I posted on this topic a few years back on the BBWC. Back then, MG (Richie) and I discussed the matter at length. Since MG touched upon this issue in a separate thread, I thought this might be a good time to reintroduce the subject.
The thread’s purpose is to examine the proper method of argumentation. The methodology of argumentation involves, first: the refinement of an individual affirmation into its simplest components, then, second: the correct combination of individual affirmations into a properly derived conclusion. The first exercise, which examines what I refer to as “The Four Levels of Affirmation,” is by far the more difficult and elusive of the two disciplines. The second, which utilizes the method of Aristotlean Logic, is amazing in its simplicity. As such, the length of discussion concerning the levels of affirmation will far exceed that of properly drawing conclusions. This said, let us begin by examining “The Four Levels of Affirmation.”
The Four Levels of Affirmation
In this discussion, we will use the term “affirmation” to describe a statement which purports to affirm a truth. An affirmation must have some cognitive basis for belief. A statement must have some observable, derivable cause of belief in order to support its consideration as an affirmation. A statement such as, “I believe that green men live at the center of the earth,” is no affirmation. The statement provides no level of reasonable truth. A negative counter-argument such as “no one has been to the center of the earth, so how can one prove otherwise,” does nothing to support the original statement. A lack of proof against a statement does not provide any support in its defense. This statement remains a zero until its advocate provides positive evidence on its behalf.
My method examines four descending levels of affirmation: Fact, Opinion, Belief, and Feeling. Each level derives its accuracy from those which precede it. As will be shown, this descending level of inheritance weakens the potential accuracy of the particular affirmation made. Each level will be individually defined so as to avoid confusion with their more generalized and popular definitions.
Level One: Fact
Our method describes a “fact” as something that is undisputably provable. A fact is objective. It is not open to interpretation. Facts come in three forms: “quantitative,” “qualitative,” and “demonstrable.” A quantitative fact is measurable. Numbers, or “quantity,” is involved. A qualitative fact involves a non-measurable attribute. It describes a “quality,” obvious upon observation. A quality describe a diversity; it requires the possibility of two or more qualities in order to exist. An observable fact requires no diversity. It is unique in its own right.
Let us use some examples in order to simplify the above definitions:
Quantitative Fact: On baseball infield, the bases are exactly ninety feet apart. The distance between the bases are measurable, in feet. In this case, they are ninety feet apart, a measurable distance.
Qualitative Fact: Brian’s eyes are blue.
Leaving a color’s wave length (which is measurable) out of the discussion, my eyes being blue is a qualitative fact. It is a quality which separates me from other humans who have brown, gray, green, or black colored eyes. (Note that a qualitative fact does not require uniqueness, only difference.)
Observable Fact: Newton’s First Law of Motion: An object in motion will retain the properties of its motion unless acted upon by an opposing force. Conversely, an object at rest will remain at rest unless acted upon by an opposing force. (Also known as “Newton’s Law of Inertia.”)
Newton’s Law of Inertia is an observable fact. It is a fact which is neither measurable nor differential. It requires no mathematical analysis or observable comparability. It is unique because it is universal. It exists simply because it exists.
Level Two: Opinion
An opinion is a statement which derives its veracity from one of more facts. This said, it requires a subjective judgement which is not a fact. Consider the following argument:
1) Joe Montana is an NFL HOF quarterback with a lifetime QB rating of 92.3.
2) Johnny Unitas is an NFL HOF quarterback with a lifetime QB rating of 78.2.
3) Joe Montana was a better NFL quarterback than Johnny Unitas.
Let us examine the facts of statements 1 & 2:
1) Joe Montana: NFL quarterback; HOF; QB rating = 92.3.
2) Johnny Unitas: NFL quarterback; HOF; QB rating = 78.2.
Both Montana and Unitas have two qualitative facts in common: both were NFL quarterbacks; both are in the HOF. Two quantitative facts also exist: Montana has a lifetime QB rating of 92.3; Unitas has a lifetime QB rating of 78.2.This said, the argument, or affirmation, that Montana was a better quarterback is based upon a predetermined judgment that a lifetime QB rating (a quantitative fact) can be used to determine the relative worth of a quarterback (a qualitative fact). This judgment becomes an opinion based upon the following:
1) It assumes that the criteria upon which the QB rating is based (a quantitative fact) truly represents the worth of a quarterback.
