more widely than to mathematics alone and which are not examined or questioned. Mathematicians, like anyone else, may be deceived by errors which arise from abstract ideas and the existence of objects outside the mind.

Berkeley is obviously correct in asserting that there may be errors in the principles applied by mathematicians (and everyone else) of which we are all unaware. The problem, to which Dr. Johnson famously objected, is that his criticism of abstractions is itself highly abstract. The objection to mathematical certainty is purely theoretical and speculative. One might easily go up to anyone involved in any activity and say: "You may be making a mistake of which neither of us is aware, due to our imperfect understanding of the higher principles which govern the activity in which you are engaged." It is unlikely, however, that they would derive much benefit from this warning.

In this particular part of A Treatise Concerning the Principles of Human Knowledge, Berkeley responds to the objections of those who argue that his subjective idealism—the notion that everything in the universe consists of ideas, not matter—is incompatible with a belief in God as traditionally conceived. As a bishop as well as a philosopher, Berkeley is understandably keen to refute such an objection, which he proceeds to do in paragraph 61 of part 1.

The argument that Berkeley seeks to dispose of is this: if the animal and vegetable life we see around us consists of nothing more than ideas, then why do they need to be so complex in their workings? Surely they could work just as easily without all their components. God could simply command them to work by a divine act of will.

With such a profusion of different bodies—both animal and vegetable—each with their own unique complex structures, how is it possible to discern any over-arching purpose, any final cause, to use the old Aristotelian terminology? If Berkeley is right, then it seems that there's no place for God in his philosophical system.

Berkeley responds in paragraph 61 by frankly admitting that his philosophy doesn't account for all the intricate workings of nature. But he quickly goes on to say that this is of no importance against that which can be proved a priori, that is to say on the basis of reasoning rather than through experience. And for him, the existence of God can be proved on such grounds.

He then turns the tables on those who maintain the existence of God's creation but not God himself. All of the characteristics of the many things that God creates, such as solidity, bulk, figure, and motion, ultimately have no activity in them; they cannot produce any effect in nature.

That being the case, those who suppose that created objects such as plants, animals, and human beings exist without being perceived, as the atheist does, are doing so to no purpose. The only use that is assigned to such objects is that they produce perceivable effects. And if we cannot perceive them, that must mean they can only be perceived by God.

In these paragraphs, Berkeley is anticipating Hume's arguments about causation, though ultimately, the overall conclusions Hume would reach a few decades later can be considered practically the opposite of Berkeley's.

Berkeley's point appears to be that when "natural philosophy" establishes a principle such as that of the attraction of bodies (in other words, gravitational force, as determined by Newton), the principle is really nothing more than an observation, extended from what is directly observable to that which is not; it is inferred from what we do see. On earth, we see gravity at work, and rather than restrict this property, the natural philosopher extrapolates it through analogy into a realm where it cannot be directly observed, as in the attraction among the bodies in the solar system.

Berkeley's argument is very much like that of Hume in asserting that when we observe two events in conjunction—such as a billiard ball striking another, followed by the motion of the second ball—we are assuming that these events, or similar ones, will always occur in conjunction, in sequence like this so that we conclude the first event "causes" the other. But both philosophers are stating that the human mind, in its tendency to draw analogies, assumes connections among different observable happenings and then claims the existence of a "law" that governs them, when in fact, no such law is observable. It's the essence of the empirical philosophy of both Berkekey and Hume that what is not directly experienced does not literally exist and needs some other factor to justify it or to establish it as provable.

For Berkeley, that "other factor" is God. The essence of things, the unobserved quality that establishes these analogized consistencies of "natural law," is the fact of their existence in the mind of the Deity. By contrast, although he starts from the same premise as Berkeley, for Hume, there is nothing. Beyond that which is directly observable at a given moment, nothing can be "proved." We see events and analogies, but beyond the immediacy of our perceptions, we have no proof that the principle of "cause and effect" exists and hence no proof, in Hume's view, that God exists. The two greatest empricists of the eighteenth century, Berkekey and Hume, start at the same point and reach opposite conclusions—the first in favor of religion and the second against it.

This is quite the recondite passage, and it requires reference to paragraph 70 to fully interpret. Briefly, in paragraph 70 Berkeley considers a critique that might be brought upon the general argument of his treatise—that there is no unperceivable substance. The critique (in paragraph 70) goes as follows: there may be particular parcels of matter, of which we have no immediate knowledge or sense of, but of which God himself is aware and which he uses to permit us to form images in our minds based on our sensation of external stimuli. Therefore, a kind of substance, not perceivable to humans but perceivable to God himself, does exist somewhere outside of man’s immediate perceptions.

Berkeley responds to this in paragraph 71, basically by saying that this indeed could be the case but that it still does not refute his underlying argument. When he says that the question being considered is no longer “of a thing distinct from Spirit and Idea,” he means to say that the perceiver and the perceived thing are no longer separate entities. This is because God, as the perceiver, is total and lacks nothing in his own existence. In any case, Berkeley concedes that this indeed may be the case—the argument that the perceived thing and perceiver may be the same object (God)—thus proving that matter can exist outside of human perception. However, he contends that the argument is so nuanced and sophisticated that it doesn’t really detract from the general points he had been making in his work up to that point.

Berkeley illustrates this idea with an allusion to a musician. A musician is driven by the musical notes on his paper to create music, which the spectator in the audience consequently hears (i.e., he perceives it). However, the notes themselves are never perceived by the audience. Rather, they are used by the musician to allow the audience members to experience a particular kind of perception (the sound of the music being played). This is, metaphorically, the same way God can use unperceivable matter or ideas to stimulate certain perception in the human mind, even if humans themselves never directly encounter the objects that have led to the perception in the first place (which only God knows).

The critical thing to keep in mind here is Berkeley’s last sentence:

Besides, it is in effect no Objection against what we have advanced, to wit, that there is no senseless, unperceived Substance.

Here he was no doubt taking influence from the work of Spinoza’s Ethics, whereby he (Spinoza) defines God as the primary substance and cause of all auxiliary substances. This is an incredibly convoluted ontological philosophy, but all you really need to know is that Berkeley believed that nothing could be known outside of sense perception; all the matter of the world only existed as images that resided in the mental world of our perceptions (and not outside of it, in the “real” world). This is what he means in this last sentence. He further borrowed from Spinoza’s definition of substance—if the primary substance is God, from which all other matter originates, and if God himself is unknowable and unperceivable, then true substance (or matter) is also not perceivable. All humans have access to are the images they form in their head, not the real substratum of matter itself. This is because, like the musician and his notes, God only gives humans the perception of a thing (the music) and not the thing itself (the musical notes on a score).