格雷厄姆·普里斯特（Graham Priest）在《Mind》上发表的文章分析，我发现了其思考的严谨与深刻。因此，我在与其直接交流的基础之上，进一步对其以往发表的文章再来一次系统地回顾和梳理。旨在就我们共同关注的深刻的根基性问题做进一步探讨。

附录：

GRAHAM PRIEST; The Limits of Thought—and Beyond, Mind, Volume C, Issue 399, 1 July 1991, Pages 361–370, https://doi.org/10.1093/mind/C.399.361

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.896.8088&rep=rep1&type=pdf 

https://core.ac.uk/display/43397348 

37．格雷厄姆·普里斯特（Graham Priest）

1. 查询：Graham Priest Mind

2. 结果：

   
   

   https://academic.oup.com/mind/article-abstract/C/399/361/2918302?redirectedFrom=PDF 
   

   2.1. 

   Is Arithmetic Consistent? 

   GRAHAM PRIEST 

   There are many possible models of paraconsistent logic that include all of the truths of the standard interpretation of arithmetic. Allowing such inconsistent arithmetics, in which n=n+1 is both true and false, has a number of advantages. For example, Uwe Petersen has provided an argument to prove that there exists a number x for which x=x+1. Paraconsistent arithmetic also avoids problems associated with Church's Theorem, Tarski's Theorem, and Godel's incompleteness theorem. Furthermore, Hilbert's Programme becomes redundant

  算术一致吗？

  有许多可能的次协调逻辑模型，包括算术标准解释的所有真理。 允许这种不一致的算术，其中n = n + 1既是真的又是假的，具有许多优点。 例如，Uwe Petersen提供了一个论证来证明存在x = x + 1的数x。 次协调算术也避免了与邱奇定理，塔斯基定理和哥德尔不完备性定理相关的问题。 此外，希尔伯特的计划变得多余。

GB/T 7714

https://academic.oup.com/mind/article-abstract/103/411/337/946881?redirectedFrom=PDF 

Priest G. Is Arithmetic Consistent?[J]. Mind, 1994, 103(411):337-349.

MLA

Priest, Graham. "Is Arithmetic Consistent?." Mind 103.411(1994):337-349.

APA

Priest, G. (1994). Is arithmetic consistent?. Mind, 103(411), 337-349.

2.2.

Title:On inconsistent arithmetics: a reply to Denyer

Author(s): Graham Priest .

Source: Mind.

Document Type: Article

Abstract :

Nicholas Denyer's criticism of an article on inconsistent arithmetics is correct in some points, but also contains some misinterpretations, ad hominem arguments and sketchy reasoning. The direct argument for accepting the least inconsistent arithmetic M rather than the standard arithmetic is unacceptable, as Denyer correctly points out. However, the indirect argument for M still stands, despite Denyer's criticisms. The indirect argument shows that M avoids some difficulties related to classical theorems such as Church's Theorem, Tarski's Theorem and Godel's Incompleteness Theorems. 

http://go.galegroup.com/ps/i.do?id=GALE|A18851893&sid=googleScholar&v=2.1&it=r&linkaccess=fulltext&issn=00264423&p=AONE&sw=w

题目：关于不一致算术：对丹耶的答复

作者：格雷厄姆牧师。

资料来源：Mind。

文件类型：物品

文摘：

尼古拉斯·丹耶对一篇关于不一致算术论的文章的批评在某些方面是正确的，但也包含了一些误解、悖论和粗略的推理。正如丹耶正确指出的那样，接受最小不一致算术m而不是标准算术的直接论点是不可接受的。然而，尽管丹耶提出了批评，但对M的间接论点仍然存在。间接论证表明，M避免了经典定理如丘奇定理、塔斯基定理和戈德尔不完全性定理的一些困难。

