An algebraically expandable (AE) class is a class of algebraic structures axiomatizable by sentences of the form $\forall \exists! \mathop{\boldsymbol {\bigwedge }}\limits p = q$. For a logic L algebraized by a quasivariety $\mathcal {Q}$ we show that the AE-subclasses of $\mathcal {Q}$ correspond to certain natural expansions of L, which we call algebraic expansions. These turn out to be a special case of the expansions by implicit connectives studied by X. Caicedo. We proceed to characterize all the AE-subclasses (...) of abelian $\ell $ -groups and perfect MV-algebras, thus fully describing the algebraic expansions of their associated logics. (shrink)

We present a theory that copes with the dynamics of inconsistent information. A method is set forth to represent possibly inconsistent information by a finite state. Next, finite operations for expansion and contraction of finite states are given. No extra-logical element — a choice function or an ordering over (sets of) sentences — is presupposed in the definition of contraction. Moreover, expansion and contraction are each other's duals. AGM-style characterizations of these operations follow.

We suggest that a restorative justice critique of current retributive policy and practice may well be a starting point for the development of more just and more effective approaches to sentencing, both formal and informal, and to a more effective approach to reentry for currently incarcerated persons. While restorative justice principles acknowledge the debt owed by offenders to their victims and victimized communities, this is a debt met neither by inflicting harm on the offender nor by removing the offender's rights (...) as a citizen. As a different normative theory, the measure of justice in a restorative approach is the extent to which harm caused by crime is repaired. While restorative justice may therefore demand a lot of offenders, their supporters, and community members, it also provides for the opportunity for victim input and reparation. Most importantly, the normative theory of restorative justice provides a different currency of repair and healing that could begin to displace the currency of punishment that knows no limits. While a restorative metric would certainly have its own limits and guidelines, the metric of uniformity as the primary gauge of justice process could at least be supplemented with a metric of stakeholder participation, satisfaction, accountability, reparation, and peacemaking. (shrink)

For $n < \omega$ , expand the structure (n, S, I, F) (with S the successor relation, I, F as the initial and final element) by forming graphs with edge probability n-α for irrational α, with $0 < \alpha < 1$ . The sentences in the expanded language, which have limit probability 1, form a complete and stable theory.

Let be a model of a theory T. Depending on wether is decidable or recursive, and on whether T is strongly minimal or -minimal, we find conditions on which guarantee that every infinite independent subset of is not recursively enumerable. For each of the same four cases we also find conditions on which guarantee that every infinite independent subset of has Turing degree 0'. More generally, let be a recursive -structure, R a relation symbol not in , ψ a recursive (...) infiniatary Π2 sentence in the language {R}, and let 0<α<ωCK1. We discuss conditions under which we can construct a recursive -structure such that ,Rψ for every Δ0α relation R on. (shrink)

Of the famous passage from Augustine’s Confessions1 that opens Philosophical Investigations, Wittgenstein writes, These words, it seems to me, give us a particular picture of the essence of human language. It is this: the words in language name objects — sentences are combinations of such names. — In this picture of language we find the roots of the following idea: Every word has a meaning. This meaning is correlated with the word. It is the object for which the word (...) stands. (PI, 2009, §1) -/- This remark has frequently been taken to simply identify as Wittgenstein’s point of departure the ‘naming theory’ of language. But as usual, closer attentiveness to Wittgenstein’s words extracts a good deal more content. Augustine’s words impart a picture not only of human language, but indeed a picture of the essence of language. So to begin, let us look briefly at the concepts of (1) picture and (2) essence as they are used here. (shrink)

The languages of finitary and infinitary logic over the alphabet of bounded lattices have proven to be of considerable use in the study of compacta. Significant among the sentences of these languages are the ones that are base free, those whose truth is unchanged when we move among the lattice bases of a compactum. In this paper we define syntactically the expansive sentences, and show each of them to be base free. We also show that many well-known (...) properties of compacta may be expressed using expansive sentences; and that any property so expressible is closed under inverse limits and co-existential images. As a byproduct, we conclude that co-existential images of pseudo-arcs are pseudo-arcs. This is of interest because the corresponding statement for confluent maps is still open, and co-existential maps are often—but not always—confluent. (shrink)

This chapter contains sections titled: Allergy to absolute truth Provisionality and truth Truth versus verification Truth and fixity Transparency, Tarski, and Carnap Truth and certainty Sentences as truth candidates Theoretical terms Varieties of instrumentalism Pragmatism and instrumentalism Systems, simplicity, reduction Crises in science Reduction and expansion.

AGM-theory, named after its founders Carlos Alchourrón, Peter Gärdenfors and David Makinson, is the leading contemporary paradigm in the theory of belief-revision. The theory is reformulated here so as to deal with the central relational notions 'J is a contraction of K with respect to A' and 'J is a revision of K with respect to A'. The new theory is based on a principal-case analysis of the domains of definition of the three main kinds of theory-change (expansion, contraction and (...) revision). The new theory is stated by means of introduction and elimination rules for the relational notions. In this new setting one can re-examine the relationship between contraction and revision, using the appropriate versions of the so-called Levi and Harper identities. Among the positive results are the following. One can derive the extensionality of contraction and revision, rather than merely postulating it. Moreover, one can demonstrate the existence of revision-functions satisfying a principle of monotonicity. The full set of AGM-postulates for revision-functions allow for completely bizarre revisions. This motivates a Principle of Minimal Bloating, which needs to be stated as a separate postulate for revision. Moreover, contractions obtained in the usual way from the bizarre revisions, by using the Harper identity, satisfy Recovery. This provides a new reason (in addition to several others already adduced in the literature) for thinking that the contraction postulate of Recovery fails to capture the Principle of Minimal Mutilation. So the search is still on for a proper explication of the notion of minimal mutilation, to do service in both the theory of contraction and the theory of revision. The new relational formulation of AGM-theory, based on principal-case analysis, shares with the original, functional form of AGM-theory the idealizing assumption that the belief-sets of rational agents are to be modelled as consistent, logically closed sets of sentences. The upshot of the results presented here is that the new relational theory does a better job of making important matters clear than does the original functional theory. A new setting has been provided within which one can profitably address two pressing questions for A GM-theory: (1) how is the notion of minimal mutilation (by both contractions and revisions) best analyzed? and (2) how is one to rule out unnecessary bloating by revisions? (shrink)

