The Principle of Contradiction and Symbolic Logic

This is the first English translation directly based on the original Polish ‘Zasada sprzeczno?ci a logika symboliczna’, the appendix on symbolic logic of Jan ?ukasiewicz's 1910 book O zasadzie sprzeczno?ci u Arytotelesa (On the Principle of Contradiction in Aristotle).     

Logic,Logic, and Logic

In his recent paper in History and Philosophy of Logic, John Kearns argues for a solution of the Liar paradox using an illocutionary logic (Kearns 2007 Kearns, J. 2007. ‘An illocutionary logical explanation of the Liar Paradox’. History and Philosophy of Logic, 28: 31–66. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). Paraconsistent approaches, especially dialetheism, which accepts the Liar as being both true and false, are rejected by Kearns as making no ‘clear sense’ (p. 51). In this critical note, I want to highlight some shortcomings of Kearns' approach that concern a general difficulty for supposed solutions to (semantic) antinomies like the Liar. It is not controversial that there are languages which avoid the Liar. For example, the language which consists of the single sentence ‘Benedict XVI was born in Germany’ lacks the resources to talk about semantics at all and thus avoids the Liar. Similarly, more interesting languages such as the propositional calculus avoid the Liar by lacking the power to express semantic concepts or to quantify over propositions. Kearns also agrees with the dialetheist claim that natural languages are semantically closed (i.e. are able to talk about their sentences and the semantic concepts and distinctions they employ). Without semantic closure, the Liar would be no real problem for us (speakers of natural languages). But given the claim, the expressive power of natural languages may lead to the semantic antinomies. The dialetheist argues for his position by proposing a general hypothesis (cf. Bremer 2005 Bremer, M. 2005. An Introduction to Paraconsistent Logics, Bern: Lang.  [Google Scholar], pp. 27–28): ‘(Dilemma) A linguistic framework that solves some antinomies and is able to express its linguistic resources is confronted with strengthened versions of the antinomies’. Thus, the dialetheist claims that either some semantic concepts used in a supposed solution to a semantic antinomy are inexpressible in the framework used (and so, in view of the claim, violate the aim of being a model of natural language), or else old antinomies are exchanged for new ones. One horn of the dilemma is having inexpressible semantic properties. The other is having strengthened versions of the antinomies, once all semantic properties used are expressible. This dilemma applies, I claim, to Kearns' approach as well.     

Vicious Regresses,Conceptual Analysis,and Strong Awareness Internalism

That a philosophical thesis entails a vicious regress is commonly taken to be decisive evidence that the thesis is false. In this paper, I argue that the existence of a vicious regress is insufficient to reject a proposed analysis provided that certain constraints on the analysis are met. When a vicious regress is present, some further consequence of the thesis must be established that, together with the presence of the vicious regress, shows the thesis to be false. The argument is provided largely through the examination of Michael Bergmann's (2006) vicious regress argument against strong awareness internalism and a partial defense of that thesis against Bergmann. 1     

Antisemitism,Definitions, and Future Cooperation

The World Council of Churches (WCC) and the International Jewish Committee for Interreligious Consultations met formally on 25–27 June 2019, in Paris, under the theme “The normalization of hatred: Challenges for Jews and Christians today.” This article outlines the presentation of WCC policies on antisemitism and the WCC’s work for human rights for all.     

Embedding If and Only If

Some left-nested indicative conditionals are hard to interpret while others seem fine. Some proponents of the view that indicative conditionals have No Truth Values (NTV) use their view to explain why some left-nestings are hard to interpret: the embedded conditional does not express the truth conditions needed by the embedding conditional. Left-nestings that seem fine are then explained away as cases of ad hoc, pragmatic interpretation. We challenge this explanation. The standard reasons for NTV about indicative conditionals (triviality results, Gibbardian standoffs, etc.) extend naturally to NTV about biconditionals. So NTVers about conditionals should also be NTVers about biconditionals. But biconditionals embed much more freely than conditionals. If NTV explains why some left-nested conditionals are hard to interpret, why do biconditionals embed successfully in the very contexts where conditionals do not embed?     

Coherence,anti-realism and the Vienna Circle

Some members of the Vienna Circle argued for a coherence theory of truth. Their coherentism is immune to standard objections. Most versions of coherentism are unable to show why a sentence cannot be true even though it fails to cohere with a system of beliefs. That is, it seems that truth may transcend what we can be warranted in believing. If so, truth cannot consist in coherence with a system of beliefs. The Vienna Circle's coherentists held, first, that sentences are warranted by coherence with a system of beliefs. Next they drew upon their verification theory of meaning, a consequence of which is that truth cannot transcend what can be warranted. The coherence theory of knowledge and verificationism together entail that truth cannot transcend what can be warranted by coherence with a system of beliefs. The Vienna Circle's argument for coherentism is strong and anticipates contemporary anti-realism.     

