XXIV. Primary Laws of Thought
Atkinson refers to the three primary laws of thought that were developed by "ancient Greek logicians" and remain valid to the present day. Most arguments and judgments, pursued for long enough, will arrive at one or more of these laws - and it is often pointless to pursue further exploration once the analysis has arrived at such a point.
The Law of Identity
This law maintains, "Whatever is, is."
In the existential sense, this law maintains that existence is not to be questioned - that if something exists, it simply exists, and does not need to be proven to exist because existence is self-evident.
In terms of judgments, if something fits the defining characteristics of a concept, then it belongs within that concept even if other qualities are not in common. A bird is a bird, whether its other characteristics cause it to be identified as an eagle, a wren, a stork, or a hummingbird. Once it has qualified as a member of a class, its other properties are incidental.
The Law of Contradiction
This law maintains, "Nothing can both be and not be."
That is to say that a creature that is a bird resides within that category: it cannot be a "bird" and "not a bird" at once. It must either be within the concept or outside of it and cannot be both.
It also maintains that existence is not comparative, but binary. One thing may be less sweet or less hot than another, but it is still essentially sweet.
And there is some matter of granularity: a single piece of iron may be hot at one end and not hot at the other - but it cannot be both hot and not hot in the same place at the same time.
The Law of the Excluded Middle
This law maintains that everything must be or not be, and that there is no middle course.
Deriving form the law of contradiction, the excluded middle maintains that if our concepts are well enough defined, they reach a point at which there is a transition from one state to another: we recognize a gradual transition between cold and hot, but there is a definite point on the gradation of temperature that an object switches from being barely cold to being barely hot.
Fallacious Application
Each of these three laws gives rise to fallacies when then are improperly applied. A fallacy is an unsound argument or conclusion that has about it enough sense to be construed as sound, but is flawed in a way that makes it entirely undependable.
For example, it is fallacious to believe that "all women lie at all times" because lying is a property that occurs in a specific situation and is not characteristic of all women at all times. While it may be accepted that all women lie at some time, it is incorrect to assume that lying or not lying is an always-or-never proposition. This is a misapplication of the law of identity.
Another common fallacy is to suggest that because something cannot be proven, it follows that the opposite must be true. The opposite judgment has not been proven. This is a perversion of the law of contradiction - that a thing cannot be and not be does not mean that if it lacks a given quality it must possess the opposite: if a thing is not red, that does not necessarily prove it is green.
A third fallacy is the binary fallacy, which insists that a thing must be one way or the other. Again, there is a gradation between opposing conditions. We do not insist that there are only two colors, black and white, but instead recognize a shade of gray as being between the two - but there is again the definite point where a gray is a "dark white" and a "light black." This is a misapplication of the law of the absolute middle.
These are not by any means the full scope of logical fallacies, but are examples of the manner in which the three basic laws of logic can be misapplied and corrupted.