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Defining vel (aka 'wedge')

In this video, we see how vel is defined using a truth-table, and in the rest of this step we take a closer look at this connective.

Key points about vel

Here’s the official defining truth-table for vel:

The defining truth-table for vel

Let’s highlight some key points about this connective.

First, vel, like ampersand, is a two-place connective (we need to plug two sentences/sentential clauses into ‘&’ to make a grammatical sentence). We can add a rule to the grammar of our language which exactly parallels the rule for ampersand:

  • (R4) If ‘α’ and ‘β’ are wffs, then ‘(α \(\vee\) β)’ is a wff

Secondly, like ampersand and tilde, vel is a truth-functional sentence connective. The truth-value of a vel sentence is fixed in all cases by the truth-value of the sentences plugged into it. A vel sentence is true in any case in which at least one of the plugged-in sentences is true. A vel sentence is false only where both of the plugged-in sentences are false.

Thirdly, we’ve suggested that vel/wedge corresponds in meaning to the English sentence-connective ‘or’. We’ll be looking more closely at this soon.

Finally, note that vel-sentences—that is, sentences which have vel as their main connective—are called disjunctions. (This term is also applied to ‘or’-sentences in English and related sentences in other natural languages.) The two clauses plugged into the main connective of a disjunction are called its disjuncts.

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This video is from the free online course:

Logic: The Language of Truth

University of York