Paradoxes, Miscellaneous

We show how removing faith-based beliefs in current philosophies of classical and constructive mathematics admits formal, evidence-based, definitions of constructive mathematics; of a constructively well-defined logic of a formal mathematical language; and of a constructively well-defined model of such a language. -/- We argue that, from an evidence-based perspective, classical approaches which follow Hilbert's formal definitions of quantification can be labelled `theistic'; whilst constructive approaches based on Brouwer's philosophy of Intuitionism can be labelled `atheistic'. -/- We then adopt what may (...) be labelled a finitary, evidence-based, `agnostic' perspective and argue that Brouwerian atheism is merely a restricted perspective within the finitary agnostic perspective, whilst Hilbertian theism contradicts the finitary agnostic perspective. -/- We then consider the argument that Tarski's classic definitions permit an intelligence---whether human or mechanistic---to admit finitary, evidence-based, definitions of the satisfaction and truth of the atomic formulas of the first-order Peano Arithmetic PA over the domain N of the natural numbers in two, hitherto unsuspected and essentially different, ways. -/- We show that the two definitions correspond to two distinctly different---not necessarily evidence-based but complementary---assignments of satisfaction and truth to the compound formulas of PA over N. -/- We further show that the PA axioms are true over N, and that the PA rules of inference preserve truth over N, under both the complementary interpretations; and conclude some unsuspected constructive consequences of such complementarity for the foundations of mathematics, logic, philosophy, and the physical sciences. -/- . (shrink)

Here, by introducing a version of “Unexpected hanging paradox” first we try to open a new way and a new explanation for paradoxes, similar to liar paradox. Also, we will show that we have a semantic situation which no syntactical logical system could support it. Finally, we propose a claim in Theory of Computation about the consistency of this Theory. One of the major claim is:Theory of Computation and Classical Logic leads us to a contradiction.

Throughout this paper, we are trying to show how and why our Mathematical frame-work seems inappropriate to solve problems in Theory of Computation. More exactly, the concept of turning back in time in paradoxes causes inconsistency in modeling of the concept of Time in some semantic situations. As we see in the first chapter, by introducing a version of “Unexpected Hanging Paradox”,first we attempt to open a new explanation for some paradoxes. In the second step, by applying this paradox, it (...) is demonstrated that any formalized system for the Theory of Computation based on Classical Logic and Turing Model of Computation leads us to a contradiction. We conclude that our mathematical frame work is inappropriate for Theory of Computation. Furthermore, the result provides us a reason that many problems in Complexity Theory resist to be solved.(This work is completed in 2017 -5- 2, it is in vixra in 2017-5-14, presented in Unilog 2018, Vichy). (shrink)

John Rawls’s difference principle says that we should change our economy if doing so is better for the worst-off group, on the condition that certain basic rights are secured. This paper presents a kind of case that challenges the principle. If we modify the principle to cope with the challenge, we open the way to a Sorites paradox.

I present a paradox concerning a person who desires to fail to achieve the goal that matters most to them. I recently encountered a similar paradox, but radical solipsism is a solution to it. This is not a solution to the paradox that I present.

هل يمكن إذن أن أكون أنا لست أنا بانطباعات الزمان على جسدي وفكري؟ أليس لي جوهرٌ ثابتٌ تتبدل عليه الأعراض من حين إلى آخر، ومن ثم لا أفقد هويتي الحقيقية؟ لقد وُلدت منذ سنوات خلت، وتعلمت وعلمت أنني هو أنا، ويعلم المحيطون بي أنني هو أنا، بل يستطيع العلم المعاصر أن يُثبت أن لي تركيبًا جينيًا وراثيًا يميزني عن غيري، وأن لي بصمات أصابع وبصمة صوت لا تتطابق مع بصمات غيري، وسيحاسبني ربي يوم العرض عليه بوصفي شخصًا واحدًا هو أنا؛ (...) والشجرة التي تظلل باب منزلي هي ذات الشجرة التي أراها منذ سنوات، حقًا لقد تغيرت أعراضها، لكن جوهرها بالضرورة ثابت؛ وكوكب الزهرة المضيء مساءً وصباحًا هو ذات الكوكب الذي أراه كل يوم، قد تعتريه تغييرات عرضية، لكن جوهره قطعًا ثابت. ألسنا جميعًا نشترك في معرفة أن هذه الأشياء هي هي مهما تغيرت أعراضها؟. (shrink)

Orice teorie care ar permite călătoria în timp ar introduce probleme de cauzalitate. Aceste tipuri de paradoxuri temporale pot fi evitate prin principiul de consecvență Novikov sau printr-o variație a interpretării multor lumi cu lumi care interacționează. Argumentul clasic împotriva cauzalității înapoi este argumentul bilking, Dacă un eveniment A provoacă un eveniment anterior B, bilking recomandă o încercare de a decorela A și B, adică de a aduce A în cazurile în care B nu a avut loc și de a (...) preveni A în cazurile în care a avut loc B. DOI: 10.13140/RG.2.2.13245.41448. (shrink)

This chapter briefly reviews the present state of judgment aggregation theory and tentatively suggests a future direction for that theory. In the review, we start by emphasizing the difference between the doctrinal paradox and the discursive dilemma, two idealized examples which classically serve to motivate the theory, and then proceed to reconstruct it as a brand of logical theory, unlike in some other interpretations, using a single impossibility theorem as a key to its technical development. In the prospective part, having (...) mentioned existing applications to social choice theory and computer science, which we do not discuss here, we consider a potential application to law and economics. This would be based on a deeper exploration of the doctrinal paradox and its relevance to the functioning of collegiate courts. On this topic, legal theorists have provided empirical observations and theoretical hints that judgment aggregation theorists would be in a position to clarify and further elaborate. As a general message, the chapter means to suggest that the future of judgment aggregation theory lies with its applications rather than its internal theoretical development. (shrink)

This paper responds to commentaries by Kaiserman and Magidor, and Hawthorne. The case of the infinite clowns can teach us several things.