2) It does not acknowledge that outside factors unique to the two quarterbacks’ playing experiences (qualitative facts) may have affected their individual quarterback ratings. Such factors would include: the era in which the respective QBs played; the offensive systems that the quarterbacks operated under; the defensive systems that the QBs played against; the quality of the supporting offensive players; the quality of opposing defenses; the quality of the playing conditions.
Level Three: Belief
For the basis of our discussion, a “belief” is an affirmation based upon one or more opinions. To put this another way: an opinion is an inference drawn solely from facts, while a belief is based at least in part upon opinion.
Let us examine our objection that adverse playing conditions (snow, rain, cold, wind, etc.) negatively affected the QB rating of Johnny Unitas vis-a-vis that of Joe Montana. We will use hypothetical quarterback ratings which we will assume to be true.
Our advocate for Montana researches the respective careers of the two players. He determines that Unitas played in 100 games in which adverse conditions existed, while Montana played in 50 such games. He then determines that, in their respective adverse conditions games, Unitas produced an overall QB rating of 70.0 and Montana a rating of 85.0.
Our Montana advocate uses this information to develop the following argument:
1) In 100 games involving adverse conditions, Johnny Unitas produced a quarterback rating of 70.0.
2) In 50 games involving adverse conditions, Joe Montana produced a quarterback rating of 85.0.
3) Since Montana maintained an approximate +15 QB rating advantage during games involving adverse conditions, then adverse conditions can be discounted when comparing the lifetime quarterback ratings of the respective quarterbacks.
Exactly as stated (and as will be shown later), the conclusion of this argument is logically sound. Yet the argument itself is flawed. How? Let us examine the affirmations put forth by our advocate.
A) Unitas’ 100 games of “adverse conditions” vs. Montana’s 50 games of “adverse conditions.” “100" and “50" are both numbers, entities that can be measured quantitatively. While it is true that Unitas played in twice as many “adverse conditions” games, Montana’s number of 50 such games is a statistically significant population from which an inference can be made. The number of games involved is a wash.
B) In the games examined, Unitas rated 70.0, Montana 85.0. Montana maintained a +15 QB rating over Unitas. These numbers are quantitative facts. (Hypothetical to our discussion, of course.)
C) The weakness in the argument involves the qualitative worth of the terminology, “adverse conditions.” Our advocate predicates his argument on the existence of only two qualitative types of playing conditions: “adverse” and “non-adverse.” He does not recognize that “adverse” conditions can differ substantially by degree. Johnny Unitas played the vast majority of his games in the Northeast. Joe Montana played a substantially larger percentage of his games under more friendly West Coast conditions. Even the casual observer will observe that a drizzling rain falling during a November game played in San Francisco will have much less effect on the quarterback play than a game played in a raging blizzard in Cleveland in December.
Our hypothetical advocate examined certain historical games that, in his opinion, exhibited weather conditions that should have had an adverse affect upon the quarterback play. He codified his argument by ignoring the qualitative differences of these games, simply combining them all into a single unified category. Given that his argument relies, in part, on opinion, he should more properly state his conclusion thus:
3) Since Montana maintained an approximate +15 QB rating advantage during games that, in my opinion, involved significantly equal adverse game conditions, then it is my belief that these adverse conditions can be discounted when comparing the lifetime quarterback ratings of the respective quarterbacks.
Level Four: Feeling
A feeling describes an affirmation that is intuitive in nature. Quite often, it is based upon personal observations and experiences. A feeling is based at least in part upon a belief. Feelings are also often based upon what the evaluator believes to be a statistical probability.
Consider a person who observes a series of coin flips. The observer notes that in five consecutive flips the result is “heads.” He develops a “feeling” that the sixth flip will come up tails. The feeling is based upon a belief that the odds that a coin will come up heads in six consecutive flips, a 64-1 improbability, dictates that the sixth flip is more likely to result in an outcome of tails. In actuality, the Laws of Probability state that the odds of any coin flip resulting in either heads or tails is exactly 1-1, or 50%. These odds remain for the sixth flip, as well as the seventh, eighth, ninth, or tenth. The odds do not change based upon previous history.
