Yet most people in a situation of near simultaneity find it easier (or perhaps just safer?) to assume they had arrived simultaneously and come to agreement on dividing the pie 'fairly', rather than argue over who got there first.
You are claiming it is a common practice. But common practice is common practice - not necessarily "fairness". We often do things precisely because they are commonly done. One common practice which is not equal is, if two cars arrive at the same intersection at right angles, then the car on the right has the right of way. This is the common practice, and we do it because it is common practice, and it is common practice because we do it.
Even if it is not common practice, dividing it into thirds may well be apt to occur to most people. This makes it a likely Schelling point. Schelling points aren't about fairness either. They are about trying to predict what the other guy will predict that you predict, all without communicating with each other. You can use a Schelling point to try to find each other in a large city without a prior agreement on where to meet. Each of you tries to figure out what location the other will choose, keeping in mind that the other guy is trying to pick the location which you're most likely to predict he's going to pick (and you can probably keep recursing).
If all we're trying to do is come to an agreement there is no need to get deeply philosophical about fairness per se.
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What we know about the causal origins of our moral intuitions doesn't obviously give us reason to believe they are correlated with moral truth.
But what we know about morality, we know purely thanks to the causal origin. If you see no obvious connection to moral truth, then either it is purely a coincidence that we happen to believe correctly, or else it is not and you're failing to see something. If it is purely a coincidence, then we may as well give up now.