Having deflected Hylas' objections for the time being, Philonous now presents his favorite argument of all, one that he says he is willing to rest everything on. The argument is intended to show that the very idea of a physical object existing outside of the mind is inconceivable. The intuition behind his claim is this: you cannot conceive an unconceived object, because in order to conceive the object you must, of course, conceive it; as soon as you have the object in your head you have conceived it. Put in plainer terms: you cannot have an object in mind, without having it in mind. So you cannot even try to meet the challenge without immediately failing.
It is easier to understand this argument if you compare it, as Philonous does, to the case of seeing. Is it possible to see an unseen object? Of course not, because the second you see it, it has been seen. The same goes for conceiving of an unconceived object. So we cannot even form the idea of an object existing out of all minds; it is an incoherent, self-contradictory notion.
In its full form the argument runs like this:(1) We can conceive of a tree existing independent of and out of all minds whatsoever only if we can conceive of the tree existing unconceived.(2) But it is a contradiction to speak of conceiving an unconceived object.(3) Hence we cannot conceive of a tree (or anything else) existing independent and out of all minds.
Hylas is impressed with this argument, but he still cannot shake the feeling that there are mind-independent objects, and he refuses to give up the good fight. What about distance?, he asks. We see the moon and stars as far off, so how can they be in our mind? Philonous, in response, points out that we perceive distance in our dreams as well. The appearance of distance does not, therefore, indicate that the "distant" object is outside of our mind. But, Hylas asks, then are our senses not somewhat deceptive if they suggest "outness" or "distance" when there is really no such thing? Philonous explains that the senses are merely indicating to us what further succession of ideas we will encounter, and it is only our own misunderstanding of these signals that has led us to believe that there is such a thing as outward distance. A blind man seeing the world for the first time, he claims, would not take these signs to indicate distance.
The "unconceived conceived thing" argument which Berkeley presents in this section is often referred to as the "Master Argument"; it is almost universally recognized today as unreliable. Some commentators, such as the Australian philosopher David Stove, go do far as to say that it is too generous to even analyze this line of thought as if it were a real argument. According to Stove, it is no argument at all: it is just a tautologically true premise (i.e. that we cannot have an object in mind without having it in mind) that in no way implies the very substantive conclusion (i.e. that it is impossible to conceive of an object that is not in mind). Stove may well be right in claiming that any real analysis of the argument is too charitable, but Stove himself also emphasizes how influential this argument has been in the history of philosophy. In his book, The Plato Cult he points out that most of the later idealists, such as Kant, Hegel, Schelling, and the British idealists, use versions of the Master Argument to bolster their immaterialist claims. Given the argument's influence, it does seem worthwhile to pay some attention to the Master Argument, and to try to analyze exactly where Berkeley went wrong in his reasoning.
The most popular diagnosis is that Berkeley failed to distinguish the perceptual act from the perceptual content. When I conceive of an idea that is my perceptual act. However, I can isolate from that act the content of the idea I am perceiving. The content of my idea can still be: unconceived tree. The fact that I am now conceiving that idea has no effect on the content itself. The content of my idea is still (unconceived tree). Berkeley is trying to say that there is an inherent contradiction in saying that there exists some X that is both unconceived and conceived by me, and he is right to say this. However, he is overlooking the fact that what is really happening when I conceive of an unconceived tree is this: I am conceiving that (there exists some X that is unconceived), with the act of conception outside of the proposition, or content of the perception.