I still mean to comment on Bowman’s 5th round, but my inner logic nerd was drawn in by some action from round 5 here, comment 19:
[Burke:] “This week I hope Rob will show Biblical evidence for the essential relationship formulae of Trinitarianism:
1. Father = ‘God’, Son = ‘God’ and Holy Spirit = ‘God’
2. ‘God’ = Father + Son + Holy Spirit . . .
[Bowman] I have already responded to this argument of yours. Your demand that I must prove these two statements “independent of each other” is an absurd demand calculated to place an unreasonable burden on me that you know cannot be met.
As you know, Dave, if statement #1 is true, and if there is only one God (one single eternal divine being), then statement #2 follows. However, you and I already agree that there is only one eternal divine being. Therefore, I do not need to argue for this premise of the doctrine of the Trinity.
Gentlemen, forgive me, but this is confused. We must clarify the meaning of “=” here. I believe that Bowman means numerical identity in 1. (I’m not sure – I think his position forces him to be unclear about this – but let that pass.) Let us, then, add the extra premise Bowman mentions (as being held in common). We then get this:
f=g & s=g & h=g
(x)(y) (Dx -> (Dy -> x=y)) [For any x and any y, x is divine only if, if y is divine, then it just is x.]
The first premise is trouble, because it implies f=s=h.
But what to make of “‘God’ = Father + Son + Holy Spirit”. What does the “+” signify? One may (and some will) think of it as the combination of parts, or some kind of conjunction of different things. But this would shift the meaning of “=”. Numerical identity is a one-to-one (actually, always a reflexive) relation – never one-to-many. So if the right hand side is read to mean some kind of conjunction, addition, or combination, then the “=” cannot mean identity. It might mean something like “consists of”, “is a whole constituted by”, or something like that. But whatever it means, it does not logically follow from 1 & 2.
But this interpretation makes 2 irrelevant to 1. It may be that Bowman is thinking this:
Df & Ds & Dh [Father is divine and Son is divine and Spirit is divine. (This "is" of predication, not the "is" of identity.)]
(x)(y) (Dx -> (Dy -> x=y))
From these, there is no reason to think any interpretation of “g = f+s+h” follows. (First we’d have to clarify the meaning of this latter claim, and then we’d have to add one or more premises, until we had a valid and sound argument.)
But this follows: f =s=h. As Homer Simpson would say: D’oh! Homework for interested readers. Why exactly is this something Bowman can’t accept? (There is more than one reason, I think.) Comment at will.
Bowman then retreats to familiar ground:
What you are really trying to do here is to claim that unless I can show some Bible verses in which the word “God” specifically refers to the Father, Son, and Holy Spirit together, my case for the doctrine of the Trinity fails.
But that is a red herring. All we need is a seemingly sound argument, for a conclusion with which Bowman agrees, and which is arguably trinitarian! Instead Bowman brings back his apparently inconsistent set of five claims; we’ve looked at those before. Insofar as they seem inconsistent, the argument will not seem sound.