二阶模态逻辑

Andrew Parisi
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引用次数: 2

摘要

摘要本文介绍了自由一阶和二阶逻辑的一种新的序演法,以及模态逻辑K、D、T、B、S4和S5的超序演法;为了获得更强模态逻辑的演算,只需要在K的演算中加入外部结构规则,而操作规则和内部结构规则保持不变。证明了所给出的所有演算的完备性和切消性。在哲学上,本文发展了一种推理主义或证明论的意义理论。它的出发点是,一个句子的意义是由它的使用规则决定的。特别地,一个句子的使用有两个特征共同决定了它的意义,即断言这个句子是连贯的条件和否认这个句子是连贯的条件。本文发展了一种量化理论,它标志着语言可以扩展的连贯方式,而情态则是我们反思支配语言断言和否认条件的规范的手段。如果所争论的量化观点是正确的,那么二阶量化和唯名论之间就没有紧张关系。特别是,人们通过使用量词而产生的本体论行为完全依赖于人们通过使用原子句而产生的本体论行为。最后,本文将发展起来的意义理论应用于形而上学的必然性和偶然性问题。本文提出并阐述了对偶然性逻辑的两个反对意见。结果表明,所得到的逻辑符合论文对量词和模态操作符的意义理论的所有要求。摘要:Andrew Parisi E-mail: andrew.p.parisi@gmail.com URL: https://opencommons.uconn.edu/dissertations/1480/
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Second-Order Modal Logic
Abstract The dissertation introduces new sequent-calculi for free first- and second-order logic, and a hyper-sequent calculus for modal logics K, D, T, B, S4, and S5; to attain the calculi for the stronger modal logics, only external structural rules need to be added to the calculus for K, while operational and internal structural rules remain the same. Completeness and cut-elimination are proved for all calculi presented. Philosophically, the dissertation develops an inferentialist, or proof-theoretic, theory of meaning. It takes as a starting point that the sense of a sentence is determined by the rules governing its use. In particular, there are two features of the use of a sentence that jointly determine its sense, the conditions under which it is coherent to assert that sentence and the conditions under which it is coherent to deny that sentence. The dissertation develops a theory of quantification as marking coherent ways a language can be expanded and modality as the means by which we can reflect on the norms governing the assertion and denial conditions of our language. If the view of quantification that is argued for is correct, then there is no tension between second-order quantification and nominalism. In particular, the ontological commitments one can incur through the use of a quantifier depend wholly on the ontological commitments one can incur through the use of atomic sentences. The dissertation concludes by applying the developed theory of meaning to the metaphysical issue of necessitism and contingentism. Two objections to a logic of contingentism are raised and addressed. The resulting logic is shown to meet all the requirement that the dissertation lays out for a theory of meaning for quantifiers and modal operators. Abstract prepared by Andrew Parisi E-mail: andrew.p.parisi@gmail.com URL: https://opencommons.uconn.edu/dissertations/1480/
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POUR-EL’S LANDSCAPE CATEGORICAL QUANTIFICATION POINCARÉ-WEYL’S PREDICATIVITY: GOING BEYOND A TOPOLOGICAL APPROACH TO UNDEFINABILITY IN ALGEBRAIC EXTENSIONS OF John MacFarlane, Philosophical Logic: A Contemporary Introduction, Routledge Contemporary Introductions to Philosophy, Routledge, New York, and London, 2021, xx + 238 pp.
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