You have had your brain replaced bit-by-bit throughout your life, through the process of cell maintenance. The OP specifies that the replacement replicates exactly the function of the neuron it replaces. I think that the word "certainly" in your post is precisely the bone of contention in this thread. As I read it, we only can be certain of your "certainly" if we deny the "precisely the same function" of the OP. If we keep the "precisely the same function", then one's conclusions regarding "certainly" are dependent on your assumptions about the relationship of experience and brain.
Hi, Merc - good to chat with you again.
Regarding neuron replacement in the brain... are you sure that's the case? I was under the impression that wasn't what was happening when neurons died - instead, I thought that the brain operates in a massively parallel fashion, so that when a neuron dies, another (or perhaps several others) are already handling the same functionality. In the case of massive trauma, even parallel systems take a loss... but if each neuron contains unique and irreplaceable information, wouldn't we be losing critical knowledge (and even maybe life functionality?) on an almost daily basis?
Doesn't sound like such a system would survive and flourish via the evolutionary process.
Anyway, regarding external replacement of cells... I guess my point is that replacing wetware with hardware may
replicate functionality, but that's not the same thing as having the original.
I thought about this last night on my way home. (Man, do I need a life!

) After some thought, I came up with an analogy for us to bat around in case the topic continued in the thread.
This is a two-stage analogy - one is essentially a prep for the second, so please bear with me.
The Mona Lisa was painted by Da Vinci. If - by means of some kind of matter duplication process - we were able to replicate the original painting molecule by molecule, we'd have an absolutely perfect and physically indistinguishuable copy of the original.
Would an art collector
knowingly pay as much for the duplicate as for the original?
I don't think so, but that's open for debate, of course.
The original was touched and created by Da Vinci himself; he mixed the pigments, applied the brushes, blended the various colors on the canvas by hand. The copy can't make that claim. Nor can the copy lay claim to the history of the painting and how it was handed down, or stolen, etc, etc. To that collector, there would be a real, non-subjective difference between the two items - the original would have a history associated with it, and the copy would merely be an extremely high-fidelity duplicate.
Sure, the collector might want the duplicate, since the original isn't really available for purchase, and is virtually priceless... but if given a choice between the original and copy, there's no doubt in my mind that a collector would always go for the original, and be willing to pay more for it than for the copy. We can debate whether the difference between the two is subjective or real... but regardless, there
is a difference to collectors, historians... and probably the general public as well. I doubt seeing a duplicate would have the same impact as seeing the original for most people... part of the wonder is the thought that you're viewing something touched by Da Vinci himself.
Now let's forget about duplication and consider replacement - which is the second part of the analogy I referred to.
Suppose - over a period of time - we were able to replace the oil paint, canvas, etc., of the Mona Lisa with a virtually indistructable material. This material would indistinguishably mimic the color, texture, feel and weight of the original paint and canvas - but of course, would be chemically composed of an utterly different substance. Not a trace of a single molecule of the original painting would remain... but this would all happen "in-place", so there wouldn't be a duplicate involved, nor would there be a "discarded original". Instead, the replacement would happen "in-place".
Once completed... is the "new" Mona Lisa still the original? Or has the original been destroyed and replaced by a perfect duplicate?
I believe that the original has been destroyed; just as I believe that the original "me" would be destroyed by replacing my wetware with hardware.
