Deductively Valid and Inductively Strong

Deductively Valid and Inductively Strong

The primary goal in argumentation is for the conclusion to follow from its basic premises either with certainty or with high probability. Technically, this means the arguer desires the argument to be deductively valid or to be inductively strong.

The concept of deductive validity can be given alternative definitions to help you grasp the concept. Below are five different definitions of the same concept. It is common to drop the word deductive from the term deductively valid:

An argument is valid if the premises can’t all be true without the conclusion also being true.

An argument is valid if the truth of all its premises forces the conclusion to be true.

An argument is valid if it would be inconsistent for all its premises to be true and its conclusion to be false.

An argument is valid if its conclusion follows with certainty from its premises.

An argument is valid if it has no counterexample, that is, a possible situation that makes all the premises true and the conclusion false.

Emeralds Green

Emeralds Green

This argument is valid:

All emeralds are green.

The stone placed in the safe deposit box is an emerald.

So, the stone placed in the safe deposit box is green.

Here is a very similar argument that is not valid. Can you see why?

All emeralds are green.

The stone placed in the safe deposit box is green.

So, the stone placed in the safe deposit box is an emerald.

That last argument has a counterexample. You can imagine a situation where all emeralds are green and the stone placed in the safe deposit box is green jade. That’s a situation where the premises are true but the conclusion isn’t. That situation is a counterexample.

An argument that is not valid is called invalid or deductively invalid. In deductive arguments, the arguer intends for the argument to meet the standard of being deductively valid. There are other, unrelated uses of the word “valid” such as when we say that word is not valid in a Scrabble game, or that is a valid way to travel from Paris to Amsterdam.

In inductive arguments, the arguer intends the argument to satisfy another standard, that the conclusion follow with high probability but not certainty from the basic premises. If it does, the argument is said to be inductively strong. Inductive strength is a matter of degree, unlike with deductively validity.

The distinction between deductive and inductive argumentation was first noticed by the Aristotle (384-322 B.C.E.) in ancient Greece. Since arguers don’t always have clear intentions about whether their goal is to create a deductive valid or an inductively strong argument, it is very often up to the logical analyst to decide which treatment works best.

When we study inductive arguments in later chapters we will see that an inductive argument can be affected by acquiring new premises (evidence), but a deductive argument cannot be. For example, this is a reasonably strong inductive argument:

Today John said he likes Romina.

So, John likes Romina today.

but its strength is changed radically when we add this premise: John told Felipe today that he didn’t really like Romina.

With inductively strong arguments there is a small probability that the conclusion is false even if all the premises are true, unlike with deductively valid arguments.

Several later chapters are devoted to exploring deductive validity and inductive strength, but it is important to note that even if your argument is deductively valid or inductively strong, it should not succeed in convincing people of your conclusion unless they know that its premises are true. If you are a critical thinker who is faced with such an argument, and you don’t know whether one of the premises are true, then you will suspend judgment about whether the argument is successful until you find out whether all the premises are true.