Member Rara Avis
To me, the hallmark of science is predictability. If A happens and then B happens, assuming the conditions C, is the inevitable result going to be X? Using this criteria, I think the word "science" as commonly meant is too vague. Just as the Eskimo's have many words for snow, we need a bit more precision when we're talking about science.
As a start, let's break it down into three "types" of science.
Let's call science that is based on pure mathematics Hard Science. If 2 + 2 does indeed always equal 4, we can say that the predictability of Hard Science is 100 percent. Much of the so-called physical sciences fall into this category. If you accelerate a particle to 97 percent the speed of light, Einstein's equations predict exactly how much energy you'll need to apply to get it up to 98 percent.
The Soft Sciences are based on experimentation, rather than on mathematics. Your medical example, Trevor, would fall in this category. If you closely examine biopsies from a thousand ulcers and find Helicobacter pylori (H. pylori) bacterium in the vast majority, you might well reach the same conclusions Australian physician Barry Marshall did. Does that mean a biopsy is always going to find H. pylori? No. Statistically, 95% of persons with gastric ulcers, and 100% of persons with chronic gastritis have this bacterium within the stomach. The organism has not been found in healthy persons (no stomach ulcers or gastritis). No guarantees, but nonetheless a high degree of predictability.
Then we have what I tend to call the Gooey Sciences. These are based on cause and effect, but the control mechanisms of the Soft Sciences rarely exist. We simply can't open up a human brain and "see" how a person's childhood affected their personality. So, in my estimation, much of psychiatry falls into the Gooey category. For different reasons, most Social sciences are Gooey; not because we can't "see," but rather because the variable are beyond our ken. I personally believe that many, many of the things we call science today are still in the Gooey stage.
All three of these categories overlap. While much of physics is Hard, there are certainly Soft portions (the Big Bang) and even a bit of Gooey (where are those damn neutrinos?). Medicine may have turned the corner to Soft, but there's still a lot of Gooey left over from our past. And psychiatry is, to some extent, becoming Softer and less Gooey every day. The criteria, again, is always predictability.
Trevor, you hit the nail when you said, "Science and math are the tools we use to define our reality," and made exactly the point I was trying to broach. How much they define our reality depends on which category of science you're going to use in your definition.
Case in point: "Bertrand Russell would ask if that red spot on the wall which appears to you is the same spot on the wall that appears to me, and is it the same spot which you see standing up and well as sitting down?"
Red is nothing more than a specific wavelength of light, very much a Hard Science. Measuring it from different angles and distances, we can determine precisely just how red the red spot really is. It doesn't matter what you see, nor does it matter what I see. As long as 2 + 2 equals 4, we can nonetheless agree. Our realities MUST mesh.
Now, if you want to talk about what affect that red spot is going to have on your mood, we start moving into a very, very Gooey realm.