The sentence "The boss fired the employee who is always late" invites the defeasible inference that the speaker is attempting to convey that the lateness caused the firing. We argue that such inferences cannot be understood in terms of familiar approaches to extrasemantic enrichment such as implicature, impliciture, explicature, or species of local enrichment already in the literature. Rather, we propose that they arise from more basic cognitive strategies, grounded in processes of coherence establishment, that thinkers use to make sense (...) of the world. Attention to such cases provides a richer and more varied landscape of extrasemantic enrichment than has been appreciated to date. (shrink)

I show that the partial truth of a sentence in a partial structure is equivalent to the truth of that sentence in an expansion of a structure that corresponds naturally to the partial structure. Further, a mapping is a partial homomorphism/partial isomorphism between two partial structures if and only if it is a homomorphism/isomorphism between their corresponding structures. It is a corollary that the partial truth of a sentence in a partial structure is equivalent to the truth of a specific (...) Ramsey sentence in a corresponding structure. Hence the partial structures approach can be expressed in standard first or second-order model theory, and it can be captured in the received view on scientific theories as developed by Carnap and Hempel. (shrink)

In the language of second-order logic, first- and second-order variables are distinguished syntactically and cannot be grammatically substituted. According to a prominent argument for the deployment of these languages, these substitution failures are necessary to block the derivation of paradoxes that result from attempts to generalize over predicate interpretations. I first examine previous approaches which interpret second-order sentences using expressions of natural language and argue that these approaches undermine these syntactic restrictions. I then examine Williamson’s primitivist approach according to (...) which second-order sentences are not offered readings in a previously understood language. I argue that the syntactic restrictions alone do not block the derivation of the paradox, unless they are backed by a principled reason that the language cannot be expanded to allow the grammatical substitution of first- and second- order variables. I argue that there is neither a syntactic nor a semantic principle that prohibits such an expansion. (shrink)

We show a sentence and modal square of opposition and equivalence to be expanded into an hexagon according to oe suggestion from William of Sherwood. This expansión is permittedby two sentence and modal rules.The logical relations of the square allow us to formulate several theorems in order to show a glimpse of the Medieval Logic complexity.

With the expansion of people’s needs, the translation performance of traditional models is increasingly unable to meet current demands. This article mainly studied the Transformer model. First, the structure and principle of the Transformer model were briefly introduced. Then, the model was improved by a generative adversarial network to improve the translation effect of the model. Finally, experiments were carried out on the linguistic data consortium dataset. It was found that the average Bilingual Evaluation Understudy value of the improved Transformer (...) model improved by 0.49, and the average perplexity value reduced by 10.06 compared with the Transformer model, but the computation speed was not greatly affected. The translation results of the two example sentences showed that the translation of the improved Transformer model was closer to the results of human translation. The experimental results verify that the improved Transformer model can improve the translation quality and be further promoted and applied in practice to further improve the English translation and meet application needs in real life. (shrink)

Belnap–Dunn’s relevance logic, \(\textsf{BD}\), was designed seeking a suitable logical device for dealing with multiple information sources which sometimes may provide inconsistent and/or incomplete pieces of information. \(\textsf{BD}\) is a four-valued logic which is both paraconsistent and paracomplete. On the other hand, De and Omori, while investigating what classical negation amounts to in a paracomplete and paraconsistent four-valued setting, proposed the expansion \(\textsf{BD2}\) of the four valued Belnap–Dunn logic by a classical negation. In this paper, we introduce a four-valued expansion (...) of BD called \({\textsf{BD}^\copyright }\), obtained by adding an unary connective \({\copyright }\,\ \) which is a consistency operator (in the sense of the Logics of Formal Inconsistency, _LFI_s). In addition, this operator is the unique one with the following features: it extends to \(\textsf{BD}\) the consistency operator of LFI1, a well-known three-valued _LFI_, still satisfying axiom _ciw_ (which states that any sentence is either consistent or contradictory), and allowing to define an undeterminedness operator (in the sense of Logic of Formal Undeterminedness, _LFU_s). Moreover, \({\textsf{BD}^\copyright }\) is maximal w.r.t. LFI1, and it is proved to be equivalent to BD2, up to signature. After presenting a natural Hilbert-style characterization of \({\textsf{BD}^\copyright }\) obtained by means of twist-structures semantics, we propose a first-order version of \({\textsf{BD}^\copyright }\) called \({\textsf{QBD}^\copyright }\), with semantics based on an appropriate notion of four-valued Tarskian-like structures called \(\textbf{4}\) -structures. We show that in \({\textsf{QBD}^\copyright }\), the existential and universal quantifiers are interdefinable in terms of the paracomplete and paraconsistent negation, and not by means of the classical negation. Finally, a Hilbert-style calculus for \({\textsf{QBD}^\copyright }\) is presented, proving the corresponding soundness and completeness theorems. (shrink)

I am often asked to explain the difference between my notion of impliciture (Bach 1994) and the relevance theorists’ notion of explicature (Sperber and Wilson 1986; Carston 2002). Despite the differences between the theoretical frameworks within which they operate, the two notions seem very similar. Relevance theorists describe explicatures as “developments of logical forms,” whereas I think of implicitures as “expansions” or “completions” of semantic contents (depending on whether or not the sentence’s semantic content amounts to a proposition). That is (...) not much of a difference. We agree that implicitures/explicatures go beyond what is said (in a strict sense) and yet fall short of being implicatures. So, what is the difference, or is it just terminological? As we will see, the real differences emerge when the two notions are situated in their respective theoretical frameworks with their contrasting conceptions of what is involved in linguistic communication. (shrink)

