It's not a matter of arbitrary classification in the cow case. The original definition still works. The heart has no experience. The continuum of consciousness exists solely within the heartless cow. Whether you want to call the heart "alive" is the same as the question about plants and sponges.
Experience is not a function of a simple "level of complexity" but of structure with specific function. The idea that you reach a certain level of complexity and just get sentience as an incidental side effect of the complexity is a fallacy for multiple reasons. Sentience results from structures specifically crafted to create sentience. In the 21st century as opposed to the 12th century we know for sure that the structures that give us sentience reside entirely in the brain. We can examine the highly complex structure of the heart and compare it to the brain and see that while the heart is complex it does not have the same structure as the brain. The heart is not sentient not because it lacks sufficient "level of complexity" but rather because it lacks a specific functional form of complexity, i.e. the heart lacks information processing structures that the brain has. We can also observe things like when there is a heart transplant the recpient does not start experiencing a change in personality from an independent "sentient" donor heart. Thus there is no evidence that sentience resides outside the brain, so why assume it might?
You could just as well assume that a rock has the processing power of a computer CPU but it just lacks input and output.
The heart of a cow (and any vertebrate) can beat on it's own. Each muscular cell of the heart beats, and they coordinate the beating when they are in contact. Also, there are a lot of neurons in the heart to synchronize the beating of the different parts of the heart.
IIRC It can keep beating even without brain signals. It's not the ideal rate of beating, and there are other problems, but the heart somewhat beats on it's own.
I don't know how many sensing neurons the heart have and how they interact with the beating. The heart is not as "smart" as a brain, but it's "smarter" than a rock.
Stealing the examples from other comments: Is the heart of a cow smarter than a planaria? Is the heart of a cow smarter than a hydra?
Yeah the heart can beat according to its internal pace maker and a CNC machine can move about and cut a work piece according to its internal program. We have no reason to believe that either is sentient. Maybe a thousand or so years ago when people did not fully understand that the brain is where consciousness takes place. Nowadays there is no excuse. Autonomy is not sentience. Your heart does not have feelings or a sense of self. Evolution did not require that to build a somewhat self regulating muscular pump. The rock vs. cpu example was a little hyperbolic I guess.
My point is simply the presence of interconnected neurons running a certain program is not sufficient to give rise to sentience or conciousness. I believe what we call sentience or conciousness is not an accident or even really an "emergent" phenomenon but rather the direct, purposeful result of specific structure that was selected for by evolution.
The phrase "level of complexity" is inartful because it implies there is one axis or dimension to complexity when that is not the case. If you make a random soup of 100 billion interconnected neurons and teach it to classify images it is highly unlikely that you will get a sentient being by accident although you may have a very efficient neural network at the task it was designed for. If however you take a 100 billion neurons and subject them to the selective pressures of evolution in the real world, where a sentient or self aware self may have advantage then it is not unlikely perhaps that you end up with a sentient or counscious being. Thus sentience is the result of specific selected for structure not the random outcome of a certain level of complexity. I don't see why this is even contraversial.
General intelligence does not exist divorced from the real world and it does not just happen as the side effect of a certian "level" of complexity.
With regard to the question is the heart of a cow smarter than a planiar (worm) whole organism I do not see this as a meaningful question because the starting premise is wrong. The starting premise assumes that there is some abstract quality "sentience" or "intelligence" that exists on a single axis, a continuum of "levels." I'd say the axis does not exist, there are no levels, what matters are functions and it is not meaningful to argue whether or not the planarian or the heart is at a higher level of intelligence because the preform different functions. Notably one is a free living creature while another is an organ inside another creater. I think they are incomparable. Neither has the specific brain structure that gives humans and other higher animals sentience so it does not make sense to argue whether one or the other is at a higher level when neither is at any level at all in terms of a structural or functional comparison with a brain. A worm is not further ahead or behind a heart when compared to a brain because neither is anything like a brain. Maybe a plannarian can learn. I doubt a heart can learn but maybe it can. But overall the idea of levels of sentience or sentience simply emerging from complexity that does not intentionally provide for it is silly in my opinion.
That's a very interesting question! (Do we have here some biologist that can try it?)
The difference between an isolated organism and a part is sometimes no so clear. For example in Clonal Colony https://en.wikipedia.org/wiki/Clonal_colony Is each trunk of Pando a different organism? Why not each branch? (Plants do very nasty things to other plants, but in slow motion. It's nice to see time lapses videos of plants "fighting".) Most examples of clonal colonies are plants, some of them have specialized members and some have identical members. If you prefer animals, one nice example is https://en.wikipedia.org/wiki/Portuguese_man_o%27_war