This work addresses the critical discussion featured in the contemporary literature about two well-known paradoxes belonging to different philosophical traditions, namely Frege’s puzzling claim that “the concept horse is not a concept” and Gongsun Long’s “white horse is not horse”. We first present the source of Frege’s paradox and its different interpretations, which span from plain rejection to critical analysis, to conclude with a more general view of the role of philosophy as a fight against the misunderstandings that come from (...) the different uses of language (a point later developed by the “second” Wittgenstein). We then provide an overview of the ongoing discussions related to the Bai Ma Lun paradox, and we show that its major interpretations include—as in the case of Frege’s paradox—dismissive accounts that regard it as either useless or wrong, as well as attempts to interpret and repair the argument. Resting on our reading of Frege’s paradox as an example of the inescapability of language misunderstandings, we advance a similar line of interpretation for the paradox in the Bai Ma Lun: both the paradoxes, we suggest, can be regarded as different manifestations of similar concerns about language, and specifically about the difficulty of referring to concepts via language. (shrink)

Brock and Glasgow recently introduced a new definition of paradox and argue that this conception of paradox itself leads to paradox, the so-called Paradox Paradox. I show that they beg the questions during the course of their argument, but, more importantly, do so in a philosophically interesting way: it reveals a counterexample to the equivalence between being a logical truth and having a probability of one. This has consequences regarding norms of rationality, undermining the grounds for the Conjunction Fallacy.

A review of Matt Cook's book Sleight of Mind: 75 Ingenious Paradoxes in Mathematics, Physics, and Philosophy.

Interesting as they are by themselves in philosophy and mathematics, paradoxes can be made even more fascinating when turned into proofs and theorems. For example, Russell’s paradox, which overthrew Frege’s logical edifice, is now a classical theorem in set theory, to the effect that no set contains all sets. Paradoxes can be used in proofs of some other theorems—thus Liar’s paradox has been used in the classical proof of Tarski’s theorem on the undefinability of truth in sufficiently rich languages. This (...) paradox (as well as Richard’s paradox) appears implicitly in Gödel’s proof of his celebrated first incompleteness theorem. In this paper, we study Yablo’s paradox from the viewpoint of first- and second-order logics. We prove that a formalization of Yablo’s paradox (which is second order in nature) is non-first-orderizable in the sense of George Boolos (1984). (shrink)

According to the so-called Lockean thesis, a rational agent believes a proposition just in case its probability is sufficiently high, i.e., greater than some suitably fixed threshold. The Preface paradox is usually taken to show that the Lockean thesis is untenable, if one also assumes that rational agents should believe the conjunction of their own beliefs: high probability and rational belief are in a sense incompatible. In this paper, we show that this is not the case in general. More precisely, (...) we consider two methods of computing how probable must each of a series of propositions be in order to rationally believe their conjunction under the Lockean thesis. The price one has to pay for the proposed solutions to the paradox is what we call “quasi-dogmatism”: the view that a rational agent should believe only those propositions which are “nearly certain” in a suitably defined sense. (shrink)

In this paper we first develop a Dialetheic Logic with Exclusive Assumptions and Conclusions, DLEAC. We adopt the semantics of the logic of paradox (LP) extended with a notion of model suitable for DLEAC, and we modify its proof theory by refining the notions of assumption and conclusion, which are understood as speech acts. We introduce a new paradox – the rejectability paradox – first informally, then formally. We then provide its derivation in an extension of DLEAC contanining the rejectability (...) predicate. (shrink)

Humility is a paradoxical virtue. This should come as no great surprise. It doesn’t take much explanation for one to realize that if someone is boasting about how humble he is, then he probably is not humble. In fact, as we shall see, the paradoxical nature of humility has a long history, going back to at least Thomas Aquinas in the thirteenth century. While it may not be a novel claim that there exists an apparent paradox of humility, I will (...) argue that there is more than one humility paradox, perhaps as many as five: the epistemic paradox, the paradox of self-attribution, the inculcation paradox, the agentic paradox, and the axiological paradox. All these paradoxes are distinct, yet seemingly intertwined. Upon examining them each in turn, we will be left with a Gordian knot of humility paradoxes. (shrink)

The paper is about 'absolute logic': an approach to logic that differs from the standard first-order logic and other known approaches. It should be a new approach the author has created proposing to obtain a general and unifying approach to logic and a faithful model of human mathematical deductive process. In first-order logic there exist two different concepts of term and formula, in place of these two concepts in our approach we have just one notion of expression. In our system (...) the set-builder notation is an expression-building pattern. In our system we can easily express second-order, third order and any-order conditions. The meaning of a sentence will depend solely on the meaning of the symbols it contains, it will not depend on external 'structures'. Our deductive system is based on a very simple definition of proof and provides a good model of human mathematical deductive process. The soundness and consistency of the system are proved. We discuss on the completeness of our deductive systems. We also discuss how our system relates to the most know types of paradoxes, from the discussion no specific vulnerability to paradoxes comes out. The paper provides both the theoretical material and a fully documented example of deduction. (shrink)

The idea of science being the best – or the only – way to reach the truth about our cosmos has been a major belief of modern civilization. Yet, science has grown tall on fragile legs of clay. Every scientific theory uses axioms and assumptions that by definition cannot be proved. This poses a serious limitation to the use of science as a tool to find the truth. The only way to search for the latter is to redefine the former (...) to its original glory. In the days well before Galileo and Newton, science and religion were not separated. They worked together to discover the truth and while the latter had God as its final destination, the former had God as its starting point. Science is based on the irrational (unproven) belief that the world is intelligible along many other assumptions. This poses a serious limitation to science that can only be overcome if we accept the irrationality of the cosmos. The motto “Credo quia absurdum” holds more truth than one can ever realize at first glance. There is nothing logical in logic, whereas there is deep wisdom in the irrational. For while the former tries to build castles on moving sand, the latter digs deep inside the depths of existence itself in order to build on the most concrete foundations that there can be: the cosmos itself. The only way forward is backwards. Backwards to a time when religion led the quest for knowledge by accepting what we cannot know, rather than trying to comprehend what we do not. Science was anyway based on that in the first place. (shrink)

