But John denies it. He says: 'La Paz is not the capital of Bolivia' (perhaps he thinks it's the capital of Colombia). In this case, there is exactly one proposition - that La Paz is the capital of Bolivia - such that Julie asserts it and John denies it. That is what genuine factual disagreement is: genuine disagreement is when there is one proposition that is asserted by one person but denied by another. If Julie and John value the truth, they will want to know whose claim is true.
But suppose now that Julie and John also disagree about the relative merits of chocolate and vanilla ice cream: Julie contends that chocolate tastes better, while John is on the side of vanilla. As we have seen, in order to make her meaning perfectly explicit, Julie would have to say 'Chocolate ice cream tastes better than vanilla to me'; John would have to say the same in order to be explicit. So what Julie is really saying is that chocolate tastes better to her, John that vanilla tastes better to him.
The proposition that Julie expresses can equally well be expressed as:
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