If Abortion,then Infanticide

Our contention is that all of the major arguments for abortion are also arguments for permitting infanticide. One cannot distinguish the fetus from the infant in terms of a morally significant intrinsic property, nor are they morally discernible in terms of standing in different relationships to others. The logic of our position is that if such arguments justify abortion, then they also justify infanticide. If we are right that infanticide is not justified, then such arguments will fail to justify abortion. We respond to those philosophers who accept infanticide by putting forth a novel account of how the mindless can be wronged which serves to distinguish morally significant potential from morally irrelevant potential. This allows our account to avoid the standard objection that many entities possess a potential for personhood which we are intuitively under no obligation to further or protect.     

On the nature of mental models of conditional: The case of If,If then,and Only if

It has recently been reported that forward inferences from if p then q sentences (i.e., from antecedent to consequent) were faster than backward inferences from consequent to antecedent (Barrouillet, Grosset, & Lecas, 2000). The standard mental model theory assumes that this directionality effect is a figural effect due to the order the information enters working memory, whereas we claim that it results from the nature of the mental models that represent oriented relations from hypothetical values introduced by the word If. We tested these hypotheses in an experiment in which adult participants evaluated conditional syllogisms from either if p then q, p only if q, or p if q statements. Contrary to the predictions resulting from the standard theory, the three forms of the conditional provoked a reversed directionality effect and denial inferences took longer to endorse than affirmative inferences for all the forms of conditionals. We argue from these results that mental models of the conditional represent oriented relations instead of mere co-occurrences between events.     

循环并不可恶--《恶性循环:非良基现象的数学》评介

上世纪初,罗素悖论和其他几个集合论悖论的出现引起了许多著名数学家的震惊。为了排除悖论,集合论学者们借助公理方法对康托尔的理论和方法进行了系统整理,建立起了多种严谨的集合论体系,当今应用广泛的ZF集合论就是其中最为著名的一种。直观上集合与类不分,一个性质决定一个类,ZF集合论不能承诺所有这些类都是集合,它用基础公理FA来保证所承诺的集合都是良基的。说一个类X为良基的,是指不能有一个由类组成的无穷序列X1、X2、…、Xn、… (不一定都不相同 )使得…∈Xn∈…∈X2∈X1∈X成立。这样的无穷序列被称为从X开始的一条无穷∈降…     

The Refined Extension Principle for Semantics of Dynamic Logic Programming

Over recent years, various semantics have been proposed for dealing with updates in the setting of logic programs. The availability of different semantics naturally raises the question of which are most adequate to model updates. A systematic approach to face this question is to identify general principles against which such semantics could be evaluated. In this paper we motivate and introduce a new such principle the refined extension principle. Such principle is complied with by the stable model semantics for (single) logic programs. It turns out that none of the existing semantics for logic program updates, even though generalisations of the stable model semantics, comply with this principle. For this reason, we define a refinement of the dynamic stable model semantics for Dynamic Logic Programs that complies with the principle.     

Traditional Logic,Modern Logic and Natural Language

In a recent paper Johan van Benthem reviews earlier work done by himself and colleagues on ‘natural logic’. His paper makes a number of challenging comments on the relationships between traditional logic, modern logic and natural logic. I respond to his challenge, by drawing what I think are the most significant lines dividing traditional logic from modern. The leading difference is in the way logic is expected to be used for checking arguments. For traditionals the checking is local, i.e. separately for each inference step. Between inference steps, several kinds of paraphrasing are allowed. Today we formalise globally: we choose a symbolisation that works for the entire argument, and thus we eliminate intuitive steps and changes of viewpoint during the argument. Frege and Peano recast the logical rules so as to make this possible. I comment also on the traditional assumption that logical processing takes place at the top syntactic level, and I question Johan’s view that natural logic is ‘natural’.     

Trust and New Communication Technologies: Vicious Circles, Virtuous Circles, Possible Futures

I approach the philosophical analyses of the phenomenon of trust vis-à-vis online communication beginning with an overview from within the framework of computer-mediated communication (CMC) of concerns and paradigmatic failures of trust in the history of online communication. I turn to the more directly philosophical analyses of trust online by first offering an introductory taxonomy of diverse accounts of trust that have emerged over the past decade or so. In the face of important objections to the possibility of establishing and fostering trust in online environments—objections that emerge especially from the perspective of virtue ethics and phenomenological approaches to how we know and navigate the world as embodied beings—I then take up three major arguments in recent work in favor of the possibilities of trust online, followed by three vicious circles that run counter to more optimistic views. I close with a summary of some additional reasons for optimism regarding trust online, followed by a final question that emerges out of recent CMC research on social networking sites that poses, I argue, fundamental challenges indeed to how we understand and may foster and experience trust online.