heart before head: the time travel problem

In mathematics, if you can prove that a statement leads to an inconsistency (or erroneous conclusion), then the statement must be wrong. Bertrand Russell, a giant of mathematics and philosophy, gave a colorful example of this.

During a popular lecture Russell explained that any statement can be proved, given a single inconsistency. (A standard remark in logic)

A heckler shouted:
Then I give to you that 2 times 2 equals 5.
Now prove to me you are the pope!

Russell: Well, subtracting three from both sides, we have two equals one.
Now my dear Sir, you agree that the pope and I are two:
therefore the pope and I are one!"

So, since Russell is not the pope, then two times two doesn't equal five, and two doesn't equal one.
Easy. So why do people not apply this when it comes to time travel?
Time travel leads to clear paradoxes and inconsistencies. If you know the effect before you perform the action, you can change the action: a clear contradiction.
Choose your poision.
1) Marty McFly traveled back in Hollywood time (in Back to The Future), and accidentally stopped his parents from marrying and having a child. He spent the rest of the movie trying to undo the error.
2) if I go back to the time of Isaac Newton, meet him, and give him the theory of gravity, where did the theory of gravity come from?
3) if I go back in time one hour and stop myself from traveling back in time (by, say, locking myself in a room), what happens to me?
and so on. Essentially, we've arrived at a point where 2=1. Therefore, the premise - time travel - must be false.

This has not stopped John Cramer, a physicist at the University of Washington, from trying to get funding to run an experiment to see if time travel exists. The idea is to extend what Einstein called "spooky action at a distance" to happen in fibre-optic cables. If so, then the information could arrive before if it is sent. There have been calls for NASA to fund this experiment .
But as Darnell Clayton of colonyworlds.com said, If NASA ever funded a project like this, I would vote for its removal as a governmental agency.
Why do we persist in dreaming of time travel, when first, there is no evidence for it, and second, it is logically impossible?
The reason is memory. The world of the past seems so real to us, it seems like a place we could visit, if only we had the vehicle. There are people, and events, and places, that we experienced and saw, that seem to us like they are in a distant land.
The way we remember leads us to believe in the past as a place, like another country, rather than a time. Travelling in time for a mere hour, as in my example above, or forwards a few days (as in the Philip K Dick story, A little something for us tempunauts), seems strange and bizarre. In fact, traveling a small distance in time seems more bizarre than travelling to a far away time. That's because nearby times, near future and near past, are more correctly represented in our heads as times, not places.
No matter how much evidence there is against the possibility of time travel, people will still believe it is possible.
It's easy to imagine, and it sounds like fun.
And the Pope and I are one.