English philosopher John Locke gives us a pretty standard way to map out boundaries of intuition. So that's where we'll start. Locke contrasts intuition to sensory perception on one side and to demonstration on the other. Sensory perception, he notices, is always about particular things. You see this pizza in front of you right now. Maybe you see that this pizza is round. But we aren't restricted to making judgements about particular things. When we judge that "No round things are square", we aren't just thinking about that particular pizza, but about a more general and abstract truth. Judging that circles are different from squares, according to Locke, is intuitive. And at least in this kind of case where Locke thinks we're recognizing features of our ideas, intuition is a perfectly good source of knowledge. We know that no round things are square through intuition. Locke also draws a contrast between intuition and demonstration. Intuition can tell us directly that a circle is not a triangle. But when we get to more complex questions, we need to use demonstration or explicit reasoning. So for example, we can figure out that the interior angles of a triangle add up to two right angles, but we have to go through a series of steps to gain this knowledge. And that’s demonstration. Demonstration requires conscious stages. Intuition is immediate. Locke notices that intuition and demonstration are connected, however.