To defend philosophy as a transcendental project is to defend it as a practice that is both cognitive and autonomous. By "cognitive" I mean it is an intellectual practice that seeks to "get it right" about something. By "autonomous" I mean it is a practice that does not borrow premises from other cognitive practices such as history, biology, physics, mathematics, etc.
In short, transcendental philosophy is self-grounding. As such, it separates itself from two competing definitions of philosophy: scientism and aestheticism. Scientism is the view that, in order for philosophy to become a science (to become a cogntive practice that achieves knowledge), it must become continuous with the natural sciences and analyze their concepts at a higher level of abstraction. Aestheticism is the view that philosophy is not primarily an inquiry into truth so much as it is a way of life; thus, the goal of philosophy is not to develop theoretical insight but rather to develop ourselves as individuals. What scientism and aestheticism share in common, and what transcendental philosophy rejects, is the idea that there is nothing cognitively distinctive about philosophy.
One can also contrast transcendental philosophy with obscurantism, otherwise known as mysticism. Obscurantists reject scientism or the view that questions of knowledge, ethics, and meaning are decided by natural causes, but rather than embracing transcendental philosophy, they posit supernatural causes. Agent Mulder on the show The X-Files is a good example of an obscurantist. Every episode is the same: Scully proposes a scientific, causal explanation for the phenomenon, but Mulder rejects Scully’s explanation in favor of a supernatural or extraterrestrial explanation. Some philosophers in the continental tradition are like this. One need only think of excessive moments in Freud’s theory of the drives, Heidegger’s apocalyptic claims about the withdrawal of Being, or Foucault’s sweeping statements about Power. All of these thinkers (not all the time, but at their worst) reject natural scientific explanation in favor of a supernatural One Big Thing which explains everything else.
As a general rule of thumb, whenever someone tells you that there is One Big Thing which does all this work and explains everything else, you should be suspicious that that person is succumbing to excess, either of the scientistic or the obscurantist variety. It matters little whether the person wants to reduce everything to the death drive or to laws of nature. More likely than not, that person is wrong.
In order to set philosophy down on the secure path of a science, it must have an object of study, just as physics, biology, mathematics, and history have their objects. What separates transcendental philosophy from other cognitive pursuits is that its object is not an entity amongst other entities but is instead the intelligibility of entities as such.
"What does it mean that something is an object of nature?" "What does it mean that something is historical?" These are the kinds of questions asked by philosophy that follows a transcendental path. A transcendental inquiry has less to do with entities themselves than it has to do with the conditions of possibility of our experience of those entities as they are.
Therefore, a transcendental argument is the kind that makes indispensibility claims about experience based upon insight into our own activity. But the kind of activity we have insight into is rational activity. This separates a transcendental claim from a psychological claim (one that relies upon causal mechanisms of the brain or the mind) or an ontological claim (one that relies upon the existence of some object). The transcendental philosopher claims that meaning is a condition of possibility of experience, but meaning is 1) not reducible to an "inner," psychological mechanism, and 2) not an object amongst other objects. We will deal with these two claims in turn.
1) Meaning is not an "inner" phenomenon. I do not first and foremost encounter value-neutral objects in the world on to which I impose a meaning from my mind. On the contrary, experience is de facto a synthesis of percepts and concepts, and it is only de jure that I make an analytical distinction between what I sense and what it means to me. I do not first see a white, rectangular shape, on to which I lay the concept "door." My most basic relationship to the entity is as a door, and it is only on the basis of this primary, meaningful relationship that I then dissect it into its components. Meaning is not a private matter; it is a public matter. This is one way of understanding what is meant by empirical realism.
2) Meaning is not an object amongst other objects. There is nothing contained in the bare perceptibility of an object that indicates its meaning. Rather, meaning is the relation that one real thing has to another. But a relation between two things is not perceptible in the same way that the color of something is perceptible. Color is real; meaning is ideal. Therefore, when we inquire into the meaning of something -- for example, what it is that makes a natural object natural -- we are not inquiring into something that is real or that we perceive directly with the sense. In the case of a natural object, we're asking after things like extension, substantiality, causality, universality, etc. We are inquiring into the ideal constitution of that entity. This is one way of understanding what is meant by transcendental idealism.
Transcendental philosophy goes beyond an investigation into the ideal constitution of entities (their meaning). It asks after the conditions under which we can have a philosophical grasp of those ideal constitutions themselves. This is how transcendental philosophy becomes a practice that is self-grounding and can account for its own knowledge. It recognizes that there are certain conditions that enable reflection as such, and that philosophy is incapable of passing beyond these conditions. This idea of a limit that is also a condition of possibility of reflection is called finitude. Therefore, transcendental philosophy is a practice that is cognitive, autonomous, and finite.
Transcendental philosophy is the only means known by which we may set philosophy down on the path of a secure science. The alternatives of scientism and aestheticism fail. Scientism does not recognize an autonomous role for philosophy, and aestheticism does not recognize a cognitive role for it. As an inquiry into the meaning of meaning (ideal constitution) and as an inquiry into the possibility of a philosophical grasp of that meaning (transcendental reflection), transcendental philosophy is the only way in which human reason may enter into its own element and set itself down safely upon a ground of its own creation.