This is a reasonable perspective. But people other than the parent sometimes read comments! I'll do my best at a level-zero explanation of "intelligence" in the literature:
Let's start by modestly noting that I routinely got the top score on Latin tests in high school (this was worth a small box of chocolates!). Someone applying the concept of "intelligence" might predict that I would also do well in math class. The traditional explanation for this given by Latin teachers is that learning Latin trains the mind to think logically, and getting high scores on Latin tests means that the training has taken. The intelligence-based explanation is that Latin and math are two of many tasks subject to the influence of g, the "general factor".
Moving to a more general level, the observation is that for many, many tests that appear to involve "mental abilities" to a greater or lesser degree, a person's score on any one of them is predictive of the same person's score on all the others. It's rare to find someone who is good at one and bad at another; instead, people tend to be uniformly good or uniformly bad (known in the literature as the phenomenon of the "positive manifold"). This suggests that there's one quality driving all the results, which we can call "intelligence", since that's the label commonly applied to people who tend to do well on those types of tests.
The question isn't, "Is there intelligence?" The question is "What is intelligence in terms of a definition?"
You're saying that if many people find you beautiful, there's a quality driving that, and it's "beauty". That's fine. Beauty exists. But aren't you almost admitting that it is a quality and therefore subject to what evaluates it? In other words, if 5 people call someone beautiful or ugly, are they beautiful? If someone is good at Latin and languages, does that mean they are intelligent? And if someone is not good at Latin, does that mean they are not?
Further, how many people do you have to find to say you are beautiful to be you are "defined" as beautiful? That's not a definition, that's just further confidence-building; the more you have the more confident you can be. But that still doesn't mean there's a point where you can say it is definitively so, and therefore you don't have a true definition.
> You're saying that if many people find you beautiful, there's a quality driving that, and it's "beauty".
That's not it.
1. Imagine that we have a system we're happy with for quantifying people's beauty.
2. Imagine that we discover that, in a sample population of 100,000 or so, higher beauty predicts lower willingness to wait in line, lower frisbee golf scores, and redder tablecloths in the home.
The idea here is that from (2) we conclude that (3) there is a single variable, "beauty", responsible for your rating in (1), but also responsible for your frisbee golf scores and the color of your home tablecloths. Now, in addition to using the system in (1), we could in theory rate people's beauty by visiting their home and checking the tablecloths, or by checking a frisbee golf score sheet (lest this sound ridiculous, I'll observe that a real test of intelligence in children consists of the instructions "draw a man", "draw a woman", and "draw yourself": https://en.wikipedia.org/wiki/Draw-A-Person_Test).
In the literature, "intelligence" or g refers to this hidden variable that explains performance across all the various IQ-driven tasks. To discredit the idea, you'd want to find a test which correlated positively with one well-accepted IQ test, and negatively (or zero) with another. Another commenter pointed out that, since we don't have a specific physical metric for intelligence, we can't rate people as having a certain number of "intelliunits". That's correct, and it means that an intelligence-discrediting test could have pretty much any content at all; all that's required is that it be positively related to one existing IQ test and negatively related to another. This turns out to be extremely difficult.
This somewhat murky nature of intelligence as defined means that you're rated in terms of a comparison to the population (we can't say "you have 70 intelliunits", but we do know how to determine that you're smarter than Bob, Carol, and Tom, but dumber than Jennifer). An IQ of 115 means, approximately, that you're smarter than 5/6 of the reference population, which is conceptually all European whites.
Thanks for taking the time to write that! You presented your ideas extremely well. (And I love this kind of debate.)
So I'll accept both premises. And for premise 1, let's imagine the system we use to quantify beauty measures pronouncement of cheekbones and thickness of lips, etc. Premise 2 remains untouched. Here's the problem: Angelina Jolie would score well, but so would Jocelyn Wildenstein (Google image search that), and Emma Watson would score poorly. We would come to wrong individual conclusions based on correlations made from larger sample sizes. In fact, Jocelyn Wildenstein might come away with the title of "the most beautiful person ever." (And if you think I'm joking, listen to any interview with a man named Chris Langan.)
Since intelligence is qualitative, like beauty or flavors of ice cream, it's about the mix of ingredients. It's about "character". So that while you can make good correlations on large sample sizes, it's that individual mix that defines "beauty", "tasty", etc. Alan Kay was wrong: point of view isn't worth 80 IQ points -- 80 IQ points is worth a better point of view. That point of view is the end result, the character that determines your intelligence.
Again, the most beautiful woman, say, may not have the combined biggest lips and highest cheekbones, but an especially good mix. If you look at Einstein and every other great thinker, the people we consider the smartest, they won't have the highest IQ scores, but they had the best intellectual character.
You asked for the definition. That is the definition. Calling it a "debate" is the kind of thing that leads Kudzu_Bob to assume that questions are asked in bad faith. Whether you're happy with it is a separate question, which you can investigate yourself; there's an extensive literature on the various life consequences of high measured IQ.