Antecedent?

[slatad12]

Hi! I am a little confused about how much importance the antecedent actually has in an "if...then" statement.

For example: "If Harry goes hiking, then Helen goes hiking" (I am using the framework of the question from a book, but changing names and whatnot)
the answer is all of the following four:
a) Every time Harry goes hiking, Helen must also go hiking
b) Harry does not go hiking unless Helen goes hiking
c) Harry goes hiking only if Helen also goes hiking
d) Helen's hiking is necessary for Harry to go hiking

I understand the first answer, that when Harry goes hiking, Helen must also. But then the rest of answers seem to flip that around. What I am confused about, is that the way the sentence is structured, "if Harry goes hiking...," reads as if Harry has to be going hiking in order for us to consider Helen going hiking. Harry hiking comes first, and then Helen goes hiking. So how is it that, in the answer, Helen becomes the necessary hiker??

I hope that makes sense!

Thank you.

[yasmin cohen]

a). "Every time" is a conditional statement indicator, and also a sufficient/ trigger/ "if" part of the conditional statement. The conditional logic is: "If" Henry goes hiking→"then" Helen goes hiking. So in order for Henry going hiking, Helen is "required" to go hiking; Helen is the "necessary", "required" or the "then" part of the conditional statement.

b). Harry does not go hiking unless Helen goes hiking. In this statement, "unless" is a conditional indicator and is known as "intruder". For the conditional logic or "if---then" statement, when we have "unless", we negate the part of a sentence that contains "unless" and make it our sufficient condition/ "if" ad we leave the other part of a sentence unchanged.
Conditional logic: If Helen doesn't go hiking, then Harry doesn't go hiking. And for the contrapositive which you both negate and reverse the statement, you will get: If Harry goes hiking, then Helen goes hiking.

c). Harry goes hiking only if Helen also goes hiking. The "only if" means "then" and "then" is always the necessary part of a conditional statement. Conditional logic: If Harry goes hiking, then Helen goes hiking.

d) Helen's hiking is necessary for Harry to go hiking. What is "necessity" or "required" for something to occur it serves as the "necessity" or the "then" part of the conditional statement. In this statement, Helen's hiking is the "then" part of the conditional logic. If Harry goes to hiking, then Helen goes to hiking.
Hope my explanation was helpful.

[rinagoldfield]

Great converstation. Yasmin Cohen, I agree with your assessment of these statements!

I have a couple of notes to add to what Yasmin wrote.

Most importantly, Slatad12, I highly recommend that you read the conditional logic chapters in our Logical Reasoning strategy guide. These chapters will clear up a lot of your confusion, I think.

Fundamentally: The “if” part GUARANTEES the “then” part. The “then” part NECESSARILY FOLLOWS from the “if” part.

You wrote:

What I am confused about, is that the way the sentence is structured, "if Harry goes hiking...," reads as if Harry has to be going hiking in order for us to consider Helen going hiking. Harry hiking comes first, and then Helen goes hiking. So how is it that, in the answer, Helen becomes the necessary hiker??

This is an incorrect interpretation of if-then statements. “If Harry… then Helen” means that Helen absolutely positively goes hiking every time Harry does. Put another way, Helen’s hiking necessarily follows from Harry’s hiking. In this sense, she is the “necessary” hiker.

However, Helen could also go hiking without Harry. The necessary condition (the “then” part) can always occur without the sufficient condition (the “if” part).

Here’s an analogy that might feel more intuitive:

If I am in Spain, then I’m in Europe.

Being in Spain absolutely positively guarantees that I’m in Europe. However, I could be in Europe without being in Spain. I could be in the Czech Republic, Norway, Austria, etc.

a) Every time I’m in Spain, I’m in Europe.
b) I can’t be in Spain unless I’m in Europe.
c) I’m in Spain only if I’m in Europe.
d) Being in Europe is necessary to being in Spain.

Hope this helps! Check out the Strategy Guide for more details