Io do una recensione dettagliata di 'The Outer Limits of Reason' di Noson Yanofsky da una prospettiva unificata di Wittgenstein e psicologia evolutiva. Inditesto che la difficoltà con questioni come il paradosso nel linguaggio e nella matematica, l'incompletezza, l'indecidibilità, la computabilità, il cervello e l'universo come computer ecc., derivano tutto dall'incapacità di guardare attentamente al nostro uso del linguaggio nel contesto appropriato e quindi alla mancata separazione delle questioni di fatto scientifico dalle questioni di come funziona il linguaggio. Discuto le (...) opinioni di Wittgenstein sull'incompletezza, la paracoerenza e l'indecidibilità e il lavoro di Wolpert sui limiti del calcolo. Per riassumere: L'Universo Secondo Brooklyn---Buona Scienza, Non Così Buona Filosofia. Coloro che desiderano un quadro aggiornato completo per il comportamento umano dalla moderna vista a due systems possono consultare il mio libro 'La struttura logica dellafilosofia, psicologia, Mind e il linguaggio in Ludwig Wittgenstein e John Searle' 2nd ed (2019). Coloro che sono interessati a più dei miei scritti possono vedere 'TalkingMonkeys--Filosofia, Psicologia, Scienza, Religione e Politica su un Pianeta Condannato--Articoli e Recensioni 2006-2019 3rd ed (2019) e Suicidal Utopian Delusions in the 21st Century 5th ed (2020) . (shrink)

Ich gebe einen ausführlichen Überblick über 'The Outer Limits of Reason' von Noson Yanofsky aus einer einheitlichen Perspektive von Wittgenstein und Evolutionspsychologie. Ich weise darauf hin, dass die Schwierigkeit bei Themen wie Paradoxon in Sprache und Mathematik, Unvollständigkeit, Unbedenklichkeit, Berechenbarkeit, Gehirn und Universum als Computer usw. allesamt auf das Versäumnis zurückzuführen ist, unseren Sprachgebrauch im geeigneten Kontext sorgfältig zu prüfen, und daher das Versäumnis, Fragen der wissenschaftlichen Tatsache von Fragen der Funktionsweise von Sprache zu trennen. Ich bespreche Wittgensteins Ansichten über (...) Unvollständigkeit, Parakonsistenz und Unentschlossenheit und die Arbeit Wolperts an den Grenzen der Berechnung. Zusammengefasst: The Universe According to Brooklyn---Good Science, Not So Good Philosophy. Wer aus der modernen zweisystems-Sichteinen umfassenden, aktuellen Rahmen für menschliches Verhalten wünscht, kann mein Buch "The Logical Structure of Philosophy, Psychology, Mindand Language in Ludwig Wittgenstein and John Searle' 2nd ed (2019) konsultieren. Diejenigen,die sich für mehr meiner Schriften interessieren, können 'Talking Monkeys--Philosophie, Psychologie, Wissenschaft, Religion und Politik auf einem verdammten Planeten --Artikel und Rezensionen 2006-2019 3rd ed (2019) und Suicidal Utopian Delusions in the 21st Century 4th ed (2019) und andere sehen. (shrink)

나는 컴퓨터로 계산과 우주의 한계에 대한 많은 최근의 토론을 읽었습니다, polymath 물리학자 및 결정 이론가 데이비드 울퍼트의 놀라운 작품에 대한 몇 가지 의견을 찾을 수 있기를 바라고 있지만 하나의 인용을 발견하지 않은 그래서 나는이 매우 간단한 요약을 제시. Wolpert는 계산을 수행하는 장치와 는 별개이며 물리학법칙과는 무관하므로 컴퓨터, 물리학 및 인간의 행동에 적용되므로 추론(계산)에 대한 제한에 대해 놀라운 불가능또는 불완전성 정리(1992년에서 2008년 참조 arxiv dot org)를 입증했습니다. 그들은 캔터의 대각선화, 거짓말쟁이 역설 및 세계관을 사용하여 튜링 머신 이론의 궁극적 인 정리가 될 (...) 수있는 것을 제공하고, 겉보기에 불가능, 불완전성, 계산의 한계, 그리고 컴퓨터로서의 우주, 가능한 모든 우주와 모든 존재 또는 메커니즘에서, 생성, 비 양자 기계적 불확실성 및 증거. 차이틴, 솔로모노프, 코몰가로프, 비트겐슈타인의 고전 적 작품과 어떤 프로그램 (따라서 어떤 장치)이 소유보다 더 큰 복잡성시퀀스 (또는 장치)를 생성 할 수 없다는 개념에 명백한 연결이 있습니다. 이 작품의 몸은 물리적 우주보다 더 복잡한 어떤 실체가 있을 수 없고 비트겐슈타인의 관점에서 볼 때 '더 복잡한'은 의미가 없다고 말할 수 있습니다(즉, 진리를 제작자나 시험하는 조건은 없습니다). 심지어 '신'(즉, 무한한 시간과 에너지를 가진 '장치')은 주어진 '숫자'가 '무작위'인지 여부를 결정할 수없으며, 주어진 '수식', '정리' 또는 '문장' 또는 '장치'(이 모든 것이 복잡한 언어 게임)가 특정 '시스템'의 일부임을 보여줄 수 있는 특정 방법을 찾을 수 없습니다. 현대 의 두 systems보기에서인간의 행동에 대한 포괄적 인 최신 프레임 워크를 원하는 사람들은 내 책을 참조 할 수 있습니다'철학의 논리적 구조, 심리학, 민d와 루드비히 비트겐슈타인과 존 Searle의언어' 2nd ed (2019). 내 글의 더 많은 관심있는 사람들은 '이야기 원숭이를 볼 수 있습니다-철학, 심리학, 과학, 종교와 운명 행성에 정치 - 기사 및 리뷰 2006-2019 2nd 에드 (2019) 및 21st 세기 4번째 에드 (2019) 및 기타. (shrink)

