Translating conditional statement

  • January 23, 2018 at 9:44 am #29923
    blenderbottle
    Participant

    Hi,

    I have a question regarding the conditional statement “I only go to work on Tuesdays.”

    I put T -> W since being Tuesday guarantees that I will be working.

    I feel like saying going to work guarantees that it’s Tuesday also makes sense. Usually, I count anything that comes after only as necc condition, but I tried to use the guarantee method. Any clarification?

    I’m also confused by the statement “Since Ted never pays attention to things he doesn’t buy.” I thought doesn’t buying would not guarantee never paying attention since Ted could not want the item even he did pay attention. This statement was similar to “Sarah will never date a funny guy,” which I correctly devised as F -> not D.

    Thank you

  • January 23, 2018 at 1:09 pm #30128
    Mike Kim
    Keymaster

    Hey there —

    Happy to try and help —

    1) “I only go to work on Tuesdays” —

    So, you know that the guarantee will either be:

    Go to work -> it must be a Tuesday

    Or

    It’s a Tuesday -> must go to work.

    If you are uncertain which way the guarantee should go, one great way to check is to consider alternatives and see how they relate to the original statement.

    So, if we want to know if

    “I only go to work on Tuesdays”

    Means

    Go to work -> it must be Tuesday —

    We can ask ourselves — would going in to work on any other day, like Wednesday, violate this rule?

    Yes, it would —

    So, Go to work -> it must be Tuesday is the right orientation of the rule.

    And to test it the other way, if we want to know if

    “I only go to work on Tuesdays”

    Means

    It’s Tuesday -> must go to work —

    We can ask ourselves — what if, on a Tuesday, we don’t go into work? Maybe we are sick or whatever. Does that violate this rule?

    No, it doesn’t —

    You can not go to work on a Tuesday and the statement “I only go into work on Tuesdays” could still be valid, so

    Tuesday -> must go to work

    is not a guarantee contained in the original statement.

    Not quite sure what your exact q is for the second conditional — whether Ted wants or doesn’t want an item isn’t of direct relevance here — but I’ll give it a shot two ways –

    1)

    “Sarah will never date a funny guy” =

    F -> not D.

    And

    “Ted never pays attention to things he doesn’t buy.” =

    won’t buy -> won’t pay attention

    Are consistent with one another.

    2)

    In addition, to test the rule out,

    Does “Ted never pays attention to things he doesn’t buy” =

    Doesn’t pay attention -> must be something he won’t buy?

    No, it doesn’t — what if he also doesn’t pay attention to the weather or to strangers walking past his house etc. — none of this would violate the original statement, and so we cannot make an inference that

    If he doesn’t pay attention to something -> it must be something he won’t buy.

    On the other hand, does “Ted never pays attention to things he doesn’t buy” =

    Something he won’t buy -> won’t pay attention?

    Yes it does — we can test it by imagining a different outcome — there is something he won’t buy, but he does pay attention to it.

    Notice this would go against the original statement.

    So, we know this is in fact a rule that we can correctly infer — if it’s something he won’t buy, then he won’t pay attention.

    Tricky stuff and very easy to get turned around but hth — MK

You must be logged in to reply to this topic.