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Defining vel (aka ‘wedge’)

In this video step, York student Natasha defines the connective vel and we note some key points about it.

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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Logic: The Language of Truth

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