Most people don't realise this - but the methodologies we use for ... project management ... are quite remarkably influenced by philosophy:
From the late 1800's to about the 1980's and 90's a philosophical paradigm known as Positivism dominated almost every aspect of thinking and shaped many of the ideas we have about how things should be done today. Positivism is grounded in empiricism and the idea that reality is an objective thing. In a project management context this would lead to thinking as tasks and user requirements as things that can be defined absolutely. You can see that the waterfall method would be a natural response to this paradigm of thought.
Interpretivism started in about the 1920's but really only managed to get serious recognition in the last couple of decades. This philosophy is based on the idea that reality is not absolute - its in our minds. This paradigm recognises that our perception of reality changes depending on the circumstances we are in. In our world - this means that users perception of reality IS reality and that reality therefore changes as users circumstances change. You can see that agile is much more aligned to this way of thinking.
The trick though is to find the middle ground between positivism and interpretivism. Both are right: realities such as budgets are absolute, but realities such as user expectations are not. The ultimate trick in all of this is not to force rigid adherence to a primary scope of work, but rather to help users and stakeholders to shape their expectations to fit the budget and the reality that is evolving in their minds as the system is being developed.
Well I found it interesting anyway. This also reminds me of the Wind and Sun Aesop's fable
The North Wind and the Sun were disputing which was the stronger, when a traveler came along wrapped in a warm cloak.
They agreed that the one who first succeeded in making the traveler take his cloak off should be considered stronger than the other.
Then the North Wind blew as hard as he could, but the more he blew the more closely did the traveler fold his cloak around him;
and at last the North Wind gave up the attempt. Then the Sun shined out warmly, and immediately the traveler took off his cloak.
And so the North Wind was obliged to confess that the Sun was the stronger of the two.
The moral was stated at the end of the fable as: Persuasion is better than force. The history of project management has focused on imposing more and more process and up-front planning and forcing the project to comply with the initial plan. Newer agile techniques have focused on persuading the project to a conclusion, through constant adjustment to changing requirements, collaboration of project team members, and ensuring developed (rather than planned) functionality meets business expectations.