Я даю подробный обзор "Внешние границы разума" Носон Янофски с единой точки зрения Витгенштейна и эволюционной психологии. Я указываю, что трудности с такими вопросами, как парадокс в языке и математике, неполнота, несоответствие, вычислительность, мозг и вселенная, как компьютеры и т.д., все это возникает из-за неспособности внимательно посмотреть на наше использование языка в соответствующем контексте и, следовательно, неспособность отделить вопросы научного факта от вопросов о том, как работает язык. Я обсуждаю взгляды Витгенштейна на неполноту, последовательность и несоответствие и нерешающость и работу (...) Вольперта на пределы вычислений. Подводя итог: Вселенная согласно Бруклин---Хорошая Наука, не так хорошая философия. Те, кто желает всеобъемлющего до современных рамок для человеческого поведения из современных двух systEms зрения могут проконсультироваться с моей книгой"Логическая структура философии, психологии, Минd иязык в Людвиг Витгенштейн и Джон Сирл" второй ред (2019). Те, кто заинтересован в более моих сочинений могут увидеть "Говоря обезьян - Философия, психология, наука, религия и политика на обреченной планете - Статьи и обзоры 2006-2019 3-й ed (2019) и suicidal утопических заблуждений в 21-мst веке 4-й ed (2019) th и другие. (shrink)

私は計算と宇宙の限界に関する最近の議論をコンピュータとして読み、ポリマス物理学者と意思決定理論家デビッド・ウォルパートの驚くべき仕事に関するいくつかのコメントを見つけることを望んでいますが、単一の引用 を見つけていないので、私はこの非常に簡単な要約を提示します。ウォルパートは、計算を行うデバイスから独立し、物理学の法則から独立している推論(計算)の限界に関する驚くべき不可能または不完全な定理(199 2年から2008年のarxiv.org参照)を証明したので、コンピュータ、物理学、人間の行動に適用されます。彼らは、カントールの対角化、嘘つきのパラドックス、ワールドラインを利用して、チューリングマシ ン理論の究極の定理である可能性のあるものを提供し、不可能、不完全性、計算の限界、そしてコンピュータとしての宇宙に関する洞察を提供し、すべての可能な宇宙とすべての存在またはメカニズムを生み出し、とりわけ 非量子機械不確実性原理と単一主義の証明を生み出します。チャイティン、ソロモノフ、コモルガロフ、ヴィトゲンシュタインの古典的な作品と、どのプログラム(したがってデバイスも)が所有するよりも複雑なシーケン ス(またはデバイス)を生成できないという考えには明らかなつながりがあります。この作品の体は、物理的な宇宙よりも複雑な存在はあり得ないので無テズムを意味すると言うかもしれませんし、ヴィトゲンチニアンの観 点から見ると、「より複雑な」は無意味です(満足の条件はありません、すなわち、真実のメーカーやテスト)。「神」(つまり、無限の時間/空間とエネルギーを持つ「デバイス」)でさえ、与えられた「数」が「ランダ ム」であるかどうかを判断したり、与えられた「公式」、定理または「文章」または「デバイス」(これらはすべて複雑な言語ゲームである)が特定の「システム」の一部であることを示す特定の方法を見つけることができ ません。 現代の2つのシス・エムスの見解から人間の行動のための包括的な最新の枠組みを望む人は、私の著書「ルートヴィヒ・ヴィトゲンシュタインとジョン・サールの第2回(2019)における哲学、心理学、ミンと言語の論 理的構造」を参照することができます。私の著作の多くにご興味がある人は、21世紀4日(2019年)の「話す猿--哲学、心理学、科学、宗教、政治」を見ることができます。 .

ノソン・ヤノフスキーの「理性の外側の限界」を、ウィトゲンシュタインと進化心理学の統一的な視点から詳しくレビューします。私は、言語や数学のパラドックス、不完全さ、デデシッド性、コンピュータとしての脳、宇 宙などの問題の難しさは、すべて適切な文脈での言語の使用を注意深く見なさなかったことから生じるため、科学的事実の問題を言語の仕組みの問題から切り離すことができなかったことを示しています。私は、不完全さ、 パラタンシ、不整合性に関するヴィトゲンシュタインの見解と、計算の限界に関するウォルパートの仕事について議論します。要約すると:ブルックリンによると宇宙---良い科学、それほど良い哲学ではありません。 現代の2つのシス・エムスの見解から人間の行動のための包括的な最新の枠組みを望む人は、私の著書「ルートヴィヒ・ヴィトゲンシュタインとジョン・サールの第2回(2019)における哲学、心理学、ミンと言語の論 理的構造」を参照することができます。私の著作の多くにご興味がある人は、運命の惑星における「話す猿--哲学、心理学、科学、宗教、政治―記事とレビュー2006-2019 第3回(2019)」と21世紀4日(2019年)の自殺ユートピア妄想st Century 4th ed (2019)などを見ることができます。 .

