1. Deductive Arguments and Valid Reasoning

In this final series of lectures we’re going to look at the distinction between deductive arguments and inductive arguments, and see how they relate to the concepts of validity and strength that we’ve previously introduced.

Both of these terms, “deductive” and “inductive”, have a life outside of their usage in logic, and they can be used in different ways so it’s helpful to be familiar with the various ways they’re used.

In this lecture we’ll look at the relationship between deduction and valid arguments.

Deduction and Valid Reasoning

In ordinary logic, the term “deductive argument” or “deductive inference” is basically a synonym for “valid argument” or “valid inference”. The terms are often used interchangeably.

However, it’s also common to describe an argument as a deductive argument even if the argument fails to be valid.

For example, someone might give an argument like this one:

1. If the match is burning then there is oxygen in the room.
2. The match is not burning.
Therefore, there is no oxygen in the room.

and they might intend for this argument to be valid. They believe the conclusion follows with certainty from the premises.

But in this case they’ve made a mistake — this argument isn’t valid, it’s invalid. Just because the match isn’t burning it doesn’t follow that there’s no oxygen in the room.

So this is an invalid argument, but it was intended as a valid argument. In this case, we’ll still want to call it a deductive argument, but it’s a failed deductive argument, a deductive argument that is guilty of a formal fallacy, a mistake in reasoning.

So, while the terms “deductive” and “valid” are sometimes used interchangeably, they aren’t strict synonyms.

• When you describe an argument as valid you’re saying something about the logic of the argument itself.
• When you describe an argument as deductive you’re saying something about the conscious intentions of the person presenting the argument, namely, that they are intending to offer a valid argument.

You need to draw this distinction in order for it to be meaningful to say things like “this is a valid deductive argument” or “this is an invalid deductive argument”, which is a pretty common thing to say in logic.