scholarly journals A Conflict Tolerant Logic of Explicit Evidence

2021 ◽  
Vol 27 (1) ◽  
pp. 124-144
Author(s):  
Thomas Studer

Standard epistemic modal logic is unable to adequately deal with the FrauchigerRenner paradox in quantum physics. We introduce a novel justification logic CTJ, in which the paradox can be formalized without leading to an inconsistency. Still CTJ is strong enough to model traditional epistemic reasoning. Our logic tolerates two different pieces of evidence such that one piece justifies a proposition and the other piece justifies the negation of that proposition. However, our logic disallows one piece of evidence to justify both a proposition and its negation. We present syntax and semantics for CTJ and discuss its basic properties. Then we give an example of epistemic reasoning in CTJ that illustrates how the different principles of CTJ interact. We continue with the formalization of the Frauchiger–Renner thought experiment and discuss it in detail. Further, we add a trust axiom to CTJ and again discuss epistemic reasoning and the paradox in this extended setting.

Author(s):  
Petr Dmitrievich Abramov

Dalai Lama notes that the Buddhist system of the objects of the realm largely coincides with such developed by Karl Popper. The subject of this article is ontology of the three worlds. The goal lies in analysis of the components of this ontology, demonstration of its prospects and advantages over dualism. First come matter or physical objects; second come mind, subjective reality; third come abstract concepts. Any object of reality is reduced to one of the three worlds and is refracted in a peculiar way in the other two. The third world is the mediator between others worlds; and the autonomous sphere that is not fully conditioned by them. We experience through representations, rather than directly, which is depicted in Buddhism as the image of a gloved hand. The knowledge concentrated in the third world contribute to development of consciousness. A thought experiment with the central and peripheral atoms reveal that there are no indivisible elements and everything exists in mutually dependent, while Buddhist logic substantiates that love and compassion can develop boundlessly. The concept of interdependent existence and non-substantiality of things draws Buddhism and quantum physics closer together. On the one hand, consciousness cannot be naturalized, reduced to matter; and on the other hand, it is inextricable from the energy processes. The conclusion is made that the three fundamental attributes of consciousness in Buddhism outlined by Thubten Gyats (13th Dalai Lama) – subjectivity, intentionality, and reflexivity, can be complemented by another two –  ability to continuously develop virtues, positive traits, and t interdependence between consciousness and subtle forms of matter. The three realms of Buddhism are such only on the phenomenal level; however, on the noumenal level, which unlike Buddhism is not recognized by Popper, is not the trinity, but the unity.


Author(s):  
D. Sowmya ◽  
S. Sivasankaran

In the cloud environment, it is difficult to provide security to the monolithic collection of data as it is easily accessed by breaking the algorithms which are based on mathematical computations and on the other hand, it takes much time for uploading and downloading the data. This paper proposes the concept of implementing quantum teleportation i.e., telecommunication + transportation in the cloud environment for the enhancement of cloud security and also to improve speed of data transfer through the quantum repeaters. This technological idea is extracted from the law of quantum physics where the particles say photons can be entangled and encoded to be teleported over large distances. As the transfer of photons called qubits allowed to travel through the optical fiber, it must be polarized and encoded with QKD (Quantum Key Distribution) for the security purpose. Then, for the enhancement of the data transfer speed, qubits are used in which the state of quantum bits can be encoded as 0 and 1 concurrently using the Shors algorithm. Then, the Quantum parallelism will help qubits to travel as fast as possible to reach the destination at a single communication channel which cannot be eavesdropped at any point because, it prevents from creating copies of transmitted quantum key due to the implementation of no-cloning theorem so that the communication parties can only receive the intended data other than the intruders.


Religions ◽  
2019 ◽  
Vol 10 (6) ◽  
pp. 389
Author(s):  
James Robert Brown

Religious notions have long played a role in epistemology. Theological thought experiments, in particular, have been effective in a wide range of situations in the sciences. Some of these are merely picturesque, others have been heuristically important, and still others, as I will argue, have played a role that could be called essential. I will illustrate the difference between heuristic and essential with two examples. One of these stems from the Newton–Leibniz debate over the nature of space and time; the other is a thought experiment of my own constructed with the aim of making a case for a more liberal view of evidence in mathematics.