Most paradoxes of self-reference have a dual or ‘hypodox’. The Liar paradox (Lr = ‘Lr is false’) has the Truth-Teller (Tt = ‘Tt is true’). Russell’s paradox, which involves the set of sets that are not self-membered, has a dual involving the set of sets which are self-membered, etc. It is widely believed that these duals are not paradoxical or at least not as paradoxical as the paradoxes of which they are duals. In this paper, I argue that some paradox’s (...) duals or hypodoxes are as paradoxical as the paradoxes of which they are duals, and that they raise neglected and interestingly different problems. I first focus on Richard’s paradox (arguably the simplest case of a paradoxical dual), showing both that its dual is as paradoxical as Richard’s paradox itself, and that the classical, Richard-Poincaré solution to the latter does not generalize to the former in any obvious way. I then argue that my argument applies mutatis mutandis to other paradoxes of self-reference as well, the dual of the Liar (the Truth-Teller) proving paradoxical. (shrink)

Some formulations of the surprise paradox involve a pair of unnecessary and controversial assumptions. After casting doubt on these assumptions, I propose a solution to the paradox.

The article is an extended critical discussion of Kevin Scharp’s Replacing Truth. Scharp’s case for the claim that the concept of truth is inconsistent is criticized, and so is his case for the claim that the concept of truth must be replaced because of its inconsistency.

I explain why research in non-applied, non-interdisciplinary, non-historical philosophy is worthwhile. The key move in the explanation is the realization that many philosophical problems can be put in the form of a set of highly plausible yet apparently jointly inconsistent claims regarding a fundamental notion.Export citation.

A paradox, according to Wittgenstein, is something surprising that is taken out of its context. Thus, one way of dealing with paradoxical sentences is to imagine the missing context of use. Wittgenstein formulates what I call the paradigm paradox: ‘one sentence can never describe the paradigm in another, unless it ceases to be a paradigm.’ (PG, p.346) There are several instances of this paradox scattered throughout Wittgenstein’s writings. I argue that this paradox is structurally equivalent to Russell’s paradox. The above (...) quotation is Wittgenstein’s version of the vicious circle principle which counteracts the paradox. The prohibition Wittgenstein describes is, however, limited to a certain language-game. Finally, I argue that there is a structural analogy between a noun being employed as a self-membered set and a paradigmatic sample being included in or excluded from the set it generates. Paradoxical sentences are not prohibited forever; they can indicate a change in our praxis with a given paradigm. (shrink)

Doy una revisión detallada de ' los límites externos de la razón ' por Noson Yanofsky desde una perspectiva unificada de Wittgenstein y la psicología evolutiva. Yo indiqué que la dificultad con cuestiones como la paradoja en el lenguaje y las matemáticas, la incompletitud, la indeterminación, la computabilidad, el cerebro y el universo como ordenadores, etc., surgen de la falta de mirada cuidadosa a nuestro uso del lenguaje en el adecuado contexto y, por tanto, el Error al separar los problemas (...) de hecho científico de las cuestiones de cómo funciona el lenguaje. Discuto las opiniones de Wittgenstein sobre la incompletitud, la paracoherencia y la indecisión y el trabajo de Wolpert en los límites de la computación. Resumiendo: el universo según Brooklyn---buena ciencia, no tan buena filosofía. Aquellos que deseen un marco completo hasta la fecha para el comportamiento humano de la moderna dos sistemas punto de vista puede consultar mi libros Talking Monkeys 3ª ed (2019), Estructura Logica de Filosofia, Psicología, Mente y Lenguaje en Ludwig Wittgenstein y John Searle 2a ed (2019), Suicidio pela Democracia 4ª ed (2019), La Estructura Logica del Comportamiento Humano (2019), The Logical Structure de la Conciencia (2019, Entender las Conexiones entre Ciencia, Filosofía, Psicología, Religión, Política y Economía y Delirios Utópicos Suicidas en el siglo 21 5ª ed (2019), Observaciones sobre Imposibilidad, Incompletitud, Paraconsistencia, Indecidibilidad, Aleatoriedad, Computabilidad, Paradoja e Incertidumbre en Chaitin, Wittgenstein, Hofstadter, Wolpert, Doria, da Costa, Godel, Searle, Rodych Berto, Floyd, Moyal-Sharrock y Yanofsky. (shrink)

Принято считать, что невозможность, неполнота, Парапоследовательность, Несоответствие, Случайность, вычислительность, парадокс, неопределенность и пределы разума являются разрозненными научными физическими или математическими вопросами, имеющими мало или ничего общего. Я полагаю, что они в значительной степени стандартные философские проблемы (т.е. языковые игры), которые были в основном решены Витгенштейном более 80 лет назад. -/- Я предоставляю краткое резюме некоторых из основных выводов двух из самых выдающихся студентов поведения о Fсовременности, Людвиг Витгенштейн и Джон Сирл, на логическую структуру преднамеренности (ум, язык, поведение), принимая в качестве (...) отправной точки фундаментальное открытие Витгенштейна, что все действительно "философские" проблемы одинаковы-путаницы AB,как использовать язык в частности контекст, и поэтому все решения одинаковы, глядя на то, как язык может быть использован в рассматриваемом контексте, так что его условия истины (Условия удовлетворенности или COS) ясны. Основная проблема заключается в том, что можно сказать что угодно, но нельзя означать (государство ясно COS для) любое произвольное высказывание и смысл возможен только в очень специфическом контексте. -/- Я вскрыть некоторые писания некоторых из основных комментаторов по этим вопросам с точки зрения Витгенштейна в framework современной точки зрения двух систем мысли (популяризировал как "мышление быстро, думая медленно"), используя новую таблицу преднамеренности и новых двойных систем номенклатуры. Я показываю, что это мощная эвристическая для описания истинной природы этих предположенных научных, физических или математических вопросов, которые действительно лучше всего подходить как стандартные философские проблемы использования языка (языковые игры в терминологии Витгенштейна). (shrink)