Prioritized bases, i.e., weakly ordered sets of sentences, have been used for specifying an agent’s ‘basic’ or ‘explicit’ beliefs, or alternatively for compactly encoding an agent’s belief state without the claim that the elements of a base are in any sense basic. This paper focuses on the second interpretation and shows how a shifting of priorities in prioritized bases can be used for a simple, constructive and intuitive way of representing a large variety of methods for the change of (...) belief states—methods that have usually been characterized semantically by a system-of-spheres modeling. Among the methods represented are ‘radical’, ‘conservative’ and ‘moderate’ revision, ‘revision by comparison’ in its raising and lowering variants, as well as various constructions for belief expansion and contraction. Importantly, none of these methods makes any use of numbers. (shrink)

Ratajczyk, Z., Subsystems of true arithmetic and hierarchies of functions, Annals of Pure and Applied Logic 64 95–152. The combinatorial method coming from the study of combinatorial sentences independent of PA is developed. Basing on this method we present the detailed analysis of provably recursive functions associated with higher levels of transfinite induction, I, and analyze combinatorial sentences independent of I. Our treatment of combinatorial sentences differs from the one given by McAloon [18] and gives more natural (...) sentences. The same method give also a combinatorial technique with no use of the cut-elimination theorem which is appropriate to study proof-theoretic strength of subsystems of first order arithmetic and some of their expansions. It was used to analyze iterated reflection principle and system of transfinite induction with a satisfaction class. (shrink)

One of the most fundamental questions in the philosophy of mathematics concerns the relation between truth and formal proof. The position according to which the two concepts are the same is called deflationism, and the opposing viewpoint substantialism. In an important result of mathematical logic, Kurt Gödel proved in his first incompleteness theorem that all consistent formal systems containing arithmetic include sentences that can neither be proved nor disproved within that system. However, such undecidable Gödel sentences can be (...) established to be true once we expand the formal system with Alfred Tarski s semantical theory of truth, as shown by Stewart Shapiro and Jeffrey Ketland in their semantical arguments for the substantiality of truth. According to them, in Gödel sentences we have an explicit case of true but unprovable sentences, and hence deflationism is refuted. -/- Against that, Neil Tennant has shown that instead of Tarskian truth we can expand the formal system with a soundness principle, according to which all provable sentences are assertable, and the assertability of Gödel sentences follows. This way, the relevant question is not whether we can establish the truth of Gödel sentences, but whether Tarskian truth is a more plausible expansion than a soundness principle. In this work I will argue that this problem is best approached once we think of mathematics as the full human phenomenon, and not just consisting of formal systems. When pre-formal mathematical thinking is included in our account, we see that Tarskian truth is in fact not an expansion at all. I claim that what proof is to formal mathematics, truth is to pre-formal thinking, and the Tarskian account of semantical truth mirrors this relation accurately. -/- However, the introduction of pre-formal mathematics is vulnerable to the deflationist counterargument that while existing in practice, pre-formal thinking could still be philosophically superfluous if it does not refer to anything objective. Against this, I argue that all truly deflationist philosophical theories lead to arbitrariness of mathematics. In all other philosophical accounts of mathematics there is room for a reference of the pre-formal mathematics, and the expansion of Tarkian truth can be made naturally. Hence, if we reject the arbitrariness of mathematics, I argue in this work, we must accept the substantiality of truth. Related subjects such as neo-Fregeanism will also be covered, and shown not to change the need for Tarskian truth. -/- The only remaining route for the deflationist is to change the underlying logic so that our formal languages can include their own truth predicates, which Tarski showed to be impossible for classical first-order languages. With such logics we would have no need to expand the formal systems, and the above argument would fail. From the alternative approaches, in this work I focus mostly on the Independence Friendly (IF) logic of Jaakko Hintikka and Gabriel Sandu. Hintikka has claimed that an IF language can include its own adequate truth predicate. I argue that while this is indeed the case, we cannot recognize the truth predicate as such within the same IF language, and the need for Tarskian truth remains. In addition to IF logic, also second-order logic and Saul Kripke s approach using Kleenean logic will be shown to fail in a similar fashion. (shrink)

The foundations of almost all Islamic sciences were laid in the first and second centuries of hijra. With the expansion of the Islamic world since the first century of hijra, the existence of a collective effort to transfer oral information into writing is notable. With the invitation of the prophet Muḥammad to Islam, an unprecedented increase in the culture of writing has been observed. Since the emergence of Islam, the world history scene has witnessed feverish writing activity. Especially in the (...) 2th/8th century, when the transition from oral culture to written culture accelerated, the founding texts of the science of language and religion, which were the carriers of these sciences related to aqāid-kalām, fiqh and uṣūl al-fiqh, tasawwuf, tafsir, and hadith, were compiled. Thanks to the founding texts containing the basic principles, the sciences have had the opportunity to develop by deepening. In this study, the contribution of Fiqh al-akbar, the founding text of the science of creed, to the science of kalam, which has made significant progress, will be discussed. In order for a text to be considered a founding and root, there must be a system that it establishes as the fruit of the tree. In this sense, Fiqh al-akbar established a moderate and defensible belief system. There is an organic link between the most concise faith texts and the most voluminous kalām books. While the creed texts, which consist of writing the goals at the end of the road, are the counting of the principles of faith, the texts of the kalām represent the walking of the road that leads to the goal of faith. Fiqh al-akbar, which marks the end of the road by finishing the roads to be walked, is the first and most important of the milestones of Islamic thought. In this study, the contribution of Fiqh al-akbar, the founding text of the science of aqāid, to the science of kalām will be discussed in the context of its belonging to its author. This text gave direction to Ahl al-Sunna theology, which would be written in the later stages of Islamic thought. In this study, the internal and external contexts of the founding text mentioned will be confirmed in terms of its relative acumen to Abū Ḥanīfa. In addition, the reason for the increase in the commentaries (Sharḥ) of Fiqh al-akbar during the Ottoman period will be shown. As a matter of fact, each annotation strengthens that it belongs to the author. In the annotations, there is no sentence stating that the text does not belong to Abū Ḥanīfa, on the contrary, the authenticity of the belonging is emphasized. Of course, not all the annotations of the relevant text will be included here, but mostly printed works will be emphasized. Theology, prophecy and the hereafter are discussed in Fiqh al-akbar. Here, how theological debates and problems related to the history of theological concepts are handled in the commentaries will be shown. In this article, within the framework of the method discussed as an example, a preparation will be made for further studies to evaluate the topics and concepts of prophecy and the hereafter in the context of commentaries. The point that should be emphasized here is that none of the scholars who commented on the text pointed out that the subject or concept was not discussed in the period of Abū Ḥanīfa. Moreover, from the early period until as late as the 7th/13th century, both theology and bibliography books did not have any doubts about the belonging of Fiqh al-akbar to Abū Ḥanīfa. Moreover, since the early period, both theological and bibliographical works did not have any doubts about Fiqh al-akbar’s belonging to Abū Ḥanīfa. (shrink)