2019 ◽  
Vol 29 (4) ◽  
pp. 419-468
Author(s):  
Henning Basold ◽  
Helle Hvid Hansen

Abstract We define notions of well-definedness and observational equivalence for programs of mixed inductive and coinductive types. These notions are defined by means of tests formulas which combine structural congruence for inductive types and modal logic for coinductive types. Tests also correspond to certain evaluation contexts. We define a program to be well-defined if it is strongly normalizing under all tests, and two programs are observationally equivalent if they satisfy the same tests. We show that observational equivalence is sufficiently coarse to ensure that least and greatest fixed point types are initial algebras and final coalgebras, respectively. This yields inductive and coinductive proof principles for reasoning about program behaviour. On the other hand, we argue that observational equivalence does not identify too many terms, by showing that tests induce a topology that, on streams, coincides with usual topology induced by the prefix metric. As one would expect, observational equivalence is, in general, undecidable, but in order to develop some practically useful heuristics we provide coinductive techniques for establishing observational normalization and observational equivalence, along with up-to techniques for enhancing these methods.


1982 ◽  
Vol 47 (1) ◽  
pp. 191-196 ◽  
Author(s):  
George Boolos

Let ‘ϕ’, ‘χ’, and ‘ψ’ be variables ranging over functions from the sentence letters P0, P1, … Pn, … of (propositional) modal logic to sentences of P(eano) Arithmetic), and for each sentence A of modal logic, inductively define Aϕ by[and similarly for other nonmodal propositional connectives]; andwhere Bew(x) is the standard provability predicate for PA and ⌈F⌉ is the PA numeral for the Gödel number of the formula F of PA. Then for any ϕ, (−□⊥)ϕ = −Bew(⌈⊥⌉), which is the consistency assertion for PA; a sentence S is undecidable in PA iff both and , where ϕ(p0) = S. If ψ(p0) is the undecidable sentence constructed by Gödel, then ⊬PA (−□⊥→ −□p0 & − □ − p0)ψ and ⊢PA(P0 ↔ −□⊥)ψ. However, if ψ(p0) is the undecidable sentence constructed by Rosser, then the situation is the other way around: ⊬PA(P0 ↔ −□⊥)ψ and ⊢PA (−□⊥→ −□−p0 & −□−p0)ψ. We call a sentence S of PA extremely undecidable if for all modal sentences A containing no sentence letter other than p0, if for some ψ, ⊬PAAψ, then ⊬PAAϕ, where ϕ(p0) = S. (So, roughly speaking, a sentence is extremely undecidable if it can be proved to have only those modal-logically characterizable properties that every sentence can be proved to have.) Thus extremely undecidable sentences are undecidable, but neither the Godel nor the Rosser sentence is extremely undecidable. It will follow at once from the main theorem of this paper that there are infinitely many inequivalent extremely undecidable sentences.


Author(s):  
Kenneth Mølbjerg Jørgensen ◽  
Anete M. Camille Strand

Material storytelling is used here to denote a material-discursive understanding of technology, and how technology works in organizations in terms of story performance. The idea is that technology configures organizations in spatial, temporal and material terms. We are inspired by Karen Barad’s work in quantum physics in developing the term material storytelling, which relies on a material-discursive understanding of storytelling. By introducing material storytelling we resituate the hegemonic relationship of discourse and language over matter. As such technology regains a central space in both understanding and managing organizations. It implies that attention is relocated to the petty and lowly everyday routines, techniques and material artifacts, which are implicit in what we do in everyday life but govern the agential possibilities for acting in this world. We frame the chapter as a story of material storytelling of a change project in a bank. We experiment with the writing style by going back and forth between two different layers of text. The first layer tells the stories of material storytelling, while the other draws out the theoretical/methodological implications of this approach in terms understanding and managing technology.


