(well, maybe not Jorge) (Whatever happened to him, anyways?) ;)
First, my apologies to any of Ben's Forum regulars I've left out. It's been a while, and its nice to see that the diehards are still live and kicking.
On to Wade's paradox.
There is no paradox.
Let's review the argument:
1) Tristam requires one year to record a day's worth of events
2) The past is an infinite amount of time.
3) If the past is an infinite amount of time, there is a 1:1 correspondence of days to years.
4) Therefore, Tristam can complete his biography.
#4 is clearly an inappropriate deduction because of the additional axiom you stated:
1) a) Tristam cannot write about a day before he has lived it
which implies that Tristam's experience of and existence in time is directional. #3 clearly follows from #2, but they are both unrelated to our hero's plight. Tristam experiences time in a linear fashion, and therefore exists within time, as you've defined it in this argument. It follows, therefore, that Tristam can never complete his autobiography, since his rate of completion is less than his rate of accumulation of new experiences to write about.
(Incidentally, I can't say I'd be very interested in reading the chapters about "The Writing Years": "I was writing and writing and writing and writing and writing and writing...")
There is technically no paradox in this argument. It appears to be paradoxical due to the fact that axiom #2 and inference #3 are lexically similar to the situation in axiom #1, but, clearly, deduction #4 is inappropriate given corollary 1.a).
Comments? Complaints? Dissent? Please let me know.
And, it's good to read all of your words again. Thanks, Ben!
