Skip main navigation

£199.99 £139.99 for one year of Unlimited learning. Offer ends on 28 February 2023 at 23:59 (UTC). T&Cs apply

Find out more

Symbolizing validity

This short step introduces the idea of entailment and the symbol used to represent it: double-turnstile.
The 'entails' symbol: a vertical line with two parallel horizontal lines attached at mid-height on its right-hand side
© University of York

One of the key things we’re going to be doing in this course is introducing carefully defined symbols to help us be clear about what’s going on with claims and arguments.

As we’ll often want to talk about whether arguments from particular premises (or particular kinds of premises) to particular conclusions (or particular kinds of conclusions) are valid, it will be helpful to have a symbol that relates to this: (models) (called double-turnstile).

Where the argument from some premises to a conclusion is valid, we say that the premises entail the conclusion. We can write that premises entail a conclusion by writing ‘(models)’ (double-turnstile) between the premises and the conclusion, like this:

  • The food has been chilled or the food is not safe to eat. The food has not been chilled. (models) The food is not safe to eat.

What we’ve written here will be true if and only if the argument really is valid.

(We’re not going to be making heavy use of double-turnstile this week, but it will play a role further down the line.)

© University of York
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