Metaphysics

Book Theta examines the concepts of potentiality and actuality, crucial to understanding Aristotle’s Metaphysics. The book distinguishes between potentialities related to change (active and passive) and those related to substance. Aristotle also addresses rational and irrational potentialities, with rational potentialities being unique to animate beings and capable of producing opposites, unlike their irrational counterparts.

In Theta 3, Aristotle counters the Megarian school’s view, which conflates potentiality with actuality. He argues for the distinctness of potentiality and actuality, demonstrating that skills like building exist as potentialities even when not actualized. This distinction underscores the need to recognize potential states separate from their actualization.

The subsequent chapters explore various facets of potentiality. Theta 4 rejects the idea of a potentiality that will never be actualized, emphasizing that potentiality, by its nature, implies eventual actualization. In Theta 5, Aristotle distinguishes between natural and acquired potentialities, noting the importance of rational choice in the realization of rational potentialities.

Theta 6 shifts focus to actuality in relation to substance and being, highlighting examples like a statue produced from wood or an actualized skill like seeing. This chapter emphasizes that actuality, as opposed to mere potentiality, represents the full realization of an entity’s nature.

In Theta 7, Aristotle explores the conditions under which something is potentially another thing. He explains that in the rational realm, potentiality is realized when the artist desires it and no obstacle exists, whereas in the irrational realm, the absence of obstacles suffices.

Theta 8 argues for the priority of the actual over the potential in thought, time, and substance. Aristotle asserts that actuality is fundamentally primary, as one cannot conceive of potentiality without first understanding actuality. He also argues that in terms of species, the actual precedes the potential.

Theta 9 connects the doctrines of actuality and potentiality with concepts of good and evil and mathematics. Here, Aristotle posits that actuality in good things is preferable to potentiality, as it precludes the actuality of corresponding evils. In mathematics, he illustrates how geometric proofs actualize potential relations in figures.

Theta 10 revisits the topic of being as truth and non-being as falsity, examined earlier in Epsilon. Aristotle discusses how statements about composite and simple things can be true or false, emphasizing that simple, non-composite things are pure actualities and therefore imperishable.

Book Iota explores the intricate concepts of unity, contrariety, and species difference. Aristotle begins by exploring the essence of unity, identifying its four primary senses: continuity, being a whole, specific unity, and numerical unity. Unity, for Aristotle, is about being indivisible in a specific and determinate way or being an indivisible whole. He uses the primary measure, especially in terms of quantity, as a clear example of this kind of unity.

Aristotle also discusses the nature of measure, essential for understanding quantity. He attributes six characteristics to measure; it is a tool for knowing quantity, the primary unit, noticeable when altered, possibly multiple for one object, and homogeneous with its object. He states that scientific knowledge and perception are measured by things, not the other way around.

Continuing, Aristotle addresses the controversial topic of whether “the one” is a substance or an attribute. He argues against the idea of “the one” as a substance, emphasizing that universals cannot be substances. Instead, unity must be a determinate property of some substance.

Aristotle then contrasts unity with multiplicity, highlighting that unity is about indivisibility, while multiplicity involves divisibility. He further associates unity with identity, similarity, and equality, each having distinct senses. For instance, identity can be numerical, formal and numerical, or purely formal. Also, similarity can range from having the same form with individual differences to possessing more equal than diverse attributes.

Next, Aristotle tackles the concept of contrariety, defining it as maximum difference and essential for understanding species difference. He points out that contraries must come in pairs and be complete or perfect differences. This leads to his argument that not all cases of contrariety result in species difference, a crucial point for understanding the diversity within a genus.

Aristotle also examines objections against his views on contrariety. One objection involves the opposition between the equal and the large and small. Aristotle resolves this by reclassifying the opposition as a privative negation, not a contrariety. The other objection concerns the one–many opposition, which he argues is not an absolute opposition but more a relational one, with the one acting as a measure for the many.

Moving forward, Aristotle clarifies the notion of an intermediary state between extremes. He asserts that intermediaries must be of the same genus as extremes, stand between contraries, and be composed of contraries.

In discussing species diversity, Aristotle stresses that species difference must involve a difference concerning a common factor within a genus, primarily a contrariety. He also argues that the diversity of species implies their indivisibility and that no species can be identical with its genus.

Finally, Aristotle uses the relationship between contrariety and species diversity to critique the doctrine of Platonic Forms. He argues that perishable and imperishable entities must be generically different, challenging the idea that the same species can include both perishable and imperishable members. This leads to his conclusion that there cannot be Forms as some philosophers propose, as this would imply a species comprising both perishable and imperishable entities.