Shadows of Syntax最新文献

Shadows of Syntax

Pub Date : 2020-10-29 DOI: 10.1093/oso/9780190086152.003.0006

Jared Warren

This chapter shows that unrestricted inferentialism/conventionalism leads to a naturalistically satisfying account of our a priori knowledge of logical validity. The chapter first lays the groundwork by discussing the general question of what conditions arguments need to meet in order to lead to knowledge of their conclusions. Following Boghossian, the chapter then argues that inferentialism/conventionalism is particularly well posed to allow rule-circular arguments to lead to a priori knowledge of the validity of our basic rules. Restricted inferentialists were often forced to complicate and sometimes abandon their accounts of logical knowledge in the face of bad company. By contrast, unrestricted inferentialism has no problem at all with bad company. All told, conventionalism gives a naturalistic account of our a priori knowledge of logic.

本章表明，不受限制的推理主义/约定主义导致我们对逻辑有效性的先验知识的自然地令人满意的说明。本章首先通过讨论论证需要满足什么条件才能得出结论这一一般性问题奠定了基础。继Boghossian之后，本章接着论证了推理主义/约定主义特别适合于允许规则循环论证导致我们对基本规则有效性的先验知识。面对糟糕的伙伴，有限的推理主义者常常被迫使他们对逻辑知识的描述复杂化，有时甚至放弃。相比之下，无限制推理主义对坏伙伴完全没有问题。总之，约定主义对我们先验的逻辑知识给出了自然主义的解释。

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Mathematical Determinacy 数学确定性

Shadows of Syntax

Pub Date : 2020-10-29 DOI: 10.1093/oso/9780190086152.003.0010

Jared Warren

This chapter addresses the second major challenge for the extension of conventionalism from logic to mathematics: the richness of mathematical truth. The chapter begins by distinguishing indeterminacy from pluralism and clarifying the crucial notion of open-endedness. It then critically discusses the two major strategies for securing arithmetical categoricity using open-endedness; one based on a collapse theorem, the other on a kind of anti-overspill idea. With this done, a new argument for the categoricity of arithmetic is then presented. In subsequent discussion, the philosophical importance of this categoricity result is called into question to some degree. The categoricity argument is then supplemented by an appeal to the infinitary omega rule, and an argument is given that beings like us can actually follow the omega rule without any violation of Church’s thesis. Finally, the chapter discusses the extension of this type of approach beyond arithmetic, to set theory and the rest of mathematics.

本章讨论了从逻辑向数学扩展惯例主义的第二个主要挑战:数学真理的丰富性。本章首先区分不确定性和多元主义，并澄清开放性的关键概念。然后批判性地讨论了使用开放性确保算术范畴性的两种主要策略;一个基于坍缩定理，另一个基于一种反溢出思想。在此基础上，提出了一个关于算术范畴性的新论证。在随后的讨论中，这个范畴性结果的哲学重要性在某种程度上受到质疑。然后，对无限欧米伽规则的呼吁补充了范畴性论证，并给出了一个论证，即像我们这样的生物实际上可以遵循欧米伽规则，而不会违反丘奇的论点。最后，本章讨论了这种方法在算术之外的扩展，到集合论和其他数学领域。

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The Facts of the Matter 事情的真相

Shadows of Syntax

Pub Date : 2020-10-29 DOI: 10.1093/oso/9780190086152.003.0014

Jared Warren

This chapter concerns the status of the conventionalist theory developed, argued for, and defended throughout the book. It begins by discussing the views that historical conventionalists had about their own conventionalist theories and addresses a recent controversy about whether Carnap was truly a conventionalist. The chapter then argues that conventionalism is the best explanation of the logical and mathematical facts, assessing it according to a number of different theoretical virtues. Then two metaobjections are considered, one based on philosophical progress, and the other based on peer disagreement. Despite the chapter’s defense of conventionalism, it ends by expressing some very personal doubts.

这一章关注贯穿全书的传统主义理论的发展、论证和辩护的地位。它首先讨论了历史上的约定主义者对他们自己的约定主义理论的看法，并讨论了最近关于卡尔纳普是否真的是一个约定主义者的争论。然后，本章论证了约定主义是对逻辑和数学事实的最佳解释，并根据许多不同的理论优点对其进行了评估。然后考虑两种元异议，一种基于哲学进步，另一种基于同行分歧。尽管这一章为传统主义辩护，但它以表达一些非常个人的怀疑结束。

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Logical Conventionalism 逻辑墨守成规

Shadows of Syntax

Pub Date : 2020-10-29 DOI: 10.1093/oso/9780190086152.003.0004

Jared Warren

This chapter argues that logical truth, validity, and necessity in any language can be fully explained in terms of the language’s linguistic conventions. More particularly, it is demonstrated that unrestricted logical inferentialism is a version of logical conventionalism by arguing for conventionalism in detail and answering various objections involving the role of metasemantic principles and semantic completeness in the conventionalist argument. The chapter then discusses how this account relates to the deflationist accounts offered by Field and others, before turning to the metaphysics and normativity of logic, which it discusses on conventionalist grounds. Overall, this chapter shows that conventionalism leads to a naturalistically acceptable and philosophically plausible theory of logic.

本章认为，任何语言的逻辑真理、有效性和必然性都可以用语言的语言惯例来充分解释。更具体地说，它证明了无限制的逻辑推理主义是逻辑约定主义的一个版本，通过详细地论证约定主义，并回答了涉及元语义原则和语义完整性在约定主义论点中的作用的各种反对意见。然后，本章讨论了这种解释如何与菲尔德和其他人提供的通货紧缩主义解释联系起来，然后转向逻辑的形而上学和规范性，这是在约定主义的基础上讨论的。总的来说，这一章表明，约定主义导致一种自然上可接受的和哲学上似是而非的逻辑理论。

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Linguistic Conventions 语言习惯

Shadows of Syntax

Pub Date : 2020-10-29 DOI: 10.1093/oso/9780190086152.003.0002

Jared Warren

What are linguistic conventions? This chapter begins by noting and setting aside philosophical accounts of social conventions stemming from Lewis’s influential treatment. It then criticizes accounts that see conventions as explicit stipulations. From there the chapter argues that conventions are syntactic rules of inference, arguing that there are scientific reasons to posit these rules as part of our linguistic competence and that we need to include both bilateralist and open-ended inference rules for a full account. The back half of the chapter aims to naturalize inference rule-following by providing functionalist-dispositionalist approaches to our attitudes, inference, and inference-rule–following, addressing Kripkenstein’s arguments and several other concerns along the way.

什么是语言惯例?这一章首先注意到并搁置了源于刘易斯有影响力的治疗的社会习俗的哲学解释。然后，它批评了将公约视为明确规定的说法。从这里开始，本章认为惯例是推理的句法规则，认为有科学理由将这些规则假设为我们语言能力的一部分，我们需要包括双边主义和开放式推理规则。本章的后半部分旨在通过为我们的态度、推理和推理规则遵循提供功能主义者-配置主义者的方法来自然化推理规则遵循，并在此过程中解决Kripkenstein的论点和其他几个问题。

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