If there was one thing that was really a pest for me this week, it was the "if and only if" statement. In English, you would normally use it to link a declaration with a condition, such that the declaration can only be made if the condition is right. For example:
I will eat apples if, and only if, it is already cut and peeled.
Most people will probably understand from this sentence that there exists a certain someone who is so lazy that he will not eat a fruit unless it is cut and peeled. Now, consider a scenario where "I" is in a room with nothing else but a table with a plate of cut apple sitting on the top. Will "I" eat the apple? According to CSC165, "I" will eat the apple. The reason being that in logic, the statement "I will eat apples if, and only if, it is already cut and peeled." is equivalent to saying something like "I will eat cut and peeled apples no matter what!". This is the same thing as saying that "if there exists cut and peeled apples, I must have eaten it". This sentence also suggests that no other person could have eaten the cut and peeled apple except of "I".
This has bugged me for the past several days now because to my knowledge "if, and only if" is used synonymously as "only if" in English. If you replaced the sentence above with "only if", then I believe that the sentence is trying to get across the same meaning. The other problem is that nothing in the sentence suggested that it is mandatory for "I" to eat the cut and peeled apple, and no other person can eat the cut and peeled apple. If they wanted to express that idea, then they could have said something like "I is the only possible person who will eat cut and peeled apple and no other apple." instead of using something confusing as "if, and only if".
At this point, the only way that I will be convinced that "if, and only if" is different from "only if" is if someone can give me a English grammar textbook and point out that they are actually different statements. Likewise, I cannot be bent to believe that "if, and only if" have a two-way implication function unless someone shows me that it can be used in such a way in real-life, not just in logic. Until then, unfortunate as it may be, I will have to brainwash myself into believing it for the assignment and next week's test. I would appreciate it if someone can post under comment section a link that "if, and only if" is just one of those grammatical thing rather than something logical.
I understand why you are trying to connect every logic symbol with a gramatical context but this might be causing you more trouble then its worth.
ReplyDeleteDifferent languages have different strengths to what they are capable of expressing and how concisely they do so. So in fact when you try to understand "if and only if" using a natural langage you are taking a very particular meaning in a well structured language and transposing it to an ambiguous language. Then its no surprise that the "if and only if" seems ambiguous in english.
With that said if a simple implication makes sense to you in english then you can think of an "if and only if " as an anded two way implication.
In other words: "if it rains it pours" and "if it pours it rains" together "it rains if and only if it pours".
come talk to me about it if you'd like.
I used wikipedia to search up for an example few days back to write this post, but the way they explained the example was not complete, I ended up confusing myself even more. As unacademic as this may sound, thinking of a way to make sense of "If and only if" in terms of English will lead me nowhere, and considering how busy I am this semester, I will just pretend that I understand what it means and just let it slide.
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