"This sentence is a lie." Thus, time passes by.

The arrow of time is one of the deepest fundamental mysteries in physics. Heuristically, we know that time advances with positive incremental changes in entropy. But what does this really imply about the human condition?

Update:
Thanks everyone for the feedback on the somewhat ill-defined prompt. I'd intended for it to be open-ended, but not open-ended beyond the point of absurdity.

In the first sentence, I had in mind the tendency of hypocritical statements to generate what one might call 'graded meanings' according to the number of times a contradiction is reached. The first time one thinks 'this sentence is false', and accepts it is true (false), the next implication is that it is false (true), but only in the context of previous statements (and the starting assertion.)

Most likely, no one would want to waste their time following hypocritical lines of reasoning (or at least, those that are deemed 'trivial'), but people tend to forget or lose track of the context of their assertions, and aren't always able to remember which approaches are wasteful. Discovering a paradox may be fun the first few times, but eventually (especially in old age) one might begin to wonder, 'How many times have I reached this point before?'. Because forgetfulness is inevitable (for me at least), it would seem important (again, for me at least) to approach the philosophical enterprise with utmost care.
The connection to the arrow of time and the second law of thermodynamics is through Landauer's principle, which tells us that the act of forgetting causes (ambient) entropy to increase, creating an indelible mark of the passage of time.
In a completely unforgetful world, would there be room for hypocrisy (beyond say, whatever trace is needed to characterize it fully)? Would time cease to exist at that point, or is there also a sense of time in the process of philosophical exploration and discovery (i.e. in the absence of incremental changes of entropy associated with some kind of memory loss)? (Hopefully this is more clear, and not totally unintelligible.)