1. Color and taste are sensed directly. Gravity and electricity1 are not sensed directly, but their effects are. Examples of the third category are necessarily more abstract, but all as-yet-undiscovered scientific knowledge (i.e. knowledge that we have the potential to discover, but just haven’t yet) falls into this category. It is even more difficult to find examples of the fourth category. (Perhaps the large-scale qualities of the universe that are impossible to understand from within the universe? Everything pertaining to other universes?) However, I do think the fourth category is possible; existence is independent of observation, at least assuming a universe that exists externally from the mind. Although these phenomena could exist, there is no meaningful way to ask questions about them. There is not even much of a reason to care about them in the first place. The only reason to care would be if there was a possibility of someday sensing or understanding them, but if that was the case, the phenomena would belong to the third category, not the fourth.
2. I suppose it is possible that physics is ultimately ununifiable, or that humans are simply incapable of discovering its underlying unity, since we can only observe the behavior of the universe from within the universe. Unification would be elegant and satisfying, and it would also suggest that physics is more than a mere human attempt to force an orderly system on the universe. Since physics provides the link connecting abstract math to the day-to-day world, this relates to the old question of whether math is created or discovered. If the branches of physics could not be unified, this would imply that math and physics are systems we have imposed on the world in order to understand it, rather than inherent qualities of the universe. Whether this matters or not depends on why you value physics. While there is a certain majesty to “physics as an inherent quality of the universe,” physics as a human system for predicting the behavior of the universe is still extremely useful, comforting, and elegant in its own right.2
3. Falsifiability is important to science because ideas that would be true no matter what the evidence say very little about the world. A statement that cannot be falsified may be an empty definitional statement or logical principle. Or, it may be an observation that is so hopelessly vague that it contains no useful information, even if it pretends to be empirical. Popper himself took issue with the Marxist interpretation of history and with Freudian principles of psychoanalysis for this reason. When Marx’s original predictions did not follow through (when they were falsified), his followers reinterpreted his principles so vaguely that all evidence could have supported them in some way. This reinterpretation allowed them to avoid acceptance that his principles were wrong, but it rendered the principles meaningless along the way. The problem Popper saw with Freud was that all conceivable human actions, even those that are polar opposites, can be explained by Freud’s ideas. Because of this, there is no real way to test his ideas’ validity. Even as Popper recognized the weakness of unfalsifiable ideas, he did not dismiss them as completely meaningless, because he realized that scientific innovation often has roots in myth or non-science. To limit all thought to strictly falsifiable ideas would be unnecessary. However, it is important to realize which ideas are not scientific.
There is another type of untestable, unfalsifiable idea: those that relate to subjective qualities. Claims of beauty are not falsifiable. Neither is most of ethics. It is not possible to do an empirical test of the statement, “It is wrong to murder.” But even so, moral claims are not useless. Right and wrong may have no objective truth, but morality is an important part of being human nonetheless, and I wouldn’t want to live in a world without moral claims. Most of religion is likewise not strictly testable, but then again religion is not meant to provide scientific truth, so this is not surprising.* It is people trying to interpret religion as scientific truth that leads to irrationality, to “woman was created from man’s rib,” and so on. But just because religion is not science, it is not automatically meaningless. In all categories of ideas, it is not necessarily true that an idea must be testable to be meaningful. What is more important is a recognition of which ideas are falsifiable, and therefore part of science, and which are not, and therefore should not be treated as scientific knowledge.3
*It is true that before scientific principles were very well-developed, many people looked to religion for a kind of pseudo-scientific truth (James Ussher attempting to calculate the age of the Earth from the Old Testament, for example). However, once empirical science was created, religion and science took on separate roles, which is why I say above that religion is not meant to provide scientific truth.
1. Our sense of bodily heaviness may depend more upon the forces of structural support than upon gravity, but I can assure you (having attempted to fix my electric blanket when I was eight years old) that electricity can be sensed directly.
2. This may be as good as it gets, as there is no way to prove a certain theory is perfectly concordant with the physical universe.
3. Perhaps one can distinguish between three categories: utterly meaningless (Cat spikes on yellow hunker-down slip storm), epistemologically meaningless (God is love), and epistemologically meaningful (Yesterday was Saturday).