ of a word or term is so important.

There are several types of definitions.  All have their purposes, and at least one is fallacious.  For those who are interested, this is an excellent summary of the different forms and functions of ‘definition:’

Logic: The Importance of Definitions

There are two important points about ‘definition’ that we need to keep in mind when we are evaluating an argument.  The first is that, if a definition is clearly explained and properly used, then it cannot be broken.  This means, if a person clearly and thoroughly defines the term(s) they are using in an argument, and they apply them properly throughout their argument, there is no way around the meaning of that word or term.  For example:

If I say something that ‘exists‘ is in a state of actual being (a state where I can prove that is has substance that can be perceived and understood), and I use this meaning for this ‘definition’ consistently in any argument where I have defined it, then there is no way around the definition.  Whatever meets the conditions of this definition must exist.

A very famous argument actually uses this same idea:

“I think, therefore I am.”

— Rene Descartes

The act of thinking is proof that the person known as Descartes exists.  Descartes may not know the full extent or objective nature of his existence, but this is not necessary to prove that he exists.  All that is necessary for Descartes to know he exists is to know that he can perceive his own thoughts.  Therefore, we can say that Descartes exists “by definition.”  This means it is not possible for Descartes to not exist because the definition demands that he must.

This brings us to the next important point we need to understand about ‘definition,’ and that is the concept of ‘logical extension.’  In short, this means that, if A is true, then B is either true because it is a part of A, or because it naturally follows from A.  Here are two examples:

If I say Descartes exists, then — by logical extension — there must be a single, unique entity defined or identified by the term (i.e. name), ‘Descartes.’  In this case, this is true because the unique individual identified as ‘Descartes’ is part of the existence of that individual: in this relationship, the two concepts cannot be separated.

At the same time, if we say that Descartes exists because he thinks, then it follows — by logical extension — that Descartes has the capacity to think.  This is because the ‘proof’ that Descartes exists is based on the ability to demonstrate he has some sort of real or perceivable form.  In this case, ‘thinking’ is the ‘proof’ that Descartes has this form.  Therefore, we can conclude that Descartes can think because this is how we proved he has form or existence.  If it helps, think of this form of ‘logical extension‘ as loosely meaning ‘implication.’

These two points are very important to us.  If we are going to properly evaluate an argument, we must be able to clearly define the terms being used.  This is true whether we are the one making the argument, or the one who is hearing or reading it.  It is also important that we be aware of the ‘logical extensions’ connected to the meaning of the words or terms being used.  Once we have a command of these concepts, we will often find that many people make mistakes because they do not consider the actual meaning of the words they are using, or the logical extensions which precede from them.