### A Wager with John Lucas

John Lucas gave a talk at the Philosophy Society tonight about the nature of time. He used an argument which is the exact reverse of an argument I have recently written into my thesis. To simplify matters I’ll give the two arguments in simple bullet points.

Lucas’s argument:

1. There is evidence from physics that there are objective probabilities.

2. If there are objective probabilities, there must be a privileged frame of reference.

3. Therefore there is a privileged frame of reference.

Jonny’s argument

1. There is evidence from physics that there is no privileged frame of reference.

2. If there is no privileged frame of reference then there can’t be objective probabilities.

3. Therefore there are no objective probabilities.

If this is a purely empirical matter, then I must bend my knee to Prof. Lucus and accept his authority. But I can’t help staying on my feet a little and questioning how it is possible to understand how a privileged frame of reference helps.

What is at issue is two interpretations of probability.

Jonny’s probability: The degree of belief a wise man would have given specific knowledge of the set up.

John Lucus’s probability: If P(A) = 1/3 then A is 1/3 true.

So I have a problem with quantum physics and Lucus has a problem with general relativity. The issue is deeply metaphysical since it is bound up in time itself. The Professor’s view has the objective truth values of propositions changing over time, whereas my view has the truth value of propositions fixed for all time, but our knowledge of them changing over time. To illustrate the difference lets imagine a wager between me and the Professor.

Day 1. We fire off a space rocket that accelerates to close to light speed. Inside the rocket is a gun powder keg attached to a Geiger counter and a delay device such that if a specific range of sub atomic events happens then at noon on Day 2 the keg will explode (keg!). Using our best physics we calculate that the probability that the keg will explode at noon on day 2 is ½ . P(keg!) = ½.

The Professor and I bet on whether the keg will explode. We both endorse contemporary physics and agree that odds of 1 : 1 are fair. He bets £1 on (keg!) and I bet £1 on ~(keg!).

Day 2. (keg time) The keg explodes. A radio signal is sent back to earth.

Day 2. (earth time) The signal arrives at earth. We now know that (keg!).

Now during his talk Professor Lucas gave the advice to use one’s opponents arguments to refute them. So to avoid paying him the pound that I owe him I offer the following argument.

1. On Day 1 P(keg!) = ½ . (According to physics)

2. On Day 1 (keg!) was ½ true and ~(keg!) was ½ true. (Lucas’s interpretation of probability)

3. (keg!) has a time index as a part of its content. (keg!) means that the powder keg explodes at noon on Day 2.

4. At the time I made the bet (keg!) was not true, but ½ true.

5. So that I have not lost the bet, since (keg!) is still not true at the time that I made the bet, it is only ½ true.

In summary, although I accept that (keg!) is now true, and has been in all locations simultaneous with noon day 2 from the privileged inertial frame of reference, this does not require me to accept that (keg!) was true before this absolute time. And it was before this absolute time that I made the bet.

Should I pay John Lucus £1? If not, are quantum mechanical statements falsifiable? When I state that some future event will happen, what do I mean?

Lucas’s argument:

1. There is evidence from physics that there are objective probabilities.

2. If there are objective probabilities, there must be a privileged frame of reference.

3. Therefore there is a privileged frame of reference.

Jonny’s argument

1. There is evidence from physics that there is no privileged frame of reference.

2. If there is no privileged frame of reference then there can’t be objective probabilities.

3. Therefore there are no objective probabilities.

If this is a purely empirical matter, then I must bend my knee to Prof. Lucus and accept his authority. But I can’t help staying on my feet a little and questioning how it is possible to understand how a privileged frame of reference helps.

What is at issue is two interpretations of probability.

Jonny’s probability: The degree of belief a wise man would have given specific knowledge of the set up.

John Lucus’s probability: If P(A) = 1/3 then A is 1/3 true.

So I have a problem with quantum physics and Lucus has a problem with general relativity. The issue is deeply metaphysical since it is bound up in time itself. The Professor’s view has the objective truth values of propositions changing over time, whereas my view has the truth value of propositions fixed for all time, but our knowledge of them changing over time. To illustrate the difference lets imagine a wager between me and the Professor.

Day 1. We fire off a space rocket that accelerates to close to light speed. Inside the rocket is a gun powder keg attached to a Geiger counter and a delay device such that if a specific range of sub atomic events happens then at noon on Day 2 the keg will explode (keg!). Using our best physics we calculate that the probability that the keg will explode at noon on day 2 is ½ . P(keg!) = ½.

The Professor and I bet on whether the keg will explode. We both endorse contemporary physics and agree that odds of 1 : 1 are fair. He bets £1 on (keg!) and I bet £1 on ~(keg!).

Day 2. (keg time) The keg explodes. A radio signal is sent back to earth.

Day 2. (earth time) The signal arrives at earth. We now know that (keg!).

Now during his talk Professor Lucas gave the advice to use one’s opponents arguments to refute them. So to avoid paying him the pound that I owe him I offer the following argument.

1. On Day 1 P(keg!) = ½ . (According to physics)

2. On Day 1 (keg!) was ½ true and ~(keg!) was ½ true. (Lucas’s interpretation of probability)

3. (keg!) has a time index as a part of its content. (keg!) means that the powder keg explodes at noon on Day 2.

4. At the time I made the bet (keg!) was not true, but ½ true.

5. So that I have not lost the bet, since (keg!) is still not true at the time that I made the bet, it is only ½ true.

In summary, although I accept that (keg!) is now true, and has been in all locations simultaneous with noon day 2 from the privileged inertial frame of reference, this does not require me to accept that (keg!) was true before this absolute time. And it was before this absolute time that I made the bet.

Should I pay John Lucus £1? If not, are quantum mechanical statements falsifiable? When I state that some future event will happen, what do I mean?

Labels: Lucas; time; probability; general relativity; quantum physics.

## 2 Comments:

I found Mellor's "Probability: A Philosophical Introduction" helpful. Also, have you checked the discussion of logical probability in Swinburne's "Epistemic Justification", ch. 4? I didn't attend the talk, and I don't know whether this is relevant, but it seems that it could be.

Thanks TCG, I've gone to the horses mouth and read about the best piece on probability that I have so far encountered. It's on John Lucas's home page at http://users.ox.ac.uk/~jrlucas/reasreal/projchp3.pdf

The man is a genius.

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