Back in May I posted an observation that my granddaughter had not yet grasped the concept of number; that she was treating number as if it were a kind of name and thus when a thing was given a number such as '3' that thing was always a three. Fast forward to July 4th when she turned 3. When told that a cousin will turn 2 next month, she said "I don't want to give him my 2. I want to give it to..." (another cousin). She still wasn't getting it. Fast forward again to last week when we were sitting her at our house. We had cooked and sliced up a hot dog for her. She stabbed two pieces with her fork but before she could eat them I asked "How many slices are on your fork?" She replied 'two'. I said 'How do you know?' She then pointed at them and counted 'one, two.' "Good job!" I commented. She is now grasping that numbers refer to quantities.
One of the things I enjoy as I babysit my four grandchildren, the oldest of which is 3 yrs, is watching them play and perceive reality around them. I've often wondered what those little percepts looked like in their little minds. Babies can perceive entities directly. That's simple enough to understand. But how do they perceive actions and relationships since they cannot conceptualize them as such? It seems to me that the baby would have to treat all attributes, actions and relationships as properties of the entity involved. This possession of attributes, actions and relationships by entities means that Rand's identification that "... (Attributes cannot exist by themselves, they are merely the characteristics of entities; motions are motions of entities; relationships are relationships among entities.)" is being perceived, right from these early stages of awareness. When the child's conceptual faculty awakens, he will reclassify these properties as attributes, actions and relationships.
I think that when a child perceives a pushed ball rolling he perceives that the ball possess pushability, the sofa does not. He perceives that the ball has rollability but the sofa does not. He will also perceive that pushability must precede rollability. Later when he learns to speak in full sentences he will eventually reclassify not the action of the ball, but the sequence of which action must come first, as cause and effect and will assign this concept to all such sequences he later encounters.
Another past example I want to relate. When my youngest grandson was about 6 months old he could sit up but not yet crawl. I would place him on a blanket on the floor and place some of his favorite toys around him, mostly stuffed animals. He would routinely toss them out of reach. Unable to reach them he would cry in frustration and grampa would come to the rescue. One day though, a toy was out of reach and he tried several times to grab it. Then he paused for a few short seconds, grabbed the blanket and pulled it toward him bringing the toy within reach. I was amazed. "How did he know to do that?" I wondered. He can't possibly conceptualise a thought process of 'if this then that' can he? No. He's too young for that. What kind of perceptual dots did he connect to perceive that something he didn't want-the blanket-could bring him what he did want, the toy?
There had to be some antecedent perceptual knowledge at work here I thought. But what kind? Anyone who ever raised or sat a baby knows that if you put something in the baby's hand, he will grab it with his fingers and, with his arm, pull it toward him, usually right to his mouth. So the baby knows from past perceptual repetitions that his hand has graspability and his arm has moveability and will bring whatever is in his hand closer. So sitting there looking at his out of reach toy, he must have perceived that the blanket, like his arm, also has moveability, and if he grasped it, he could bring it closer. Then he acted on that perception.
One last anecdote. When my oldest boy was around 6 months old, he would sometimes jabber himself to sleep at night. One night however, he was jabbering then he stopped. There was silence. Then a sound. Then silence. Then another sound but this one was followed by laughter. Then a louder sound followed by louder laughter. This went on for a few more minutes. The wife and I looked at each other and I commented "He's just discovered that it is he who is making those sounds and that's making him happy." I never experienced this with any other child or grandchild, just him.
For me, observing such experiences is priceless.
(The above Rand quote is from "Introduction to Objectivist Epistemology".)