How does the color exclusion problem challenge logical atomism


Recently tried diving into Wittgenstein and I’ve encountered a fair bit of discussion over the color exclusion problem. I’m mainly interested in what exactly is meant by logical atoms necessitating logical independence?

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Logical independence is a core belief of logical atomism. Logical atomism is basically the assertion that: all statements about the world can be broken down into atomic statements (statements that cannot be broken down any further) whose truth does not depend on any other statement.

If either of these (that atomic statements exist and that they are independent) are false, then logical atomism is false, by definition.

Color exclusion is a presented as a problem for logical atomism by presenting a an atomic statement (some object in some place and time is a given color) is not independent (because any other statement being another color is necessarily false).