> Reality is ontologically enriched logic. It is a logic that is animated, alive with thought, infinitely aware of its own infinite self. And it is, simultaneously, a logic that is embodied, a logic that generates itself in space, resulting in the material world. > – Betraying Spinoza, Rebecca Goldstein In "Kamii, Constance, and Leslie Baker Housman. Young Children Reinvent Arithmetic: Implications of Piaget’s Theory. New York: Teachers College Press, 2000", the authors discuss how children acquire the ability to count by combining the concept of order with the concept of hierarchy. The third form of knowledge that Piaget was interested in learning more about was logical-mathematical knowledge, which is that of relationships. As we learn more about the different logical relationships in reality, we have to develop new vocabulary for it. Language aims at the same level of precision as mathematics. It just does so without abstracting from the properties of reality. There needs to be words that capture every step along a gradient or dimension of reality. For instance, words for anger should range from upset to rage. (Karla McLaren). But there are other words that need to capture inclusivity as it moves along the gradient, that retain the older properties, rather than jettisoning them. Whole new vocabularies need to be developed when we start making discoveries in orthogonal directions. Perhaps the Model of Hierarchical Complexity only applies to left hemispheric thinking. It deals best when reality is seen as snapshots in a time series, and we are tracking different variables across this series. But we need some kind of model of intuition that captures how our right hemisphere works. (Iain McGilchrist)