After introducing luck in general, Dr. James then tried to define luck. For example, an event is lucky if and only if it is lucky for some people (or subjects) and potentially unlucky for some people. Lucky events are either good or bad for a subject. In other words, lucky events have valence. Valence just means that lucky events are always either lucky or unlucky for someone and that lucky events are always good or bad for someone. In addition to valence, lucky events must also be beyond a person's control. Events that a person has full control over are not lucky events.
Latus thinks that such a definition of luck is insufficient. He came up with some counterexamples that fit these criteria but are not instances of luck. For example, the sun rises every day is a good occurrence and it is beyond our control, but it's not lucky. Another example is gravity. It's good for us that we don't just drift out into space, but we're not lucky that gravity exists.
In response to Latus, someone might say that luck requires that the event is an accident that was unintended. This addition to the definition of luck is also problematic, since winning the lottery is a case of luck but winning the lottery is not unintentional. A person wants to win the lottery when he or she buys a ticket.
Another attempt to improve the definition of luck is to say that lucky events are matters of chance. However, there is another counterexample to this definition. For example, there may be a forecast for a 90% chance of rain tomorrow. But if it does rain tomorrow, this is not a result of luck.
Someone might try to further refine the definition of luck by saying that lucky events are events that had a low probability of happening. Only things that happen "against odds" are lucky. But consider Russian Roulette, a game where a gun is loaded with a single bullet. A person who plays this game has a low chance of dying (1/6) but this person is still lucky to be alive. In spite of the fact that there was a high probability that the person would live, we still say that a person is lucky to survive Russian Roulette.
Yet another improvement of the definition of luck is to say that an event is lucky if the person who experienced the event was not in a position to know that the event would occur. If a person does not have evidence that an event will occur, then perhaps these events are lucky. But imagine this counterexample: imagine that some all-knowing entity, such as God, a superphysicist or a psychic, tells you that you will win the lottery. Although you expect to win the lottery after hearing this, it is still a matter of luck that you win the lottery.
Still a different definition of luck is to say that an event is lucky if the event did occur but could easily have not occurred. In other words, if circumstances were only slightly different, then the event would not have happened. A counterexample to this is a case where a person is born with a terrible genetic disease. It is not possible that this person could have been born without the disease. He or she could not have easily been born without the disease, yet this person is unlucky to have the disease.
Rescher wants to draw a distinction between luck and fortune. Perhaps getting a disease is unfortunate, but because it happens in the natural course of things, it is not unlucky. Another example is that a person may be fortunate to be born beautiful, but he or she is not lucky. Rescher thinks that fortunate things happen in the natural course of events but lucky or unlucky things somehow happen outside of the natural course of events. For example, having a cold is unfortunate but having a cold on the day that you happen to have a final exam is unlucky. Or being born ugly is unfortunate but being born ugly in a family full of beautiful people is unlucky.