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When someone is sharpening the saw, they are taking time out, learning and improving so that they can be more effective in their job.

When someone has an axe to grind, they are angry, and looking for an excuse to take it out on someone.

Now perhaps the former image is that of the careful thoughtful craftsman. Perhaps the second image is one of sparks flying off a piece of metal in a grinder – but they seem too similar not to have some common origin.

My question is: Why do sharpening the saw and has an axe to grind mean two completely different things?

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Tough the two sayings refer to similar actions, their meanings depends on their origin and their usage.

As for have an ax to grind, it appears that the notion of "having ulterior motives" comes from:

  • The story is a cautionary fable concerning the author's recounting of an incident from his youth, where a passing stranger takes advantage of him and, by flattering him, dupes him into turning a grindstone to sharpen the stranger's axe. Miner then uses having an axe to grind as a metaphor for having an ulterior motive:

    • When I see a man holding a fat office, sounding 'the horn on the borders' to call the people to support the man on whom he depends for his office. Well, thinks I, no wonder the man is zealous in the cause, he evidently has an axe to grind."

(The Phrase Finder)

Sharpening a saw, refers to a story of a frustrated lumberjack and conveys the notion that:

  • We get frustrated by life and our inability to cope, but instead of developing ourselves and taking the time to become more effective, we keep struggling with a blunt saw.

(betterlifecoachingblog.com)

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