It seems like a very 101-level question that someone like me shouldn't have, but I am actually confused.

Is there a strict, black-and-white, approximately universally agreed upon definition? I don't get the impression that there is. People seem to use the term to mean different things.

Furthermore, I get the sense that -- I'm not sure how to say this -- it's a typicality thing. That science is something for which there are more and less typical examples of.

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In How to Think Straight About Psychology Keith Stanovich writes: 

Psychology is an immensely diverse discipline covering a range of subjects that are not always tied together by common concepts. Instead, what unifies the discipline is that it uses scientific methods to understand behavior. 

The scientific method is not a strict set of rules; instead it is defined by some very general principles. Three of the most important are that 

(1) science employs methods of systematic empiricism; 

(2) it aims for knowledge that is publicly verifiable; and 

(3) it seeks problems that are empirically solvable and that yield testable theories (the subject of the next chapter). 

The structured and controlled observations that define systematic empiricism are the subject of several later chapters of this book. Science renders knowledge public by procedures such as peer review and mechanisms such as replication.

I think Keith Stanovich book is good about explaining how science works in the case of psychology. When I use the term 'science' I often speak about something that follows those criteria. I think that most people who use the term science would respond "yes" when I ask them "Do you mean the thing that Keith describes?"

One important aspect is that the knowledge itself has to be publically verifiable. A superforcaster who makes a specific forecast has knowledge but whether or not the individual forecast is right is not publically verifiable. You can just look at the overall track record of the superforcaster. As a result the act of superforcasting isn't science. 

If a meditate, I can learn in the process knowledge about myself but that knowledge can't be publically verified, so it's also not scientific knowledge. 

In the field of therapy, a therapist learns a lot of implicit knowledge about how the mind works by working with clients in a way that's not systematically organized for learning, so that knowledge also isn't scientific even if the therapist has a good understanding that he can use to guide his therapy interventions. 

The knowledge only becomes scientific if it's written down in a way where it has testable theories that allow for public verification. 

Like most common words that have been around for a long time, it doesn't have a "strict, black-and-white" definition, certainly not a universally agreed or used one.

It will vary widely based on context and audience - it's not just typicality, it's actual different uses.  And because some meanings have social status, it'll be used misleadingly fairly often, in a motte-and-bailey way, without ever really specifying either the motte nor the bailey.

If you're in a context where you need more precision, you'll have to use more words to describe the thing you're talking about, rather than thinking there's an authoritative reference somewhere that causes people to understand the full meaning of a single word.

Controlled experiments and a connected body of theory. The set-up of experiments needs to be freely adjustable to check that most particularities and circumstances of the experiment can indeed be ignored and what remains has qualities of a "natural law".

This is a strong definition, it somewhat excludes cosmology and a good deal of biology.