In "Is Arithmetic Consistent?" (1994a--hereafter, IAC) I drew attention to the fact that there are inconsistent but nontrivial theories that contain all the sentences true in the standard model of arithmetic, "N". The theories are not, of course, classical theories, but paraconsistent ones. I also argued that it is not as obvious that "N" is the correct arithmetic as one might suppose and that there are reasons for taking one of the inconsistent arithmetics, "M", with least inconsistent number, "m", to be the correct one. Two reasons were given. The first was a direct one; the second an indirect one, to the effect that "M" avoids most of the limitative theorems of classical metatheory. In "Priest's Paraconsistent Arithmetic" (1995--hereafter PPA), Nicholas Denyer gives a critique of the paper. The first four sections attack the indirect argument, the fifth the direct argument, and the sixth and final, section is an "ad hominem" attack. The paper is a mixture of insightful criticism, over-swift argument and misreading. The purpose of this note is to point out which parts are which.

https://www.mendeley.com/catalogue/inconsistent-arithmetics-reply-denyer/ 

在“算术一致吗？”（1994年a——此后，IAC）我提请注意一个事实，即在标准的算术模型“n”中，有不一致但不平凡的理论包含了所有的句子。当然，这些理论不是古典理论，而是准一致的。我还认为“n”并不像人们想象的那样明显是正确的算术，并且有理由将不一致的算术中的一个“m”（数字不一致的最小值为“m”）作为正确的算术。给出了两个原因。第一个是直接的，第二个是间接的，因为“m”避免了经典元理论的大多数极限定理。在“牧师的帕拉一致性算术”（1995年——以下简称“ppa”）中，尼古拉斯·丹耶对这篇论文进行了评论。前四节攻击间接论点，第五节直接论点，第六节和最后一节是“自动寻人”攻击。这篇论文是一篇综合了深刻的批评，过快的争论和误读。本注释的目的是指出哪些部分是什么。

GB/T 7714

PRIEST, G. On Inconsistent Arithmetics: A Reply to Denyer[J]. Mind, 1996, 105(420):649-659.

MLA

PRIEST, and G. "On Inconsistent Arithmetics: A Reply to Denyer." Mind 105.420(1996):649-659.

APA

PRIEST, & G. (1996). On inconsistent arithmetics: a reply to denyer. Mind, 105(420), 649-659.

  https://academic.oup.com/mind/article-abstract/105/420/649/945409?redirectedFrom=PDF 

  2.3.

  Logicians have been trying to solve the Liar Paradox and its associated family of insolubiles for the best part of two and a half thousand years; so one might well have thought that there could be no very new views on the topic. The subject is deep and hard, however; and this is not the case. In Replacing Truth , Kevin Scharp has come up with one.

  The main idea is a variation of the thought that truth is an inconsistent concept (as endorsed by, e.g., Chihara, Eklund, and dialetheists). Its main novelty lies in the idea that it should be replaced by two notions. One of these, descending truth, D , satisfies the T -schema from left to right: . The other, ascending truth, A, satisfies it from right to left . Neither converse holds. (Here, 

在两千五千年的时间里，逻辑学家一直在试图解决“说谎者悖论”及其相关的不可解性家族；因此，人们可能会认为在这个问题上可能没有什么新的观点。然而，这个主题是深刻而艰难的；事实并非如此。为了取代事实，凯文·沙普想出了一个。

主要的观点是，真理是一个不一致的概念的思想的变体（如千原、埃克隆德和狄尔忒派的赞同）。它的主要新颖之处在于它应该被两个概念所取代。其中之一，下降真理，d，满足从左到右的t-图式：forumla。另一个，上升的真理，A，从右到左满足它。都不支持。（这里，

  https://academic.oup.com/mind/article-abstract/125/498/553/2583542?redirectedFrom=PDF 

GB/T 7714

Priest G . Replacing Truth, by Kevin Scharp[J]. Mind, 2016, 125(498):fzv117.

MLA

Priest, Graham . "Replacing Truth, by Kevin Scharp." Mind 125.498(2016):fzv117.

APA

Priest, G. . (2016). Replacing truth, by kevin scharp. Mind, 125(498), fzv117.

