Well, having a good bash at that particular problem. Not sure if Russell and Whitehead actually succeeded.
"Work is of two kinds: first, altering the position of matter at or near the earth's surface relatively to other such matter; second, telling other people to do so. The first kind is unpleasant and ill paid; the second is pleasant and highly paid."
How does programming fit into this? It feels a bit in-between. On the one hand, you tell the computer what to do, in a way that feels similar to Type 2; on the other hand, you actually have to do the work of programming, which feels much like Type 1, except you're not moving physical matter around, but stuff in 'concept space'.
In all seriousness, I've long thought of what I do as moving electrons around, getting pits onto CDs in the right place, things like that. Whatever I do in, say, C++-land, is a means to those ends. An intermediate step. I arrived at that way of thinking after trying to define 'work', and deciding that it always consists of moving matter around (transporting it, putting it into a desired configuration).
Interesting conclusion. However, notice that most of the energy (in thermodynamical sense) in this "work" is not spent on moving electrons in the computer around, nor even in the C++-land, but in concept-space. We do our work by building castles in the air out of abstract mental structures, and only then we formalize it in code that moves electrons around.
When I look at the end results of work, I come to the same conclusion that indeed it ultimately consists of reconfiguring matter. That's what we need to do to reach whatever goals we have. Maybe the conceptspace work maps to the levels of intricacy of the end-result matter configuration, i.e. the more complex, precise thing you want to get, the more energy you need to expend on thinking rather than arranging atoms. It's easier to move a ton of bricks from one place to another than to design a microprocessor.
So I guess that ultimately I agree with your comment.
I disagree. What programming is doing is "telling [something] what to do." The difference is that instead of telling people what to do, we are telling inanimate idiots what to do, and therefore it is not necessarily pleasant, and highly pedantic.
The output of a programmer is the output of their mind, not of their muscles. I've stacked boxes in a warehouse and that sort of work is altogether different from telling transistors when to output a high voltage instead of a low voltage, which is fundamentally what we are doing when we are programming.
Which is quite significant I would say. Suddenly we can no longer talk about what is objectively true and false, only what is subjectively useful. That last sentence is of course also neither objectively true nor false, just like this one. See it's a mess :)
It really depends on what is meant by "objectively true or false".
You're right that some statements within a formal system are true or false.
However, the theorem does imply that the behavior of the "world out there" (and any explanation of it) is either contradictory or not following a fixed set of rules.
So yes, we can state something to be "objectively" true or false but only if we're willing to use a contradictory explanation - which we usually are in the name of usefulness, not in the name of "absolute objective truth".
Notwithstanding that small matter of formally defining the logical foundations of all mathematics.