Define atheism :: Logical consistency
Logic is a natural and useful intellectual tool for testing the consistency of our understanding of concepts and ideas, claims and assertions, hypotheses and theories, mathematics and philosophy, and many other subjects that require the use of logic that even includes casual day-to-day decision-making.
Hereunder, we rely on the symbolic keymap (immediately above) to logically clarify the meanings of select vocabulary that is used in public discourse, philosophical debates, epistemological studies, etc. These particular words of interest are: atheism, anti-theism, and theism, all of which pertain to the subject of belief, and agnosticism and gnosticism, both of which pertain to the subject of knowledge.
Excluded Middle, the principle of
The Principle of the Excluded Middle is a well-known logical law that asserts that a logical statement can only be "true" or "false." While this law is useful, the law itself it is not exempt from causing false dichotomies when applied where more than two options are logically valid possibilities, and so in the spirit of striving for objectivity it is important that practitioners of logic be aware of the risk of bifurcated thought that can arise from unnecessarily or illogically excluding additional options and/or positions.
As a straight-forward example, a false dichotomy arising from the incorrect application of the "excluded middle" can be demonstrated with a basic system of signal lights on a motor-vehicle. While these signal lights are best known for communicating the driver's intention to perform a left-hand or right-hand turn or lane change, limiting the options to "left" and "right" signalling is a false dichotomy because it unnecessarily excludes the default of "not signalling." (Also, this is not the only possibility since a well-known fourth "hazard lights" option utilizes both sets of signal lights simultaneously to indicate a temporary full stop due to a mechanical breakdown, etc.)
Along this line of thought is that "not believing that deities exists" (atheism) is distinctly different from "believeing that deities do not exist" (anti-theism) and its opposite of "believing that one or more deities do exist" (theism). While for former does not carry a burden of proof since it is not an assertion, a belief, or a claim, the remaining two are actively-held beliefs that do carry burdens of proof insofar as they are like claims or assertions, and/or when others are also expected to hold the same beliefs.
In summary, applying the Principle of the Excluded Middle to choices that aren't naturally limited to "true" and "false" is illogical, even though some debaters have been known to use it in an attempt to force a burden of proof onto adversaries who have not taken a position. Therefore, the attitude that an individual only has the option of "believing in deities" (theism) or "believing that deities don't exist" (anti-theism) is illogical and qualifies as a bifurcation fallacy because it excludes the valid and default option of "not believing in any deities" (atheism).
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