An explanandum is an experience we seek to explain, such as the changing seasons. An explanans is a set of claims which explain the experience, such as that the earth orbits of the sun once every 365 days, that the earth is tilted by 23.5 degrees on its axis, that surfaces orthogonal to light sources absorb more heat, and so on.
An explanans must logically entail its explanandum, but not vice versa. The consequence class of the explanandum must be a proper subset of the explanans. In other words, an explanans is “bigger” than its explanandum. Claims about planetary orbits, axial tilts, heat absorption and so on, together entail our experience of the changing seasons. However, our experience doesn’t entail anything about planetary orbits, axial tilts, or heat absorption, because our experience is consistent with many explanations.
Attempting to derive an explanans from an explanandum is an ill-posed problem. Inverse optics and Gettier problems are examples of the same issue. It’s impossible to determine, from an explanandum alone, a unique solution except by prejudice or caprice. When we seek justification for our explanations, however, we must attempt to solve this ill-posed problem. That is, our experience (the explanandum) is supposed to justify claims about planetary orbits, axial tilts, and heat absorption (the explanans). But this is logically impossible.
Explanation and justification run in opposite directions. When confronted with this opposition, we can either abandon justification or explanation.
Scientific anti-realists abandon explanation. They repudiate the goal of explaining our experiences at all. They normally adopt an instrumentalist attitude toward our explanations. That is, “explanations” are merely useful tools for categorising and predicting experience, but the anti-realist assiduously refrains from claiming they are an attempt to describe anything real, out there, or beyond appearances. Anti-realists assent to no explanation of our experience, because the music cannot be explained by a non-existent orchestra, and they refuse to either affirm or deny the existence of the orchestra.
Scientific realists should abandon justification. Unfortunately, most of them want to have their cake and eat it. They understand that realism is the best explanation of our experiences, because insofar as anti-realism may be construed as an alternative explanation, it’s a bad one. That is, anti-realism says that it’s just as though our best explanation of our experience of the seasons is true (or proximately true), but actually something else altogether is true. This is a quintessentially bad explanation. The problem is not that it conflicts with experience, but rather that it includes a fudge factor. The unspecified ‘something else’ has no function except to deny the truth of our explanation, and it can be adjusted ad hoc to fulfill that purpose. However, realists also tend to crave justification, and so they find themselves arguing from a compromised position.
