Philosophy is typically "justified" by observing the world. "Justifying" tends to be a term used when you are forcing other alternatives out. However, many of the softer sides of philosophy do not force out other options, so they need less justification.
The approach of needing justification comes from science's ability to cause both harm and good. A scalpel, used properly, can save lives, or it can take them. But, no matter what it does, the effect is decisive. Thus, we need justifications to use this decisive tool, or else we might do too much harm.
The alternative approach is well described by the phrase "do no harm." Acupuncture needles are generally recognized as very safe. Science doesn't find acupuncture does any harm (it just doesn't find any good in it). Acupuncturists feel less need to "justify," in the Western sense, because whether their techniques are true or false, they aren't doing any harm. They permit time to sort out the true and false techniques. As best as I can tell (disclaimer: I am not an acupuncturist) the idea is that as long as you're not doing bad, and patients are walking away happy, and sometimes even fixed (a good thing), then you're at least doing good, and you can afford to wait to know the truthood or the falsehood of your approach.
(It is worth noting that western medicine absolutely abhors the placebo effect, while eastern medicine is more than happy to allow your mind to fix the problem for you. Much of this difference can stem from the differences in approaches.)
This is, of course, a gradient, not an easy grouping of two categories. And TCM is not even perfectly "do no harm," unless you were already comfortable spending your time and money at it. Modern Western medicine is also not entirely justified. There's plenty of cases where we pay doctors to have good instincts part way through an operation. They're not just trained robots.
However, as you start to get down towards the "do no harm" end, where justification becomes less and less essential, you find justification in more places. Sometimes, you may not even be able to put the justification into words. For many westerners, the inability to put the justification into words immediately gets treated as "having no justification." If you accept this policy, then it is entirely reasonable for philosophy to have no justification simply by justifying itself using a billion tiny details absorbed through a lifetime.
Now I am talking about philosophy in general. Western philosophy loves to justify itself all over the place, but even in those cases, you find the circular reasonings you mention. The best of these become softer, until they can be justified through living. Some of those that cannot be justified that way? Well, wars have been fought to defend a belief.