## Wednesday, August 7, 2013

### The logician's daughter

Yesterday, my eldest daughter burned the dessert she was baking. You see, the recipe at one point (after a fair amount of baking at a lower temperature) said to bake "for fifteen minutes or until golden brown." She knew the second disjunct was already true at the beginning of that period, but decided to opt for following the first disjunct, as apparently allowed by the recipe. The dessert was black when she was done (though some of the inside was edible).

Tullius said...

She should have known that imperatives do not have truth value and thus are impervious to the rules of implication.

Skylar said...

Even if all imperatives lack truth value, there could be some statements that look (or sound) like imperatives but are not.

Suppose somebody robs me in a dark alley and says, "Give me all your money or I'll shoot!" I understand (rightly, I hope) this statement in disjunctive form: either I give him all of my money, or else he will shoot me.

In this case, instructions about baking seem to be like the example I just gave. Perhaps the (funny) mistake was reading the "or" as inclusive: either cook for 15 minutes or until golden brown (or both).

Alexander R Pruss said...

No, inclusive satisfaction would be perfectly ok, if after 15 minutes it was golden brown.
The problem with the directions was that there was an implicit "whichever comes first".

Dagmara Lizlovs said...

Ah, Live and learn little one. This reminds of the time many, many rains ago, when my sister and I returned home from our respective music camps. We decided to serve our family something we called "music camp pancakes."

Tullius said...

I don't know, Skylar; you seem to undermine the analogy by demonstrating that the baking instance has an implicit unity between disjuncts. As Mr. Pruss states, "whichever comes first" is the idea. Thus, in the baking example you add "or both," which would be problematic in the stick-up scenario. I'm much less likely to hand over money if the statment is not a set of exclusive disjuncts. Therefore, I would reply, "I will give you my money, ONLY IF you do not shoot me."

I'm not comfortable translating the criminal's remarks as "Either you give me your money or I shoot you (or both—that is, whichever comes first)."

Tullius said...

Oh, I reread your remarks. I should have added that in logic, unless otherwise specified, the "or" is always inclusive. The joke applies because the whole statement is true even if only one disjunct is true. So in your example (the indicative version of it) I can take comfort in the fact that as long as he shoots me, he was telling the truth.

Alexander R Pruss said...

Well, maybe it's inclusive in the shooter case, too? If you give him the money he still MIGHT shoot you (and you can't complain that he broke the bargain), but if you don't, then for sure he will (and if he doesn't, you can complain that he broke the bargain :-) ).

Dagmara Lizlovs said...

When we bake our Latvian pirogues (filled with bacon and ham typically, although I've done bacon and venison), the cookbook we have says to bake 15 min. Only we don't do that. Here's our secret, we bake for only 12 or 13 minutes, check the bottom of the pirogues, and add a minute if needed. At that point it is one minute or until the smoke alarm sounds which ever comes first. Then they're done. They taste wonderful when they're fresh out of the oven. They taste even better with beer.

As for the shooter case. I grew up in the Detroit area. There they just shoot you.