If there's a real-world definition to the Thinking function, in my mind, it's simply our ability to influence, manipulate and change the nature of the non-human sensory information we receive. Introversion vs. extraversion simply determines whether we do this best inside our own heads, or whether this is more effective by changing the external sensory data.
Back in the "Ti is not objective" thread, Ivy mentioned that this could be a decent subject. Here's my stab at it - Ti is not objective because it depends on accurate external sensory information, something none of us have because our sensory systems are wired to be "just good enough" for survival/reproduction purposes. There's also the observer effect - you automatically change the nature of the sensory information by one's own presence. This makes every bit of information we receive fundamentally subjective.
That's not a bad thing - it's just how we're built.
Feel free to offer your own thoughts on the subject.