Intelligence
Most definitions of intelligence that I have seen mention problem-solving or goal-pursuit, and I agree. A thing can't be intelligent unless it's pursuing some kind of goal. This is a handy way to preclude most ordinary objects from being called intelligent.
But my definition still has two important terms that need further explanation: data and goal.
Data is a synonym for information. Data must be symbolically encoded, and it must be stored in some kind of storage structure. Otherwise, it's not data. This means we can exclude all the possible information out there in the world that hasn't been encoded and stored yet. That doesn't count as data.
A book has symbols that encode information. This is a kind of token encoding because one material object encodes or points to another object. For example, the ink on the page spells the word "dog," which points to an actual dog.
The human brain has its own data storage system, which is how we use our memory. However, our brain does not encode sensory inputs in the form of tokens, like one object to indicate another object. Instead we encode our sensory inputs in the structure of our brain's neural network. That still counts as encoding, and this is an important distinction between token encoding and network encoding.
As far as I know, every information structure in the universe was built by a living entity - except for the genetic code of DNA, which apparently arose naturally. DNA could not have been built by a living entity, because DNA is the fundamental basis of life itself. And a life surely cannot build itself. Note: If God created life, he cannot possibly be made of DNA.
A goal is also a particular kind of information structure. In order for something to have a goal, it's not enough to move persistently toward a thing. For example, a river flows to the sea, trying its hardest to overcome every obstacle. Why couldn't we say the river has a goal of getting to the sea? It's because a goal is a stored data structure.
The Mississippi River at St. Louis has no concept of its own mouth below New Orleans. Nothing about the river indicates where it is going. In fact, the river has no stored data and no informational structure at all.
It seems therefore that every goal is held by a living entity, and there are no goals except those pursued by living entities.
Since my whole definition of life is based on evolution by natural selection, and since pursuit of the root goal is an inescapable condition of evolution, then we can say that every goal is part of the hierarchy of goals, and every goal leads up to the root goal.
Since all data is organic and all goals lead up to the root goal, we can say that all intelligence is a matter of living things pursuing the root goal.