Logical negation - polar vs logical opposites

[amagari]

Sometimes when I'm doing logical negation of a sentence, the logical negation works out and other times it doesn't.

Many times, using the polar opposite will work as the logical opposite. For example, "I went to the park" becomes "i didn't go to the park."

Often the polar opposite is the same as the logical opposite as above. But when the concept I'm negating has a range of possibilities such as "hot & cold," I understand that "not hot" is the logical opposition of hot. So in cases like that it's clear, but there are other concepts that apparently have ranges that I wouldn't normally think have a range of possibilities. Such as the concept of "like"

I would think the logical opposite of "dislike" would be "like" but apparently it's not because you can be neutral towards someone also.

how do I systematically know when the logical opposite is the polar opposite and when it wont' work because there is a range of options? If this makes sense.

[Dave Killoran]

Hi Amagari,

Thanks for the question! You actually know more about this than you suspect, you've likely just been caught off-guard a few times and now feel like you might have missed something. I'm sure you haven't, and part of the value of preparing systematically is that you get to identify and address issues like this.

Basically, items will fall into one of two groups: things that are binary and have just two states, or things that have a range of three or more states. Let's talk about both briefly.

• Binary (two states)
  
  These are things that only have two properties, which is often a variation of On and Off. For example, a light switch is either on or off. People are either alive or dead. There's no middle ground or "neutral" to these outcomes.
  
  Range (three or more states)
  
  These are sets with multiple elements, often in a gradient. For example, temperature ranges from hot to cold, but is on a scale that changes degree by degree. Music has has similar scale, but is is more limited in range. And even things we don't immediately expect to have a range, such as liking something, often do because of the possibility of the third "neutral" state.

That's a super fast overview there, but it might help you realize that you are probably more comfortable with these ideas than you think, and that's it;s mostly your experience and learning that tells you what has ranges and what does not.

Please let me know if that helps. Thanks!

[amagari]

I understood your explanation but unfortunately my intuition says that "liking something" is binary. How can I tell the difference?

I've read that you can put "it is not the case that" something to help but then I don't know what to do to make sure I do the negation correctly.

Thanks

[Dave Killoran]

Hi Amagari,

Thanks for the reply. What you've mentioned is fortunately just a single instance, and the good news is that now you know that isn't binary. However, I suspect you did know that existed but just didn't connect it (think: love-hate-indifference, each of which is terms you were almost certainly already familiar with). That lack of connection is what has you concerned, but it won't happen again in that same arena, and the chances of them catching you out on that again are low (especially as it's now in your mind).

The problem is that there's no way to know every gradient and non-gradient range in the world, simply because you might not have ever encountered some of them before. This is where the LSAT has the advantage, and aside from talking about it like this, there's nothing that can cover every single scaling in existence.

To your question, the negation of any term is typically "not the term." So, the negation of cold is "not cold (or it's equivalent)." The negation of "like" is "not like" and so on. That still won't suggest "neutral" to you automatically, but such a system for doing that doesn't exist unless you've thought about it before or alternately experienced everything in the world (neither of which is possible!). The thing is that you know that now, and so you can at least consider a third possibility such as neutral (or whatever passes for the middle ground) instead of simply assuming it's binary. that's enough here in almost every instance. Plus, some of the other common LSAT scalings, like truth or certainty, you've already seen.

I realize this is a concern for you, but very likely you've resolved most of this problem simply by now being aware of it, and the remainder of the issue will be resolved by becoming more familiar with the scalings they tend to use.

Please let me know if that helps. Thanks!

[tizwvu34]

So, am I correct in my understanding then, that if something is truly and indisputably binary, like on or off, then the logical opposite of 'on' could be both 'not on' or more simply put, 'off'?

[Adam Tyson]

That would work, tizwvu34. We see that in terms of true/false, for example. We call that a two-value system, where if you are not one thing then you must be the other thing, and it is common in logic games especially to take advantage of that. For example, if there are two groups, A and B, and every variable must be in exactly one of those groups, then "not in A' is the same as "in B." That's very helpful when creating contrapositives, such as:

If R is in Group A, Q must also be in Group A

the contrapositive is:

If Q is in Group B, R must be in Group B

Be aware of those true binary opportunities, those two-value systems, and use them to your advantage!