(Theory question) Why do you negate a conditional by negating the necessary?

CinnamonTea

Specifically, I am looking at PT 68.S2.Q23, the second sentence: "We must therefore reject Tolstoy's rash claim that if we knew a lot about the events leading up to any action, we would cease to regard that action as freely performed").

So that would be diagrammed out as:
Not (know about events ---> ~freely performed)
Which I was told turns into:
(Know about events ---> freely performed)

My question is a theoretical one, and that is: WHY do you negate a conditional by introducing the sufficient and denying the necessary?

2 follow up questions:
1) (Theory) Why is it incorrect to say when you negate a conditional, the sufficient could OR could not lead to the necessary?
2) Is there is this lesson in the CC (negating a conditional?) I could not find it.

DumbHollywoodActor

So that would be diagrammed out as:
Not (know about events ---> ~freely performed)
Which I was told turns into:
(Know about events ---> freely performed)

This is incorrect. When you negate a conditional relationship, you create new intersectional relationship.

The logical equivalent of "Not (know about events ---> ~freely performed)" is
"know about events <-SOME -> freely performed" (Sometimes, we can know a lot about the events leading up to any action and regard that action as freely performed)

Now to answer your question 1: you can! Why? I ask you a question: What does it mean to say A is a sufficient condition of B? It's saying that the presence of A guarantees or triggers B. Another way of saying it is that if A exists, B must exist as well. By negating the conditional relationship we are essentially saying that sometimes when A happens B does not happen.

Pertininent Lessons.
https://classic.7sage.com/lesson/advanced-negate-some-statements
https://classic.7sage.com/lesson/advanced-negate-all-statements
https://classic.7sage.com/lesson/deny-the-relationship
https://classic.7sage.com/lesson/how-to-negate-statements-in-english

CinnamonTea

Thanks so much @DumbHollywoodActor! To clarify, in the 3rd CC link you sent, JY said that to negate A--->B, you could say EITHER that:
A <--some-->~B OR A and ~B.

So in the case above, that would mean: Not (know about events--->~freely performed)
Translates to:

know about events <--some---> freely performed
OR
Know about events and freely performed

Is that correct? Thanks in advance.

DumbHollywoodActor

All correct. Well done!

CinnamonTea

Thanks for the help!

Stimmy Turner

Thank you for your comments this thread helped me understand a separate problem with similar elements!