Meaningfulness and Invariance

Few disavow the principle that scientific propositions should be meaningful in the sense of asserting something that is verifiable or falsifiable about the qualitative, empirical situation under discussion. What makes this principle tricky to apply in practice is that much of what is said is formulated not as simple assertions about empirical events — such as a certain object sinks when placed in water — but as laws formulated in rather abstract, often mathematical, terms. It is not always apparent exactly what class of qualitative observations corresponds to such (often numerical) laws. Theories of meaningfulness are methods for investigating such matters, and invariance concepts are their primary tools.

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