Hi Elton!
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Your guess is very good. But maybe not perfect. I would like to know where you read or heard this sentence, because it is an idiom that is no longer used today.
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It was popular at one time. There are many examples of this idiom in books and stories from the mid to late 1800s, including famous ones such as "Little Women" (1868). The idiom is used more than once in the novel "Gone with the Wind" (1936). But, of course, this novel's story is set in the American Civil War period (1861+), so again, we see that the idiom was used in the mid-1800's. But there are examples of it being used in the 1920s and 1930s. I do not know when the idiom went out of fashion (stopped being used). But it has.
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So enough of that.
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To be simple, "Don't be a goose" means "Don't be a goose. Don't act like a goose. Don't be gooselike. Don't be unthinking. Don't be foolish. Don't be brainless. Don't be mindless. Don't be stupid. Even, sometimes, Don't be ridiculous. And yes, Don't be silly--as long as by silly, we mean 'unthinking.' "
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"Do not act or be like a goose." In the sense that a goose, in popular conception, is a bird that does not use its brain. There is an old nursery rhyme or Christmas carol that starts: "Christmas is coming. The goose (or geese) is getting fat." This means that the goose is eating and eating and getting fatter and fatter; but it does not realize that when it gets fat enough, it will be killed by its owners and eaten for Christmas dinner! So this is a good example of what "Don't be a goose" means. It means; "Don't be brainless." "Don't be mindless." Or, only in this sense, "Don't be silly" or even "Don't be stupid."
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It can mean: "Don't be stupid," if by stupid we mean foolish. Or mindless or even, sometimes, ridiculous.
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It can mean "Don't be silly." But we have to be careful. Silly has at least two meanings. One meaning of silly is good for this phrase: this meaning is foolish or mindless. (But silly can also mean frivolous, which does not fit