Fundamental Philosophy, Vol. 2 (of 2) — Context and Discussion

Geometrical Ideas and Sensible Intuition

Balmes devotes several early chapters to the difference between a geometrical idea and the sensible representation that accompanies it. He observes that when we think of a triangle, we may picture a particular shape, yet the idea of triangle applies to all triangles regardless of size or orientation. The sensible image is always determinate—a specific figure with a definite size—while the idea is universal. Balmes argues that the intellectual act grasps the universal, whereas the senses provide only the particular. He uses this to critique Condillac's statue, which attempts to derive all knowledge from sensation alone. For Balmes, the statue could never generate the idea of a triangle from mere sensory inputs; it would remain trapped in particular impressions.

The Conception of the Infinite

In chapters on infinite extension and infinite number, Balmes explores how the mind conceives of the unlimited. He distinguishes between the pure conception of infinite lineal value—formed by uniting the general ideas of lineal value and negation of limit—and the sensible intuition that might represent it. The sensible intuition, he notes, requires imagining a space without limit, then summing all possible lines drawn in all directions. This process reveals a tension: the conception is clear, but the sensible representation is elusive. Balmes applies the same reasoning to infinite number, arguing that we can conceive of a number greater than any given limit, even if we cannot enumerate all units. The idea of infinite number, he claims, is not contradictory; it arises from the general idea of number combined with the negation of limit.

Universal Reason and the Foundation of Possibility

Balmes introduces the notion of a universal subsisting reason that grounds pure possibility and necessity. He argues that ideas are not merely subjective constructs but have a foundation in an objective, necessary order. For example, the necessity involved in geometrical truths—that a triangle must have three sides—cannot be explained by sensation or by arbitrary convention. Balmes posits that such necessity reflects a universal reason that is not dependent on individual minds. He connects this to the idea of being, which he treats as the most fundamental and indeterminate concept, serving as the form of the understanding itself. All science, he claims, is founded on the postulate of existence.

Language, Innate Ideas, and the Limits of Intuition

In the final chapters of Book Fourth, Balmes examines the relation of language to ideas, arguing that words are not mere labels for pre-existing concepts but play a role in shaping and fixing general ideas. He rejects the notion of innate ideas in the Cartesian sense, yet maintains that the capacity for intellectual intuition is inherent. He distinguishes between intuitive and discursive cognition: the former grasps truths directly, the latter proceeds by reasoning. Balmes also discusses the limits of our intuition, noting that we cannot intuit the infinite directly but can conceive it through the combination of general ideas. This interplay between the limited and the unlimited, the sensible and the intellectual, structures the entire volume.

Readers will find that Balmes builds his arguments through careful distinctions and repeated returns to the same core problem: how the mind moves from particular sensations to universal ideas. The book rewards attention to his precise terminology—especially the difference between idea, intellectual act, and sensible intuition. Those interested in the history of philosophy will note his engagement with Condillac, Kant, and the Aristotelians, though Balmes always subordinates historical critique to systematic analysis.