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Word of the Day: Theory and Law

A novel of Christian apologeticsLet’s start with a few definitions within mathematics and logic. An axiom or postulate is a proposition (statement) taken as a given. A lemma is an intermediate proposition or stepping stone rather than the final result, which is a theorem. A corollary follows readily from a theorem—it’s often simply another way of stating the theorem. Lemmas, theorems, and corollaries are all proven, but proofs are only possible within mathematics and logic, not within science.

By contrast, all scientific statements are provisional. A scientific hypothesis is a testable explanation for a phenomenon. It explains and predicts. Once a hypothesis has proven itself, it becomes a scientific theory. A scientific law is a description of a natural phenomenon, often an equation. Laws and theories are both well-tested, widely or universally accepted within the field, and falsifiable. The main difference is that a theory explains while a law describes.

For example, germ theory, quantum theory, and the theory of evolution are explanations. Boyle’s law, Ohm’s law, and Newton’s law of gravity are all descriptions (and are all equations).

A common misconception is that scientific hypotheses mature to theories, which mature to facts or laws. Instead, facts (the observations from an experiment, for example) lead to hypotheses (a plausible but immature explanation), which lead to theories (well-evidenced explanations). In the category of scientific explanations, a theory is as good as it gets and it doesn’t graduate to become a law.

Photo credit: Marvin (PA)

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About Bob Seidensticker
  • RandomFunction2

    Hi Bob,

    All UNIVERSAL scientific statements are provisional. But some particular scientific statements are definitive. Here is a scientific statement: some gorillas have a self-awareness. It is not provisional, it is definitive. At least as far as the methods of observation and interpretation are reliable*. It is definitive because it is modest. It could not be disproven by a counterexample, or even by lots of them.

    * Actually, researchers left an odorless spot of yellow on a gorilla’s head, so that the gorilla could not see it by himself. And then they showed a mirror to the gorilla. The gorilla detected the spot on him. He knew that the one he saw in the mirror was not another gorilla, but was himself, and that’s why he was able to find the spot.

    • Bob Seidensticker

      I see this distinction … but isn’t it possible that the conclusion of this experiment would be reinterpreted? For example, “We were wrong–what we thought was gorillas being self aware was really X” vs. “We were wrong–Newton’s Law of Motion doesn’t always apply.” The latter sounds less likely.

  • RandomFunction2

    Hi Bob,

    Still, if you start with a universal scientific statement which is, as you stress, provisional, if you manage to disprove it, you get a new statement which, though more modest and limited, is a proven truth. In logic, we say that the contradictory opposite of “All X are Y” is “some X are not Y”. So that either of these statements HAS to be true.

    Let’s take a better example: “some nonhuman animals practice infanticide”. It’s a proven statement. It will never be disproven. The theory that attempts to explain this statement, sociobiology, may be disproven, though.

    • Bob Seidensticker

      I tend to agree, but I think this could be quibbled with as well. What if we find out that this “proven statement” comes from researchers whose work is later discovered to be fraudulent? If they’d claimed cold fusion, their work would’ve been scrutinized, but this infanticide conclusion didn’t raise any alarm and so was not duplicated (in my imaginary example).

      Sounds to me like we’ve moved to the domain of “facts”–that is, the fodder from which hypotheses and then theories come from. For example: “I dropped a ball and made these speed measurements” would be a fact–a simple observation.

      You could overturn a theory, but you probably wouldn’t “overturn” a fact. You might say instead that the equipment malfunctioned. In other words, your original fact mistakenly lacked the qualifier “Using the lab’s Acme oscilloscope” or whatever.

      I think we’re in agreement on the interesting things and are parsing definitions now.

      • RandomFunction2

        Hi Bob,

        Yes, a fraud or a gross mistake are theoretically possible, especially when the stakes are high (genetics and IQ, the paranormal, gender, etc.). Scientists are not gods.

        If you take things in that sense, few things beyond everyday experience remain certainties.

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