Counterintuitively, defining big "profound" ideas like life or consciousness is easier than defining everyday objects.
Bowls are for soup, right? Okay, [bowls hold liquids].
Is a cracked bowl not a bowl? Is a bowl in orbit not a bowl? Is an overturned bowl not a bowl?
Okay okay, what about a bowl shape?
Now you have a sorites paradox. At which coefficient of curvature is the bowl not bowl-like enough? Is a plate with a lip just a very shallow bowl? How is a cup not merely a slightly atypical bowl? There's no inflection point here, making it all arbitrary. Mountains are merely very incompetent bowls?
Okay okay okay, descriptive definition: things that are called "bowl" are bowls. Know it when you see it, right? Now whether a bowl is a bowl depends on time and place. It depends on who you're talking to or how you select your reference average. Ultimately you are speaking to distinct individuals who will or will not agree any particular phenomenon is a [bowl].
It turns out humans actively silo-ize their artifacts so they don't have to invent new in-between words. Cultures will have typical bowls and avoid the grey in-between zones so they don't have to think about it.
Individuals have a finite vocabulary. Every new in-between artifact needs a new word, which takes a word away from something else, which is likely a non-in-between entity.
Likewise, the space for remembering distinctions or holding them in conscious attention is sharply limited. The handles are of distinctly finite size, and it's not that small.
However, it's important to remember these things are artifacts of non-boundless cognitive power. Although it's good enough as long as you aren't working at high energies or in the grey areas, there isn't really any such thing as a [bowl]. It's a handle, not the thing itself.
A truly precise definition would have sub-atomic precision, but all artifacts decay over time; this definition would have exactly one member, at exactly one moment in time, and then it would shift away and have zero members for the rest of time.
Ultimately, names are just tags. It doesn't matter exactly how you define "bowl," but it's necessary to define it for the purposes of discussion. Handles are not the thing itself, but nevertheless you need a handle. You don't need to know what everyone else means by "bowl" but you do need to know what you yourself mean.
The bowl-like things in reality aren't really [bowls] but they are really something, and you can group them into a category that doesn't vary within the limits of mortal perception. If you can't see the difference even indirectly, it doesn't matter to you. There are, as a matter of fact, a bunch of instances of curved flatware which hold liquid enough to make soup consumption convenient. ("But what's a soup??!?")
Logic can be used to learn many non-obvious things and it's cheap. No billion-dollar supercolliders here. However, it's necessary to know which things, exactly, you're learning about. Use explicit verbal definitions. Invent a new word, or assign a jargon definition to an existing word, use it until you're done learning, and then discard it. Write it down with the proof so you don't have to keep all these artisanal ideas in mind.
You want to think about things because logical thinking is extraordinarily powerful. E.g. Logical thinking about emotions, a.k.a. Stoicism, grants near-total psychological self-mastery. Definitions allow you to think without your train of thought skipping a track. Or rather, you still skip a track, but then you notice and fix it, rather than being unable to think in straight lines. Compounded because the result in cached; the engine doesn't run down the track again, it links the start and end points and skips all the middle. This is a problem if you've committed a fallacy in the middle. E.g. when doing math it's easy to accidentally divide by zero without noticing; you don't know that A = 2B yet, but you divide by (a-2b)...
Find the phenomena you wish to think about.
Try to find words that create a category fencing off the phenomena.
Try thinking with this definition.
It probably doesn't work, so try again until it does.
Meanwhile, you learn about how words and events relate to each other.
You learn more about the words that didn't work than about the words
that did. You likewise learn more about the sense-perceptions you
accidentally roped off than about the ones you roped off on purpose.
P.S. With practice it's easy to re-construct definitions on the fly. I keep the dictionary definition in permanent memory, then add perturbations to match whatever is being locally used in a particular time and place. Dictionaries are more than good enough most of the time - I checked by independently deriving wide-scope average definitions and I find it matches the dictionary to like three nines or something like that. The method is not overly labour-intensive and highly consistent and reproducible.
Having tried tens of thousands of definitions, I can instantly tell when someone is using a divergent definition. I'm experienced with the hallmarks of divergence.
That said, in general the dictionary definition, although accurate as far as folk
cognition goes, will be noticeably broken with regards to the actual
phenomena. E.g. gathering together fish and whales. Okay they're both
fish-shaped, but this commonality is only relevant for fluid dynamics...
Average folk suffer tremendous cognitive privation, and must commit
these solecisms more often than not to conserve scare mental resources.
Every time they're taught the distinction between fish and manatees or between tomatoes and vegetables, a distant distinction dies untimely. They forget the difference between bullying and retribution, or between feast and holiday.
P.P.S. As a functional matter, the brain defines things using a type specimen and a perturbation threshold. There is one ur-[bowl], working exactly like Plato's forms except it's entirely personal and idiosyncratic instead of some external universal, upon which is added some tolerance for deviation. Within the limits of mortal perception you can in fact exactly match the definition of [bowl], it's just that it will match exactly one person's definition. If you wanted you could measure everyone's deviation tolerance and find they're all different with weird divoted coastlines.
P.P.P.S. The serious part about the soup joke is the fact that if you're doing proper logic you really do need to go all Socrates, question everything, and define every term. Later you might find you've defined bowls that aren't bowls if they're upside-down. The proof will still be valid, but it will perhaps not be on the topic you wanted it to be. Then go back and try again using a different definition until you're talking about the phenomenon you're interested in.