# Author B Van Kerkhove

Van Bendegem J. P. & Van Kerkhove B. (2009) Mathematical arguments in context. Foundations of Science 14(1/2): 45–57. https://cepa.info/321

Van Bendegem J. P. & Van Kerkhove B.
(

2009)

Mathematical arguments in context.
Foundations of Science 14(1/2): 45–57.
Fulltext at https://cepa.info/321
Except in very poor mathematical contexts, mathematical arguments do not stand in isolation of other mathematical arguments. Rather, they form trains of formal and informal arguments, adding up to interconnected theorems, theories and eventually entire fields. This paper critically comments on some common views on the relation between formal and informal mathematical arguments, most particularly applications of Toulmin’s argumentation model, and launches a number of alternative ideas of presentation inviting the contextualization of pieces of mathematical reasoning within encompassing bodies of explicit and implicit, formal and informal background knowledge.

Van Kerkhove B. (2011) Dialectics in Action, World at Stake. Review of “Bridges to the World. A Dialogue on the Construction of Knowledge, Education, and Truth” by David Kenneth Johnson & Matthew R. Silliman. Constructivist Foundations 7(1): 78–80. https://cepa.info/246

Van Kerkhove B.
(

2011)

Dialectics in Action, World at Stake. Review of “Bridges to the World. A Dialogue on the Construction of Knowledge, Education, and Truth” by David Kenneth Johnson & Matthew R. Silliman.
Constructivist Foundations 7(1): 78–80.
Fulltext at https://cepa.info/246
Upshot: This is a deceptively profound, compact book that can be inscribed in the grand tradition of philosophical dialogue. It confronts naive realism and radical constructivism, arriving at a seemingly workable conciliatory position.

Van Kerkhove B. & Van Bendegem J. P. (2008) Pi on earth, or mathematics in the real world. Erkenntnis 68(3): 421–435.

Van Kerkhove B. & Van Bendegem J. P.
(

2008)

Pi on earth, or mathematics in the real world.
Erkenntnis 68(3): 421–435.
The authors argue in favor of the view that in mathematics, which increasingly relies on computers to warrant mathematical results, the hunt for absolute certainty will become more and more expensive.

Van Kerkhove B. & Van Bendegem J. P. (2012) The Many Faces of Mathematical Constructivism. Constructivist Foundations 7(2): 97–103. https://cepa.info/251

Van Kerkhove B. & Van Bendegem J. P.
(

2012)

The Many Faces of Mathematical Constructivism.
Constructivist Foundations 7(2): 97–103.
Fulltext at https://cepa.info/251
Context: As one of the major approaches within the philosophy of mathematics, constructivism is to be contrasted with realist approaches such as Platonism in that it takes human mental activity as the basis of mathematical content. Problem: Mathematical constructivism is mostly identified as one of the so-called foundationalist accounts internal to mathematics. Other perspectives are possible, however. Results: The notion of “meaning finitism” is exploited to tie together internal and external directions within mathematical constructivism. The various contributions to this issue support our case in different ways. Constructivist content: Further contributions from a multitude of constructivist directions are needed for the puzzle of an integrative, overarching theory of mathematical practice to be solved.

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