Does this sound familiar?
Yes. I see nothing here not already covered by this, this, and this.
Your final conclusion is like saying that the computation done by computers doesn't involve arithmetic. It's *flow of electric charge*. The charge flows around, then settles down in some stable point in the sea of possible distributions. ETA: On that point, see also this.
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By Wittgenstein's time, there were already plenty of philosophers who thought definitions aren't quite captured by necessary and sufficient conditions.
And the recognition that the process that ordinary people went though had pretty much NOTHING in common with "necessary and sufficient conditions" was not made by philosophers.
Ordinary people struggle to decide whether dolphins are fish or penguins are birds. And they often get it wrong if they haven't been explicitly taught otherwise; even then, some still screw up their answers.