logical opposite (tense, conditionals)

[fhsh13]

Hi,

When I was studying the logical opposite in LRB, I was confused about the following questions. Really hope to get your help!

# Q1: Does tense matter?

I am comfortable with the past/present groups when considering their logical negation, (ie: did--didn't, do-- do not); but as for the future tense (ie: "will"), I was kind of confused. What's the logical negation of the word "will"? Will not, or might not? I feel that there may be a difference between these two words, but probably I was wrong. And I feel the similar difference when I was dealing with the MUST/Not necessarily situation and Attack Conclusion/Attack reasoning situation.

"The tax increase will result in more revenue for the government."

How to deal with the logical negation with the future tense (ie: will)? Is the"Will not" a subset of the "might not"?



# Q2: logical opposite of conditional logic "If A, then B."

Which one is correct answer?

(1) If A, then /B.
(2) There exists "A and /B"

For example, "All berries are red". (If berry, then red.)

I would say "Some berries are not red (2)" is the correct negation, and I don't think "If berry, then NOT red (1)" is the correct negation.

However, as for the example like "If the policy is implemented, the education budget will be cut",

I would say "If the policy is implemented, the education budget will be NOT cut (1)" may also be correct for logical negation.

Really confused. Need your help!

[Robert Carroll]

fhsh,

I don't think tense is what's causing you trouble here, but rather degree of certainty. To say "the tax increase will result in more revenue for the government" is not just to make a claim about the future but to make a claim about how certain it is that something will happen in the future. It "will" happen - it's necessary. The opposite of necessity is the possibility that something won't happen. So we can rephrase, without changing the meaning, our original sentence: "It is necessary that in the future, the tax increase will result in more revenue for the government." The opposite is then: "It is possible that the tax increase will not result in more revenue for the government."

The logical opposite of a conditional is always a conjunction. The logical opposite of A B is "sometimes A and not B". Your intuition in the berries case is 100% correct - the logical opposite of "all berries are red" is "there are some berries that are not red".

In the education budget case, the same should apply - the logical opposite of "if the policy is implemented, the education budget will be cut" should be "the policy might be implemented even if the education budget weren't cut" (or equivalents). A conditional is an expression of necessity. As I said above, the opposite of necessity is the possibility that something isn't true. When you posit that the opposite of the education budget conditional is another conditional, you're saying the opposite of a necessity is another necessity. That's not accurate. The opposite of "necessarily A" is "possibly not A". That's why your intuition in the budget case is incorrect. I hope this helps!

Robert Carroll

[fhsh13]

Thanks so much, Robert! Your analysis is exactly what I need for this question.