Against the somewhat populist mantra of atheists like Sean Carroll (that the term ‘God’ is not now, nor seemingly ever, clearly defined), I have insisted that analytic theologians, at least, have provided a very clear definition of God which is serviceable for the purposes of philosophical analysis. When(ever) defining theism, therefore, I have been very insistent upon the roughly Anselmian definition (i.e., that God is that than which nothing greater could be conceived – or, put more simply, that God is an altogether perfect being) which is also adopted, in a refined form, by analytic theologians engaged in the project of what is called perfect being theology. Perfect being theology (PBT) suggests that God is that which exemplifies the largest compossible package of great-making (or ‘perfect-making’) properties. For all its philosophical and rhetorical advantages, however, there is an important sense in which this definition dislocates the term ‘God’ from the way it is often used in the real world. For instance, while the monotheistic Hindu, or the (follower of) Bahá’í, or the Muslim, or the deist will, on this definition, be included among the ranks of theists, the Mormon, who professes belief in the God of the Bible, may turn out to be an atheist (this, for those unfamiliar with Mormonism, is because the Mormon concept of the God of the Bible is – to the best of my understanding – of a finite material non-necessary definitely-old humanoid being on a nearby planet who has his own god, and that god, in turn, has his own god (regress ad infinitum) – a being, in short, which is categorically lacking every perfection). Indeed, insisting upon the philosophically sophisticated definition introduced by Anselm and refined by analytic theologians makes the believers in the Roman pantheon of gods (as well as other ancient polytheists) non-theists. Polytheists (of the imagined variety) are something of a rarity in the modern world, which may appear to mitigate the seriousness of the problem they pose, but the fact that our definition can’t make sense of our colloquial language (insofar as we want to call polytheists theists, and certainly don’t want to call them atheists) remains a problem. More seriously, it turns out that several philosophically/theologically high-profile theists in our own time who reject PBT (e.g., open-theists/process-theologians) turn out to be atheists on the definition on which I am in the habit of insisting, even though they believe in a transcendent incontingent intentional/personal omnipotent entity responsible for the existence of everything not identical to itself. More exotically, the Anselmian definition of theism alluded to above will both exclude Wittgensteinian theists and include neo-Meinongian atheists (I’m thinking here of a hypothetical neo-Meinongian who adopts PBT and insists that non-existence is a great-making property; for them, “God exists” is false, but there is really such a thing as the God defined by PBT).
Though the Anselmian definition of God seems, at first blush, intuitive and uncontroversial (it seems to accord well with what theists mean when they use the term ‘God,’ as well as vindicating religious sentiments expressed as worship), the corresponding definitions of theism and atheism tangle us up with especially awkward commitments. How are we to resolve this problem responsibly? One solution might be to regard theism as having no strict definition, no set of necessary and sufficient conditions, but to, instead, regard any instance of ‘theism’ as picked out by a kind of family resemblance (perhaps we could have disjunctive sets of sufficient conditions none of which are necessary for theism). Another strategy is to define theism more than once (offering a wide, and a narrow definition, or some set of definitions running along a scale from widest to narrowest), leaving people to specify in which sense they mean to use the term when deployed in conversation. On this suggestion we could give ‘theism’ a technical definition for the purposes of doing analytic philosophy or natural theology, and then a more general definition in order to accommodate its real-world use. I am open to either strategy. For instance, I would be happy to accept the latter strategy (of defining theism multiple times), allowing its most general meaning to be defined as something like “[that] there is a being to whom religious/unrestricted worship is appropriately directed,” provided only that I could then provide a more philosophically careful definition for the purposes of philosophical interrogation (plug in Anselm’s or PBT’s definition here).
What this reflection is meant to surface to the reader’s attention is that defining theism may actually not be as easy as rhetorical responses to Sean Carroll (and others of his ilk) suggest. Perhaps, in place of being so dismissive of Carroll et alia as illiterate pedestrian theological-invalids, we should, instead, welcome the implicit challenge of defining God clearly and then offer the Anselmian definition as a proposal to be considered seriously.
