Is Philosophy Useless?

Oftentimes I hear that "philosophy is just navel gazing; it doesn't have any progress like science. Look at how science has cured diseases and put us on the Moon! Philosophy has never achieved anything like that! So philosophy is useless."

There are at least two problems with this viewpoint. For one thing, it assumes that philosophy is a sort of competitor to science. But they are not competitors any more than science and art are competitors. "What has art achieved compared to science?!" would be a ridiculous question. Science and philosophy are working at different things, with philosophy asking the more abstract questions that go alongside science. And this leads into the second problem:

In order to say that philosophy is useless, you must...

• Define "useful" and "useless". In order to define these, you must...
• Explain why we ought to value X rather than Y. In order to explain this, you must...
• Engage in value theory, wherein you theorize about what what type of knowledge and projects are valuable, and why we ought to strive for things that are valuable. But to engage in knowledge and value theory you are...
• Engaging in ethics and epistemology. To engage in these you are...
• Engaging in philosophy, which is allegedly useless.

So in order to say that philosophy is useless, you must engage in philosophy, which is useless.

So the statement "philosophy is useless" refutes itself. It is either false, or if true then it renders itself false. So it can't be anything other than false.