David Hume's Account of Demonstration in Book I of 'A Treatise of Human Nature'

The dissertation has three intertwined goals. The first is to uncover some of the key components of Hume's use of demonstration in Book I of A Treatise of Human Nature, noting the standards and scope of this form of reasoning. Because Hume does not tell us what makes for a successful demonstration, we must rely on his destructive arguments to see why Hume thought his opponents failed in their attempted demonstrations. This allows us to reconstruct his criteria for a successful demonstration. Using these findings, I examine the arguments of three passages – "Of the ideas of space and time" (T 1.2), "Why a cause is always necessary" (T 1.3.3), and "Of the immateriality of the soul" (T 1.4.5) – to reconstruct and evaluate the arguments contained therein in light of the discoveries about demonstration. Despite not featuring prominently in interpretations of Hume, these passages are important to Hume's overall argument and were very important to his contemporaries. Finally, I raise the question, whose arguments are potentially defeated by Hume's claims about the nature of demonstration? Each passage causes trouble for natural theology or metaphysics as practiced by the religious metaphysicians (such as Samuel Clarke and other Boyle lecturers) that proliferated in Britain in the fifty years before Hume wrote the Treatise. Each of these passages has an irreligious consequence.;An under-appreciated aspect of his rejection of infinite divisibility in "Of the ideas of space and time" is his argument that we have no adequate idea of infinity and adequate ideas are required for demonstrations, so all his opponents' attempted demonstrations fail. He does not explicitly state what makes an idea adequate, but he appears to conjoin a high demand on adequacy with a controversial requirement that demonstrations must involve adequate ideas. Significantly, it follows that there can be no demonstration of the existence of God, since it was widely accepted that our idea of God is inadequate because we have no adequate idea of an infinite being. While perhaps not convincing to his opponents, Hume's argument against infinite divisibility is more sophisticated than has been realized by most critics today.;In "Why a cause is always necessary," Hume claims that successful demonstrations follow merely from ideas and are based on an unalterable relation between the ideas. His list of unalterable or constant relations (identified elsewhere as the philosophical relations that produce certainty or scientific knowledge) place severe limits on what can be demonstrated. These unalterable relations are a key component of his argument that it is neither intuitively nor demonstratively certain that a cause is always necessary. The argument's success might rest on assuming the distinctness of the causal relata. I resist drawing too heavily on statements Hume made after publishing the Treatise that intended to downplay the irreligious and skeptical consequences of his rejection of the intuitive and demonstrative certainty of the maxim that a cause is always necessary.;Hume's argument against a substantial self in "Of the immateriality of the soul" appeals to both adequacy and unalterable relations in arguing that we should reject the existence of an immaterial soul. He argues against the possibility of us having an idea of an immaterial soul, and I examine the three arguments he gives. I also lay out the interesting critique he offers of the religious metaphysicians who ridicule Spinoza's metaphysics. If Spinoza's metaphysics is full of contradictions, then so too must that of the theologians.;In a brief chapter on "Of scepticism with regard to reason," I discuss Hume's argument that knowledge degenerates into probability. Rather than negate the need for an examination of demonstration like I have provided, Hume's approach to demonstrations in this passage is compatible with and even supported by his earlier approach. The conclusion of the dissertation provides evidence that Hume's theory of demonstration did not change greatly after the Treatise..