If forms exist in a transcendent realm separate from sensible particulars, as Plato claims, then it is impossible to explain change, because forms are eternal and unchanging while change is inherently transient, creating a logical contradiction.

The concept of final cause is foundational to all subsequent Western moral theory, particularly intentionalism, which judges an action morally based on its purposes and intentions rather than consequences alone (e.g., getting an 'A for effort').

Aristotle introduces the concept of potentiality (potencia)—a middle state between non-existence and full being—to solve the logical problem of change: a boy is not a non-man, nor is he yet a man, but is potentially a man; under correct conditions, he will naturally develop toward that end-state.

Material cause is the physical substratum or basic stuff of which a thing is made (e.g., a lectern is made of chipboard with plastic veneer), answering the question 'What is it made of?'

Final causality avoids infinite regress in explanation because once you understand the purpose of an action, you need not ask 'what caused the purpose?'—the purpose is the end-state and requires no further explanation.

Plato argued that numbers are not found in nature, therefore they exist in the intelligible realm; Aristotle countered that numbers are not essences but abstractions from the magnitude property of things—we abstract magnitude from all other properties and study it independently, without positing transcendent numerical essences.

Aristotle's four causes—formal cause (essence/definition), material cause (physical substratum), efficient cause (agent of change), and final cause (purpose or end-state)—constitute the complete framework for explaining how things exist and change in the universe.

Efficient cause is the agent or agency through which a change occurs—the agency that brings something about (e.g., I release the paper, causing it to fall; I push the button, causing the blender to turn on).

Final cause is the end or purpose towards which a process naturally moves (e.g., health is the final cause of exercise; the acorn's final cause is to become an oak tree; a chicken crosses the road to get to the other side).

Things exist in different modes or categories—some exist as primary beings (complete, unified substances like myself or this lectern), while others (like the color of my clothing, the sound of my voice) exist only as accidents dependent on primary beings and lack self-subsistence.

Aristotle criticizes Plato's doctrine of the forms on the principle of simplicity (Occam's Razor): Plato's theory multiplies entities unnecessarily—for every particular thing there is also a separate form, and potentially a form of that form—creating an 'ontological slum' that impedes scientific explanation.

Scientific explanation attempts to create simplicity by using the smallest number of moving parts to explain a phenomenon; the principle of parsimony (later articulated by William of Ockham as Occam's Razor) states that if two explanations equally account for phenomena, the one with fewer entities is better.

Murray Gell-Mann, a physicist working on grand unified theory, stated that you will know when you have achieved the grand unified theory because the explanation will be incredibly beautiful and simple with almost no moving parts—an intuition reflecting Aristotle's view that simplicity and elegance indicate correct scientific explanation.

The form of things is often defined in functional terms—a lectern has the shape and structure it does because it serves the purpose of providing a place to lean and speak from; a chair has a bottom and back because its function is to allow sitting.

Teleology—the doctrine that the universe has purpose and that things have natural end-states toward which they tend—became fundamental to Christian worldview; Christian thinkers saw Aristotle's teleology as pointing to a divine creator with purposes, though Aristotle himself conceived purpose differently.

Aristotle distinguishes between inanimate objects (which change only through external efficient causation or gravitational teleology) and animate objects (which possess soul and can induce motion from within themselves without external winding or pushes).

Plants possess only the nutritive soul, enabling growth and nutrition; animals possess both nutritive and sensitive souls, enabling growth, nutrition, movement, and sensation; humans possess all four types of soul—nutritive, sensitive, desiderative, and rational—placing us at the top of the scale of being.

God, in Aristotelian thought, is not the active creator or causal agent like in Judeo-Christian tradition; rather, God causes motion by being the final cause—the object of desire toward which everything naturally moves and strives to emulate perfect being.

Aristotle argues that God must be perfect in actuality and unchanging; if God were to think about anything external to himself, his mental state would change, and change implies imperfection; therefore, God can only think about himself—he is eternally self-contemplative and self-sufficient.

According to Aristotelian realism, the nine categories are not merely linguistic or mental constructs but are absolutely essential or real properties of things in themselves; this doctrine of realism about categories became one of the major bones of contention in subsequent philosophical tradition.