Help understand "unless"

Question

The statement "r unless s" is defined as "if $\sim s$ then $r$."

Now, I can proceed as follows:

$$\sim s \rightarrow r $$

$$\equiv \; \sim (\sim s) \vee r$$

$$\equiv \; s \vee r$$

Which means that when $s$ and $r$ both are true, the statement is true. This violates the definition of "unless", which implies mutual exclusion.

Of course when $s$ is true, $\sim s$ is false and the conditional $\sim s \rightarrow r$ is true, but how does that help resolve this apparent paradox? I mean, this way, it seems that both $s$ and $r$ can occur together, which is the very opposite of the definition of "unless".

Please help.

The phrase "$r$ unless $s$" should be viewed as shorthand for "$r$ unless $s$, in which case who knows?" This doesn't imply mutual exclusion. — goblin GONE, Nov 26 '13 at 01:30
@user18921 Sometimes 'unless' implies mutual exculsion. E.g., 'you may have soup with that unless you choose salad, sir'. — Quinn Culver, Jan 15 '14 at 14:25

score 0 · Accepted Answer · answered Jan 14 '14 at 14:47

0

Answering it myself in order to close it. As explained in a comment above: "The phrase "r unless s" should be viewed as shorthand for "r unless s, in which case who knows?" This doesn't imply mutual exclusion."

answered Jan 14 '14 at 14:47

ankush981

2,033

Help understand "unless"

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