ughaibu wrote:………

in the two observation argument, the one that demonstrates a contradiction, there is another observation which is independent of the coin toss.

ughaibu wrote:If we assume that the first claim is true, then there is a time one at which the description and the laws mathematically entail all the future behaviour of two humans A and B. At time two A says "heads you buy, tails I do" and B agrees, at time three A tosses a coin that lands tails up and at time four A buys the drinks for both of them. This is an everyday situation that I'm sure any reader has been in at some time, so you know this behaviour is unproblematically possible, but more to the point, it is another example of a procedure for recording an observation, so it is required by our ability to do science that we can behave like this. In short, if we have the experimental apparatus, in this case a standard coin, and we have the recording equipment, in this case someone selling drinks and enough money to buy a round, then either science is impossible or we can toss the coin and record the result by one of us buying the drinks. [ ] Now consider a different proposal by A, "if your birthday is closer to today, I buy, if mine's closer, you buy". Again, this is equivalent to recording an observation, so they must be able to buy according to the proximity of their birthdays, or there is no science. But this entails that if they combine the methods, then the two methods must agree, otherwise one of the observations can't be recorded. Now we can cut out the drinking and simplify the experiment; if claim 1 is correct, then either there is science or we can find out which of two people's birthdays is closer to today by tossing a coin. Of course we can't do this and there is science, so claim 1 is incorrect.

You are not describing a fully deterministic universe. OK, at time four a certain person buys a round and this is mathematically entailed by the laws of science in that universe. Fine, time four is determined. But time two, in your scenario, is seriously undetermined. At time two, you are saying there are (at least) two different possibilities:

1) At time two A says "heads you buy, tails I do", or

2) At time two A says "if your birthday is closer to today, I buy, if mine's closer, you buy".

If the universe is fully determinate, then there’s no way both of those possibilities are open at time two. Accordingly, you are not talking about a determinate universe, but an indeterminate one, and your argument has no bearing on whether science is possible in a determinate universe.