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In the first dialogue, Philonous wants to show that all sensible objects are mind-dependent. He begins by trying to show that all sensible qualities are mind-dependent. In other words, he wants to prove that there is no such thing as, say, a blue ball out in the world. Blueness cannot exist outside of the mind. This, of course, sounds wrong to us. We do not think that blueness, or sweetness or roundness or whatever, depends on our mind. We think that these qualities belong to objects out in the world. We think that the ball is inherently blue and round and would be even if there were no one around to see it.
But there is one quality that we can all agree exists only in our own minds: pain. There is no such thing as pain out in the world. No one would say that a knife contains pain, though a knife can cause pain in us if it cuts our flesh. Pain only exists when it is being perceived. We would never say that someone was in pain, but that they just could not feel it. The essence of pain is a feeling. Berkeley uses our intuitions about pain to get us to admit that all the qualities are just like pain in this respect: they all exist only when perceived. Just as there is no such thing as pain that is not perceived, there is also no such thing as blue than is not perceived, or sweetness that is not perceived, or roundness that is not perceived.
Berkeley accomplishes this by linking up all the qualities with pain (or pleasure, which has the same relevant features as pain). He begins by linking heat with pain. Intense heat, he tells us, is experienced as pain. This seems undeniably true. The way that we perceive intense heat is as pain; the pain is indistinguishable from any other sensation of the heat which we might have. But if intense heat is felt as pain, then just as pain cannot exist outside of the mind, intense heat cannot exist outside of the mind. As a form of pain, intense heat only exists when it is being perceived. Since intense heat is mind- dependent, we can conclude that all degrees of heat are mind-dependent. Otherwise, we would be forced to say that as heat went up in degree, it moved from outside to inside the mind.