- PhilosophyPhilosophical studies
Two defences of conservative deflationism are considered: Waxman’s committed either to a non-purely expressive notion of truth, or to a conception of mathematics that does not allow them to justifiably exclude non-conservative theories of truth.
There May Be Many Arithmetical Gödel Sentences†
We argue that, under the usual assumptions for sufficiently strong arithmetical theories that are subject to Gödel’s First Incompleteness Theorem, one cannot, without impropriety, talk about the…
On the Truth of G\"odelian and Rosserian Sentences
There is a longstanding debate in the logico-philosophical community as to why the Godelian sentences of a consistent and sufficiently strong theory are true. The prevalent argument seems to be…
Mathematical Proofs and Scientific Discovery
It is argued that the axiomatic view is inadequate as a view of the method of mathematics and that the analytic view is to be preferred, which means that the advancement of knowledge cannot be mechanized.
On the Arithmetical Truth of Self-Referential Sentences
We take an argument of Godel's from his ground-breaking 1931 paper, generalize it, and examine its validity. The argument in question is this: the sentence $G$ says about itself that it is not…
Why We Shouldn’t Reason Classically, and the Implications for Artificial Intelligence
It is shown that arguments for the existence of fundamental Godelian limitations on artificial intelligence are undermined by the idea that the authors should reason reticently, not classically, but in accordance with a weaker ‘reticent logic’.
A metasemantic challenge for mathematical determinacy
This paper investigates the determinacy of mathematics and poses a serious challenge for most philosophical theories of mathematics, since it puts considerable pressure on all views that accept a non-trivial amount of determinacy for even basic arithmetic.
Mechanical intelligence and Godelian Arguments
In the present paper we attempt to evaluate the legacy of Turing’s ideas concerning the consequences of Godel’s Incompleteness Theorems for philosophy of mind. These Theorems were almost immediately…
今度こそわかるゲーデル不完全性定理 = Gödel's incompleteness theorems
第１章 自然言語 第２章 理論の完全性とわかりやすさ 第３章 表現可能性 第４章 初等自然数言語の不完全性定理の証明 第５章 古典的理論と現代的理論 第６章 形式化 第７章 完全性 第８章 ゲーデルの不完全性定理 第９章 ゲーデルの第２不完全性定理 第１０章 新しい論理学
On the necessary philosophical premises of the Goedelian arguments
Lucas-Penrose type arguments have been the focus of many papers in the literature. In the present paper we attempt to evaluate the consequences of Godel’s incompleteness theorems for the philosophy…
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Fundamentals Of Measurement And Representation Of Natural Systems
- Computer Science
Real People: Personal Identity without Thought Experiments
- Psychology, Philosophy
Part 1 Thought experiments: what thought experiments are first difficulty - the background parenthesis - relevance and natural kinds second difficulty - imagination and possibility conditions of…
Philosophical Perspectives in Artificial Intelligence
Philosophy of mathematics: What numbers could not be
- Mathematics, Art
THE attention of the mathematician focuses primarily upon mathematical structure, and his intellectual delight arises (in part) from seeing that a given theory exhibits such and such a structure,…