This is a linkpost for https://www.anshuljain.me/the-world-is-continuous-not-discrete/
I fear you're mixing ambiguity with uncertainty with un-quantized states. A sensible definition of dead would be "never again going to take action". There is a bright line where this is the case, though there's uncertainty whether it's been crossed. Hearts can start beating again, though I don't know of any cases of post-cremation resurrection.
Healthy vs sick is similar regarding uncertainty and ambiguity. Outside of movies, doctors don't pronounce you absolutely healthy. They can say relatively healthy - better shape or less risk than some comparison group.
This is true, but implementing it as general policy may benefit from a multilevel world model, where you're aware of the continuous underlying reality but set discrete thresholds anyway. The space of states may be nearly continuous, but that is true on many axes at once, whereas the number of actions we can take in a given window of time to move along those axes is bounded, and we need to make discrete choices of how to prioritize. And ideally, set aside time periodically to review the prioritization process. That last one seems to be where a lot of people stumble, recognizing that the approximations aren't eternal.
My own experience is that in many contexts there models live in different peoples' heads. Biologists and (most?) doctors know there is a spectrum of health, but use simpler discrete models for treatment decisions. It creates its own problems (when insurers and regulatory agencies enforce them rigidly, for example), but also lets them help more people on average.
We have a bias towards using discrete mental models over continuous ones because they're more convenient. But they're not always the best choice.
I've heard a lot of different definitions for "dead". Some people say living things have souls, and they die when the soul leaves. Other people say death is when the heart stopped beating. Some people say it's when the "brain dies".
None of these definitions ever satisfy me. There are always questions people can't answer. What about someone whose heart stops beating but starts again? Can we look at a scan of someone's brain and point to the moment they die? What if we revive someone from cryonic suspension - does that mean the soul never left?
You could say this is a question of definitions. If we define death as "heart not beating" then we can definitively say when someone is dead. Of course, this would mean that we can bring people back to life after they've died because CPR works when you are "heart-stopped-dead". But what if someone is too far gone, and we can't bring them back? What if they're "actually-dead", then what's the definition of that kind of dead? We're back to square one.
The problem is that alive and dead aren't binary states where something is either dead or not. Instead, it's a continuous spectrum of "more dead" to "less dead". You could measure it as "probability we can bring back to life". The question of "what does it mean to die" doesn't make sense because there is no single point where someone is fully dead. Why was this not obvious to begin with?
Language is discrete by nature. Words usually represent distinct states and ideas because they themselves are discrete. Describing continuity is an abstract task where we draw a line between two discrete points using multiple words. For example to describe the spectrum of alive to dead I need you to visualise each endpoint and the continuum between them. Because language is discrete, a lot of our communication and thinking also becomes discrete. This is at odds with the world, which is mostly continuous.
I'm not making a claim about the nature of reality or the underlying physics. That's above my pay grade. I'm saying, at the level of abstraction we operate at, the world mostly acts as if it is continuous. Yes, some things are discrete, like the number of trees in a forest or the number of buildings in a city. But for the most part, moments in time, objects in space, or states of the world are part of a continuum. For example, we're comfortable thinking about time as continuous because we speak about it in numbers which we already intuitively understand are on a spectrum.
Discrete language trades accuracy for convenience. Because language is discrete, we need more words when we speak about continuous things. Most of the time the extra speed and convenience are a good thing. Saying I'm hungry or full is usually enough - I don't need to put a number on it. But sometimes accuracy is more valuable than speed and in those cases, it's valuable to be aware of the bias so you can correct it.
If you go to the doctor for a check-up and he says you're healthy, that isn't true. You are always at least a little bit "sick" because you're somewhere on the sick to healthy spectrum. Saying you're healthy means you're above an arbitrary point on that spectrum where there are no obvious signs of illness. But if you walk out of their office thinking you're healthy, you're less likely to take action until you dip below that threshold, at which point you've done more damage than was necessary.
Sick vs. healthy, dead vs. alive, happy vs. unhappy, hungry vs. full, smart vs. stupid. All of these are actually continuous spectrums. Treating them as discrete states is a less accurate mental model, that leads to poor decisions. When you notice yourself categorising things into discrete states, ask yourself what spectrum they live on.