2021 ◽  
Author(s):  
◽  
Samuele Tonello

<p>This thesis in divided in two main parts. First, I develop the claim that current democracies are unable to properly defend what I deem the pivotal feature to evaluate the quality of a political system - namely the people’s liberty - due to what I call a twofold democratic dilemma. On the one hand, common citizens are affected by biases that compromise their ability to successfully maintain forms of self-government. On the other hand, even representative forms of democracy that limit to a certain degree the people’s power are threatened by an oligarchic power. That is, oligarchs are using their wealth power to sway governments towards pursuing oligarchic interests rather than common ones, thus hindering the people’s liberty. For this reason, I argue that we ought to rely on Pettit’s view of liberty as non-domination to resolve the democratic dilemma. The thesis conceives these two threats as two forms of domination that must be avoided and focuses on adding a supplementary editorial and contestatory dimension of democracy to the classical participatory one. Republicanism could offer a solution to both sides of the dilemma. On the one hand, citizens’ political task would be more compatible with the people’s biases, since citizens would limit their participation to control that government’s policies do not entail oligarchic domination. On the other hand, framing liberty as a battle between dominating masters and dominated slaves, republicanism could offer the many the institutional means to counteract elites’ political domination. In this way, I conclude the first part of the thesis, but this opens the gates to the main question of the thesis, namely to how we should structure this contestatory democracy. The problem is that whereas republican scholars agree on the importance of setting freedom as non-domination at the basis of our political systems, there is no such agreement on the best way to institutionally enhance the republican ideal. I analyse this debate, maintaining that while Pettitt’s ideal is the view to pursue, we should reject his editorial solution because small committees of experts are likely to increase oligarchic domination rather than to protect the people’s liberty. Rejecting Pettit’s model does not yet imply refusing any editorial model, since I argue that critical scholars mistakenly identify the editorial component of democracy with Pettit’s answer only. In this way, they neglect alternative solutions to Pettit’s, such as Bellamy’s and McCormick’s. Having explained that Bellamy’s solution does not resolve the democratic dilemma, since this scholar rejects editorial bodies, I argue that McCormick’s “Machiavellian Democracy” framed on a divided conception of the populace offers instead the solution I am looking for. Institutionally recognizing the social differences among the populace, we could create modern bodies similar to the Roman “Tribune of the Plebs” to offer the weaker part of the population a class-specific institution to use as defence from oligarchic domination. The problem is how to implement a modern “Tribune of the plebs” making sure that these bodies are effective but popular in character at the same time. I thus explain how modern editorial tribunates could work in practice, drawing from McCormick’s “thought experiment”. I agree with most of McCormick’s ideas – lottery selection, wealth threshold exclusion, large size tribunates, etc. - but I suggest that we must review some of his suggestions with features more concerned with improving the people’s knowledge – specialization, education selection, etc. Hence, I conclude the thesis describing my thought experiment of a system of Specialized Ministerial Tribunates. In this way, I argue that we could better resolve the democratic dilemma. On the one hand, tribunates’ editorship would be more specific and would not require members of the tribunate to analyse the operation of governments on a too broad spectrum, thus reducing the problems of the people’s biases. On the other hand, tribunates’ operation could be primarily connected to detecting oligarchic features in the policies enacted by single ministries, thus challenging more precisely any oligarchic influence over governments. In sum, I argue that an editorial dimension could produce significant improvements to the people’s liberty. Thanks to a modern “Tribune of the plebs”, citizens could participate more meaningfully in politics, while taming more efficiently the influence oligarchs have on how modern societies are politically directed.</p>


