In the recent analytic philosophy literature on the meaning of the word/name 'God', it is common to begin by distinguishing two positions. In the first place, we might think of 'God' as abbreviating a definite description like 'the being than which none greater can be conceived' or 'the being which is worthy of worship' or 'the omnipotent, omniscient, and perfectly good creator of the universe'. Some philosophers stipulate that they are using the word this way, but this kind of account is unsatisfactory as a description of how the word 'God' is used in English (or how its translations are used in other languages). Speakers don't have these kinds of descriptions in mind and, furthermore, both philosophers and ordinary folks seem to be capable of considering the possibility that God exists but fails to satisfy them.
In the second place, then, it might be supposed that 'God' is a proper name. On the Kripkean account of proper names (which is often applied here), this would involve holding that someone initially had some way of designating God and applying this name. For instance, perhaps Abraham or someone had a religious experience in which God was manifested and introduced a name to refer to that being. Or perhaps someone hypothesized the existence of a being who satisfied some description—sole creator of the universe, for instance—and gave that being a name. Then, there is a chain of transmission of the name from one speaker to another, with each speaker simply intending to use the name to designate the same being to whom the name was initially applied. This conception is very flexible in terms of what speakers might believe about the being so-named. Among Kripke's examples are that a person might know nothing about Feynman other than that he is 'a famous physicist', and therefore not be able to describe Feynman in a way that distinguishes him from Einstein or Noether, and yet use 'Feynman' as a name of Feynman and not any other famous physicist. An even more extreme example given by Kripke is that a person asked who Gödel was might be able to say nothing but 'the person who proved the incompleteness theorems', yet such a speaker would use 'Gödel' to refer to Gödel even on the assumption that Gödel didn't really prove those theorems.
As applied to God, however, many philosophers have thought that the Kripkean theory of proper names was too permissive. It seems to many people that the meaning of the word 'God' places limits on how different a being could be from the traditional conception and still be the referent of that word.
Some philosophers have sought to incorporate this fact within an account of 'God' as a Kripkean proper name. For instance Meghan Sullivan has applied the concept of 'reference drift' here: sometimes the chain of transmission of reference breaks down in such a way that the reference of a name shifts. For instance, in actual history, what began as fictional stories or legends about the historical person Saint Nicholas of Myra eventually became stories about an entirely fictional person, so that the name 'Saint Nicholas' no longer referred to the historical person. The vulnerability of the name 'God' to reference drift (because of the difficulty of reidentifying its referent) might help explain why there seem to be limits on how wrong the traditional picture of God could be before we have to say that God does not exist.
Alternatively, some philosophers have tried to develop views that are in some way in between the definite description theory and the proper name theory. I think Aquinas has such a view, and I think his view is different from any I've seen in the contemporary literature in ways that are interesting and worthy of attention.
In ST Iq13a8, Aquinas argues (citing Ambrose) that the word 'God' is a name of the divine nature. In this sense, the word 'God' is more like the word 'human' than the name 'Mary'. And, indeed, Aquinas goes on to say (Iq13a9r2) that "This name God is an appellative name, and not a proper name," i.e., it's semantic function is that of what we call a common noun. This is supported by the fact that one occasionally finds the plural 'gods' even in Scripture (and the typographical distinction between 'God' and 'god' often employed in modern English has no equivalent in Scripture or in medieval Latin). This, however, raises an important question, which Aquinas expressed as "Whether the name 'God' is communicable?' (Iq13a9). That is, could it in principle be the case that this name applied to many things? If indeed it is an appellative (common) noun, this would seem to be the case (Iq13a9o2).
In response to this issue, Aquinas makes a very interesting move. According to him, the fact that 'God' is a common noun explains why it is communicable in opinion, that is, why it is possible for competent language users to be polytheists. According to Aquinas, "a Catholic saying that an idol is not God contradicts the pagan asserting that it is God; because each of them uses this name God to signify the true God" (Iq13a10r1). Thus, it appears that Aquinas would think that our typographical 'God'/'god' distinction is a mistake, because the pagan and the monotheist, according to him, actually signify the same thing by 'god' and they have a perfectly straightforward first-order disagreement regarding whether one or many things have that nature.
What is 'incommunicable', according to Aquinas, is the divine nature itself. It is not because of the semantics of 'God', but rather because of the metaphysics of God, that, necessarily, there is exactly one God.
One way of translating this view into analytic philosophy would be to say that 'God' is not a Kripkean proper name, but rather a Kripkean natural kind term. For Kripke, natural kind terms, like names, are introduced by ostension, i.e., by (literal or metaphorical) pointing at the stuff in question, and then are perpetuated by semantic deference, in which each speaker intends to refer to the same kind as the previous speaker. This fits quite nicely with Aquinas's claim that, since we don't know the divine nature except by its effects, the name 'God' was introduced by means of those effects, yet it refers to the nature and not the effects (Iq13a8o2). So we, as it were, 'ostend' God as First Cause and say 'let "God" name that kind of being'. The peculiarity here is not about the word, but about the kind itself: necessarily, that kind has exactly one instance.
This seems to me to be appropriately classed among the 'in-between' views. If 'God' is a natural kind term, that certainly explains the intuition that something that was too different from the paradigm simply wouldn't be (a) God. On the other hand, it doesn't require speakers to have a shared definite description in mind in order to use the word 'God' competently. Further, it simplifies our understanding of the disagreement between atheists, monotheists, and polytheists. This turns out to be just what the 'surface grammar' suggests: a disagreement about how many instances a certain kind has.
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