science is about convincing other humans that your experiments are correct

... and the best way to do that is, in theory, to do good experiments. Hence replication and so forth. That's the basic idea of Science. (Alarmingly, some modern "scientists" have indeed been found cutting out the middle-man, as it were.)

art is about convincing other humans that what you have made is art

Yes, this seems like a reasonable assessment. Some people have other goals in influencing the minds of their viewers, although this tends to edge into advertising etc.

parenting is about convincing other humans that you are a good parent

No, this is only the lower bound that allows you to retain a child. Most of the rewards etc. of parenting are unrelated.

working for a living is about convincing other humans to pay you a living

Definately.

competitions are about convincing other humans that you have won

This seems quite analogous to law, if the layer is themself the defendant.

teaching is about convincing other humans that you are teaching

In practice, sadly, it is. The incentive structure for teachers is pathetic, because no-one actually cares about it..

being intelligent is about convincing other humans that you are intelligent

living is about convincing other humans that you are not yet dead

Not sure what to make of these last two, they don't seem remotely analogous to the OP.

More seriously, law is also about predicting what those humans will be most easily convinced of.