2021 ◽  
Author(s):  
◽  
Samuele Tonello

<p>This thesis in divided in two main parts. First, I develop the claim that current democracies are unable to properly defend what I deem the pivotal feature to evaluate the quality of a political system - namely the people’s liberty - due to what I call a twofold democratic dilemma. On the one hand, common citizens are affected by biases that compromise their ability to successfully maintain forms of self-government. On the other hand, even representative forms of democracy that limit to a certain degree the people’s power are threatened by an oligarchic power. That is, oligarchs are using their wealth power to sway governments towards pursuing oligarchic interests rather than common ones, thus hindering the people’s liberty. For this reason, I argue that we ought to rely on Pettit’s view of liberty as non-domination to resolve the democratic dilemma. The thesis conceives these two threats as two forms of domination that must be avoided and focuses on adding a supplementary editorial and contestatory dimension of democracy to the classical participatory one. Republicanism could offer a solution to both sides of the dilemma. On the one hand, citizens’ political task would be more compatible with the people’s biases, since citizens would limit their participation to control that government’s policies do not entail oligarchic domination. On the other hand, framing liberty as a battle between dominating masters and dominated slaves, republicanism could offer the many the institutional means to counteract elites’ political domination. In this way, I conclude the first part of the thesis, but this opens the gates to the main question of the thesis, namely to how we should structure this contestatory democracy. The problem is that whereas republican scholars agree on the importance of setting freedom as non-domination at the basis of our political systems, there is no such agreement on the best way to institutionally enhance the republican ideal. I analyse this debate, maintaining that while Pettitt’s ideal is the view to pursue, we should reject his editorial solution because small committees of experts are likely to increase oligarchic domination rather than to protect the people’s liberty. Rejecting Pettit’s model does not yet imply refusing any editorial model, since I argue that critical scholars mistakenly identify the editorial component of democracy with Pettit’s answer only. In this way, they neglect alternative solutions to Pettit’s, such as Bellamy’s and McCormick’s. Having explained that Bellamy’s solution does not resolve the democratic dilemma, since this scholar rejects editorial bodies, I argue that McCormick’s “Machiavellian Democracy” framed on a divided conception of the populace offers instead the solution I am looking for. Institutionally recognizing the social differences among the populace, we could create modern bodies similar to the Roman “Tribune of the Plebs” to offer the weaker part of the population a class-specific institution to use as defence from oligarchic domination. The problem is how to implement a modern “Tribune of the plebs” making sure that these bodies are effective but popular in character at the same time. I thus explain how modern editorial tribunates could work in practice, drawing from McCormick’s “thought experiment”. I agree with most of McCormick’s ideas – lottery selection, wealth threshold exclusion, large size tribunates, etc. - but I suggest that we must review some of his suggestions with features more concerned with improving the people’s knowledge – specialization, education selection, etc. Hence, I conclude the thesis describing my thought experiment of a system of Specialized Ministerial Tribunates. In this way, I argue that we could better resolve the democratic dilemma. On the one hand, tribunates’ editorship would be more specific and would not require members of the tribunate to analyse the operation of governments on a too broad spectrum, thus reducing the problems of the people’s biases. On the other hand, tribunates’ operation could be primarily connected to detecting oligarchic features in the policies enacted by single ministries, thus challenging more precisely any oligarchic influence over governments. In sum, I argue that an editorial dimension could produce significant improvements to the people’s liberty. Thanks to a modern “Tribune of the plebs”, citizens could participate more meaningfully in politics, while taming more efficiently the influence oligarchs have on how modern societies are politically directed.</p>


1975 ◽  
Vol 40 (2) ◽  
pp. 141-148 ◽  
Author(s):  
Martin Gerson

We present two finitely axiomatized modal propositional logics, one between T and S4 and the other an extension of S4, which are incomplete with respect to the neighbourhood or Scott-Montague semantics.Throughout this paper we are referring to logics which contain all the classical connectives and only one modal connective □ (unary), no propositional constants, all classical tautologies, and which are closed under the rules of modus ponens (MP), substitution, and the rule RE (from A ↔ B infer αA ↔ □B). Such logics are called classical by Segerberg [6]. Classical logics which contain the formula □p ∧ □q → □(p ∧ q) (denoted by K) and its “converse,” □{p ∧ q)→ □p ∧ □q (denoted by R) are called regular; regular logics which are closed under the rule of necessitation, RN (from A infer □A), are called normal. The logics that we are particularly concerned with are all normal, although some of our results will be true for all regular or all classical logics. It is well known that K and R and closure under RN imply closure under RE and also that normal logics are also those logics closed under RN and containing □{p → q) → {□p → □q).


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