What makes our utterances mean what they do? In this work I formulate and justify a structural constraint on possible answers to this key question in the philosophy of language, and I show that accepting this constraint leads naturally to the adoption of an algebraic formalization of truth-theoretic semantics. I develop such a formalization, and show that applying algebraic methodology to the theory of meaning yields important insights into the nature of language. ;The constraint I propose is, roughly, this: the (...) meaning of an utterance of a natural language sentence is derived from the place of that sentence within a system that includes other sentences, and is structured in virtue of primitive semantic facts about complete sentences. This constraint calls for a formal semantics program where the meaning of natural language sentences is represented by an appropriate assignment of the elements of an algebraic structure to sentences, an assignment that represents facts concerning complete sentences. I call the above constraint 'The Algebraic Thesis', and the corresponding formal semantics program 'Algebraic Semantics.' ;I introduce AT by carving it out of the holistic views of language of Quine and Davidson, and I show that it is independent of other important features of these philosophers' views. I then argue for AT, taking into account recent work by Brandom, Dummett, Fodor and Lepore, Gaifman and Perry. In developing Algebraic Semantics I present structures of two basic types: Boolean algebras and cylindric algebras; these structures are construed in the context of AT in a novel way: they are treated as applying to classes of sentences as numbers apply to physical objects in measurement. Applying algebraic methodology to formal semantics and to the theory of meaning, I develop these results: ; An account of the semantics of necessity and possibility that avoids both Quine's dismissal of these notions and their reduction by David Lewis to quantification over possible worlds; ; The application of the model-theoretic notion of expansion to capture the process of our learning progressively more of the meaning of expressions in our first languages. (shrink)

Lackey’s (2007) class of “selfless assertions” is controversial in at least two respects: it allows propositions that express Moorean absurdity to be asserted warrantedly, and it challenges the orthodox view that the speaker’s belief is a necessary condition for warranted assertibility. With regard to the former point, I critically examine Lackey’s broadly Gricean treatment of Moorean absurdity and McKinnon’s (2015) epistemic approach. With regard to the latter point, I defend the received view by supporting the knowledge account, on which knowledge (...) is the necessary condition for warranted assertion. After examining two defenses of KA, by Montminy and Turri, I propose two alternative approaches. Although I remain neutral between them, I develop in more detail the view which classifies “selfless assertions” as “presentations”, a type of assertives distinct from genuine assertions. This account is motivated further by allowing for the expansion of the normative approach to other assertives, a feature we may be interested in, in the light of a recent wave of normative accounts of speech acts. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Living the Truth: A Theory of ActionBenjamin J. BrownLiving the Truth: A Theory of Action Klaus Demmer Washington, D.C.: Georgetown University Press, 2010. 179 pp. $34.95.Klaus Demmer is one of the most influential Catholic moral theologians in Europe since Vatican II. Unfortunately, he is relatively unknown in America. Living the Truth is only the second of his works to be translated into English, although other translations are anticipated. (...) In Living the Truth, Demmer provides an incredibly balanced and nuanced work of fundamental moral theology and brims with insights. Not content with easy answers or oversimplifications, Demmer seeks in this book not only to chart a way between apparent opposites but also to synthesize the best of both into a new unity.For example, Demmer returns regularly to the question of the foundation and role of moral norms. Norms are indispensable in the life of the “ethical personality,” the person who is fully alive as a human being. They serve to open a person to the truth and to freedom and help to make a space for genuinely good, free, and vibrant action. However, norms are not at the heart of Demmer’s ethics, either as a discipline or in actual life. He also speaks of the ways in which a person establishes norms for herself even as he is careful to avoid relativism or subjectivism. Acknowledging that norms derived from a natural law ethics are true and important and that Christian morality may not be able to add any propositional content to natural law, he also argues at length that Christianity does in fact significantly shape a natural law ethics into something that is both deeper and more expansive. For Demmer, the Christian context changes the basis and meaning of morality. Although frustratingly spare with examples, he brings to the fore the difference between grounding human dignity in human nature as reason can grasp it and grounding it more specifically in the image and likeness of God and the love shown in the incarnation and redemption.Demmer’s moral theology is profoundly human and existential; it is immersed in the context and texture of real human experience. In many ways, it is very pastoral. It certainly manifests a depth of psychological insight into the nature and workings of the human mind, for example, in analyzing the ways in which people fall into pride and self-deception (33–37).Living the Truth’s concern with truth and truthfulness is an important and timely theme. Once again, Demmer synthesizes distinct elements. Truthfulness is a multifaceted reality, referring both to internal and external forces. Systematically [End Page 227] grounding his ethics in a robust classical metaphysic, Demmer understands the “true,” the “good,” and “being” to be related as transcendentals (42). The “truth” opens one up to “goodness,” which in turn allows for the flourishing of the human person. Far from being restrictive, the truth opens up possibilities for true freedom. But this only occurs when it is internalized as “truthfulness,” a virtue of many dimensions that Demmer unfolds throughout the book, particularly in the last of the three main parts.Living the Truth is very dense. It definitely is not an undergraduate text. Both the meaning of individual sentences and the flow of Demmer’s thought are elusive at times. Many subsections discuss a range of ideas and seem at times to wander. Even readers with a strong background in moral theology will find it necessary to reread and think carefully in order to catch the precise meaning of specific phrases and follow the argument. Nonetheless, the rewards are well worth the effort. Every moral theologian owes it to herself to read this book. [End Page 228]Benjamin J. BrownLourdes UniversityCopyright © 2012 Society of Christian Ethics... (shrink)

