Kempson et al. (2016) deliver a well-reasoned, subtle and interesting critique of the current orthodoxy in linguistics, and also offer an alternative approach which, they would argue, goes a long way to remedying the problems that they have uncovered. I find their approach very appealing: I think that the issues which they have uncovered are genuine issues, and that their proposed resolution of these issues is a very plausible first step, but, I would argue, does not go far enough. First some words about my understanding of the main thesis of Kempson et al. (2016); the two main problems of the current linguistic authodoxy are propositionalism – the thesis that the fundamental objects of interest are propositions, that these are what language-using humans interact with, and consequently that these are the objects that linguistics must study – and antipragmatism, the thesis that pragmatics is not constitutive of the semantics or syntax of human language. By contrast, Kempson et al. (2016) advocate an approach to syntax which is resolutely higher order: the fundamental linguistic objects are what would, orthodoxly, be called sentence fragments, that humans use such sentence fragments against a context which provides them with a semantics, that, in the case of linguistic interaction, this context is shared between the participants, and that linguistic interaction typically operates on both context and sentence fragment, extending the sentence fragment, while simultaneously manipulating the context, until an assertion is made. From the present author’s standpoint – that is, against a background of algebraic geometry, the semantics of programming languages, and philosophy – this is a position which makes a great deal of sense: the evaluation of salient items against a context is well established in both algebraic geometry (Grothendieck 1970) and in the semantics of programming languages (Winskel

中文翻译：

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动态句法与证明理论

Kempson等。（2016）对当前语言学中的正统观念进行了理性，微妙和有趣的批判，并提供了另一种方法，他们认为，这对于解决他们发现的问题大有帮助。我认为他们的方法非常吸引人：我认为他们发现的问题是真正的问题，他们对这些问题的拟议解决是非常合理的第一步，但我认为这还远远不够。首先说一下我对肯普森等人主要论文的理解。（2016）；当前语言学方法论的两个主要问题是命题主义–感兴趣的基本客体是命题的论点，这些命题是使用语言的人与之互动的，因此，这些是语言学必须研究的对象以及反实用主义的论点，即语用学不是人类语言的语义或语法的构成。相比之下，肯普森等。（2016）提倡一种绝对更高阶的句法方法：基本的语言对象通常被称为句子片段，即人类在提供语义的上下文中使用这些句子片段，在这种情况下就语言交互而言，这种上下文是在参与者之间共享的，并且语言交互通常在上下文和句子片段上进行操作，扩展了句子片段，同时操纵了上下文，直到断言为止。从当前作者的角度来看-即在代数几何的背景下，