The two most prominent figures in the tradition are Thomas Reid and G. E. Moore. Reid was a contemporary of David Hume, and started a tradition of Scottish Common Sense Philosophy that lasted for over a century. Reid's works include An Inquiry into the Human Mind on the Principles of Common Sense, Essays on the Intellectual Powers of Man, and Essays on the Active Powers of the Human Mind. G. E. Moore was an early 20th century philosopher who was influential in the early stages of analytic philosophy, and is the most commonly read common sense philosopher today. Others who have been influenced by this tradition include J. L. Austin, Roderick Chisholm, and, most recently, Michael Huemer, whose web page can be found by clicking on the link to right, and who was personally responsible for my interest in common sense philosophy.
Yes. The arguments in favor of privileging common sense don't show that it is impossible for common sense to be wrong. Rather, their aim is to show that it is not possible (at least in the absence of serious incoherence within common sense itself) to ever be justified in abandoning any significant aspect of common sense. No procedure for formulating beliefs, other than refusing to believe anything at all, can possibly guarantee immunity from error. What we need to find out is what our best means available are for getting at the truth. If it turns out that even when doing our best we are still wrong that is unfortunate, but is not an objection to a philosophical method.
The reason that is most often appealed to in defense of privileging common sense centers on the nature and the structure of our evidence, or our reasons to form beliefs. When we come to know something, we do so because, in one way or another, it's truth became apparent to us. Some things, such as that there are trees and buildings, are apparent merely by opening our eyes, and paying attention. Others need to be brought into the light in some way. One common way to try to make a claim seem true is by placing in light of a set of other claims that we might think are correct, and evaluating them in light of those other claims. This is why we give arguments for views. However, in any argument, the evidence we have for the conclusion depends upon the reasons we already had to accept the premises. Given this, we can never have more reason to believe something that isn't obvious on its own than we have to believe the claims that we use in support of it. Common sense beliefs, however, are both obvious on their own and serve as a central component in what makes it the case that other things seem true to us. Given the dependence of our other beliefs on common sense, we can never have more reason to believe anything else than we have to believe the tenets of common sense. Therefore, if, in your attempts to explain things, you wind up saying things that are incompatible with them, it is always more rational to believe you made a mistake than to believe that common sense was wrong.
Common sense philosophy is a branch of philosophy that places restrictions on the legitimate results of philosophical investigations requiring such results to be compatible with common sense. It views the appropriate role of philosophical inquiry as the codification and gradual extension of our pre-theoretical understanding of reality, rather than as the development of new and counter-intuitive worldviews that would overthrow some significant aspect of that common sense worldview.
Most philosophers believe that the purpose of philosophy is to get beyond our superficial understanding of reality in order to find out what the true, underlying nature of reality is. Common sense philosophers also want to acquire a deeper understanding of the nature of reality, but they don't believe that one can have successfully discovered that underlying nature if it is significantly at odds with our superficial observations and our basic conceptualization of the nature of the world. Most philosophical methods place some restrictions on what sorts of views deserve legitimate consideration, but common sense philosophy is unusual in its insistence that cohering with our common sense view of the world is a pre-requisite for a view to be deserving of serious consideration.
The phrase “common sense,” as common sense philosophers use it, refers to a broad set of foundational beliefs that are presupposed in human discourse and action and help to make possible our ability to engage in everyday life. For example, when you want to buy something at a store, you and the shopkeeper both assume a large number of things that you would never have to actually state: that the item you are bringing to the register really exists, that you and the shopkeeper both exist, that you both have minds capable of understanding what is happening, that time will continue to move forward throughout the transaction, that the floor beneath your feet is real, that you can choose whether or not you want to buy the item, that it would be wrong for you to torture and kill the shopkeeper and then steal the item for no good reason, that you have both existed for more than five minutes, and probably a vast number of other beliefs. A fundamental, shared understanding of the world is presupposed in all ordinary human action and conversation, and the elements of that understanding are the principles of common sense. Common sense philosophers believe that if your philosophical worldview is at odds with any significant portion of that understanding, then your philosophical view should be rejected.