..., we have no ultimate ground for logic either.
As happens with many words, the term "logic" can have multiple meanings. Sometime it is used as synonymous with "reasoning" or "thinking". This makes it subjective, since it is the mental activity of a subject. Others use the term to mean the mechanistic following of fixed rules of inference, and we can treat that as an objective meaning.
NWR makes this to-do about the word "belief"--says it's always emotional. I just mean by "belief" the idea of being convinced by some proposition. Unlike NWR, apparently, I think it is possible to reason objectively--no doubt another naive idea of mine.
You are reading too much into this.
I am attempting to account for why people can have beliefs, while it is generally agreed that computers cannot have beliefs.
Reasoning is done by a subject, so in inherently subjective. However a reasoner (as a subject) can follow objective principles of reasoning. When you use the expression "objective reasoning", are you intending that to single out the principles followed in the reasoning (which can be objective), or are you intending to single out that there is a reasoner (a subject)? Okay, that was a rhetorical question, so no need to answer.
I think you are seeing a profound disagreement between us, when it is more likely that I am trying harder to avoid ambiguity by being careful in my use of terminology.