Counter-intuitive feelings often crop up in sports prognostications. For example, a particular sports fan might affirm that a winless team is “due” to win a game. Conversely, the fan might feel that this team’s upcoming opponent, which has been playing very well, is getting “cocky,” and is therefore “due” for a loss. The fan ends up predicting an upset win by the heavy underdog.
Let us interject a “feeling” into our hypothetical Montana/Unitas comparison. Our Montana advocate has utilized historical facts with which he forms an opinion that Joe Montana was a better quarterback that John Unitas. He then utilizes opinion to form a belief that Montana would uniformly outperform Unitas in adverse weather conditions. He might then raise the argument:
“It is my feeling that, if both Montana and Unitas were able to play in snowy December game for the 2007 New England Patriots, Joe Montana would statistically outplay Unitas by about a +15 quarterback rating.”
Aristotlean Logic is an argumentative discipline that is beautiful in its simplicity. It is “deductive” in nature. By “deductive” we mean that it utilizes a method that unites two inter-related premises, both which are accepted to be true, into an irrefutable conclusion. In its basic form, the method works thus,
Premise One: All of “A” is “B.”
Premise Two: All of "C” is “B.”
Conclusion: “C” is “A.”
A bit confusing at first? Let us use a simplified example:
Premise One: All New York Football Giants wear blue home uniform jerseys.
Premise Two: Jared Lorenzen is a New York Football Giant.
Conclusion: Jared Lorenzen wears a blue home uniform jersey.
The above example represents a correct application of Aristotlean Logic. Note that the premises, which we accept to be true, may not be entirely accurate.( The Giants do, after all, occasionally play a home game in red uniforms.) In fact, a solidly deduced conclusion can be flat out false if it is based upon an incorrectly accepted premise:
Premise One: All New York Giant quarterbacks are right-handed.
Premise Two: Jared Lorenzen is a New York Giant quarterback.
Conclusion: Jared Lorenzen is right-handed.
The above argument deduces a correct conclusion. The problem is: the conclusion is observably incorrect. Jared Lorenzen is left-handed. The problem does not lie in our methodology, which is rock-solid. Rather, the mistake results from us accepting as true a premise (Premise One) which is in fact false. Not all Giant quarterbacks are right-handed. Good argumentative method, bad science.
The Fallacy of the Undistributed Middle
An improper application in methodology can result in a logical mistake referred to as “The Fallacy of the Undistributed Middle.” Here, two accepted premises, both of which may be perfectly true, may be improperly connected to derive an incorrect conclusion. In other words, both the premises and conclusion may be independently true, but the argument itself is false. The Fallacy of the Undistributed Middle looks thus:
Premise One: All of A is B.
Premise Two: All of C is B.
Conclusion: Therefore, all of C is A.
To use a concrete example, consider the following argument:
Premise One: All New York Football Giants wear blue home uniform jerseys.
Premise Two: Jared Lorenzen wears a blue home uniform jersey.
Conclusion: Jared Lorenzen is a New York Football Giant.
Both the premises utilized and the conclusion drawn are empirically true. This said, the qualitative fact that Jared Lorenzen wears a blue home uniform jersey does not support the argument that he is a New York Giant. Wearing a blue home jersey is not exclusive to the New York Football Giants. Although the conclusion is qualitatively correct (Lorenzen is a Giant), the methodology used is not. Therefore, the argument itself is false.
We can see that proper Aristotlean methodology requires that both premises are accepted as true. But premises, as proposed, are often lacking as independently supportable truths. Premises are, after all, “Affirmations.” This said, the strength of a premise depends upon the level of affirmation that it reflects: fact, opinion, belief, or feeling. The lower the level of affirmation utilized, the weaker the reliability of the conclusion.
In conclusion, proper argumentation requires two basic criteria: correctly defined premises and properly utilized methodology. We must recognize both the correct level of affirmation that a premise reflects and properly define the subject matter being discussed. We must also use the proper methodology that allows us to arrive at a correctly derived conclusion. Arguments which begin with a conclusion and then work backwards to find improperly supportive premises are both all too common and all too recognizable. And they are flat out wrong. Period.
Big Hitter Dalama