It's one of those phrases you hear and think you know what it means. Something about simplicity. This definition crossed my screen via A.Word.A.Day and I thought it nice and succinct.
Ockham's razor states that "entities should not be multiplied needlessly". It's also called the principle of parsimony. It's the idea that other things being equal, among two theories the simpler one is preferable. Why razor? Because Ockham's razor shaves away unnecessary assumptions. Ockham's razor has applications in fields as diverse as medicine, religion, crime, and literature. Medical students are told, for example, "When you hear hoofbeats, think horses, not zebras."
Variations on this theme: "Simple chess is best." "To do the necessary in the fewest possible steps: that is grace."
The point, for our purposes, is to apply this notion to composition. It is always correct to cut what is not needed, to go with the simpler sentence over the complex, to be parsimonious in your use of modifiers.
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