So, sometimes if you don't press the handle hard enough, the toilet does a partial flush. Would this count as a half-job done by the toilet and not comparable to the firing of the neurons? Just how is a 'partial-flush' similar to a neuron firing?
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The partial flush would be like a 'graded potential' meaning it doesn't reach the threshold to make an action potential (I think the threshold is -55?) So yea, a graded potential would not cause an action potential, but once the threshold is reached, it's an all or nothing! there is no way of stopping it. I'm really not sure about the mechanics of a toilet but I assume it's the same way.
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I would not consider them the same. The all or nothing law states that either an actin potential occurs or it does not. There is no half job as in your example.