LogicWarrior Demand Reason

25Dec/090

Opposite vs. Not

Basic Idea: In a rigorous argument, one must differentiate between when one wants "opposite" to mean "conceptual opposite" vs. "logical opposite" aka "not".  In the first case, one is taking the conceptual inverse of a claim but in the latter merely claiming diagreement with a specific claim.  For instance, the conceptual opposite of "hot" is cold" while the logical opposite of "hot" is "not hot".

More Detail: When one disagrees with a claim, some arguers will assume their opponents simply mean the opposite.  This is sloppy and can lead to ridiculous arguments.  For instance, if someone disagree with me on the existence of global warming he or she is probably not advocating global cooling.   Debate demands a simple way of saying "your claim is not the case".  This is symbolically represented by the "not" operator.  "Not" and "non" don't always roll of the tongue; something that causes harm but not a lot of it is not necessarily harmful and is more accurately called not harmless.  Again, awkward wording.  So, let's take a deeper look at using "not".

The Law of the Excluded Middle teaches us that either a statement or its opposite must be true if the statement is properly formed.  I find this comforting in that it means between any two properly statements one must be true.  What do I mean by properly formed?  Some statements make assumptions.  For instance, I have no sisters.  What is the logical value of the statement "my sister is left-handed"?  If we say it's false because my sister doesn't exist, the inverse of that statement must be true making my sister right-handed (excluding ambidexterity and such things).  This is meaningless as one could reasonably start with either claim of handedness, call it false, and conclude the opposite.  Always check assumptions.

Saying "not" allows one to be very specific.  When taking the negative in argument, one has no requirement to either replace that which is being negated with a positive truth or defend the rhetorical opposite of a position.  If I claim that someone is not guilty of a crime, I have no obligation to find the real guilty party.  Do not get cowed into providing an alternative.  If one doesn't believe that man is the cause of global warming don't feel obliged to provide an alternative.  One may, and if backed by fact, one should provide an alternative but it often the case with preliminary phenomenon that you don't know what's right but you do know what's wrong.  Unexplained phenomenon blamed on ghosts are prime examples of some people's need to fill the void with an explanation.

Rhetorical Opposites and "Not"- Quantity Claims: Conceptual opposites share a common distance from a center point. The opposite of hot is cold and the opposite of cool is warm.  Each term is equally distant from neutral as its opposite.  Lukewarm isn't diametrically opposite of frigid.  These distances may seem obvious, but what about with claims of quantity?  What is the opposite of all?  The diametric opposite of all is none, but the logical opposite of all is simply not all, a number of elements less than the total in a set.  The diametric opposite of none is all, but the logical opposite of none is not none, a number of elements more than an empty set.  So, some can then mean "any number of elements less than the total" or "any number of elements greater than zero".  Tricky...

Identifying Overlap and Pitfalls: Sometimes there is overlap, when a case can only have two possible outcomes.  Do not succumb to a false dichotomy as there is often a middle ground.  The conceptual opposite of a positive number is a negative number, the logical opposite is simply "not positive" which includes a negative number and zero.  Moral arguments seem disposed to ignoring neutrality.  My father claims someone is a good kid and I disagree.  I don't think he's a bad kid, I simply think he's not a good one and my dad assumes me the cynic.  Be clear, when using the logical opposite preface it with "simply" or follow up with a clarifying.  "I don't think he's a good kid.  I'm not claiming he's a bad one, just not a good one."

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