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Theological noncognitivists argue in different ways, depending on what one considers the "theory of meaning" to be.
One argument holds to the claim that definitions of God are irreducible, self-instituting relational, circular. For example, a sentence stating that "God is He who created everything, apart from Himself", is seen as circular rather than an irreducible truth.
George H. Smith uses an attribute-based approach in an attempt to prove that there is no concept for God: he argues that there are no meaningful attributes, only negatively defined or relational attributes, making the term meaningless.
An example: Consider the proposition of the existence of a "pink unicorn". When asserting the proposition, one can use attributes to at least describe the concept such a cohesive idea is transferred in language. With no knowledge of "pink unicorn", it can be described minimally with the attributes "pink", "horse", and "horn". Only then can the proposition be accepted or rejected. The acceptance or rejection of the proposition is distinct from the concept.
It is asserted by Steven J. Conifer that to be a positive atheist, one who not only lacks a belief in gods but who furthermore denies that gods exist, is to give credence to the existence of a concept of something for God to refer to, because it assumes that there is something understandable to not believe in.
Notes and references
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