Logical Opposite

[andriana.caban]

Can someone please explain why the logical opposite of Cannot be true is could be true? ....How can the opposite of something not being true is that it could be true?

[Dave Killoran]

Hi Andriana,

Thanks for the question! Probably the best place to start here is to first ask, What is an opposite and what does that word really mean? And, for example, what is the opposite of Cold?

I'm going to start there, and then based on your answer, we'll keep working through the idea until it all makes sense.

Thanks!

[andriana.caban]

Opposite of cold is not hot. But then, the opposite is could be true or could be false so why not this: not necessarily false.

[Dave Killoran]

Opposite of cold is not hot. But then, the opposite is could be true or could be false so why not this: not necessarily false.

Hi Andriana,

Thanks for the reply! Ok, I think I see partially where you are going astray. First, we want to try to stick within terms that can cover an entire range together. So, that means:

• "Opposite of cold is not hot." — Cold and hot are what are known as polar opposites; they sit at the far ends of the scale. But if we just use cold and hot, we miss a whole lot of temperatures such as lukewarm or tepid or anything in the middle. Logical opposites divide the spectrum into two parts (not necessarily of equal size, just two parts). So, the logical opposite of "cold" is "everything but cold," which is just as easily stated as "not cold." When we use "cold" and "not cold," every single temperature will fall into one of those two categories.
  
  As an aside, perhaps you misspoke by saying "not hot?" Because "not hot" includes cold, and the opposite of a statement can't include that statement.
  
  
  "the opposite is could be true or could be false so why not this: not necessarily false." — Here we again want to avoid mixing up terms, in this case "true" and "false." It can be done, but to successfully do so you need to know exact equivalents, such as that "Could Be True" is identical to "Not Necessarily False."
  
  If we define Cannot Be True on a scale of 0% to 100% (let's say the scale is about truth), then Cannot Be True is the same as none of the truth, or 0%. What would it's opposite be? Everything else, or 1%-100%. That happens to be exactly what Could Be True means (and yes, that includes the idea of Must Be True, just the same way that Some includes the idea of All).
  
  Also, while Could Be True overlaps with Not Necessarily True, they are not identical. In fact, each include the opposite of the other! Numerically, we could say:
  
  Could Be True = 1%-100%
  
  Not Necessarily True = 0%-99%
  
  Thus, Could Be True includes Must Be True (which is 100%, and the exact opposite of Not Necessarily True). And, Not Necessarily True includes Cannot Be True (0%), which is the exact opposite of Could be True.
  
  So, between 1% and 99% they are identical and overlap, but at the extremes they differ considerably!
  
  And just for reference on this scale:
  
  Must Be True = 100%
  
  Cannot Be True = 0%

So, we want to first keep the terms in the same region or area, and then second it appears that the overlap of Could and Not Necessarily is causing some concern for you, so take a closer look at that. And if you let me know what materials of ours you have, I can direct you to where this is explained in detail.

Thanks!