Asking "and how do you define...?" is often unnecessary and unreasonable.

Up until just several years ago, I believed that a discussion can't really be meaningful if a critical term in it is not defined. For example, if I heard a debate about free will I would often think: why don't they first formulate a clear definition of "free will" so that everybody's on the same page on what they are talking about? Maybe once they agree on a specific definition their disagreement will evaporate.

I wasn't completely wrong there, but I now realize there is something I was missing. And here it is: 

In many cases it is unreasonable and unnecessary to define terms. It is perfectly possible to have a meaningful discussion without formulating, or even being able to formulate, a definition of critical terms.

Rather than giving a long comprehensive (and probably sleep-inducing) defense of this thesis, I'll just give you one example - I think it'll be enough to illustrate the point. We can agree, I'll boldly assume, that we can have a meaningful discussion about dogs. But try to formulate a definition of what a dog is, it's not so easy, in fact pretty darn well impossible!

I know you are probably very dubious at this point, you may think - how can it be impossible to define such a simple concept as a dog, something that even a three-year-old easily understands. Well, suppose for a second that I am wrong, and there is a nice and clear definition of a dog. But you would probably still concede that:

(a) a three-year-old, or even a seven-year-old child probably wouldn't be able to come up with such a definition,

(b) yet, this same child is perfectly capable of meaningfully talking about dogs - two children talking about, for example, what sounds dogs make aren't just talking meaningless jibberish!

If you agree with (a) and (b) then you already hopefully see that my thesis is correct, even if you disagree that a smart adult can't define a dog. But to strengthen my point, let's in fact see whether I am wrong about that. The easiest way to do that is to see how a dictionary tries to cope with this task. I'm going to do this: I will google "dictionary definition of dog" and use whichever one comes up first. I haven't pre-screened the results before writing this, I promise.

And here's what comes up, this definition is from Oxford languages:

A domesticated carnivorous mammal that typically has a long snout, an acute sense of smell, non-retractable claws, and a barking, howling, or whining voice.

But that's a terrible definition! It's no definition at all in fact - a definition must provide a necessary and sufficient condition for being a dog, but this "definition" provides neither. In simpler terms, there's no way to use this definition to adjudicate whether something is a dog or not.

That doesn't prove that some other definition couldn't do the job, of course. There's no way for me to survey all possible definitions, so I am relying here on your intuition. The fundamental point is that the way we decide whether a certain label, such as "dog" or "chair", applies to some entity is actually extremely complicated and cannot be summarized in a text of any reasonable length.

One fun fact to help you appreciate how complex an algorithm in your brain is for adjudicating "dog-ness" is that for the longest time extremely sophisticated AI algorithms could not reliably do what any two-year-old can do with no effort - reliably distinguish a dog from a cat. Rule-based algorithms are powerless here, there's simply no set of simple rules that can do that - the task is performed through extremely complex pattern recognition. Only in the last few years large multi-layer neural networks became reasonably successful at this benchmark computer science task. Neural networks are notoriously inscrutable - they can be trained to do amazing tasks but there's almost never a clear interpretation of how or why a trained neural network succeeds in accomplishing its task.

The fact is that many concepts, even seemingly simple ones, are simply not definable by a short set of rules, instead they are learned by our brains through pattern recognition and that's how they are "defined" - as a mind-bogglingly complex pattern recognition algorithm that our brains eventually settle on after being exposed to many examples.

Luckily for us, our brains are sufficiently similar that children eventually arrive at sufficiently similar algorithms for adjudicating "dog-ness", "chair-ness", etc. We can then use words like "dog" and "chair" (or most other words) and mean by them more or less the same thing - it's rare enough for two people to disagree on whether a label ("dog", "chair", ...) applies to a particular thing/situation/property that we can meaningfully use these words and be understood - well, most of the time!

To rephrase and summarize:

  1. We all have slightly different internal definitions of words (we all speak slightly different languages).
  2. A lot of the time these internal definitions are complicated pattern recognition algorithms, which cannot be boiled down to a set of rules that could be formulated as a definition.
  3. In most, but certainly not all, cases our definitions for various words are similar enough to allow for meaningful communication.
So the next time somebody asks: "how do you define...?", with the assumption that you have no business discussing something until you can give a clear definition, don't be flustered if you can't formulate a definition - challenge their incorrect assumption instead! 

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