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Mark Balaguer's Platonism and AntiPlatonism in Mathematics presents an intriguing new brand of platonism, which he calls plenitudinous platonism, or more colourfully, fullblooded platonism. In this paper, I argue that Balaguer's attempts to characterise fullblooded platonism fail. They are either too strong, with untoward consequences we all reject, or too weak, not providing a distinctive brand of platonism strong enough to do the work Balaguer requires of it. 

A formal theory of quantity T Q is presented which is realist, Platonist, and syntactically secondorder (while logically elementary), in contrast with the existing formal theories of quantity developed within the theory of measurement, which are empiricist, nominalist, and syntactically firstorder (while logically nonelementary). T Q is shown to be formally and empirically adequate as a theory of quantity, and is argued to be scientifically superior to the existing firstorder theories of quantity in that it does not depend upon empirically (...) 

Platonism about mathematics (or mathematical platonism) is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our language, thought, and practices. In this survey article, the view is clarified and distinguished from some related views, and arguments for and against the view are discussed. 

Everything red is colored, and all squares are polygons. A square is distinguished from other polygons by being foursided, equilateral, and equiangular. What distinguishes red things from other colored things? This has been understood as a conceptual rather than scientific question. Theories of wavelengths and reflectance and sensory processing are not considered. Given just our ordinary understanding of color, it seems that what differentiates red from other colors is only redness itself. The Cambridge logician W. E. Johnson introduced the terms (...) 





The global/local contrast is ubiquitous in mathematics. This paper explains it with straightforward examples. It is possible to build a circular staircase that is rising at any point (locally) but impossible to build one that rises at all points and comes back to where it started (a global restriction). Differential equations describe the local structure of a process; their solution describes the global structure that results. The interplay between global and local structure is one of the great themes of mathematics, (...) 

Mathematical fictionalism (or as I'll call it, fictionalism) is best thought of as a reaction to mathematical platonism. Platonism is the view that (a) there exist abstract mathematical objects (i.e., nonspatiotemporal mathematical objects), and (b) our mathematical sentences and theories provide true descriptions of such objects. So, for instance, on the platonist view, the sentence ‘3 is prime’ provides a straightforward description of a certain object—namely, the number 3—in much the same way that the sentence ‘Mars is red’ provides a (...) 