यह आमतौर पर सोचा जाता है कि असंभवता, अपूर्णता, Paraconsistency, अनिर्णितता, Randomness, Computability, विरोधाभास, अनिश्चितता और कारण की सीमा अलग वैज्ञानिक शारीरिक या गणितीय मुद्दों में कम या कुछ भी नहीं कर रहे हैं आम. मेरा सुझाव है कि वे काफी हद तक मानक दार्शनिक समस्याओं (यानी, भाषा का खेल) जो ज्यादातर 80years पहले Wittgenstein द्वारा हल किए गए थे. -/- "क्या हम 'इस तरह के एक मामले में कहने के लिए' कर रहे हैं, ज़ाहिर है, दर्शन नहीं है, लेकिन (...) यह अपने कच्चे माल है. इस प्रकार, उदाहरण के लिए, क्या एक गणितज्ञ वस्तुपरकता और गणितीय तथ्यों की वास्तविकता के बारे में कहने के लिए इच्छुक है, गणित का दर्शन नहीं है, लेकिन दार्शनिक उपचार के लिए कुछ है। विटगेनस्टीन पीआई 234 -/- "Philosophers लगातार उनकी आँखों के सामने विज्ञान की विधि को देखने और irresistibly पूछने के लिए और जिस तरह से विज्ञान करता है में सवालों के जवाब परीक्षा कर रहे हैं. यह प्रवृत्ति तत्वमीमांसा का वास्तविक स्रोत है और दार्शनिक को पूर्ण अंधकार में ले जाती है। विटगेनस्टाइन -/- मैं आधुनिक समय के व्यवहार के सबसे प्रतिष्ठित छात्रों में से दो के प्रमुख निष्कर्षों में से कुछ का एक संक्षिप्त सारांश प्रदान करते हैं, लुडविग Wittgenstein और जॉन Searle, जानबूझकर की तार्किक संरचना पर (मन, भाषा, व्यवहार), मेरे प्रारंभिक बिंदु के रूप में ले रही Wittgenstein की मौलिक खोज - कि सभी सही मायने में 'लोकप्रिय' समस्याओं को एक ही हैं एक विशेष संदर्भ में भाषा का उपयोग करने के बारे में भ्रम, और इसलिए सभी समाधान एक ही हैं-कैसे भाषा के संदर्भ में इस मुद्दे पर इस्तेमाल किया जा सकता है पर देख इतना है कि इसकी सच्चाई शर्तें (संतोष या COS की शर्तें) स्पष्ट हैं. मूल समस्या यह है कि एक कुछ भी कह सकते हैं, लेकिन एक मतलब नहीं कर सकते (राज्य स्पष्ट COS के लिए) किसी भी मनमाने ढंग से कथन और अर्थ केवल एक बहुत ही विशिष्ट संदर्भ में संभव है. -/- मैं सोचा की दो प्रणालियों के आधुनिक परिप्रेक्ष्य के ढांचे में एक Wittgensteinian दृष्टिकोण से इन मुद्दों पर प्रमुख टिप्पणीकारों में से कुछ के कुछ लेखन विच्छेदन (के रूप में लोकप्रिय 'तेजी से सोच, धीमी गति से सोच'), की एक नई मेज रोजगार जानबूझकर और नई दोहरी प्रणाली नामकरण. मैं बताता हूँ कि यह इन putative वैज्ञानिक, शारीरिक या गणितीय मुद्दों जो वास्तव में सबसे अच्छा कैसे भाषा का इस्तेमाल किया जा रहा है के मानक दार्शनिक समस्याओं के रूप में संपर्क कर रहे हैं की सही प्रकृति का वर्णन करने के लिए एक शक्तिशाली heuristic है (Witgenstein में भाषा का खेल शब्दावली) -/- यह मेरा तर्क है कि जानबूझकर की मेज (तर्कसंगतता, मन, सोचा, भाषा, व्यक्तित्व आदि) है कि यहाँ प्रमुखता से सुविधाएँ अधिक या कम सही वर्णन करता है, या कम से कम के लिए एक heuristic के रूप में कार्य करता है, हम कैसे सोचते हैं और व्यवहार करते हैं, और इसलिए यह शामिल नहीं केवल दर्शन और मनोविज्ञान, लेकिन सब कुछ (इतिहास, साहित्य, गणित, राजनीति आदि). ध्यान दें कि विशेष रूप से जानबूझकर और तर्कसंगतता के रूप में मैं (Searle, Wittgenstein और अन्य लोगों के साथ) यह देखने के लिए, दोनों सचेत विचार विमर्श भाषाई प्रणाली 2 और बेहोश स्वचालित prelinguistic प्रणाली 1 कार्रवाई या सजगता भी शामिल है. (shrink)

