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> Other more quaint languages like Java may have type systems that check properties such as "The program does not add numbers and strings"

Poor example. In Java, number + string means "convert the number to a decimal string then concatenate", and it can be invoked unintentionally.

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Does it? I thought string + number does that, but number + string does not compile.

That's not a counter-example. I'm not saying that Java doesn't allow syntax that might look like "number + string", just that it does not actually add them, like C does where: 3 + "4" means something very surprising.

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