11 found
Sort by:
  1. Jessica Carter (2014). Mathematics Dealing with 'Hypothetical States of Things'. Philosophia Mathematica 22 (2):209-230.
    This paper takes as a starting point certain notions from Peirce's writings and uses them to propose a picture of the part of mathematical practice that consists of hypothesis formation. In particular, three processes of hypothesis formation are considered: abstraction, generalisation, and an abductive-like inference. In addition Peirce's pragmatic conception of truth and existence in terms of higher-order concepts are used in order to obtain a kind of pragmatic realist picture of mathematics.
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  2. Jessica Carter (2013). Handling Mathematical Objects: Representations and Context. Synthese 190 (17):3983-3999.
    This article takes as a starting point the current popular anti realist position, Fictionalism, with the intent to compare it with actual mathematical practice. Fictionalism claims that mathematical statements do purport to be about mathematical objects, and that mathematical statements are not true. Considering these claims in the light of mathematical practice leads to questions about how mathematical objects are handled, and how we prove that certain statements hold. Based on a case study on Riemann’s work on complex functions, I (...)
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  3. Jessica Carter (2012). The Role of Representations in Mathematical Reasoning1. Philosophia Scientiae 16:55-70.
    No categories
    Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  4. Tinne Hoff Kjeldsen & Jessica Carter (2012). The Growth of Mathematical Knowledge—Introduction of Convex Bodies. Studies in History and Philosophy of Science Part A 43 (2):359-365.
    Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  5. Jessica Carter (2010). Diagrams and Proofs in Analysis. International Studies in the Philosophy of Science 24 (1):1 – 14.
    This article discusses the role of diagrams in mathematical reasoning in the light of a case study in analysis. In the example presented certain combinatorial expressions were first found by using diagrams. In the published proofs the pictures were replaced by reasoning about permutation groups. This article argues that, even though the diagrams are not present in the published papers, they still play a role in the formulation of the proofs. It is shown that they play a role in concept (...)
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  6. Jessica Carter (2008). Categories for the Working Mathematician: Making the Impossible Possible. Synthese 162 (1):1 - 13.
    This paper discusses the notion of necessity in the light of results from contemporary mathematical practice. Two descriptions of necessity are considered. According to the first, necessarily true statements are true because they describe ‘unchangeable properties of unchangeable objects’. The result that I present is argued to provide a counterexample to this description, as it concerns a case where objects are moved from one category to another in order to change the properties of these objects. The second description concerns necessary (...)
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  7. Jessica Carter (2008). Structuralism as a Philosophy of Mathematical Practice. Synthese 163 (2):119 - 131.
    This paper compares the statement ‘Mathematics is the study of structure’ with the actual practice of mathematics. We present two examples from contemporary mathematical practice where the notion of structure plays different roles. In the first case a structure is defined over a certain set. It is argued firstly that this set may not be regarded as a structure and secondly that what is important to mathematical practice is the relation that exists between the structure and the set. In the (...)
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  8. Jessica Carter, Jussi Haukioja, Mariska E. M. P. J. Leunissen & Brendan Larvor (2007). Book Reviews. [REVIEW] International Studies in the Philosophy of Science 21 (2):213 – 225.
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  9. Jessica Carter (2005). Individuation of Objects – a Problem for Structuralism? Synthese 143 (3):291 - 307.
    . This paper identifies two aspects of the structuralist position of S. Shapiro which are in conflict with the actual practice of mathematics. The first problem follows from Shapiros identification of isomorphic structures. Here I consider the so called K-group, as defined by A. Grothendieck in algebraic geometry, and a group which is isomorphic to the K-group, and I argue that these are not equal. The second problem concerns Shapiros claim that it is not possible to identify objects in a (...)
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  10. Jessica Carter (2005). Motivations for Realism in the Light of Mathematical Practice. Croatian Journal of Philosophy 5 (1):17-29.
    The aim of this paper is to identify some of the motivations that can be found for taking a realist position concerning mathematical entities and to examine these motivations in the light of a case study in contemporary mathematics. The motivations that are found are as follows: (some) mathematicians are realists, mathematical statements are true, and finally, mathematical statements have a special certainty. These claims are compared with a result in algebraic topology stating that a certain sequence, the so-called Mayer-Vietoris (...)
    No categories
    Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  11. Jessica Carter (2004). Ontology and Mathematical Practice. Philosophia Mathematica 12 (3):244-267.
    In this paper I propose a position in the ontology of mathematics which is inspired mainly by a case study in the mathematical discipline if-theory. The main theses of this position are that mathematical objects are introduced by mathematicians and that after mathematical objects have been introduced, they exist as objectively accessible abstract objects.
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation