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Rules of conversation again

We see how the idea of rules of conversation can explain what we feel about some strong apparent cases of mismatch between vel and 'or'.
Two minions have a chat
© University of York

Let’s look more closely at the example involving Alex, Mattie, and Sarah.

Think about a situation in which Alex is meeting with Mattie and meeting with Sarah: ‘Alex is meeting with Mattie’ is true; ‘Alex is meeting with Sarah’ is true. Now, let’s just suppose for the moment that ‘or’ always has the same truth-table as vel, and we’ll see if we can explain what we think and feel about people saying ‘Alex is meeting with Mattie or Alex is meeting with Sarah’ in this sort of situation.

There are two kinds of case.

First, suppose the speaker knows that Alex is meeting with Mattie and Sarah. We’re trying out the idea that ‘or’ has the same truth-table as vel, so the sentence the speaker has used is true. But, using Grice’s idea about rules of conversation, we can still explain why we think it would be wrong to use that sentence in this situation. Look at the rule of Quantity.

The rule of Quantity says: provide an amount of information appropriate to the conversation you’re having — not too much and not too little.

The more information someone gives, the more specific they are: the more information you get, the more it narrows down the range of possibilities.

Let’s look at this with a truth-table. Let’s define basic sentences like this:

  • M: Alex is meeting with Mattie
  • S: Alex is meeting with Sarah
M S   M or S   M and S
T T   T   T
T F   T   F
F T   T   F
F F   F   F

We’ll say that someone who says ‘M or S’ has spoken truly. (Remember that we’re working with the idea that ‘or’ has the same truth-table as vel and seeing if we can explain what we feel about these conversations.) But, if the speaker knows that both ‘M’ and ‘S’ are true, they could have given more information by saying ‘M and S’, which is also true but narrows down the range of possibilities further.

Saying only ‘M or S’ only narrows the range of possibilities to those covered by the first three rows of the truth-table (leaving rows 2 and 3 as ‘live’ options), but saying ‘M and S’ narrows things down to row 1. So, it’s more informative.

This makes ‘M or S’ a bad thing to say in this situation, without us having to say it’s false.

The second sort of situation is one in which it is in fact true that Alex is meeting with both Mattie and Sarah, but the speaker doesn’t know that—although they are confident that Alex is meeting with at least one of them. Do we want to say that the speaker would say something false in this situation, if they said ‘Alex is meeting with Mattie or Alex is meeting with Sarah’? Probably not: here we don’t even want to say they’ve spoken wrongly.

© University of York
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Logic: The Language of Truth

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