Rules of Logic

There need to be a few things clarified in what we are about to discuss. First, let me briefly define what an argument is and what it isn’t. An argument is a collection of statements – which assert something is or is not the case – in which one statement (the conclusion) is said to follow from the other statements (premises). In other words, the premises are meant to provide support for the conclusion. A statement which asserts/claims something is the case or is not the case is a proposition. Second, if an argument follows the rules of logic, then it is a valid argument. To say an argument is valid is to say the conclusion follows from the premises. An argument being valid has nothing to do with the premises and the conclusion being true or false. An argument being valid is concerned with the form or structure of the argument; it is not concerned with the truth of the premises or the conclusion. By contrast, if the conclusion fails to follow from the premises that preceded it, then the entire argument is invalid. For an argument to be a sound argument the conclusion has to follow from the premises and the premises have to be true. But in this blog post we will not be discussing the soundness of an argument but its validity.

Rule #1

Modus Ponens

This is a rule, which is very simple and straightforward to understand. The rule Modus Ponens can be defined as follows: A rule of inference in which a certain truth is automatically implied by another truth that precedes it: P implies Q. P; Therefore, Q. I will show a few examples on how this is worked out.

Example #1

-            Since I am hungry for Italian food right now, I will go to Olive Garden to eat.

-            I am hungry for Italian food right now.

-            Therefore, I will go to Olive Garden to eat.

Example #2

-            Anything that comes into existence has to have a cause

-            The universe came into existence

-            Therefore, the universe has to have a cause

Example #3

-            If it is raining outside, then I will stay inside

-            It is raining outside

-            Therefore, I will stay inside

              Rule #2

                  Modus Tollens

Modus Tollens is similar to Modus Ponens but has a critical difference. In Modus Tollens, the second half of a premise (the consequent) is denied or negated in the second premise of an argument:

P > Q (the > sign means implies. Q is implied by P or is a consequence of P)

~Q (the ~ sign means negation or denial. Q is being denied in this case)

~P

Whatever is true of P is also true of Q and vice versa. There is never a time in which something is true of either P or Q but false of the other variable. Let’s look at some examples.

Example #1

-            If God does not exist, then objective moral values do not exist

-            Objective moral values do exist (Notice that this premise is a *denial* of the second part of the first premise)

-            Therefore, God exists

Example #2

-            Since the Pacers have tied the series 2-2 with the Heat, they will win the remaining games of the Eastern Conference Finals

-            They will not win the remaining games of the Eastern Conference Finals

-            Therefore, the Pacers have not tied the series 2-2 with the Heat

Example #3

-            Whatever comes into the marketplace to be sold must be fresh food

-            Raspberries are not fresh food

-            Therefore, raspberries did not come into the marketplace to be sold

In the next blog post pertaining to logic I will talk about a hypothetical syllogism and a disjunctive syllogism. Stay tuned!