This, I’m afraid, seems to be the best we can do (without doing serious violence to our normal use of ‘god’-language).
 For example, Sean Carroll in his very successful debate with William Lane Craig back in 2015, insisted several times that theism is just not sufficiently well defined (e.g., “Theism does not even try to do this because ultimately theism is not well defined[,]” “you do not see graphs like this in the theological papers trying to give God credit for explaining the fine-tuning because theism is not well defined[,]” and, of course: “It’s not hard to come up with ex post facto justifications for why God would have done it that way. Why is it not hard? Because theism is not well defined. That’s what computer scientists call a bug, not a feature.” The popularity of this debate noticeably boosted the popularity of this rhetorical strategy. To his credit, Carroll does say: “… theism is not well defined. I’m going to be emphasizing this… point because if you ask a theist about the definition they will give you some very rigorous sounding definition of what they mean by God. The most perfect being, the ground for all existence, and so forth. There are thousands of such definitions, which is an issue, but the real problem is not with the definition, it’s when you connect the notion of God to the world we observe. That’s where apparently an infinite amount of flexibility comes in and I’m going to be inveighing against using that in cosmology.” He acknowledges, therefore, that there are rigorous(-sounding?) definitions on offer but persists in thinking (and suggesting) that ‘God’ is not sufficiently well defined.
See: William Lane Craig and Sean Carroll, God and Cosmology: The Existence of God in Light of Contemporary Cosmology, accessed February 10th, 2020. https://www.reasonablefaith.org/media/debates/god-and-cosmology-the-existence-of-god-in-light-of-contemporary-cosmol/
 Or, perhaps, the Mormon might turn out to be an agnostic, regarding the question of whether a perfect being exists to be an open question on which the Church of Latter-Day Saints makes no pronouncements either way – or, indeed, some Mormons might be theists, others atheists, others agnostics, others Wittgensteinians, others theological non-cognitivists (and so on) so that Mormonism is strictly not determinative of theism in this widely adopted Anselmian sense.
 For instance, see Joseph Smith Junior’s King Follett sermon, where he says, among other things:
“I am going to tell you how God came to be God. We have imagined and supposed that God was God from all eternity. I will refute that idea, and take away the veil, so that you may see.”
“Here, then, is eternal life—to know the only wise and true God; and you have got to learn how to be gods yourselves, and to be kings and priests to God, the same as all gods have done before you, namely, by going from one small degree to another, and from a small capacity to a great one; from grace to grace, from exaltation to exaltation, until you attain to the resurrection of the dead, and are able to dwell in everlasting burnings, and to sit in glory, as do those who sit enthroned in everlasting power.”
However, interestingly, there are parts even of this sermon which appear, on first reading, to make room for an ultimate God, a God who is the head of all gods, and who created the world (though, of course, not ex nihilo: “Now, I ask all who hear me, why the learned men who are preaching salvation, say that God created the heavens and the earth out of nothing? The reason is, that they are unlearned in the things of God, and have not the gift of the Holy Ghost; they account it blasphemy in any one to contradict their idea. If you tell them that God made the world out of something, they will call you a fool. But I am learned, and know more than all the world put together.”). For example: “In the beginning, the head of the Gods called a council of the Gods; and they came together and concocted [prepared] a plan to create the world and people it.”
See: Joseph Smith Jr., The King Follett Sermon, accessed February 10, 2020. https://www.churchofjesuschrist.org/study/ensign/1971/04/the-king-follett-sermon?lang=eng
 See: D.Z. Phillips, “Wittgensteinianism: Logic, Reality, and God,” in The Oxford Handbook of Philosophy of Religion, edited by William J. Wainwright, (Oxford: Oxford University Press, 2005): 447-471.