|Abstract||We argue that the language of Zermelo Fraenkel set theory with definitions and partial functions provides the most promising bedrock semantics for communicating and sharing mathematical knowledge. We then describe a syntactic sugaring of that language that provides a way of writing remarkably readable assertions without straying far from the set-theoretic semantics. We illustrate with some examples of formalized textbook definitions from elementary set theory and point-set topology. We also present statistics concerning the complexity of these definitions, under various complexity measures|
|Keywords||No keywords specified (fix it)|
|Categories||No categories specified (fix it)|
|Through your library||Only published papers are available at libraries|
Similar books and articles
Stewart Shapiro (2000). Set-Theoretic Foundations. The Proceedings of the Twentieth World Congress of Philosophy 2000:183-196.
Peter Schreiber (1996). Mengenlehre—Vom Himmel Cantors Zur Theoria Prima Inter Pares. NTM International Journal of History and Ethics of Natural Sciences, Technology and Medicine 4 (1):129-143.
Gianluigi Oliveri (2006). Mathematics as a Quasi-Empirical Science. Foundations of Science 11 (1-2).
J. P. Studd (2012). The Iterative Conception of Set: A (Bi-)Modal Axiomatisation. Journal of Philosophical Logic.
Michał Walicki (2012). Introduction to Mathematical Logic. World Scientific.
Cheng-Hung Tsai (2010). Practical Knowledge of Language. Philosophia 38 (2).
Harry C. Bunt (1985). Mass Terms and Model-Theoretic Semantics. Cambridge University Press.
Cheng-Hung Tsai (2006). On the Epistemology of Language. Southern Journal of Philosophy 44 (4):677-696.
Barry C. Smith (2006). What We Know When We Know a Language. In Ernest Lepore & Barry C. Smith (eds.), Oxford Handbook of Philosophy of Language.
Nicolas D. Goodman (1981). The Experiential Foundations of Mathematical Knowledge. History and Philosophy of Logic 2 (1-2):55-65.
Sorry, there are not enough data points to plot this chart.
Added to index2010-09-11
Total downloads2 ( #234,778 of 556,895 )
Recent downloads (6 months)2 ( #39,122 of 556,895 )
How can I increase my downloads?