The author uses the word "immediacy" (line 39) most likely in order to express
PeterXon June 11, 2020
Sufficient and Necessary: If vs. Only if Statements
Is this right?
If statement Example:
If he has a golf club, he can play golf. = C --> PG
Sufficient: Club
Necessary: Play Golf
Contrapositive: ~PG --> ~C. He cannot play golf if he doesn't have a golf club.
Only if statement example based on video:
A person plays golf only if he has a club. PG --> C
Sufficient Plays Golf PG
Necessary Club C
Contrapositive: ~C --> ~PG. He did not have a club, he could not play golf.
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Your breakdown of the If statement is correct until the very end. As you identified, the contrapositive is: ~PG -> ~C. In written form, this is: If he cannot play golf, then he does not have a club. Here, "not play golf" is sufficient and "not have a club" is necessary.
You wrote this contrapositive out as "he cannot play golf if he doesn't have a golf club." We can rephrase this into "if he doesn't have a golf club, he cannot play golf." This would be diagrammed as: ~C -> ~PG, which is different from what we are wanting to say.
Your breakdown of the Only If statement is also correct, although we would write the contrapositive out as "If a person does not have a club, then he does not play golf." We do this so that we make sure to include the sufficient/necessary language.
Your basic logic seems to be correct. If statements introduce sufficient, whereas Only If statements introduce necessary. This is the key difference between the two, which is why they are diagrammed differently.
Does that make sense? Hope it helps! Please let us know if you have any other questions.
PeterXon June 12, 2020
Hi Skylar,
Thanks for the clarification. I had a follow-up question for "If" statements.
Statement: If he has a golf club, he can play golf. = C --> PG
You mentioned that in the second paragraph, the contrapositive should state: "if he doesn't have a golf club, he cannot play golf."
I would annotate this as ~C --> ~PG. Is this the contrapositive? It sounds like we are just negating the sufficient and the necessary rather than the nonexistence of the necessary brings out the nonexistence of the sufficient. I'm going based off what is taught in the Suff/Necessary video.
Skylaron June 12, 2020
@PeterX, happy to help with any follow up!
To find the contrapositive, you should always both reverse and negate. The contrapositive of the statement C -> PG is ~PG -> ~C. The contrapositive of the statement PG -> C is ~C -> ~PG. Your original diagrams are correct, but the written form of your contrapositives are where the logic is inconsistent.
In the second section of my previous explanation, I was referring to your written explanation of the contrapositive of the If statement being incorrect. You wrote the diagram ~PG -> ~C out as "he cannot play golf if he doesn't have a golf club." This is equal to "If he doesn't have a golf club, then he cannot play golf." This would be diagrammed as ~C -> ~PG, which is incorrect. Instead, the diagram ~PG -> ~C should be written out as "if he cannot play golf, then he does not have a club." Essentially, the second section of my explanation was meant to show why your written explanation of the contrapositive was incorrect, not to suggest it was what the contrapositive should state.
Does that make more sense? Please let us know if you have any other questions!
PeterXon June 12, 2020
I think I got it now; I wrote the original contrapositive as "He cannot play golf if he doesn't have a golf club."
It would read that "if he doesn't have a golf club" would be the sufficient part which is actually the necessary. I didn't put the if in the first part of the sentence next to cannot play golf; that makes all the difference between which part of the sentence is the sufficient and which isthe necessary. Thanks for the clarification!
Skylaron June 14, 2020
@PeterX, glad it makes sense now. Best of luck with the rest of your studies and please don't hesitate to let us know if you come across any other questions!