In noun phrase coordinate constructions, there is a strong tendency for the syntactic structure of the second conjunct to match that of the first; the second conjunct in such constructions is therefore low in syntactic information. The theory of uniform information density predicts that low-information syntactic constructions will be counterbalanced by high information in other aspects of that part of the sentence, and high-information constructions will be counterbalanced by other low-information components. Three predictions follow: lexical probabilities will be lower in (...) second conjuncts than first conjuncts; lexical probabilities will be lower in matching second conjuncts than nonmatching ones; and syntactic repetition should be especially common for low-frequency NP expansions. Corpus analysis provides support for all three of these predictions. (shrink)

Takfir is an accusation against someone as an infidel—those having different beliefs or expressing a different view or committing any acts of infidelity. Sentences or labels toward infidels vary and are accompanied by a fatwa from labeling the accused as ‘infidels’ to having the right to eradicate the infidels. This article discussed the development of the takfir doctrine which separates some groups not only based on theological aspects but also on socio-political aspects. Moreover, the expanding meaning of ‘infidel’ is (...) also accompanied by an obligatory, individual jihad to fight against internal enemies and external enemies. The expansion is even emphasized on any occasions on several hatred acts, such as hating infidels, which are propagandized to promote and establish Islamic laws. Specifically, this article discussed how Ayman al-Zawahiri expanded the doctrine into global acts framed in a modern way, such as secularism, capitalism, human rights, and environmental destruction, to attract local jihad groups to fight together in global spheres. (shrink)

In 1969, De Jongh proved the “maximality” of a fragment of intuitionistic predicate calculus forHA. Leivant strengthened the theorem in 1975, using proof-theoretical tools (normalisation of infinitary sequent calculi). By a refinement of De Jongh's original method (using Beth models instead of Kripke models and sheafs of partial combinatory algebras), a semantical proof is given of a result that is almost as good as Leivant's. Furthermore, it is shown thatHA can be extended to Higher Order Heyting Arithmetic+all trueΠ 2 0 (...) -sentences + transfinite induction over primitive recursive well-orderings. As a corollary of the proof, maximality of intuitionistic predicate calculus is established wrt. an abstract realisability notion defined over a suitable expansion ofHA. (shrink)

Wilkie 5 397) proved a “theorem of the complement” which implies that in order to establish the o-minimality of an expansion of with C∞ functions it suffices to obtain uniform bounds on the number of connected components of quantifier free definable sets. He deduced that any expansion of with a family of Pfaffian functions is o-minimal. We prove an effective version of Wilkie's theorem of the complement, so in particular given an expansion of the ordered field with finitely many C∞ (...) functions, if there are uniform and computable upper bounds on the number of connected components of quantifier free definable sets, then there are uniform and computable bounds for all definable sets. In such a case the theory of the structure is effectively o-minimal: there is a recursively axiomatized subtheory such that each of its models is o-minimal. This implies the effective o-minimality of any expansion of with Pfaffian functions. We apply our results to the open problem of the decidability of the theory of the real field with the exponential function. We show that the decidability is implied by a positive answer to the following problem ): given a language L expanding the language of ordered rings, if an L-sentence is true in every L-structure expanding the ordered field of real numbers, then it is true in every o-minimal L-structure expanding any real closed field. (shrink)

Justice for rape victims has become synonymous with punitive state punishment. Taking rape seriously is equated with increasing convictions and prison sentences and consequently most feminist activism has been focused on reforming the conventional criminal justice system to secure these aims. While important reforms have been made, justice continues to elude many victims. Many feel re-victimized by a system which marginalizes their interests and denies them a voice. Restorative justice offers the potential to secure justice for rape victims, but (...) feminist resistance has resulted in few programmes tackling such crimes. In After the Crime, Susan Miller evidences the positive outcomes of a restorative justice programme tackling serious offences including rape and recommends their development. However, her vision is ultimately limited by her recommendation of only post-conviction restorative processes and the implicit endorsement of the conventional criminal justice system. I argue that feminist strategy and activism must rethink its approach to what constitutes justice for rape victims, going beyond punitive state outcomes to encompass broader notions of justice, including an expansive approach to restorative justice. (shrink)

Revision operation is the consistent expansion of a theory by a new belief-representing sentence. We consider that in a paraconsistent setting this desideratum can be accomplished in at least three distinct ways: the output of a revision operation should be either non-trivial or non-contradictory (in general or relative to the new belief). In this paper those distinctions will be explored in the constructive level by showing how the remainder sets could be refined, capturing the key concepts of paraconsistency in a (...) dynamical scenario. These are preliminaries results of a wider project on Paraconsistent Belief Change conduced by the authors. (shrink)

By replacement is meant an operation that replaces one sentence by another in a belief set. Replacement can be used as a kind of Sheffer stroke for belief change, since contraction, revision, and expansion can all be defined in terms of it. Replacement can also be defined either in terms of contraction or in terms of revision. Close connections are shown to hold between axioms for replacement and axioms for contraction and revision. Partial meet replacement is axiomatically characterized. It is (...) shown that this operation can have outcomes that are not obtainable through either partial meet contraction or partial meet revision. (shrink)

Temporal logic as a modern discipline is separate from classical logic; it is seen as an addition or expansion of the more basic propositional and predicate logics. This approach is in contrast with logic in the Middle Ages, which was primarily intended as a tool for the analysis of natural language. Because all natural language sentences have tensed verbs, medieval logic is inherently a temporal logic. This fact is most clearly exemplified in medieval theories of supposition. As a case (...) study, we look at the supposition theory of Lambert of Lagny, extracting from it a temporal logic and providing a formalization of that logic. (shrink)

