|Abstract||We develop a point-free construction of the classical one- dimensional continuum, with an interval structure based on mereology and either a weak set theory or logic of plural quantification. In some respects this realizes ideas going back to Aristotle,although, unlike Aristotle, we make free use of classical "actual infinity". Also, in contrast to intuitionistic, Bishop, and smooth infinitesimal analysis, we follow classical analysis in allowing partitioning of our "gunky line" into mutually exclusive and exhaustive disjoint parts, thereby demonstrating the independence of "indecomposability" from a non-punctiform conception. It is surprising that such simple axioms as ours already imply the Archimedean property and that they determine an isomorphism with the Dedekind-Cantor structure of R as a complete, separable, ordered field. We also present some simple topological models of our system, establishing consistency relative to classical analysis. Finally, after describing how to nominalize our theory, we close with comparisons with earlier efforts related to our own|
|Keywords||No keywords specified (fix it)|
|Through your library||Only published papers are available at libraries|
Similar books and articles
Michael J. White (1988). On Continuity: Aristotle Versus Topology? History and Philosophy of Logic 9 (1):1-12.
Anne Newstead (2001). Aristotle and Modern Mathematical Theories of the Continuum. In Demetra Sfendoni-Mentzou & James Brown (eds.), Aristotle and Contemporary Philosophy of Science. Peter Lang.
Craig Harrison (1996). The Three Arrows of Zeno. Synthese 107 (2):271 - 292.
Athanassios Tzouvaras (1997). The Order Structure of Continua. Synthese 113 (3):381-421.
Geoffrey Hellman (1994). Real Analysis Without Classes. Philosophia Mathematica 2 (3):228-250.
Piotr Błaszczyk, Mikhail G. Katz & David Sherry (2013). Ten Misconceptions From the History of Analysis and Their Debunking. Foundations of Science 18 (1):43-74.
Geoffrey Hellman (2006). Mathematical Pluralism: The Case of Smooth Infinitesimal Analysis. Journal of Philosophical Logic 35 (6):621 - 651.
Philip Ehrlich (2012). The Absolute Arithmetic Continuum and the Unification of All Numbers Great and Small. Bulletin of Symbolic Logic 18 (1):1-45.
Richard Jozsa (1986). An Approach to the Modelling of the Physical Continuum. British Journal for the Philosophy of Science 37 (4):395-404.
Daniel Dzierzgowski (1995). Models of Intuitionistic TT and N. Journal of Symbolic Logic 60 (2):640-653.
Anne Newstead & Franklin James (2008). On the Reality of the Continuum. Philosophy 83 (01):117-28.
Added to index2012-11-07
Total downloads19 ( #64,378 of 549,075 )
Recent downloads (6 months)13 ( #5,011 of 549,075 )
How can I increase my downloads?