alt Hacker NewsOne can build scientific theories without rigorously defining terms: a stipulative definition is enough.
Best example is Darwin's "Origin of Species"; here, Darwin didn't rigorously define "species": 'No one definition has as yet satisfied all naturalists; yet every naturalist knows vaguely what he means when he speaks of a species.'
Many in the social sciences fetishize definitions, operating under the false notion that formulating a precise definition is the primary goal of inquiry. In reality, a robust scientific theory is a structured set of hypotheses; when combined with auxiliary theories, it derives a specific set of testable consequences.
Even within this framework, one must remain vigilant against ad hoc explanations. An ad hoc explanation fails to provide genuine systemic insight because it is engineered solely to fit the target phenomenon; it eliminates the explanatory gap by simply re-stating or absorbing the explanandum without offering any independent predictive or falsifiable power.
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I'd say that comes down to a matter of degree, and as a quibble it's certainly not a scientific theory if it's not worded sufficiently precisely to be testable and falsifiable. With Darwin it was really about where did all the variety of animals come from, and with speciation/variation being a process rather than an event, it really doesn't make much difference how one defines "species" (can't interbreed is a useful starting point). Of course Darwin was also just speculating about some mechanism of hereditability existing, so at the time this was more of a thought experiment than theory.
The trouble with discussion of "consciousness" is the sheer degree of ill-definedness - it is such a hand wavy and multi-facted concept, that it's not possible to even begin any meaningful discussion without defining a better vocabulary and breaking the concept down into pieces. Are you talking about subjective experience, mental awareness, free-will, altered state of consciousness, or what, or more likely simultaneously some mish-mash of all of the above and more!
But with "consciousness" we don't have even a stipulative definition, more like 40 different competing definitions (https://philpapers.org/rec/VIMMAT) which are in many cases only loosely related, and generally are talking about very different things. When the situation is this bad, I am skeptical you can make scientific progress.