Conditional Reasoning - Question

[oshkoshofjosh]

Hi there,

I was reading this PowerScore article and had a question. The article is listed: https://blog.powerscore.com/lsat/bid-28 ... -equation/

In the article, they list a conditional statement under "multiple necessary conditions." They state: Unless you try and trust yourself, you won’t succeed. And PowerScore states that the correct translation of this is, "if you don't try or don't trust yourself, you won't succeed" ( ~try or ~ trust → ~succeed). The contrapositive of this is, "if you succeed, you try and trust yourself."

My question is, since the logical term "unless" negates part of a conditional and makes the part sufficient, if we negate the first part of the sentence, are we also negating the "and"? Is that why the translated version has an "or" in its translation?

Because if I saw this statement "Unless you try and trust yourself, you won’t succeed" on the LSAT, I would just tell myself, "okay, if you don't try and don't trust, then you won't succeed." Contrapositive would be, "if you succeed, then you either tried or trusted." This is incorrect, right?

So whenever I see a statement like this, "Unless A and B, thus C," I translate this to: "not A or not B, thus C"?

Likewise, if it said, "Unless A or B, thus C," would that mean I translate it to: "not A and not B, thus C"?

I've just been used to DeMorgan's Law, which is when you do a contrapositive of multiple sufficient/ necessary conditions, you negate the statement, and change "or" to and "and," vice versa.

Please let me know as this has confused me a bit and would like clarification!

[Dave Killoran]

Hi Josh,

Thanks for the message! I have some comments for you below, but first I want to note that the blog you are reading isn't just about diagramming Unless, it's specifically about the advantages of using the Unless Equation. More specifically, it's getting at the fact tyhat "if not" can create diagramming mistakes for students when they are faced with compound conditions. So, some of the points you are referring to below are using that specific part of the discussion. I suspect that might have lead to some of your uncertainty here.

In the article, they list a conditional statement under "multiple necessary conditions." They state: Unless you try and trust yourself, you won’t succeed. And PowerScore states that the correct translation of this is, "if you don't try or don't trust yourself, you won't succeed" ( ~try or ~ trust → ~succeed). The contrapositive of this is, "if you succeed, you try and trust yourself."

In the article, what we actually say the correct diagram is for the statement above is:

• Try
  
  Succeed         +
  
  Trust

But, the contrapositive is indeed "not try or not trust not succeed," which matches the above. The discussion there was showing how using "if not" as a substitute for "unless" can confuse people on the negation of the "and" there.

As a side note, another advantage is how the Unless Equation typically produces a nice clean statement free of negatives.

Because if I saw this statement "Unless you try and trust yourself, you won’t succeed" on the LSAT, I would just tell myself, "okay, if you don't try and don't trust, then you won't succeed." Contrapositive would be, "if you succeed, then you either tried or trusted." This is incorrect, right?

Yes, that is incorrect. Your statement of "if you don't try and don't trust" is supposed to reflect "not (try and trust)," which from De Morgan's becomes "not try or not trust."

So whenever I see a statement like this, "Unless A and B, thus C," I translate this to: "not A or not B, thus C"?

Likewise, if it said, "Unless A or B, thus C," would that mean I translate it to: "not A and not B, thus C"?

This is the part of the article I think you may have missed since we actually wouldn't initially diagram them this way (although they aren't wrong, they are just the contrapositive of what we'd diagram).

So, to diagram these statements, we use the Unless Equation, which will turn "Unless A and B, thus C," into: "not C A + B." And "Unless A or B, thus C" would become "not C A or B."

I've just been used to DeMorgan's Law, which is when you do a contrapositive of multiple sufficient/ necessary conditions, you negate the statement, and change "or" to and "and," vice versa.

Yes, you should continue to do this! As you can see from the above, everything we do is consistent with De Morgan's.

Thanks!

[oshkoshofjosh]

Hi Dave,

Thank you for the quick reply! This totally makes sense. I understand the Unless Equation now and I'll definitely put it in my logic toolbox. I've started with 7Sage so I've always been used to translating "unless" as "negate anything, and make it sufficient, while leaving the rest as necessary." But, the Unless Equation works equally well!

I guess my thought process here (my apologies I don't know how to use the reference thing you did), "Because if I saw this statement "Unless you try and trust yourself, you won’t succeed" on the LSAT, I would just tell myself, "okay, if you don't try and don't trust, then you won't succeed." Contrapositive would be, "if you succeed, then you either tried or trusted." This is incorrect, right?" is definitely wrong and I can see why.

I should've realized that since "unless" negates anything and makes it sufficient, according to 7Sage, I should've negated not only the 2 terms, but also negated the "and/or" in accordance with DeMorgan's Law. But, in the future, I'll definitely use the Unless Equation as it works equally well on tough translations!

Thank you for this Dave!