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."

21Oct/093

Basic Laws of Logic

Before I can launch into diatribes about overcoming fallacies and pwning abusers of heap arguments the rules of the game need be established. Luckily, logic only has three. Yep, three laws rule all of logic and rule with an iron fist. Each has a cute name and a seemingly innocent definition, but it’s the ramifications of these statements that slay arguments and spawn doctoral theses. Let’s meet ‘em in some detail:

Law of Identity

Definition: a given something is a given something (tricky shit, eh?)

It may be a bit of jump, but the Law of Identity implies that all things have characteristics, because without characteristics, something can’t be identified and therefore we could call something a something in the first place. Things are identified by those characteristics, so if you’re given something without characteristics in an argument, you really haven’t been given anything (happens a lot with bad definitions of God, mind and other abstracts). A lot of discussion on the Law of Identity uses fruity terms like essence, usia (Greek for essence), nature and so on, but these words have too much baggage for my tastes. The Law of Identity’s opposite is also useful, a something isn’t a not something. Pimps aren’t hoes, light isn’t dark and a shit load of other things that are profoundly obvious.

Uses: The Law of Identity is great for dismissing ridiculous claims and crystal-waving bullshit from the start. Someone making claims that “the God and the pigeon are one” can be dismissed outright as being non-logical so you can skip arguing and go straight to calling the speaker a fucktard. The Law of Identity also quickly cuts down people that abuse analogies. “Blah A is like blah B which has this property so blah A must too” is a fallacy of association that can be dismissed simply by saying “but Blah A isn’t Blah B, it’s Blah A”. Some discretion is needed in using this argument as Blah A and Blah B can be the same if they’re just two words for the same thing. A lot of art-house arguments depend on abusing analogies; the Law of Identity is the shotgun of logic with high stopping power against these arguments that never runs out of ammo.

Law of Non-Contradiction

Definition: a given something can’t be both that something and not that something.

This law is another seemingly obvious point but in practice the Law of Non-Contradiction is the foundation of argumentative validity. The Law of Non-Contradiction makes logic truth preserving so that you’ll never go from a true point and arrive at a false point. Contradiction negates logic, and while true paradox may be something fun which to reflect unless you’re attempting to unite with the godhead by reaching nirvana, contradiction simply has no place in logic. This is not to say that something can’t appear to be self-contradictory and this idea is the basis of a lot of statements of reflection. In the course of debate another definition may become useful: Both a claim and not that claim can’t be true. So, if a statement holds even a teensy weensy bit of falseness, it must be entirely false.

Uses: The Law of Non-Contradiction allows one to throw out any argument which allows something and its negation to both be true. I was once arguing with a dullard in an Intellectual Heritage class that said Christianity and Hinduism were essential the same and he then proceeded to point of the similarities. I asked him if he thought Hinduism had many Gods, to get him in the non-contradiction trap of saying one was polytheistic and the other was monotheistic. He said everything came from Brahman. I asked him if Brahman was a conscious force, to which he rightly replied no. The contradiction now came in that one believed God was conscious while the other stated he wasn’t.

Abuses: The Law of Non-Contradiction only applies to two qualities of the same characteristic at the same time. Stuff can change or be analyzed in different lights creating some false counter arguments. The Rational Argumentator has a dubious article “proving” that light can’t be both a particle and a wave via the Law of Non-Contradiction. This argument ignores the fact that physicists don’t treat light as a particle and a wave at the same time. The Argumentator’s argument would be similar to saying a human can’t be both a child and an adult ignoring the fact that with time one turns into the other and that no one is arguing that one’s both the same at the same time. Their argument also uses non-Scientific definitions and is selectively rigorous, but that’s for later.

Law of the Excluded Middle

Definition: A statement must be either true or false.

Note: The phrases “truth value” or “logical value” will pop up periodically and these merely refer to whether a statement is true or false.

Two things happen because of the Law of the Excluded Middle, the first is limiting logical statements the second is the slaying of the word “maybe”. The Law of the Excluded Middle implies that only statements that can have a truth value can be looked at logically. For instance, “I can has cheezburger?” has no logical value because a question can’t be true or false. Also, “Blow me” has no logical value because commands can’t be true or false. The Law of the Excluded Middle also rules out logical statements answered with “sometimes” or “maybe”. A statement may have to be adjusted to get a proper truth value. Like the statement “Tim has always been a cock jockey” can’t be answered true because there are times when Tim’s cock jockeyness is in dispute. So we can retool the statement to “Tim is currently a cock jockey” or “Tim is usually a cock jockey” to get our sought value of true.

Uses: The Law of the Excluded Middle pops up a lot in discussions of free-will. Some people are inclined to come up with some 3rd option that is neither true nor false when they really should be redefining or attacking the question. In most cases, these answers are simply elaborate forms of free will or non-free will. These arguments also involve some assumptions that may be invalid. The question “free will exists” is different from “all actions are governed by free will” and “perfect information prevents free will” where some lazy arguers will assume they’re the same. In cases where “maybe” seems like the right answer, seek to redefine the question or point out the flaws of the statement. The Law of Non-Contradiction can work with the Law of the Excluded Middle to point out deficiencies of ethical arguments that leave no room for moderation.

Abuses: The Law of the Excluded Middle can be abused to create false dilemmas such as occurs with the “either you’re with us or against us mentality” or “if you’re not part of the solution, you’re part of the problem”. In both cases, a party may be neutral or non-involved. The Law of the Excluded Middle only applies to cases with two options. Truth values are either true or false so the Law applies to those. Many arguers assume that “not x” is the same as “the opposite of x” and this is where many false dilemmas are born.

Closing

Keep in mind that the laws of logic have no proof and have come to be accepted not because they’re provable but because they’re both largely obvious and the most philosophers could ever get to agree on. Even at that, Immanuel Kant based logic on values rather than truth. Crazy bastard.