Metaphysics

Book Lambda of Aristotle’s Metaphysics delves into general philosophy with a strong focus on theology. Aristotle splits the book into two halves: the first half explores natural philosophy, while the latter half presents his mature theology.

1. Substance and Change (Lambda 1 & 2):

Aristotle starts by examining the concept of substance, categorizing it into three types: perceptible and perishable, perceptible and imperishable, and those immune to any change. He asserts that understanding these substances is crucial for both natural science and logic/mathematics. Theology, he suggests, should investigate if there is a common source for all substance. Aristotle then examines the nature of change, stressing that for any change, there is something persistent, which he associates with matter. He concludes that there are three fundamental causes or principles for perceptible substances: form, privation, and matter.

2. On Immaterial Form (Lambda 3):

Shifting focus to substance, Aristotle discusses immaterial form, suggesting that while it may not apply to artifacts, it could be relevant for natural entities. He refutes the idea of the Forms as temporally prior to the composite, highlighting the non-separability of efficient and formal causes.

3. The Role of the Efficient Cause (Lambda 4):

In a critique of idealism, Aristotle rejects the concept of a more fundamental constituent underlying the categories of being. He emphasizes the uniqueness of the efficient cause in addition to form, privation, and matter, asserting the necessity of an eternal, unmovable substance.

4. Actuality and Potentiality (Lambda 5):

Aristotle adds actuality and potentiality to his explanation of universal principles. He argues that material potentiality alone cannot explain the production of the composite, necessitating an eternal substance that is never potential and always actual.

5. The Necessity of an Eternal Substance (Lambda 6):

Arguing for the existence of an eternal, unchanged substance, Aristotle suggests that without such a substance, everything would be perishable. He identifies this eternal substance with pure actuality, explaining that it can never be merely potential, thus ensuring the continuity of its existence.

6. The Prime Mover as God (Lambda 7):

Aristotle posits that the eternal actual substance is the prime mover and equates it with God. He reasons that the prime mover must cause processes by being an object of desire, emphasizing that the prime mover’s existence is supremely desirable. Aristotle describes the prime mover as engaged in a continuous, self-reflective contemplation, which is the highest form of life.

7. Multiple Prime Movers? (Lambda 8):

In a controversial shift, Aristotle raises the possibility of multiple prime movers, based on the number of eternal movements in the heavens. The conclusion, however, is inconclusive and somewhat contradictory.

8. Reflexive Nature of Divine Thought (Lambda 9):

Returning to the concept of divine thought, Aristotle argues that the prime mover’s thought must be about itself to avoid dependencies or unworthy objects. He suggests that the prime mover is conscious of its contemplation in a way that surpasses human thinkers.

9. Conclusion: The Goodness of the Universe (Lambda 10):

Aristotle concludes by asserting the universe’s goodness, drawing an analogy with an army whose excellence stems from its general. He reiterates the unity of the composite secured by the identification of the efficient with the final cause.

Book Lambda is a complex exploration of natural philosophy and theology, where Aristotle investigates the nature of substance, change, and the role of the prime mover, culminating in his portrayal of God as an eternal, contemplative being.

Book Mu highlights the nature of substance, focusing on the question of whether there are imperceptible substances beyond the perceptible world. Aristotle investigates two prime candidates: mathematical objects and Platonic Forms. His analysis forms a crucial part of his broader metaphysical inquiry.

Aristotle begins by setting the agenda: examining mathematical objects and Forms, not as mere abstract entities, but as fundamental constituents of reality. This exploration occupies the entirety of Books Mu and Nu, with several interpolated discussions. The central thesis revolves around the existence and role of imperceptible substances, contrasting with perceptible ones previously discussed in his Physics.

Mu sections 2 and 3 question the existence of mathematical objects as separate entities. Aristotle argues against the notion that geometry deals with ideal entities separate from our world. Instead, he posits that mathematical disciplines like geometry and arithmetic abstract from physical objects, considering them in a specific, non-physical manner. He contends, “Universal assertions in mathematics are not about separable entities which are beyond and apart from magnitudes and numbers. They are about these very things, only not qua such things as have magnitude and are divisible” (398).

The next sections, reworked from Book Alpha, scrutinize Platonic Forms. Aristotle critically examines the foundations of Plato’s Theory of Forms, especially its claim that Forms are stable, non-fluctuating entities necessary for knowledge. He dissects various arguments for Forms, exposing inconsistencies and logical flaws. Aristotle stresses the implausibility of Forms being both particular and universal, a central contradiction in Plato’s theory.

Mu sections 6 to 8 dissect various Platonic and Pythagorean theories of number, critiquing their postulation as fundamental substances. Aristotle systematically dismantles these theories, revealing their contradictions and implausibility, particularly in the notion of numbers as separate, ideal entities. He questions the relationship between numbers, Forms, and the physical world, concluding that none of the posited theories of numbers as separate substances withstand scrutiny.

In the final chapters, Aristotle addresses an objection to the search for principles: whether they are universal or particular, and thus, whether they can be substances or intelligible. He argues that principles can be particular without losing their explanatory power. This sets the stage for exploring principles and causes in the natural world in Book Nu.

Aristotle’s critique in Book Mu is methodical, examining the proposed theories of imperceptible substances through rigorous logical analysis. He emphasizes the need to distinguish between physical reality and mathematical abstraction, arguing against the existence of separate mathematical entities or Platonic Forms. His exploration raises fundamental questions about the nature of substance, knowledge, and the relationship between the perceptible and imperceptible worlds.

Book Nu continues the investigation into the nature of substances, specifically focusing on the principles and causes of the natural world in relation to numbers and Forms.

The central facet of Book Nu is the critique of the Platonic and Pythagorean views on numbers as fundamental principles of the world. Aristotle starts by challenging the idea that the elements of number must be opposite principles. He argues against both the opposition between principles and the characterization of principles themselves by the Platonists: “So the problem we propose applies to contraries head on, given that contraries are in all cases of some subject and never separable things” (431). Aristotle asserts this, emphasizing the conceptual errors in the Platonic approach.

Aristotle then turns to the concept of eternal substances and their composition, arguing that anything eternal should not be composed of elements, as this would imply the presence of matter, which contradicts the notion of eternality: “It would be possible for it not to exist” (435), he states, highlighting the contradiction in the Platonic theory of eternal substances having elements.

The book continues with a critique of the role of numbers in explaining the natural world. Aristotle examines various theories, including those of the Pythagoreans and advocates of mathematical number, and finds them lacking. He questions their foundational principles and the roles attributed to numbers, arguing against their causal relationship with the physical world. Aristotle points out, “It is just crazy, just impossible that some single nature could, by coming to be, be the cause of its being the case that one thing was a this, one thing a such, one thing a so much, one thing an over there!” (436).

Aristotle also addresses the connection between the doctrine of principles and the concept of the Good, a central idea in Plato’s philosophy. He critiques two interpretations of accommodating the Good to the notion of principles, one by Speusippus and the other by Plato himself. Aristotle concludes that neither approach successfully integrates the Good with principles: “That, then, is the dilemma, primary sovereignty or not?” (445).

Toward the end of the book, Aristotle reflects on the idea of numbers as causes, dissecting the logic behind such claims and finding it wanting. He uses practical examples to illustrate the limitations of numbers as explanatory causes in the natural world. Aristotle effectively demonstrates that the supposed connections and causal relationships attributed to numbers are insufficient and often coincidental.