Objectivist: The concept of a triangle includes those that are either equilateral, or isosceles, or scalene.
According to Binswanger: "The Realist theory of concepts says just the opposite. Locke, for example, says that "triangle" is a concept of what is neither equilateral nor scalene "but all and none of these at once" [Locke, IV, VII, 9]. (Binswanger skipped Locke including "equicrural", a synonym of isosceles.)
I admit that Locke is vague and even apparently contradictory here. How can the concept triangle be both all and none of these sub-kinds at once? But I think Binswanger interprets Locke uncharitably. Locke's phrase can be interpreted as "but all and none of these singly." That dissolves the apparent contradiction. And isn't that what the general idea triangle is -- a flat shape that has three straight sides and three angles? The units of the general idea include equilateral and isosceles and scalene triangles, but the general idea triangle itself is not limited to any one of these sub-kinds.
Neither Locke nor Binswanger present a visual model that captures the general idea of triangle, but I offer the following. Imagine a manipulable triangle on a computer screen that allows one to grab any vertex where two lines intersect and move the vertex anywhere desired with such two intersecting lines remaining straight and unbroken. It would be like the one on this page with two revisions. The stationary vertex would be movable, and the movable vertexes could be moved off the x-axis.
Bishop George Berkeley cited Locke's passage about the abstract idea triangle and then, plainly with ridicule, said, "All I desire is that the reader would fully and certainly inform himself whether he has such an idea or no" (The Principles of Human Knowledge, Introduction, paragraph 13). I hereby reply, "Yes, I do!"
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