When we say what applications philosophy has then I think the missing word is “practical” — practical applications, and this draws us to the distinction established by Kant if not earlier between Practical and Pure Reason. (http://en.wikipedia.org/wiki/Critique_of_Practical_Reason) I recently wrote about this in my last chapter of my dissertation at http://about.me/emergentdesign. Practical reason in the Greek world was called Metis (http://en.wikipedia.org/wiki/Metis_(mythology)). Odysseus had metis as his singular quality (http://depthome.brooklyn.cuny.edu/classics/course/ingenuity.html). It tended to have the meaning of trickery. But Kant raised the question to a higher level as meaning to excel at the practical arts but also considering ethics as the epitome of Practical reason. Pure reason had to be reigned in, but practical reason is useful. The person who in modern times explored this question in the most interesting way is P. Bourdieu in his logic of practice . . . and other relevant books pictured here. (http://en.wikipedia.org/wiki/Pierre_Bourdieu)
This is his ground breaking book on Practice and how it is different from Theoretical reason’s understanding, and basically about how it is a black box which we cannot see into.
This book is a summary of his position on Practice.
This book is basically a rewrite of the Logic of Practice, seemingly meant to just sell more books, no substantive difference.
He was concerned with the question that Levi Strauss raised in Structuralism which was how cultures can produce structural pattens and not be aware of them. There is clearly a distinction between Theory and Practice, and practice can produce structural patterning that escapes our knowledge but exists, like in the relation beween Kinship patterns and village layout.
But the wonderful thing is the answer M. de Certeau (http://en.wikipedia.org/wiki/Michel_de_Certeau) gives to this question. (http://en.wikipedia.org/wiki/The_Practice_of_Everyday_Life)
de Certeau points out that there is practice in the art of narrative and that we can get insight into other types of practice though the rhetorical and stylistic practices within narrative composition.
So what Certeau is saying is that Practice is not a completely black box as Bourdieu believes.
Whether philosophy has an application depends on how we take this relation between theoretical reason and practical reason, because anything which ‘an application’ must the the result of practical reason. But basically the way things have gone since practical reason was basically ethics and crystal clear as application of rules to behavior, until recently practical reason became more and more opaque to theoretical reason. Then Certeau made that a grey box rather than black by noting that narrative, by which we explain practical behaviors itself has it own rhetorical and narrative and stylistic devices. And since we can understand narratives, we must get some insight into practice from by seing how these stylistic devices are used.
For Plato, and his version of Socrates, the practical application of philosophy was civil life of the man of leisure in the interaction with others in the politics of the city. Socrates gives us many narratives with dramatic settings, historical characters, and plenty of rhetoric, irony and other tricky devices such as the use of made up myth. So from Certeau’s point of view the practice of philosophy would be seen in these stylistic, rhetorical, and tricky ways that Plato uses dialogue to express his opinions though the voices of others. The one thing you can be sure of in a Platonic Dialogue is that Plato is not saying directly what he believes, but he is presenting us endless veils of irony to indirectly indicate what he might believe, but one can never be sure. Thus if we take Plato as the guide in this the application of philosophy would be elevated civil discourse among equals searching for the truth together in a dialectical form of discourse. But actually we see little of that and much more pontificating by Socrates, or the Stranger, or the Statesman or the Sophist . . . See John Sallis Being and Logos fur the most accessible introduction to this side of Plato. In someways the forging of a civilization by civil speech in public seems to be Plato’s idea of the application of Philosophy (the love of wisdom) but it is also the elevation of the soul and the giving of laws to society, organizing society for the human good. Since it is a narrative from Certeau’s point of view, we can have insight into that practice via the rhetorical, stylistic, and twists and turns of tropes that appear in the dialogues.
One good source of some insight into this is Alan Blum’s books on Theorizing and Socrates.
My belief is this. The application of philosophy is the way that it changes the way you look at the world and the way in which it helps to understand the worldview in which we find ourselves living. The structures of the worldview are incredibly ancient at the level that Philosophy understands them. And this understanding is quite different from our everyday understanding from the naive point of view within the lifeworld. We have just forgotten so much, about our own worldivew. It is a great mystery to us, what seems so mundane and ever-present and real. But there are features to the worldview that have persisted for a very long time in spite of new facts, novel theories, disruptive paradigms, shattered epistemes, smashed ontologies, pulverized existences, and obliterated absolutes. There are certain things that all the emergence that has occurred in our worldview has not changed like the meta-levels of Being for instance. They were there in the vedas as the difference between the Gods, they survived in mythology, and they were known by Plato, and finally they were rediscovered in continental philosophy. Knowing that the world has stair steps to nowhere through kinds of Being completely alters the view of the world. Knowing that Nihilism is the fundamental thing produced by the worldview, and that is so that it can have its nihilistic opposite emergence recognized when it occurs. But that emergence does not change the basic structure of the worldview in the slightest even though it changes everything else. To know that myth preserves these ontological differences and makes them accessible though its stories offering a handbook to the worldview. Knowing that every novel operates within these constraints. There is always Author/Reader//Character/Narrator, just as there is always Heaven/Earth//Mortals/Immortals. The entire worldview is laid out for us to read, but we cannot see it because we are looking at things, not at Being (Sein), less well at Beyng (Seyn). The structure is found in the Old English (Anglo-Saxon) structures of Being verbs. It is found in the Philosophical Principles discovered by Peirce and elaborated by B. Fuller. And it is ensconced in the great philosophy books of our tradition, such as those of Plato, Aristotle, Descartes, Leibniz, Spinoza, Kant, Hegel, Husserl, Heidegger, Merleau-Ponty, Sartre, Derrida, Deleuze, Bataille, Baudrillard, Zizek, Badiou, etc. Continental Philosophy rediscovered this deep structure of the worldview lost in our tradition in our own time. Thus we live in a renaissance in which we finally can have some insight into the our worldview which is dominating globally, really for the first time in thousands of years. It is like when they found the rosetta stone, or they could translate Mayan or Cuneiform of the Sumerians, or the text of Ugarit. Whole worlds opened up to us, just as we are destroying world and languages throughout the globe, if not the viability of life on the globe itself. People read fake mysteries like those of Dan Smith and get all excited, but are missing the greatest mystery adventure of them all, which is here right before our eyes and effects everything in sight within the world. Anyway it is an available intellectual adventure for any that are up to the challenge. I really believe that in my works I have only scratched the surface of what is available now that we can read the kinds of Being as meta-levels in the worldview, and thus in all phenomena in our lifeworld around us, including in the depths of our Self, because what are we but a reflection of our worldview.
So for me the application of philosophy is finally knowing something significant about our selves and the worldview which all who live on the earth should be interested in because though colonialization and globalization it is affecting everyone on the planet profoundly. We should know something about it, and perhaps if we did we could limit in some way its greatest excesses and perhaps save ourselves and some of the other species we are killing off at such an alarming rate. This i an intellectual adventure on the scale of an Indiana Jones spectacular but which everyone can participate in because of the plethora of open questions that abound once we get a glimpse of the structure of the worldview.