"Do I love her" is a hard question because there aren't that many people in the world who can answer it. I couldn't look up the answer on Wikipedia or conduct a double-blind study using a control group. In fact, I am the only person who knows whether I love my wife. You might infer that it is likely that I love her based on my behavior, but my love-like behavior might be motivated by a fear of loneliness or physical attraction or a sense of duty. Only I know for sure whether I love her or not.
Significantly, science cannot answer for me whether I love my wife. Science is really good at answering lots of questions. But it can't answer this one and it is an important question because I have to decide how to act based on my answer.
Limitations of science
One of the dangers of the post-scientific revolution era is that we might worship science so fanatically that we lose sight of its limitations. Again, science is really good at answering lots of questions and is responsible for extraordinary improvements in quality of life over the past 500 years. But it would be a mistake to believe that science is the only source of knowledge or even that it is the best source of knowledge in all domains.
Naseem Taleb points out that a major limitation of science is that it can't confirm a truth, it can only disprove a hypothesis. Until 1697, scientists believed that all swans were white. All the data supported this hypothesis. But in 1697, an explorer discovered black swans in Western Australia. This discovery conclusively disproved the "all swans are white" hypothesis. No amount of data could ever prove that all swans are white. But one instance of a black swan disproved it forever.
The scientific method is one of making hypotheses and then trying to disprove them. When we can't disprove a hypothesis, we call it a theory or occasionally, when we think it is very important, we call it a law. But science cannot prove any of these theories or laws. It can only claim that no one has yet disproved them and wait for someone else to try.
How do we know what we know?
David Eagleman is the man behind the Possibilianism movement. It is a sort of active agnostic philosophy. He claims that we know too much to accept any of the existing religious traditions, but we don't know enough to reject the idea of a supreme creator. In other words, we should entertain a broad field of possibilities that includes every possibility that we can conceive of (we are an alien experiment, we are living out God's dream, etc.) and then use the tools of science to test those possibilities.
I am intrigued by Possibilianism because it has such an honest epistemology (epistemology is a method of arriving at knowledge). Its epistemology is: We don't know much, but what we do know, we can confirm using science. It is an honest epistemology, but it is limiting.
I think most Possibilians, including Eagleman, would acknowledge that we know some things that can't be known through the scientific method. One example is love for your wife. You know you love your wife even if you can't prove it scientifically.
A valid criticism that Possibilians could make of most religions is that they do not have a coherent epistemology. I'm not an expert on all religions, but when I have asked a Protestant, "How do you know to be a Protestant?" their answer has been, "The Bible tells me to be a Protestant." If I ask, "How do you know the Bible is true?" they answer by saying either, "The Bible says it is true" or "Archaeological evidence says that it is true." The first answer is circular and is of no help to a Buddhist who does not start with a traditional belief in the Bible. The second claim is not really true. There may be historical evidence to support some or all of the events in the Bible. But there is historical evidence that supports the events in the Quran and other sacred texts. How am I to decide which is true?
The epistemology of most other Western religions is similarly incoherent or non-existant. I don't mean this to be a criticism of those religions. Many, including Protestant Christianity, teach beautiful moral doctrines. But they don't have anything to offer the rationally skeptical Possibilians because they have no way of sharing the certainty of the traditional believer.
A suggestion for Possibilians
I have just one suggestion for Possibilians and rational skeptics of all kinds: keep an open mind. That might sound like an echo of exactly what Eagleman's Possibilians are doing, but Eagleman is actually saying, "Keep an open mind to things that can be proven or disproven by science." But there are other ways to know things. Science isn't the only way to find truth.
The virtue of science is that it creates collective knowledge. I can basically trust that experiments that purport to follow the scientific method and have been published in scientific peer-reviewed journals are accurate without repeating every single experiment myself. So, step-by-step we build collective knowledge that we can share with the whole human race. But I might know things that the scientific community doesn't know.
I might know that I love my wife and children and that I find Hemmingway novels beautiful. Those are personal, individual pieces of knowledge. I can't share them scientifically, but that doesn't mean I don't know them.
Maybe one day a Possibilian will come to know something outside of the scientific method. Maybe she will be able to share it with other Possibilians (through a method we haven't discovered yet) and maybe she won't. But she'll still know.