Skip main navigation

Introducing deductive validity

In this video, Dr Barry Lee introduces the key concept which is the focus of our work in this course: deductive validity.
0
Here, we’re going to introduce the key idea for the course. It’s worth pausing to emphasize just how important this idea is. It’s at the heart of everything else we’ll do from now on. Our key concept is that of deductive validity. Here’s a first go at outlining the notion. A deductively argument is one in which, if the premises are all true, then the conclusion must be true. The intuitive idea here is of a kind of argument where it’s not just that the truth of the premises would somehow make it more likely or plausible that the conclusion is true. Instead, it’s that the truth of the premises would rule out the possibility of the conclusion being false.
52.9
If the premises are true, there’s no wriggle room, no way for the conclusion to be false. If the premises are true then the conclusion has to be true. Talk of possibilities here is helpful. We can use it to give a sharper, clearer statement of the kind of feature were interested in. Here’s the revised version, putting deductive validity in terms of possibility. An argument is deductively valid if, and only if, it’s not possible for it to be the case that both, 1) all of its premises are true and 2) it’s conclusion is false, as it were, at the same time. This will be our official definition of deductive validity. Note that in what follows, we’ll often shorten ‘deductively valid’ to ‘valid’.
98.4
A quick note on ‘if and only if’. It has, pretty obviously, two components. We can understand these by working through the definition of deductive validity. First, ‘if’ bit. If an argument is such that it’s not possible for all of its premises to be true and its conclusion false, then it’s valid; that is in every case in which an argument is like that, it’s valid. And now the ‘only if’ bit.
127.9
An argument is valid only if it’s such that it’s not possible for all of its premises to be true and its conclusion false; that is, in every case in which an argument is valid, it has that feature Putting the two bits together, that’s one way for an argument to be valid and indeed it’s the only way.

Here we introduce the key concept of deductive validity. Here’s our official definition of the concept:

  • An argument is deductively valid if, and only if, it is not possible for it to be the case that both (i) all of its premises are true and (ii) its conclusion is false

(Because this is an important step, we’ve included a formatted text version in case you’d like to review and refer back to that once you’ve watched the video. Please see the link below.)

This article is from the free online

Logic: The Language of Truth

Created by
FutureLearn - Learning For Life

Our purpose is to transform access to education.

We offer a diverse selection of courses from leading universities and cultural institutions from around the world. These are delivered one step at a time, and are accessible on mobile, tablet and desktop, so you can fit learning around your life.

We believe learning should be an enjoyable, social experience, so our courses offer the opportunity to discuss what you’re learning with others as you go, helping you make fresh discoveries and form new ideas.
You can unlock new opportunities with unlimited access to hundreds of online short courses for a year by subscribing to our Unlimited package. Build your knowledge with top universities and organisations.

Learn more about how FutureLearn is transforming access to education