Michael friedmans behandlung Des unterschieDes zwischen arithmetik und algebra bei Kant in Kant and the exact sciences
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Kant-Studien 101 (1):75-88 (2010)
In the second chapter of his book Kant and the Exact Sciences Michael Friedman deals with two different interpretations of the relation or the difference between algebra and arithmetic in Kant's thought. According to the first interpretation algebra can be described as general arithmetic because it generalizes over all numbers by the use of variables, whereas arithmetic only deals with particular numbers. The alternative suggestion is that algebra is more general than arithmetic because it considers a more general class of magnitudes. This means that arithmetic is concerned only with rational magnitudes, whereas algebra is also concerned with irrational magnitudes. In this article, I will discuss which of the two aforementioned approaches is to be considered the most plausible interpretation of Kant's theory of algebra and arithmetic. According to Friedman, the first interpretation cannot be reconciled with certain statements made by Kant on various occasions. The second interpretation is developed by Friedman himself. It is meant to be an attempt to avoid such inconsistencies. By a detailed analysis of the texts Friedman himself cites I shall examine the soundness of his arguments against the first interpretation and the compatibility of his own interpretation of the difference between algebra and arithmetic with the relevant passages in Kant's texts. It will turn out that the reasons that make Friedman reject the first interpretation are invalid as they are based on misunderstandings and that his own interpretation does not expound Kant's notions on that subject correctly, whereas the first interpretation is compatible with these passages. Thus, I conclude that the interpretation rejected by Friedman, unlike his own approach, is actually the more adequate interpretation of Kant.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Werner Loh (1992). Kant-Forschungen Als Beispiel Für Selbstverschuldeten Methodenmangel. Journal for General Philosophy of Science 23 (1):105 - 128.
Benjamin Vilhauer (2004). Can We Interpret Kant as a Compatibilist About Determinism and Moral Responsibility? British Journal for the History of Philosophy 12 (4):719 – 730.
Kenneth R. Westphal (1998). ‘Buchdahl’s “Phenomenological” View of Kant: A Critique’. Kant-Studien 89 (3):335-352.
Daniel Sutherland (2006). Kant on Arithmetic, Algebra, and the Theory of Proportions. Journal of the History of Philosophy 44 (4):533-558.
Michael Friedman & Graham Bird (1998). Kantian Themes in Contemporary Philosophy. Aristotelian Society Supplementary Volume 72 (1):111–130.
Andrew Janiak (2004). Kant as Philosopher of Science. Perspectives on Science 12 (3):339-363.
Joshua Glasgow (2007). Kant's Conception of Humanity. Journal of the History of Philosophy 45 (2):291-308.
Michael Friedman (1992). Kant and the Exact Sciences. Harvard University Press.
Kristina Engelhard & Peter Mittelstaedt (2008). Kant's Theory of Arithmetic: A Constructive Approach? [REVIEW] Journal for General Philosophy of Science 39 (2):245 - 271.
Added to index2010-03-21
Total downloads17 ( #108,108 of 1,413,281 )
Recent downloads (6 months)1 ( #154,925 of 1,413,281 )
How can I increase my downloads?