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I'm with Utopian/hoglagoo too. It's a matter or degree. Coarse hones remove lots of metal, medium hones remove less, and fine remove very little. The 4k cuts, while an 8k polishes. A pasted strop is more agressive than a non pasted strop. A strop is more aggressive than colored newsprint. Each sharpens much less then its predecessor, relatively.
It's a simple question: Does stropping keep the razor sharp? Well... does your razor get more dull from stropping? No. Does it stay the same? No. It gets sharper!
Grass is green, water is wet, and sharper is still sharper... even if you aren't removing metal!!
Here's the semantic problem we are banging our heads against:
The cutting ability of the razor (sharpness) is independent of the action of the stone or strop on the edge (metal removed, metal aligned, nicks smoothed, etc.).
I completely agree, whether it removes metal or just aligns the edge, if it means it cuts hair easier, I say its made it sharper. If stropping put a smily face on your razor and that cut hair better, I would count that as sharper.