Does the statement " If you get an A, then you can eat ice cream" logically concludes that "if you don't get an A then you can not eat ice cream"?? Why doesn't it work mathematically? Because P-->Q and not P --> not Q don't have the same truth table.
-
2That's correct. You can get a C- and explain to your parents that it's perfectly logical for you to get some ice cream anyway. And you'd be right. But you still wouldn't get any ice cream, because they're your parents. Logic only goes so far in the real world.– user4894Commented Nov 23, 2021 at 21:49
-
2"If" statements in natural language are context-dependent and not always equivalent to the material conditional, see the indicative conditional. For example, your English statement could also be interpreted as an "if and only if", the biconditional. It could also be taken as a statement about possible worlds and formalized with modal logic (though in modal logic propositions you'd still have the choice of material conditional or biconditional)– HypnosiflCommented Nov 23, 2021 at 22:24
-
1they mean IFF. if and only if. parents are like that– user56815Commented Nov 23, 2021 at 22:24
-
4Because colloquial speech is a shorthand, much is implied but not spelled out, see Grice's conversational implicatures. In this case, the converse statement is implied by context: you get a reward for achievement, saying that you don't get it without is redundant under common sense. Once you spell out what is implied it does work "mathematically".– ConifoldCommented Nov 24, 2021 at 0:26
Add a comment
|
2 Answers
It depends. There are many things involved here. At least one IF structure to be chosen (there is not only one), a logical statement to be tested, at least a result.
Let's see some options we got here:
IF i get an A THEN I get ice cream END IF.
In this case you can get ice cream ONLY and ONLY IF you get an A.
IF i get an A THEN I get vanilla ice cream ELSE I get chocolate ice cream. END IF.
In this case you can get ice cream in all scenarios but different flavor.
So the scenario "If you get an A, then you can eat ice cream" The only fact that apply here, as it is are the following: If you get an A, then you can eat ice cream If you don't get an A, then you can't eat ice cream.
If reality does not apply to what your statement says, then you should make a more realistic statement. Example: If you got an A, OR mom is in good mood, then you can eat ice cream. That is a different story.
There are 4 states:
Get A, eat ice cream - this is allowed Get A, don’t eat ice cream - also allowed Don’t get A, eat ice cream - undefined Don’t get A, don’t eat ice cream - undefined
It’s often assumed that only states 1 and 4 are permissible, although in fact only state 1 is confirmed and the others are speculative