Hal ini sering berpikir bahwa kemustahilan, ketidaklengkapan, Paraconsistency, Undecidability, Randomness, komputasi, Paradox, ketidakpastian dan batas alasan yang berbeda ilmiah fisik atau matematika masalah memiliki sedikit atau tidak ada dalam Umum. Saya menyarankan bahwa mereka sebagian besar masalah filosofis standar (yaitu, Permainan bahasa) yang sebagian besar diselesaikan oleh Wittgenstein lebih dari 80years yang lalu. -/- "Apa yang kita ' tergoda untuk mengatakan ' dalam kasus seperti ini, tentu saja, bukan filsafat, tetapi bahan baku. Jadi, misalnya, apa yang seorang matematikawan cenderung mengatakan (...) tentang objektivitas dan realitas fakta matematika, bukan filsafat matematika, tetapi sesuatu untuk pengobatan filosofis. " Wittgenstein PI 234 -/- "Filsuf terus melihat metode ilmu di depan mata mereka dan tak tertahankan tergoda untuk bertanya dan menjawab pertanyaan dalam cara ilmu tidak. Kecenderungan ini adalah sumber nyata metafisika dan memimpin filsuf menjadi gelap gulita. " Wittgenstein -/- Aku memberikan ringkasan singkat dari beberapa temuan utama dari dua siswa yang paling terkemuka perilaku zaman modern, Ludwig Wittgenstein dan John Searle, pada struktur Logis intensionality (pikiran, bahasa, perilaku), mengambil sebagai titik awal Penemuan fundamental Wittgenstein – bahwa semua masalah ' filosofis ' adalah sama — kebingungan tentang bagaimana menggunakan bahasa dalam konteks tertentu, sehingga semua solusi sama — melihat bagaimana bahasa dapat digunakan dalam konteks yang menjadi masalah sehingga kebenaranNya kondisi (kondisi kepuasan atau COS) jelas. Masalah dasar adalah bahwa seseorang dapat mengatakan apa-apa, tetapi orang tidak dapat berarti (negara yang jelas cos untuk) sembarang ucapan dan makna hanya mungkin dalam konteks yang sangat spesifik. -/- Saya membedah beberapa tulisan dari beberapa komentator utama pada isu ini dari sudut pandang Wittgensteinian dalam kerangka perspektif modern dari dua sistem pemikiran (Dipopulerkan sebagai ' berpikir cepat, berpikir lambat '), mempekerjakan meja baru intensionality dan baru sistem ganda nomenklatur. Saya menunjukkan bahwa ini adalah heuristik yang kuat untuk menggambarkan sifat sebenarnya dari hal ini ilmiah, fisik atau matematika masalah yang benar-benar terbaik didekati sebagai masalah filosofis standar bagaimana bahasa yang akan digunakan (permainan bahasa di Wittgenstein's terminologi). -/- Ini adalah pendapat saya bahwa tabel intensionality (rasionalitas, pikiran, pikiran, bahasa, kepribadian dll) yang fitur mencolok di sini menggambarkan lebih atau kurang akurat, atau setidaknya berfungsi sebagai heuristic untuk, bagaimana kita berpikir dan berperilaku, dan sehingga mencakup tidak hanya filsafat dan psikologi, tetapi segala sesuatu yang lain (sejarah, sastra, matematika, politik dll). Perhatikan terutama bahwa intensionalitas dan rasionalitas sebagai I (bersama dengan Searle, Wittgenstein dan lain-lain) melihatnya, mencakup baik sistem linguistik pertimbangan sadar 2 dan tidak disadari otomatis sistem prelinguistik 1 tindakan atau refleks. (shrink)

I consider a puzzling case presented by Jose Benardete, and by appeal to this case develop a paradox involving counterfactual conditionals. I then show that this paradox may be leveraged to argue for certain non-obvious claims concerning the logic of counterfactuals.

I identify an assumption that the students should not rely on: if the teacher believes that the exam would not be a surprise on a certain day, the teacher will not give the exam on that day. The reason I present for not making this assumption does not involve doubting the moral goodness of the teacher. But it does involve making a value judgment.

The perhaps most important criticism of the nontransitive approach to semantic paradoxes is that it cannot truthfully express exactly which metarules preserve validity. I argue that this criticism overlooks that the admissibility of metarules cannot be expressed in any logic that allows us to formulate validity-Curry sentences and that is formulated in a classical metalanguage. Hence, the criticism applies to all approaches that do their metatheory in classical logic. If we do the metatheory of nontransitive logics in a nontransitive logic, (...) however, there is no reason to think that the argument behind the criticism goes through. In general, asking a logic to express its own admissible metarules may not be a good idea. (shrink)

This paper presents a case for the claim that the infamous miners paradox is not a paradox. This contention is based on some important observations about the nature of ignorance with respect to both disjunctions and conditional obligations and their modal features. The gist of the argument is that given the uncertainty about the location of the miners in the story and the nature of obligations, the apparent obligation to block either mine shaft is cancelled.

The students’ argument against the possibility of a surprise exam assumes that the following would not occur: the teacher decides to give the exam on a certain day; the teacher believes that the exam would be a surprise on that day; but, actually, the exam would not be a surprise on that day. I give a reason to reject this assumption, and I point out that an attempt to reformulate the surprise exam paradox in order to allow for the assumption (...) does not result in an acceptable argument. (shrink)

Beall and Murzi :143–165, 2013) introduce an object-linguistic predicate for naïve validity, governed by intuitive principles that are inconsistent with the classical structural rules. As a consequence, they suggest that revisionary approaches to semantic paradox must be substructural. In response to Beall and Murzi, Field :1–19, 2017) has argued that naïve validity principles do not admit of a coherent reading and that, for this reason, a non-classical solution to the semantic paradoxes need not be substructural. The aim of this paper (...) is to respond to Field’s objections and to point to a coherent notion of validity which underwrites a coherent reading of Beall and Murzi’s principles: grounded validity. The notion, first introduced by Nicolai and Rossi, is a generalisation of Kripke’s notion of grounded truth, and yields an irreflexive logic. While we do not advocate the adoption of a substructural logic, we take the notion of naïve validity to be a legitimate semantic notion that points to genuine expressive limitations of fully structural revisionary approaches. (shrink)

Hili Razinsky, free downlad at link. ABSTRACT: Emotional perceptions are objectivist (objectivity-directed or cognitive) and conscious, both attributes suggesting they cannot be ambivalent. Yet perceptions, including emotional perceptions of value, allow for strictly objectivist ambivalence in which a person unitarily perceives the object in mutually undermining ways. Emotional perceptions became an explicandum of emotion for philosophers who are sensitive to the unique conscious character of emotion, impressed by the objectivist character of perceptions, and believe that the perceptual account solves a (...) worry about the possibility of a conflict between an emotion and a judgement. Back into the 1980s Greenspan has argued that emotional ambivalence is possible, her reasons implying that objectivist accounts of emotion are inconsistent with ambivalence. Tappolet has more recently replied that perceptual accounts allow for emotional ambivalence since the opposed values seen in ambivalence are good or bad in different senses. The present paper identifies strict objectivist ambivalence between judgements and between emotional perceptions by contrasting them with such ambivalence of separate values such as evoked by Tappolet. (shrink)

