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The 'entails' symbol: a vertical line with two parallel horizontal lines attached at mid-height on its right-hand side

Symbolizing validity

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.)

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This article is from the free online course:

Logic: The Language of Truth

University of York