What 1 philosophy do most conservatives adhere to? Also, what 1 philosophy do most progressives adhere to?
Good question. I have thought about this myself. Let me offer an answer which may seem cryptic and a little overly abstract and philosophical. But then I will try to offer an explanation: Conservatives believe in ultimate truths and final ends. Liberals believe in method over final ends.
OK, so what does this mean? To answer this, think about science. In science, many people think that the enterprise is involved in finding final answers about facts and truth. This is certainly true. But the emphasis is on method. No matter how well established a certain Scientific principle, if the proper observations, logic, and methods are pursued to question those conclusions, science will go in that direction. There are no final, fixed dogmas or unquestionable, sacred foundations. All is open to question, provided that the proper methods are used to do so.
Conservatives, on the other hand, believe that certain things are final and sacrosanct. This usually involves appeals to notions of habits, culture, traditions, "commonsense" (which is nothing more than just the kind of worldview that one has happened to grow up with). These are often seen as the best, with appeals to "The wisdom of the ages" to shut down further questioning of what they see as common sense foundations.
A good example of this, in my mind, was the idea that the earth is the center of the universe vs that it goes around the sun. When Galileo suggested that the earth is not the center of the universe this in the 1600s based on observations he had made , it went against religious dogma that had been taught by the church for 16 centuries. There were lots of scripture that they used to support this. And besides, where else would God put the culmination of his creation, man, right? It was the commonsense belief of the whole world up to that point, of course, projected as usual to notions of commonsense and eternal truth. When Copernicus and Galileo made observations which seemed to contradict that idea, it rattled the church. They almost burned them alive at the stake for daring to make such a counterintuitive claim. The church only accepted the idea that the Earth goes around the sun, not vice versa, in the 1820s- about 200 years later! They only forgave Galileo for this "heresy" only in the 1990s!
Liberalism, and of the European enlightenment in general, was based on this idea that we do not know ultimate truth, and can probably never know them. But that's not what's important. We can make progress by admitting our ignorance of such ultimate truth. But rather than leading to nihilism, as conservatives sometimes fear, this led to endless and restless questioning and search after better ways of seeing and doing things. It led to debates and thinking. This kind of approach has been found to be very fruitful not just in the sciences, but in the area of social policy as well. Why should we continue with slavery? Why should women not be allowed to vote? But do we think that those things the ultimate moral truth now? No. We can never make that claim, just like we can never make ultimate claims on any scientific conclusions. We liberals are always open to better ideas, and better logic. But until you can provide us with those, we can be quite dogmatic about what we feel is progress.
Hope this helps.