A descriptor is a set of sentences that are truth-functional combinations of expressions of the form \ , where \ is a metalinguistic belief predicate and p a sentence in the object language in which beliefs are expressed. Descriptor revision ) is an operation of belief change that takes us from a belief set K to a new belief set \ where \ is a descriptor representing the success condition. Previously studied operations of belief change are special cases of (...) descriptor revision, hence sentential revision can be represented as \ , contraction as \ , multiple contraction as \ , replacement as \ , etc. General models of descriptor revision are constructed and axiomatically characterized. The common selection mechanisms of AGM style belief change cannot be used, but they can be replaced by choice functions operating directly on the set of potential outcomes . The restrictions of this construction to sentential revision ) and sentential contraction give rise to operations with plausible properties that are also studied in some some detail. (shrink)

We investigate the theory Peano Arithmetic with Indiscernibles ( \(\textrm{PAI}\) ). Models of \(\textrm{PAI}\) are of the form \(({\mathcal {M}},I)\), where \({\mathcal {M}}\) is a model of \(\textrm{PA}\), _I_ is an unbounded set of order indiscernibles over \({\mathcal {M}}\), and \(({\mathcal {M}},I)\) satisfies the extended induction scheme for formulae mentioning _I_. Our main results are Theorems A and B following. _Theorem A._ _Let_ \({\mathcal {M}}\) _be a nonstandard model of_ \(\textrm{PA}\) _ of any cardinality_. \(\mathcal {M }\) _has an expansion (...) to a model of _ \(\textrm{PAI}\) _iff_ \( {\mathcal {M}}\) _has an inductive partial satisfaction class._ Theorem A yields the following corollary, which provides a new characterization of countable recursively saturated models of \(\textrm{PA}\) : _Corollary._ _A countable model_ \({\mathcal {M}}\) of \(\textrm{PA}\) _is recursively saturated iff _ \({\mathcal {M}}\) _has an expansion to a model of _ \(\textrm{PAI}\). _Theorem B._ _There is a sentence _ \(\alpha \) _ in the language obtained by adding a unary predicate_ _I_(_x_) _to the language of arithmetic such that given any nonstandard model _ \({\mathcal {M}}\) _of_ \(\textrm{PA}\) _ of any cardinality_, \({\mathcal {M}}\) _has an expansion to a model of _ \(\text {PAI}+\alpha \) _iff_ \({\mathcal {M}}\) _has a inductive full satisfaction class._. (shrink)

In this paper I introduce and develop an approach to tenses and temporal expressions that is a mix between eternalism and temporalism consisting in appeal to ‘variadic operators’. The type of variadic operator I will be concerned with is the expansive variadic operator, which takes as input predicates of a certain adicity and yields new predicates with one additional degree of adicity. Appeal to variadic operators has proven useful in giving the semantics of several types of expressions: adverbs ), (...) prepositional phrases ), relational terms ), etc. The focus of this paper is on tenses and temporal expressions, with the aim of showing how these are treated by appeal to temporal variadic operators. First I define the temporal variadic operator and then show how it can be used to account for simple tensed sentences. I also give a rough sketch of how it can accommodate more complex phenomena like sequence of time, interaction between tenses and temporal adverbials, temporal anaphora, later-than-matrix and double-access readings, etc. (shrink)

An unconventional formalization of the canonical square of opposition in the notation of classical symbolic logic secures all but one of the canonical square’s grid of logical interrelations between four A-E-I-O categorical sentence types. The canonical square is first formalized in the functional calculus in Frege’s Begriffsschrift, from which it can be directly transcribed into the syntax of contemporary symbolic logic. Difficulties in received formalizations of the canonical square motivate translating I categoricals, ‘Some S is P’, into symbolic logical notation, (...) not conjunctively as \, but unconventionally instead in an ontically neutral conditional logical symbolization, as \. The virtues and drawbacks of the proposal are compared at length on twelve grounds with the explicit existence expansion of A and E categoricals as the default strategy for symbolizing the canonical square preserving all original logical interrelations. (shrink)

We define the notion of a combinatorics of a first order structure, and a relation of covering between first order structures and propositional proof systems. Namely, a first order structure M combinatorially satisfies an L-sentence Φ iff Φ holds in all L-structures definable in M. The combinatorics Comb(M) of M is the set of all sentences combinatorially satisfied in M. Structure M covers a propositional proof system P iff M combinatorially satisfies all Φ for which the associated sequence of (...) propositional formulas 〈Φ〉 n , encoding that Φ holds in L-structures of size n, have polynomial size P-proofs. That is, Comb(M) contains all Φ feasibly verifiable in P. Finding M that covers P but does not combinatorially satisfy Φ thus gives a super polynomial lower bound for the size of P-proofs of 〈Φ〉 n . We show that any proof system admits a class of structures covering it; these structures are expansions of models of bounded arithmetic. We also give, using structures covering proof systems R * (log) and PC, new lower bounds for these systems that are not apparently amenable to other known methods. We define new type of propositional proof systems based on a combinatorics of (a class of) structures. (shrink)

