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background: I recall in my undergrad linguistics class being given the prompt "What is a dog?" The key takeaway is that one can remove almost any single trait (e.g. has four legs) and still have something which is clearly a dog.

I would like to propose a framework for answering this type of question, and I'll use a car to be more humane. The framework requires a hypothetical dismanteling of the object. (It is also conceptually related to the Banach Tarsky principal/paradox.)

Framework: Assume you have something that can be agreed to be a car. Rather that asking if it is still a car when you remove one of the doors, I would ask if the door alone is a car. answer:it is not. But, can you pull out the right set of parts and reconstruct them such that the new arrangement is a car, but also the parts you left behind are still a car?

Next, we'll use Dennet's intuition pump to create a metric which can help arrange various concepts along a continuum. Start with one million cars of the same make and model. It seems uncontroversial that we could create a million-and-one such cars by rearranging the parts. There are two knobs to turn on the intuition pump: Knob 1: keep rearranging the parts and see how many "cars" you can make. it's OK for the answer to be fuzzy. Maybe most people will agree you can make 1.2 million cars, but then concensus starts dropping off, and by the time you're trying to make 1.8 million "cars", things look murky. That's fine. we have learned some metrics about "car-ness" Knob 2: reduce the original number and see if you can still make "one more". This may seem like the same knob, but something special happens at small numbers. Can you make 4 dogs from the parts of 3?... (assuming Frankenstein-like powers of reanimation)

For some items, we only have 1 object to start with, so Knob 2 isn't available. For example, can you make 2 cities from one? probably. Can you make 2 San Franciscos from 1? more dubious. 3 San Franciscos?

Proposal: Before trying to answer "what is a car", first use the multiplication-via-rearrangement framework to find where on the spectrum of many-from-fewer the concept lies. I suspect that concepts which share locality on this spectrum can also share other results. This spectrum shows that cars are like functioning-cities but perhaps functioning-cars are more like living-dogs.

Have you seen something like this before? Do you find it useful? Thanks.

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