It's tough to judge a 'theory' when you won't define a part of it. I get your analogy to vessels. But that feels shaky since you have defined the other vessel as 'larger'. If you are saying sentience is 'larger' or different to intelligence then I'd argue you are defining it, at least partially. Which is good.

One problem I have with a lot of this 'AI isn't sentient' stuff is - who is saying it is? Is their opinion of any value? I see AI companies make marketing claims about AGI and the singularity. But their opinion is without value in this debate, because of their bias. No big name in AI academia or philosophy of mind seems to have made a strong claim about sentience in AI that we currently have. A lot of laymen have made claims, without defining sentience, or consciousness. And it just seems like a reactionary kneejerk opinion based on being able to hold a conversation with an LLM. That doesn't feel like enough for these discussion pieces - you're reacting to a flawed vox populi.

"Those are a lot of unknowns and conjectures, my hope is that a new field emerges that would study intelligence with the same rigour and formalism as computation and mathematics, and that this field would be studied abstractly without being tied to an individual organism be it a man or an animal."

This exists. It is called Cognitive Studies. Language students, Philosophy students, AI students, have all taken modules in this area for decades. The topic is often tied to, but not limited to animals, humans, and machines depending on the specific studies/theories. LLMs will be drastically changing this area now, of course, but we have academic rigour for the general area already established.

"Weakly, I also think it’s possible that intelligence is a binary characteristic i.e, it’s either present or not."

Strongly, I think it's far from binary, it's an emergent property based on size of the network of connections and underlying training data (be that human sensory input or machine vectors). Trim an LLM down and you won't see 'intelligence' disappear at a binary boundary, it'll degrade gradually to various different points of usability.

"This isn’t helped by the fact that extremely motivated people are making bad faith arguments and pushing complex babbling machines as sentient which need to be schooled in morality by employing religious leaders."

Nailed it. 100% agree. The agony some feel though, does need to be accounted for because those babbling machines are clearly a milestone moment on our journey TO machine sentience. We don't know when we'll actually see machine sentience but the conversation does need to be had of how we handle it responsibly, and every bad faith argument from biased sources is, to me, a warning that we will probably fuck it up majorly if/when it does happen.