There are certain ideas and practices that, by their very nature, it would be self-defeating to oppose. This is most obvious when the act of opposition is itself an instance of what is being opposed. Argument, communication, persuasion and evaluation could all be examples of this. Perhaps also philosophy itself, since meta-philosophy (which would include the denial of philosophy's worth) is still, in a sense, a philosophical topic.
The sheer invincibility of philosophy is often overlooked. Various principles have been proposed which, if true, could cut much philosophy out of the picture -- but themselves along with it! Consider the thesis that there is no truth - is it true? If all truths are scientific truths, is this scientific? If all knowledge is derived from experience, when did you experience that? We ought not discuss ethics, did you say? There's no justification for epistemology? You believe in eliminative materialism? Hey, don't tell me to shut up!
Anyway, this self-referentiality is all very fun, but does it actually amount to much? Does the mere fact that a practice cannot be opposed (without thereby engaging in the practice and so implicitly condoning it) provide any positive justification for the practice? Perhaps there are inexpressible truths. Perhaps arguing really is a waste of time, even if it would be self-defeating to argue this.
I probably need to distinguish between theoretical and practical self-defeation. A principle is theoretically self-defeating if its truth implies its falsity (e.g. "there is no truth") - such principles cannot possibly be true. But other principles are merely practically self-defeating. These are the ones which cannot be advanced without violating themselves (e.g. "never argue"). But it seems they might nevertheless be true, even if no-one can ever advance them as such. Tricky.
So, if there were 'invincible ideas' that were nevertheless false, could we know it?