Statement Negation Drill #2 - council member

[leslie7]

the council member could reverse her position (p 383 ed. 2020)

I added "not" to could to produce the logical opposite as in "could not" which is synonymous with cannot.

However, depending on the context of the statement the word "could", could be translated as "might" which is another option. In that case, would the logical opposite here be "might not"?

And relatably, would we have to rely on context to determine what the word "could" means?

In this example specifically how did we know that "could" meant "can"?

[Adam Tyson]

The logical opposite of "could" is "cannot," leslie. "Could" means "it's possible," and so the opposite must be something that means "it is not possible." So "could not" would not be a good negation of that statement, as it means "might not" rather than "cannot."

Yes, there may be some contexts in which "could not" means "cannot" or "was unable to," like "despite John's past felony convictions, he could have been hired for the job." To negate that we might say "his past convictions meant he could not have been hired" But you are safest negating a "could" statement with some form of "cannot." Treating "could not" as "cannot" would be the exception rather than the general rule.

Something similar occurs with the use of the word "some." "Some mammals lay eggs" is not negated by "some mammals do not lay eggs," because both statements can be true at the same time. Instead, you have to change "some" to some version of "none" - "no mammals lay eggs."

[NJL2022]

Regarding the negation of COULD (1-100), is another possible answer "WILL NOT (0)?"

I understand the usage of CANNOT (0), however am under the impression that "WILL NOT" is also a logical opposite that satisfies the required negation. I'm guessing because it's the logical opposite of "WOULD" vice "COULD" it would be considered incorrect. Or does it come down to a temporal difference (if there is one)? It doesn't fall into either a quantity, time, or space categorization so I'm uncertain how to deal with this issue.

I'm most likely overthinking it, but am looking to wrap my head around Formal Logic and would appreciate any clarification on the matter. Thanks.

[Robert Carroll]

NJL,

I hope my answer in this thread viewtopic.php?f=1361&t=35039&p=88030#p88030 helps, and if you need further clarification, let me know!

Robert Carroll