 The American philosopher-mathematician Charles Sanders Peirce’s (1839–1914) view of the  continuum[38]  was, in a sense, intermediate between that of Brentano and the arithmetizers. Like Brentano, he held that the cohesiveness of a continuum rules out the possibility of it being a mere collection of discrete individuals, or points, in the usual sense. And even before Brouwer, Peirce seems to have been aware that a faithful account of the continuum will involve questioning the law of excluded middle. Peirce also held that any continuum harbors an unboundedly large collection of points—in his colorful terminology, a supermultitudinous collection—what we would today call a proper class. Peirce maintained that if enough points were to be crowded together by carrying insertion of new points between old to its ultimate limit they would—through a logical “transformation of quantity into quality”—lose their individual identity and become fused into a true continuum.