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pragmatist comments on [Poll] Less Wrong and Mainstream Philosophy: How Different are We? - Less Wrong
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In relativity you still have temporal ordering of events, but it is not a total order. In a Newtonian world, every event is either earlier than, later than or simultaneous with every other event. In relativity, some events can still be unambiguously described as earlier than or later than others. Event A is earlier than event B if it is in B's past light cone. There is no longer a relationship of simultaneity, however, and some pairs of events are not related by the earlier than/later than relation. The temporal order is a partial order.
That makes sense. Although it looks like you either have all information regarding where/when all events occurred relative to each other (which would necessarily give information about where/when all events happened in relation to an observer) or you have a partial ordering, which means you don't have all the information.
The more I think about this, the more confused I get. How exactly does A differ from the information of what is in the observer's past light cone and what isn't? Or is this based on the idea of there being a single, consistent "present time" throughout the universe?
The partial ordering actually encodes a surprising amount of information about space-time. Specifying the temporal ordering relationship between space-time points also fixes the topological structure of space-time, its differential structure, and the metric up to a conformal factor. It doesn't let you reconstruct the full metric, and maybe you think that certain metrical facts count as "temporal facts" (which seems right), in which case the definition of B-theory I gave above should be modified to include the claim that those metrical facts are provided as well. I don't want to make the definitions too technical though, and I think the current version gets the essential idea across, so I'm going to leave it as is.