Are there "natural kinds"?

I would suspect that nobody would think as you propose. It’s obvious to anyone that the choice is arbitrary and not in any way “natural”. The number of protons in a nucleus, on the other hand, is in no way arbitrary and describes a number of atoms that all behave in almost identical ways (small exceptions of mass and, for a few, stability). Perhaps you might want to claim that “natural” vs. “conventional” is a sliding scale, with driving direction at one extreme and elements at the other. And perhaps the boundary is fuzzy. For example, the geologic eras and periods were mostly defined originally to be carved up at times of maximal taxic turnover. As such, they’re somewhere in between natural and conventional.

I think you are now getting into a completely different sense of “natural”, which does not advance your point.

Conventional? Is there no such thing as 5 apples, a different thing from 4 apples, other than by convention? I’d say that the natural numbers are abstracted from real phenomena. There is no alternative way to count apples.

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The seems to imply that all indigenous groups should count the same way, and use the natural numbers. That does not seem right.

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Do you know of an alternative?

Hi @nwrickert,

You might like to peruse this article, by astrophysicist Ethan Forbes: What Are We Getting Wrong About Schrodinger’s Cat?. Here’s an excerpt:

In fact, Erwin Schrödinger himself didn’t present his “cat” idea as a proposed experiment. He didn’t devise it to ask deep questions about the role of a human being in the observation process. He didn’t actually claim that the cat itself would be in a superposition of quantum states, where it’s part-dead and part-alive simultaneously, the way a photon appears to pass partly through both slits in the double-slit experiment.

Every idea along these lines is itself a myth and misconception that runs counter to Schrödinger’s original purpose in putting forth this thought experiment. His true purpose? To illustrate how easy it is to arrive at an absurd prediction — such as a prediction of a simultaneously half-dead and half-alive cat — if you misinterpret or misunderstand quantum mechanics.

In other words, pretty much everything you’ve ever heard about Schrödinger’s cat is probably a myth, with the sole exception of the fact that quantum systems actually are well-described by a probabilistically weighted superposition of all possible, allowable states, and that an observation or measurement will always reveal one and only one definitive state…

In reality, the cat itself is a perfectly valid observer. The fact of the door or gate opening, and the mechanism controlling it getting triggered, is a perfectly valid observation. Throwing a Geiger counter in there, an instrument which is sensitive to radioactive decays, would count as an observation. And, in fact, any non-reversible interaction that occurs within that system, even if it’s completely sealed off from the outside world in that box, will reveal one and only one definitive state: either the atom has decayed or it has not.

… In reality, the decay (or non-decay) of the atom will trigger (or fail to trigger) the door mechanism, and that alone, right there, is where the transition from this bizarre quantum behavior to our familiar classical behavior occurs.

I hope that clears up matters.

Please also note that quantum theory assumes the existence of discrete quantities, so the discovery that an element’s atomic number is always an integer is perfectly in accord with quantum theory. Cheers.

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Only if it clears them up for you.

QM describes the world in terms of probability waves. You won’t find sharp distinctions there. We create sharp distinctions when we categorize.

It is my impression that many indigenous groups have only a very limited counting – perhaps counting up to 5 or so, and then going to many. It is an important aspect of what we call “natural numbers”, that they are unlimited.

I don’t see the relevance. The natural numbers are unlimited, but that doesn’t mean the names have to be unlimited. A person without a name for “6” would just call it “5 and one more”. It’s still 6.

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