The question about epistemic nature of norms is a special case of discussing the non-standard definition of knowledge. Is it possible to expand the understanding of knowledge beyond the proposi­tions expressed by narrative sentence and describing what takes place? Might a moral norm, an aesthetic ideal, a religious symbol be taken as specific types of knowledge? Thesis on the special epistemological status of science, its empirical basis and methods lies in the basis of naturalistic revision of epistemology by Quine. White, (...) on the contrary, considers scientific observations and moral experiences equal means to justify objective and normative content in science as well as in morality and art. With regard to the contemporary expansion of the subject matter of epistemology White is more advantageous, although both sides ultimately do not extend beyond reduction of all cultural phenomena to the facts of individual consciousness. The resolution of the dispute under consideration can be provided by the turn of epistemological reflection to the study of the cognitive content of cultural objectivizations of human activity and communication, to the analysis of specific forms of representation and functions of whatever cognitive phenomena in the social artifacts. On the one hand, this extends the subject-matter of traditional epistemology by involving all the diversity of consciousness and on the other hand, this prepares methodological insights for cultural and reli­gious studies, ethics, aesthetics, and political science. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Milton and Political CorrectnessMary Ann McGrail (bio)In the opening of the title essay of Persecution and the Art of Writing, Leo Strauss speculates:We can easily imagine that a historian living in a totalitarian country, a generally respected and unsuspected member of the only party in existence, might be led by his investigations to doubt the soundness of the government-sponsored interpretation of the history of religion. Nobody would prevent him (...) from publishing a passionate attack on what he would call the liberal view. He would of course have to state the liberal view before attacking it; he would make that statement in the quiet, unspectacular and somewhat boring manner which would seem to be but natural; he would use many technical terms, give many quotations and attach undue importance to insignificant details; he would seem to forget the holy war of mankind in the petty squabbles of pedants. Only when he reached the core of the argument would he write three or four sentences in that terse and lively style which is apt to arrest the attention of young men who love to think. That central passage would state the case of the adversaries more clearly, compellingly and mercilessly than it had ever been stated in the heyday of liberalism, for he would silently drop all the foolish excrescences of the liberal creed which were allowed to grow up during the time when liberalism had succeeded and therefore was approaching dormancy. His reasonable young reader would for the first time catch a glimpse of the forbidden fruit. The attack, the bulk of the work, would consist of virulent expansions of the most virulent utterances in the holy book or books of the ruling party. The intelligent young man who, being young, had until then been somehow attracted by those immoderate utterances, would now be merely disgusted and, after having tasted the forbidden fruit, even bored by them. Reading the book for the second and third time, he would detect in the very arrangement of the quotations from the authoritative books significant additions to those few terse statements which occur in the center of the rather short first part.[24–25]This description of exoteric writing—that is, writing with two teachings: “a popular teaching of an edifying character, which is in the foreground; and a philosophic teaching concerning the most important subject, which is indicated only between the lines” [Strauss 36]—is the principle of reading most closely associated with Strauss and Straussians. What Strauss describes here is the practice of “writing between the lines” by authors holding heterodox views, constrained by the prejudices of their audience or the vested interests of the regimes within which they write. The term is broadly misused by both opponents and students of Strauss’s work themselves and has helped to gain Straussians the mythopoetic status of hermetic school. The popular version of this theory [End Page 98] is that there are writers with secret teachings, and this occasionally lends itself to different kinds of scholarly deception and grandstanding.Strauss, in this passage, refers to the position of a writer in a totalitarian country. This might lead a writer or critic in a liberal, democratic country to conclude wrongly that this kind of writing would not appear in a liberal society where there is no direct suppression of freedom of speech. I wish to suggest in this article that Milton’s Areopagitica uses a form of exoteric writing, what Macaulay calls a “peculiar art,” which addresses itself not just to the dangers of suppression of thought from above, but also to the potential dangers of suppression of thought from below. In liberal regimes, de Tocqueville located the origins of the latter, the suppression of thought from below, in what he called the tyranny of the majority. One contemporary form of this is “political correctness,” an insistence that public writings and speeches be purified to conform to a particular view of what constitutes “unprejudiced” language. Geoffrey Hill has referred to these communally enforced constraints as “the thuggish stereotypes of political correctness,” a phrase which conveys the paradox of a concept which is based simultaneously on a certainty about the incapacity of writers... (shrink)

In Quine's philosophy stance, the most clearly is not his "real" view. Perhaps he is most concerned about the experience and the theoretical relationship between the content of experience, evidence, and the wide expanse between scientific theories associated. "True," this concept in his theoretical philosophy, it seems to swing in between different stance. For example, speaking, Quine's theory of experience equal to what is really home and country-style stance , Davidson is the support that the coherence theory of truth management (...) results. On the other hand, Quine seems to think that Tarski's truth language management frame, the true theory should provide management In order to meet reasonable description. Of course, Quine is also abbreviated true doctrine of the early advocates of management theory, one clear description of the "truth is quoted to eliminate ". This will be Quine's own theory, based on digestion of Quine quotes for "real" coherence "true" symbol should be "true" or inner "true" of諸-like ideas. I want regardless permit, we must take seriously Quine's digestion quotes "true" theory, so in order for him above on the "real"諸as of speech, proposed the same explanation. In my opinion, not in the digestion Quine quotes "real," but also suggested that regardless of any knowledge or ontology of "true." All his report on the "real" considerations, are can and should to counteract quotes "true" interpretation of the theory as a starting point. "Real" word in the context of the emergence of many, should be regarded as a collection of words, abbreviations or the expression is a common feature associated with the "real" language sentence only. Among Quine's philosophy, his account on truth is probably the mistiest part. Perhaps what concerns him most is the relation between experience and scientific theories, is the relation between empirical content, evidence, and scientific theories in the broad sense. His attitude toward the conception of truth seems to vacillate between different theories, due to his various philosophical positions. For instance, regarding Quine's sectarian position of which empirically equivalent theories should be taken as true, Davidson thinks that it is the consequence of holding the coherence theory of truth. On the other hand, Quine appears to consider Tarski's T schema as giving the correspondence theory of truth a sensible account. Moreover, Quine is one of the trail-blazers of the deflationary theory of truth, stating specifically "Truth is disquotation". This paper is based on Quine's own theory, discussing his multiple claims regarding disquotational truth, coherent truth, correspondence truth, or immanent truth. What I would like to argue is that, in order to consistently explain his various claims concerning truth, we have to take Quine's disquotational theory of truth seriously. I think that, except his disquotational account, Quine does not make any claim of epistemological truth or ontological truth. All of his consideration regarding truth can be and should be explained in terms of his disquotational theory of truth. The appearance of the word 'true' / 'truth' in many contexts should be seen as playing a collective term, as abbreviating or expressing true sentences with the same feature. (shrink)

