In a nutshell, those who claim to be theological noncognitivists claim:
"God" does not refer to anything that exists.
"God" does not refer to anything that does not exist.
"God" does not refer to anything that may or may not exist.
"God" has no literal significance, just as "Fod" has no literal significance.
The term God was chosen for this example, obviously any theological term [such as "Yahweh" and "Allah"] that is not falisifiable is subject to scrutiny.
Many people who label themselves "theological noncognitivists" claim that all alleged definitions for the term "God" are circular, for instance, "God is that which caused everything but God", defines "God" in terms of "God". They also claim that in Anselm's definition "God is that than which nothing greater can be conceived", that the pronoun "which" refers back to "God" rendering it circular as well.
Others who label themselves "theological noncognitivists" argue in different ways, depending on what one considers "the theory of meaning" to be. Michael Martin, writing from a verificationist perspective, concludes that religious language is meaningless because it is not verifiable.
George H. Smith uses an attribute-based approach in an attempt to prove that there is no concept for the term "God": he argues that there are no meaningful attributes, only negatively defined or relational attributes, making the term meaningless.
Another way of expressing theological noncognitivism is, for any sentence S, S is cognitively meaningless if and only if S expresses an unthinkable proposition or S does not express a proposition.[original research?] The sentence X is a four-sided triangle that exists outside of space and time, cannot be seen or measured and it actively hates blue spheres is an example of an unthinkable proposition. Although some may say that the sentence expresses an idea, that idea is incoherent and so cannot be entertained in thought. It is unthinkable and unverifiable. Similarly, Y is what it is does not express a meaningful proposition except in a familiar conversational context. In this sense to claim to believe in X or Y is a meaningless assertion in the same way as I believe that colorless green ideas sleep furiously is grammatically correct but without meaning.
Some theological noncognitivists assert that to be a strong atheist is to give credence to the concept of God because it assumes that there actually is something understandable to not believe in. This can be confusing because of the widespread claim of "belief in God" and the common use of the series of letters G-o-d as if it is already understood that it has some cognitively understandable meaning. From this view strong atheists have made the assumption that the concept of God actually contains an expressible or thinkable proposition. However this depends on the specific definition of God being used. However, most theological noncognitivists do not believe that any of the definitions used by modern day theists are coherent.
As with ignosticism, many theological noncognitivists claim to await a coherent definition of the word God (or of any other metaphysical utterance purported to be discussable) before being able to engage in arguments for or against God's existence.