  2.4.

Hegel"s Dialectical Logicby Ermanno Bencivenga

Review by: Graham Priest 

Mind 

Vol. 111, No. 443 (Jul., 2002), pp. 643-646 

Published by: Oxford University Press on behalf of the Mind Association 

https://www.jstor.org/stable/3093626 

Page Count: 4 

GB/T 7714

Priest G. Hegel's Dialectical Logic by Ermanno Bencivenga[J]. Mind, 2002, 111(443):643-646.

MLA

Priest, Graham. "Hegel's Dialectical Logic by Ermanno Bencivenga." Mind 111.443(2002):643-646.

APA

Priest, G. (2002). Hegel's dialectical logic by ermanno bencivenga. Mind, 111(443), 643-646.

黑格尔的辩证逻辑论

  2.5

Studia Logica

June 1982, Volume 41, Issue 2–3,  pp 249–268| Cite as

https://link.springer.com/article/10.1007%2FBF00370347 

To be and not to be: Dialectical tense logic

Graham Priest

1. Philosophy Department, University of Western Australia, Nedlands, Australia

Abstract

The paper concerns time, change and contradiction, and is in three parts. The first is an analysis of the problem of the instant of change. It is argued that some changes are such that at the instant of change the system is in both the prior and the posterior state. In particular there are some changes from p being true to ℸp being true where a contradiction is realized. The second part of the paper specifies a formal logic which accommodates this possibility. It is a tense logic based on an underlying paraconsistent prepositional logic, the logic of paradox. (See the author's article of the same name Journal of Philosophical Logic 8 (1979).) Soundness and completeness are established, the latter by the canonical model construction, and extensions of the basic system briefly considered. The final part of the paper discusses Leibniz's principle of continuity: “Whatever holds up to the limit holds at the limit”. It argues that in the context of physical changes this is a very plausible principle. When it is built into the logic of the previous part, it allows a rigorous proof that change entails contradictions. Finally the relation of this to remarks on dialectics by Hegel and Engels is briefly discussed.

Keywords

Formal Logic Basic System Model Construction Computational Linguistic Final Part 

.

逻辑学

1982年6月，第41卷，第2-3期，第249-268页，引用为

存在与不存在：辩证时态逻辑

普里斯特

1 澳大利亚 内德兰西澳大利亚大学 哲学系

摘要

本文涉及时间、变化和矛盾，分为三个部分。第一个是对变化瞬间的问题的分析。有人认为，有些变化是这样的，即在变化的瞬间，系统同时处于前后状态。尤其是在矛盾实现的情况下，从P为真到_P为真有一些变化。本文的第二部分详细说明了一种适应这种可能性的形式逻辑。它是一种基于潜在的副一致介词逻辑即悖论逻辑的时态逻辑。（见同名《哲学逻辑杂志》1979年第8期作者的文章）通过规范的模型构造，并简要考虑了基本体系的扩展，建立了完整性和完整性。论文的最后一部分讨论了莱布尼兹的连续性原理：“任何能达到极限的都能达到极限”。它认为，在物理变化的背景下，这是一个非常合理的原则。当它被嵌入到前一部分的逻辑中时，它允许一个严格的证明，即变化会导致矛盾。最后简要讨论了这与黑格尔、恩格斯关于辩证法评论的关系。

关键词

形式逻辑 基础系统 模型构建 计算语言 最后部分

   2.6.

Discussion. The import of inclosure: some comments on Grattan-Guinness：Structural similarity or structuralism? Comments on Priest's analysis of the paradoxes of self-reference'' [Mind 107 (1998), no. 428, 823–834; MR1667172 (2000d:03003a)]. 

 G Priest  

Mind, Volume 107, Issue 428, October 1998, Pages 835–840, https://doi.org/10.1093/mind/107.428.835 

Published: 01 October 1998 

http://xueshu.baidu.com/usercenter/paper/show? paperid=cac114cf5de115391f7b13dc267fba60&site=xueshu_se