Mathematical Thinking in Hegel’s Science of Logic

Author(s):  
Pirmin Stekeler-Weithofer
1996 ◽  
Vol 41 (1) ◽  
pp. 80-80
Author(s):  
Daniel Stalder ◽  
Shubhangi Stalder

PsycCRITIQUES ◽  
2010 ◽  
Vol 55 (23) ◽  
Author(s):  
Gordon Pitz

2020 ◽  
Author(s):  
Jennifer McDonald ◽  
Rebecca Merkley ◽  
Jacqueline Mickle ◽  
Lisa Collimore ◽  
Daniel Ansari

Research in cognitive development has highlighted that early numeracy skills are associated with later math achievement, suggesting that these skills should be targeted in early math education. Here we tested whether tools used by researchers to assess mathematical thinking could be useful in the classroom. This paper describes a collaborative project between cognitive scientists and school board researchers/educators implementing numeracy screeners with kindergarten students over the course of three school years. The Give-A-Number task (Wynn, 1990) was used with first-year kindergarten students and the Numeracy Screener [BLINDED] with second-year kindergarten students. Results indicated that educators (N = 59) found the tools feasible to implement and helpful for exploring their students’ thinking and targeting instruction. The Educators’ feedback also helped inform improvements to the implementation of the tools and future directions for both the schools and the researchers. This work emphasizes the importance of transdisciplinary collaboration to address the research-practice gap.


Author(s):  
Huaping Lu-Adler

This book is both a history of philosophy of logic told from the Kantian viewpoint and a reconstruction of Kant’s theory of logic from a historical perspective. Kant’s theory represents a turning point in a history of philosophical debates over the following questions: (1) Is logic a science, instrument, standard of assessment, or mixture of these? (2) If logic is a science, what is the subject matter that differentiates it from other sciences, particularly metaphysics? (3) If logic is a necessary instrument to all philosophical inquiries, how is it so entitled? (4) If logic is both a science and an instrument, how are these two roles related? Kant’s answer to these questions centers on three distinctions: general versus particular logic, pure versus applied logic, pure general logic versus transcendental logic. The true meaning and significance of each distinction becomes clear, this book argues, only if we consider two factors. First, Kant was mindful of various historical views on how logic relates to other branches of philosophy (viz. metaphysics and physics) and to the workings of common human understanding. Second, he first coined “transcendental logic” while struggling to secure metaphysics as a proper “science,” and this conceptual innovation would in turn have profound implications for his mature theory of logic. Against this backdrop, the book reassesses the place of Kant’s theory in the history of philosophy of logic and highlights certain issues that are still debated today, such as normativity of logic and the challenges posed by logical pluralism.


Author(s):  
Robert B. Pippin

Hegel famously says in the “Preface” to The Philosophy of Right that that outline or Grundriss presupposes “the speculative mode of cognition.” This is to be contrasted with what he calls “the old logic” and “the knowledge of the understanding” (Verstandeserkenntnis), a term he also uses to characterize all of metaphysics prior to his own. He makes explicit that he is referring to his book, The Science of Logic, but he does not explain the nature of this dependence anywhere in the book. This chapter attempts to explain the nature of this dependence, and to show that it is indeed crucial to understanding the argument of the work.


Author(s):  
Michael Ernst

In the foundations of mathematics there has been an ongoing debate about whether categorical foundations can replace set-theoretical foundations. The primary goal of this chapter is to provide a condensed summary of that debate. It addresses the two primary points of contention: technical adequacy and autonomy. Finally, it calls attention to a neglected feature of the debate, the claim that categorical foundations are more natural and readily useable, and how deeper investigation of that claim could prove fruitful for our understanding of mathematical thinking and mathematical practice.


ACM Inroads ◽  
2014 ◽  
Vol 5 (1) ◽  
pp. 35-36 ◽  
Author(s):  
Peter B. Henderson ◽  
Allan M. Stavely

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