Statement Negation & The Assumption Negation Technique

[jordandowne16]

Hello,

I have 2 questions regarding the Assumption Negation Technique...

1) I just completed the "Statement Negation Drill" which employs the ANT, and a lot of my answers were wrong because I used "did not" instead of "may not", or "will go to school" instead of "could go to school" (for example). I guess my question is, when approaching Assumption questions and negating the statements, do we use "could", "may", and "not necessarily" instead of words like "not", "won't", and "will"? I'm just confused because when learning how to negate statements with Sufficient and Necessary terms they used "solid" words like not/won't/will. (For example: If A -> B has a contrapositive of If not B -> not A ... it isn't "If not B -> not necessarily A".) I don't know if my question makes sense or not...

2) I'm getting really confused with using the ANT on statements that use "unless". Earlier in my PS course, I learned how to negate these statements (I.e. unless/without/except/until = the necessary term and then you must negate the sufficient term). In Assumption questions, how does this work? Do we negate the original sentence and then negate it again? One example I have that I was confused with is this one (where it asks us to use the ANT):

Original statement: Happiness is impossible unless we profess a commitment to freedom.
Converting/negating it: If happiness -> we professed a commitment to freedom
Would I then use the ANT like this?: If happiness -> we may not have professed a commitment to freedom (in other words, happiness still could happen even if we may not have professed a commitment to freedom?)

If this is true, then we essentially negated the statement twice (first when converting it and second when using ANT). Thank you in advance and looking forward to hearing back!

[Robert Carroll]

jordandowne16,

Some of what I wrote here viewtopic.php?p=88030#p88030 is relevant to answering your first question. The negation of a statement expressing necessity ("All students must take the exam") is a statement expressing possibility ("Some students might not have to take the qualifying exam").

Also relevant to your first question, when contraposing, we're negating each component of the conditional. Those individual components didn't use necessity, so their negations didn't use possibility. The conditional as a WHOLE expresses necessity, but often the parts don't do so. Compare:

"All Greeks are Europeans."

This conditional expresses necessity, so its negation expresses possibility: "Someone might be Greek without being European." But "Greek" and "European" as PARTS don't use necessity wording at all.

To your second question, the Unless Equation diagrams the conditional expressed by the statement that uses the word "unless" (or "except", "until", or "without"). The negation of a statement is not that statement. It's the logical opposite of it. So when you use the Unless Equation, you're diagramming the conditional. You're not diagramming the negation of anything. The Equation involves a step where you negate a part of the SENTENCE to get a part of the CONDITIONAL, but, again, you're not finding the logical opposite of anything.

"One can't be Greek unless one is European" =

Greek European

What I just diagrammed IS the conditional. I haven't negated anything. I could negate it now: "One might be Greek without being European" or something equivalent. But that's not the Unless Equation. That's a separate, new step to do something different with the conditional.

So when you say "converting/negating", you're confusing two entirely different processes.

Using the Assumption Negation Technique on an "unless" statement would just be two steps. Use the Unless Equation to convert it, and then negate by negating the entire conditional you just diagrammed.

Robert Carroll

[jordandowne16]

Hi Robert! Okay great, thank you so much for the clarification. I appreciate it!