Paradoxes and their Resolutions is a ‘thematic compilation’ by Avi Sion. It collects in one volume the essays that he has written in the past (over a period of some 27 years) on this subject. It comprises expositions and resolutions of many (though not all) ancient and modern paradoxes, including: the Protagoras-Euathlus paradox (Athens, 5th Cent. BCE), the Liar paradox and the Sorites paradox (both attributed to Eubulides of Miletus, 4th Cent. BCE), Russell’s paradox (UK, 1901) and its derivatives the (...) Barber paradox and the Master Catalogue paradox (also by Russell), Grelling’s paradox (Germany, 1908), Hempel's paradox of confirmation (USA, 1940s), and Goodman’s paradox of prediction (USA, 1955). This volume also presents and comments on some of the antinomic discourse found in some Buddhist texts (namely, in Nagarjuna, India, 2nd Cent. CE; and in the Diamond Sutra, date unknown, but probably in an early century CE). (shrink)

The principle of universal instantiation plays a pivotal role both in the derivation of intensional paradoxes such as Prior’s paradox and Kaplan’s paradox and the debate between necessitism and contingentism. We outline a distinctively free logical approach to the intensional paradoxes and note how the free logical outlook allows one to distinguish two different, though allied themes in higher-order necessitism. We examine the costs of this solution and compare it with the more familiar ramificationist approaches to higher-order logic. Our assessment (...) of both approaches is largely pessimistic, and we remain reluctantly inclined to take Prior’s and Kaplan’s derivations at face value. (shrink)

Lewis Carroll’s 1895 paper, 'What the Tortoise Said to Achilles' is widely regarded as a classic text in the philosophy of logic. This special issue of 'The Carrollian' publishes five newly commissioned articles by experts in the field. The original paper is reproduced, together with contemporary correspondence relating to the paper and an extensive bibliography.

There are three questions associated with Simpson’s Paradox (SP): (i) Why is SP paradoxical? (ii) What conditions generate SP?, and (iii) What should be done about SP? By developing a logic-based account of SP, it is argued that (i) and (ii) must be divorced from (iii). This account shows that (i) and (ii) have nothing to do with causality, which plays a role only in addressing (iii). A counterexample is also presented against the causal account. Finally, the causal and logic-based (...) approaches are compared by means of an experiment to show that SP is not basically causal. (shrink)

A consideration of the relationship between conscious self-aware systems and art. I introduce my art practice and demonstrate the connections language has to self-conscious reflexivity. The document of research can be considered part of a creative practice that also uses language as a material. The specialist use and subversive manipulation of information in science and art as practiced in the service of culture are discussed to show how this informed the creation of Access Restricted-Operational Reasons as a response to my (...) environment. (shrink)

A number of contemporary philosophers think that the unqualified statement “X is unspeakable” faces the danger of self-referential absurdity: if this statement is true, it must simultaneously be false, given that X is speakable by the predicate word “unspeakable.” This predicament is in this chapter formulated as an argument that I term the “ineffability paradox.” After examining the Buddhist semantic theory of apoha (exclusion) and an apoha solution to the issue, I resort to a few Chinese Buddhist and Hindu philosophical (...) materials to rationally reconstruct a strategy for resolving the paradox. By introducing the mode of expression termed “indication,” together with the relevant notions of superimposition and of gesturing beyond the horizon, I show that expressing the ineffable does not necessarily involve irresoluble contradiction. It is also suggested that philosophers may need to acknowledge the relevance of the notion of ineffability for contemporary philosophizing. (shrink)

Is there a notion of contradiction—let us call it, for dramatic effect, “absolute”—making all contradictions, so understood, unacceptable also for dialetheists? It is argued in this paper that there is, and that spelling it out brings some theoretical benefits. First it gives us a foothold on undisputed ground in the methodologically difficult debate on dialetheism. Second, we can use it to express, without begging questions, the disagreement between dialetheists and their rivals on the nature of truth. Third, dialetheism has an (...) operator allowing it, against the opinion of many critics, to rule things out and manifest disagreement: for unlike other proposed exclusion-expressing-devices (for instance, the entailment of triviality), the operator used to formulate the notion of absolute contradiction appears to be immune both from crippling expressive limitations and from revenge paradoxes—pending a rigorous nontriviality proof for a formal dialetheic theory including it. (shrink)

We examine how Frege’s contrast between identity judgments of the forms “a=a” vs. “a=b” would fare in the special case where ‘a’ and ‘b’ are complex mental representations, and ‘a’ stands for an introspected ‘I’-thought. We first argue that the Fregean treatment of I-thoughts entails that they are what we call “one-shot thoughts”: they can only be thought once. This has the surprising consequence that no instance of the “a=a” form of judgment in this specific case comes out true, let (...) alone a priori true. This further reinforces Glezakos’s objections against the set-up of Frege’s puzzle, while also raising what we think is an acute problem for Fregeans, insofar as I-thought (and indexical thinking more generally), understood in their way, turns out to be incompatible with some basic features of rationality. (shrink)

Today it would be considered "bad Platonic metaphysics" to think that among all the concrete instances of a property there could be a universal instance so that all instances had the property by virtue of participating in that concrete universal. Yet there is a mathematical theory, category theory, dating from the mid-20th century that shows how to precisely model concrete universals within the "Platonic Heaven" of mathematics. This paper, written for the philosophical logician, develops this category-theoretic treatment of concrete universals (...) along with a new concept to abstractly model the functions of a brain. (shrink)