Statement Negation Drill #2 and #5

[NJL2022]

#2 Orig: The councilmember COULD reverse her position.
Neg: The councilmember CANNOT reverse her position.

Can this negation be changed to WILL NOT? The reason I ask is I'm still struggling with logical opposition and WILL NOT (0) seems to fulfill the requirement as the logical opposite of COULD (1-100). However, I assume this a difference in the base meaning of WILL vs. CAN (willingness vs. ability) and not where it falls in the spectrum.

#5 Orig: Organic farming methods promote crop resistance to pest attack.
Neg: Organic farming methods DO NOT promote crop resistance to pest attack.

Why would this not be negated with DO NOT NECESSARILY (0-99)? My understanding is the original statement is an assurance the methods promote crop resistance (100) and the logical opposite would be a statement falling in the (0-99) range. Am I missing that "to promote" is not a guarantee, and is more akin to COULD (1-100)?

Also, tracking that logical opposites require the least amount of work and want to ensure I'm not overthinking it. Big picture is I'm looking for a crystal clear understanding of logical opposition. Appreciate any clarification, thanks!

[Robert Carroll]

NJL,

There's more to "can" and "could" than just the quantities involved. The quantification of terms like "some" (1-100) and "none" (0) captures all those terms are taking about, but "can" and "could" talk about possibilities that might never be actual. I could have taken the LSAT in 2021, but I didn't. So I can correct say "No one who lives in my house took the LSAT in 2021" (0 people did), but also "Some people who live in my house could have taken the LSAT in 2021" or even "All people who live in my house could have taken the LSAT in 2021." Something can be possible even if it hasn't happen. So the logical opposite of "could" should not express what has happened but rather what is possible. The logical opposite of a possibility is an impossibility; the logical opposite of "could be true" is "cannot be true".

In the second example, there is no possibility language, so the logical opposite should not introduce possibility.

In short, there are two different kinds of scales we're talking about - possibility (from impossibility on one end to necessity on the other) and quantity (from none on one end to all on the other). The logical opposite of a statement that speaks in possibility-language should include possibility-language; the logical opposite of a statement that involves quantity-language should involve quantity-language.

Robert Carroll

[NJL2022]

Robert,

Thanks for the reply. Bottom line, sounds like I need to ensure I've nailed down the differences between Possibility and Quantity and be able to recognize the language used for each. Appreciate the clarification.

NJL

[jupiterlaw]

Hi,

I am trying to understand these differences from reading the forum but I am still confused.

For #3 and #5 I see the explanation that you can't use "not necessarily" because possibility is not introduced. So for both to negate you would have #3: "...did not change..." and #5: "...do not promote..."

And following this logic, #1 & #7 introduce possibility by using the term "will" in their original statements, which is why you can choose "will not" OR "might not" to negate? How come then for #9, the option for "might not" and only "will not" is given in the answer key, is this intentional or did they simply choose not to mention it but either is an option?

I am a little confused as to why in the previous pages the LRB emphasizes not over-stepping with polar opposites but then many of the answers for this drill seem to use them, it threw me off in my understanding.

Lastly, for #4 could you negate with "...must be determined..." as opposed to "...is necessarily determined..." I interpreted "not necessarily" as the logical opposite of must be in terms of truth, but does the book choose necessarily because of the use of the word "determined"?

Thank you

[Jeff Wren]

Hi jupiter,

You're correct that for #9, "might not" is an option.

While it's generally important not to over-step with polar opposites, negating conditional statements can be tricky for many people, especially in terms of diagramming. The easiest way to capture a negated conditional statement in terms of diagramming is to simply negate the necessary condition. However, when reading that diagram, people often read the negated necessary condition as "will not" rather than "not necessarily." As discussed under the discussion of negating conditional statements, using "will not" is overstating the case but still works in these conditional statements.

For #4, you could use "must be determined" instead of "is necessarily determined" as they are logically equivalent. Often, if the statement is already expressed in the negative (with the word "not" for example), the easiest way to negate it is to simply remove the word "not."