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A potential mismatch case for ‘&’ and ‘and’

In this video, Dr Barry Lee introduces a case in which an 'and' sentence might seem to different in truth-value from the corresponding '&' sentence.
We can start to introduce ideas around semantics and pragmatics with a story. Notoriously, in 2011, at a special dinner for White House journalists, which Donald Trump attended, President Barack Obama made some very sharp jokes at Trump’s expense. Many of those present laughed at these jokes; Trump did not. Some people suggested that being publicly mocked in this way was what made Trump decide to run for president, to ‘get’ Obama and the Democrats. Now, someone who believes that there was a connection might say
this: “Obama made fun of Trump and Trump decided to run for President”. In the context of the conversation about what happened at that dinner and subsequently, it would be pretty natural to hear someone who said that, as in some sense, saying that there was a connection between the two facts. Effectively, that the first at least contributed to bringing about the second. But is that idea, the idea of connection, included in the meaning of the sentence that we’re supposing that they said? If the idea of connection is built into the meaning of the ‘and’ sentence, then we have a potential mismatch between ampersand and ‘and’. There’s no mention of connection in our definition of ampersand.
Remember that ampersand is truth- 01:29.400 –> 01:32.700 functional, so an ampersand-sentence will be true
in any case in which the sentences plugged into it are true, whether the relevant facts are connected or not. If the idea of connection is built into the meaning of the ‘and’ sentence in the Obama/Trump case then it might be that the corresponding ampersand sentence is true, because “Obama made fun of Trump”, as a sentence, and
“Trump decided to run for President”, as a sentence, are both true, but the ‘and’ sentence, false. Suppose the people who think that being mocked by Obama made Trump run for President are just wrong. We could suppose here that Trump already hated Obama as much as one human being could hate another and that he decided to run for unconnected reasons. The connection claim would be false and, on the assumption that the idea of connection is built into the meaning of ‘and’ at least in this sort of case, the sentence, “Obama made fun of Trump and Trump decided to run for President” would be false.
This would mean the first line of our truth table for ‘and’ would be wrong, not because it would always be false with true plugged-in sentences, but because it would be false in some cases like this, where there is no connection, and true in others, where there was a connection. Is there a real mismatch in this case? In the next few steps, we’ll see that it almost certainly isn’t a real mismatch case, but in looking at why, we’ll encounter some interesting and useful ideas. We’ll also see how careful we need to be when we’re looking at claims and arguments expressed in natural language.

This video describes a potential mismatch case for ‘and’ and ampersand: a situation in which it might seem like an ‘and’-sentence might differ in truth-value from the corresponding ampersand-sentence.

If this really was a mismatch case, that would show at least that we can’t always represent claims involving the sentence-connective ‘and’ by using ‘&’.

Investigating whether this is a real mismatch case will introduce some interesting ideas about meaning and how we express ourselves in natural language. These ideas will be useful as we look at further sentence-connectives.

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Logic: The Language of Truth

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