3. Make a list of all possible logical sentences of the form IF route 1 is taken THEN I will arrive at such-and-such a time AND IF route 2 is taken THEN I will arrive at such-and-such a time AND ...
Because the algorithm was created without including the additional assumption (used later on in the “proof”) that if route 1 route is taken, then route 2 would NOT be taken (and vice versa). If you include only that additional piece of information, then the statements generated in step 3 are “logically” equivalent to:
“IF route 1 is not taken AND IF route 2 is taken THEN I will arrive at Time” (or “IF route 1 is taken I will arrive at Time AND route 2 is not taken”).
And that (again from our route 1 XOR route 2 assumption) is equivalent to a list of :
IF route # is taken, THEN I will arrive at time
for all possible combinations of route and time, with no conjunctions at all.
Ah, so the error is back here:
3. Make a list of all possible logical sentences of the form
IF route 1 is taken THEN I will arrive at such-and-such a time AND IF route 2 is taken THEN I will arrive at such-and-such a time AND ...Because the algorithm was created without including the additional assumption (used later on in the “proof”) that if route 1 route is taken, then route 2 would NOT be taken (and vice versa). If you include only that additional piece of information, then the statements generated in step 3 are “logically” equivalent to:
“IF route 1 is not taken AND IF route 2 is taken THEN I will arrive at Time” (or “IF route 1 is taken I will arrive at Time AND route 2 is not taken”).
And that (again from our route 1 XOR route 2 assumption) is equivalent to a list of :
IF route # is taken, THEN I will arrive at time
for all possible combinations of route and time, with no conjunctions at all.