Results for 'countabilism'

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  1. Countabilism and Maximality Principles.Neil Barton & Sy-David Friedman - manuscript
    It is standard in set theory to assume that Cantor's Theorem establishes that the continuum is an uncountable set. A challenge for this position comes from the observation that through forcing one can collapse any cardinal to the countable and that the continuum can be made arbitrarily large. In this paper, we present a different take on the relationship between Cantor's Theorem and extensions of universes, arguing that they can be seen as showing that every set is countable and that (...)
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  2. Is (un)countabilism restrictive?Neil Barton - manuscript
    Let's suppose you think that there are no uncountable sets. Have you adopted a restrictive position? It is certainly tempting to say yes---you've prohibited the existence of certain kinds of large set. This paper argues that this intuition can be challenged. Instead, I argue that there are some considerations based on a formal notion of restrictiveness which suggest that it is restrictive to hold that there are uncountable sets.
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    Metasemantics and the Continuum Hypothesis.Neil Barton - manuscript
    The Continuum Hypothesis featured top of Hilbert's list of 23 problems in 1900. Today, we still consider the question, with various programmes pulling in different directions. This conceptual diversity raises a puzzle: In what sense do we disagree when we talk about it? A standard assumption takes it that the content of our thought about classes and the Continuum Hypothesis has not changed. Assuming a moderate view of how content is determined, I reject this assumption but also argue that whilst (...)
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