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<p>In this paper, I present several philosophical applications of pure type systems. As I explain, many pure type systems are more expressively powerful than the higher-order languages—like the simply typed lambda calculus—on which philosophers have focused. Consequently, pure type systems support the formulation of more general, and more unified, metaphysical theories. To illustrate this, I use pure type systems to formulate some extremely general principles of grounding: these principles describe ground-theoretic connections among items drawn from across the hierarchy of types. I also present both informal theories, and formally rigorous theories, of what pure type systems say about the world.</p>

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Pure type systems and generalized grounding

  • 期刊论文

  • 发表日期：

    2025年7月4日

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  • Isaac Wilhelm

摘要

In this paper, I present several philosophical applications of pure type systems. As I explain, many pure type systems are more expressively powerful than the higher-order languages—like the simply typed lambda calculus—on which philosophers have focused. Consequently, pure type systems support the formulation of more general, and more unified, metaphysical theories. To illustrate this, I use pure type systems to formulate some extremely general principles of grounding: these principles describe ground-theoretic connections among items drawn from across the hierarchy of types. I also present both informal theories, and formally rigorous theories, of what pure type systems say about the world.