..., they simply have a basic intuition that there couldn’t be abstract mathematical objects. ⁴ If pressed, they may simply say that such objects are too ‘mysterious’ or ‘spooky’ to be admitted into one's ontology. It is easy to be dismissive of such inchoate intuitions. However, I will argue...

...Focuses on an issue about the objectivity of mathematics—the extent to which undecidable sentences have determinate truth‐value—and argues that this issue is more important than the issue of the existence of mathematical objects. It argues that certain familiar problems for those who postulate...

...Chapter 7 provides a noneist account of mathematical and other abstract objects, and of worlds (possible and impossible). It then discusses a number of objections, such as that this is just a form of platonism in disguise. abstract objects mathematical objects non existence non existent objects...

...This chapter introduces the indispensability argument for the existence of mathematical objects, presenting it as relying on three premises: (P1) Naturalism, (P2) Confirmational Holism, and (P3) Indispensability. It lays out the argumentative strategy of the book, noting that, while the assumptions...

... and objectivity in mathematics. It then considers the modern problems of the continuum that exist in ancient Greek geometry, along with the so-called methodological platonism of modern mathematics and its focus on mathematical objects. Finally, it describes the Axiom of Completeness and the Riemann Hypothesis...

...). ⁹⁴ Also, of the next sentence there were two different versions: Knowing how Aristotle reads Plato, it should come as no surprise that he attributes the doctrine of the intermediate status of mathematical objects to Plato, making explicit what the “logic of Plato’s argument requires.” Bonitz...

... Houdé O Newell A Tzourio Mazoyer N conditional sentences modus ponens rule of logic production system theories mathematical objects number learning number meaning concepts of number math schemas mathematical knowledge D.S. Age: 6 years, 2 months: D.S.: The numbers only go to million...

... the explanatoriness, of universals and mathematical objects across the board (or at least across the natural sciences), is there anything persuasive for the realist to say? Some things the realist about Platonist mathematical objects may want to say can look like reducing the puzzle of appeal to mathematical objects...

... a more venerable indispensability argument in the philosophy of mathematics, which takes the indispensability of mathematical objects to the practice of scientific theorizing to be grounds for belief in the former. This chapter explores the parallels between the two types of argument, suggesting...

...; that there are several candidate metaethical analogues of ‘easy-road’ nominalism about mathematical objects; and that in some respects Enoch’s version of the indispensability argument is on safer grounds compared to the more common ones in the philosophy of mathematics. nominalism Quine Putnam indispensability argument...

..., formalization, and constraints over mathematical objects and statements. The chapter also considers gender-neutral mathematical language in the context of sexuality. Combinatorics generating functions interpretation in mathematics variables and unknowns contradiction Turing Alan Wittgenstein Ludwig...

.... It then discusses the cognitive interpretation of mathematical objects, arguing that the meaning of the mathematical line is the protomathematical object obtained by identification of the visual line and the vestibular line. It also contends that what makes the narration or the mathematics interesting...

... is to be understood by taking nominalism simply as the thesis that there are no distinctively mathematical objects: no numbers, sets, functions, groups, and so on. As to the nature of such objects (if there are any), it can be said that it has come to be fairly widely agreed, under the influence...

...The properties and relations that perform a role in mathematical reasoning arise from the basic relations that obtain among mathematical objects. It is in terms of these basic relations that mathematicians identify the objects they intend to study. The way in which mathematicians identify...

... of the doctrine which is discussed in this chapter was Plato's own one). The first subsection of this section considers the problems raised by the concept of Forms as causes, more specifically in relation to the notion that they were, in some way or other, mathematical or quasi-mathematical objects. At lines...

... that the mathematical realist has to solve in order to formulate an acceptable epistemology, and I hint at the direction in which one might hope to find the solution to these puzzles. One of the puzzles, that was first clearly formulated by Paul Benacerraf, is that since mathematical objects are supposed to be causally...

... way whatever: for they are abstractions in thought, just as mathematical objects are. The reply is that [PIB] is separate from definitional priority as it supports the distinction between real and nominal definitional priority. More importantly, [PIB] is distinct from, and more fundamental than, real...

...Are moral properties intellectually indispensable, and, if so, what consequences does this have for our understanding of their nature, and of our talk and knowledge of them? Are mathematical objects intellectually indispensable, and, if so, what consequences does this have for our understanding...

... that they are employed on a regular basis. As generation follows upon generation, the knowledge of how the mathematical enterprise had been launched begins to die out and is eventually lost altogether. People begin thinking of mathematical objects 242 as genuinely there. Some, ironically enough, take the theoretical...