Nearly one in every 100 adults in the United States is in jail or prison today. In a period dominated by calls to roll back the government in all areas of social and economic policy, we have witnessed its massive expansion in the realm of penal policy since the 1970s. The U.S. incarceration rate is now more than 737 per 100,000 people, or five to 12 times the rate of Western European countries and Japan . The reach of the U.S. (...) carceral state extends far beyond the 2.2 million men and women currently in prison or jail in the United States. On any given day, over 7 million people__or 1 in every 32 adults__are incarcerated or on probation or parole . This rate of state supervision is unparalleled in U.S. history.These overall figures on incarceration belie the enormous and disproportionate impact that this bold and unprecedented social experiment has had on certain groups in U.S. society. If current trends continue, one in three black men and one in six Hispanic men are expected to spend some time in jail or prison during their lives . The number of incarcerated African_American men has grown so rapidly over the past quarter_century that today more black men are behind bars than enrolled in colleges and universities .[1]Some contend that growing public dismay over the crushing economic burden of incarcerating and monitoring so many people heralds the beginning of the end of the prison boom . As evidence, they point to recent penal developments in the states. Severe budget deficits prompted by the 2001 recession forced some states to close prisons and lay off guards. Dozens of states experimented with new sentencing formulas, mostly directed at nonviolent offenders.[2] Fiscally conservative Republicans previously known for being penal hard_liners championed some of these recent relaxations in penal policy. This fueled speculation that law_and_order Republicans, troubled by mounting costs, are well poised to roll back the carceral state, much as red_baiter Richard Nixon was ideally situated to breach the great political wall with China.We should be cautious, however, about assuming that fiscal pressures and the recent softening of public opinion sparked by the plummeting crime rate over the past decade will automatically forge a durable consensus that will dismantle the carceral state.[3] It was mistakenly assumed three decades ago that shared disillusionment on the right and the left with the rehabilitative ideal would shrink the prison population. Instead, it exploded. Criminal justice policies often confound conventional distinctions between left and right, particularly on issues related to crime victims. The relationship between political leaders, social movements, interest groups, and governing institutions is highly contingent and volatile in the case of penal policy because the left_right divide is more blurred and because of certain institutional features of the U.S. criminal justice system and welfare state.[4]While economic arguments against the carceral state are important and compelling, they have their limitations. If properly pitched, they can help forge a consensus to reverse the prison boom. But they can also be used to propel mean_spirited budget cuts that do not significantly reduce the size of the prison population__or save much money__ but do render life in prison and life after prison leaner and meaner. Criminal justice reform to reverse the prison boom is a highly fragile project that cannot be underwritten primarily by fiscal concerns. Without some broader vision and movement for change, the U.S. carceral state, trimmed down a little by a few modest sentencing and drug law reforms, will be here to stay. Such a movement is beginning to coalesce in the United States. Opponents have begun to portray the carceral state not only as a financial liability but also as a moral liability and a pressing civil and human rights issue that perverts cherished democratic institutions, like the right to vote. They have also begun to focus public attention on how the prison boom has exacerbated economic and social inequalities and is a growing menace to public health. (shrink)

Morton White proposes two patterns of expansion for sentences of the form "Possible (x is Q)" in "On What Could Have Happened" (Philosophical Review, 1968). His attempts in "Ands and Cans" (Mind, 1974) and in "Positive Freedom, Negative Freedom, and Possibility" (Journal of Philosophy, 1973) to simplify these two patterns and his argument for abandoning the first pattern are mistaken. Although I question a number of White's claims, my purpose is to improve his treatment of possibility rather than to (...) refute it. Our understanding of what constitutes "the same circumstances" largely determines whether a given condition is appropriately mentioned in a first-pattern expansion. This point helps support the form of compatibilism White advocates. (shrink)

THE THEME, "The Intelligibility of Nature," is exceedingly broad. It stretches like a vast domain in which one can only hope to leave a few footprints, some fragile impressions that are all but lost in the expanse. In attempting to understand the natural world, the enterprise that is most familiar to many of us is inherited from the Greeks and their Latin heirs, both classical and mediaeval, and this enterprise continues in our own day in the form of the modern (...) sciences of nature. Nowadays, we are more informed about the knowledge acquired by the Egyptians, Babylonians, and others prior to the Greeks. We are more conscious of the achievements of the Chinese in physics and the Indians in mathematics. And we are more aware of the medical and zoological lore present in oral traditions, such as those of Africa. Moreover, we are only now beginning to appreciate their contributions and their potential for new forms of enquiry, including other ways of approaching nature. The terms in which the topic is here designated, however, are conceived in Greek and expressed in Latin. Nevertheless, even within this cultural tradition of natural enquiry, the topic is quite broad enough. Like a grammarian of old parsing a sentence, I am forced to begin by distinguishing parts of the theme. (shrink)

The subject of the presented work is the analysis of situations changeability in frame of constructed logic LCG. In the suggested interpretation, substantial change ( substantial movement ), which consists of the disappearing of a certain substance a 1 and the coming into being of substance a 2 , for which a 1 is an active potentia , is understood in the following manner - the elementary fact: essence a 1 exists becomes fiction and a new fact arises: essence a (...) 2 exists , which is enabled by the previous one. In the language of our formalisation this "transition" from fact to fiction, which occurs in the case of the situation: essence a 1 exists , described as C-change . The second component of substantial movement (or rather its situational equivalent) is the occurring of a new fact: essence a 2 exists , which is possible under the condition of an earlier occurring of the fact: essence a 1 exists . We describe this aspect of movement as G-change , which is an expansion of a set of formulas by a new elementary sentence and expressions in which this sentence occurs. Within the range of the LCG calculus operators C and G obtain an interpretation wider than the one which can be determined upon the basis of the Aristotelian theory of change expressed in terms of situational ontology. Semantical and syntactical characteristics of the LCG logic gives the possibility to compare it with such known calculi of changes like sentential systems of von Wright, Clifford and Wajszczyk. (shrink)