Conditional Reasoning Question

[Oz29xr8]

Hello can someone clarify why this happens in conditional reasoning? What I've realized today when practicing diagramming conditional statements is that when a premise contains the words "not" and "unless" it becomes a positive premise. Why does this happen and how does it make sense? For example, a premise can say something like: "Today will not be a good day unless it is sunny outside". The diagram will come out as GD---->SO. If anyone can explain this, it would really help me. Thank you.

[Dave Killoran]

Hi Oz,

Good question! It's really a matter of choice as to how it appears but what's causing that is the nature of the word "unless" (and any equivalent, such as "until" or "without"). "Unless" brings up the case of an exception, which turns things upside down, so to speak. It makes the original statement not true.

So, when you look at a statement such as "Today will not be a good day unless it is sunny outside," the "sunny outside" is the exception to today will not be a good day. That exception effectively removes the "not", telling us that if it is a good day, it is sunny.

However, the above form is produced using the Unless Equation, and there is an alternative approach that keeps everything negative. You can substitute "if not" for "unless," which would result in:

• Not sunny outside today is not a good day

So in that case you see the "not" is retained. Both statements mean the same thing (they are contrapositives of each other), but we prefer the positive form produced by the Unless Equation because more people find it harder to process negative statements than positive ones.

Thanks!