Brandon here has pointed out that it is not inconsistent to hold that there are three persons in the Trinity, but only one God. For the following statements are consistent:
Jack has an F
John has an F
Jack /= John
There is only one F
However, this is true so long as we do not read 'is God' in 'the Father is God' as an identity statement, but as something like ' has the divine nature'. If, on the other hand, we read 'God' as a logically proper name, and 'the Father is God' as an identity statement, it is clearly inconsistent to hold that three things (the Father, the Son and the Holy Ghost) are identical with a fourth thing (God).
Is that right? It is certainly consistent with what Aquinas says here, that no name signifying any individual thing is 'properly communicable to many', except by way of similitude; as a person can be called "Achilles". Thus the name 'God', can only be communicated by way of similitude. 'But if any name were given to signify God not as to His nature but as to His "suppositum," accordingly as He is considered as "this something," (hoc aliquid) that name would be absolutely incommunicable; as, for instance, perhaps the Tetragrammaton among the Hebrew; and this is like giving a name to the sun as signifying this individual thing.'
It suggests that our ordinary words for God only signify by description (as philosophers now say) not 'by reference'. But is that right?