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Consider these sentences, please:

  1. A bicycle can be defined as a two-wheeled vehicle propelled by human energy.

  2. A bicycle is defined as a two-wheeled vehicle propelled by human energy.

Q1) Does the "can" in (1) suggest, as opposed to sentence (2), that the "definition" is newly created by the writer (their own opinion), and is understood not to be a standard one used by other people?

Q2) Can I replace the "can" with "could" or "may"?

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    It would be more exact to say the "can be defined" would mean this is an acceptable definition for the purposes of the discussion, which likely will cover more of the topic. It can be the most or least common definition, or even an opinion, but we can't tell which by the context. I didn't put this as an "answer," because I don't know if you can use "could." But "may" is acceptable. Apr 20 '21 at 18:10
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The answer to Q1 is no.

The question of which verb combination you use comes down to context. The choice is likely to depend on what the author wants to say.

Examples:

Most dictionaries would agree that the bicycle is (generally defined as) a two-wheeled vehicle propelled by human energy.

Most dictionaries would agree that while the bicycle can/may be defined for most purposes as a two wheeled vehicle, there are also three-wheeled bicycles in existence. So, strictly speaking, bicycles should be defined simply as wheeled vehicles propelled by human energy.

On the other hand, some bicycles are now either assisted or driven by battery power, which requires them to be redefined as wheeled vehicles that are driven either by human propulsion and/or entirely or partly by battery power.

And so. You choose the combination that fits the purpose of your sentence.

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    In the academic literature, I often see "can be defined" or "can be expressed," possibly to avoid a reviewer reacting to "is defined" with "Well, I don't define it that way." It sidesteps the issue of what the correct definition or expression is and lets you know how the author is choosing to define or express the point of interest. "Here, we define [or express]" achieves the same goal. Apr 21 '21 at 20:35

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