What is the Question to Which Husserl’s Fifth Cartesian Meditation is the Answer?

Interpreters generally agree that the Fifth Cartesian Meditation fails to achieve its task, but they do not agree on what that task is. In my essay, I attempt to formulate the question to which the Fifth Cartesian Meditation gives the answer. While it is usually assumed that the text poses a rather ambitious question, I suggest that the text asks, “How is the Other given to me on the most basic level?” The answer would be that the Other is given as accessible in the mode of inaccessibility. Husserl’s failure to convey this question clearly seems rooted in ambiguities concerning the concepts of solipsism and the sphere of ownness.     

Against mereological nihilism

I argue that mereological nihilism fails because it cannot answer (what I describe as) the special arrangement question: when is it true that the xs (the mereological simples) are arranged F-wise? I suggest that the answers given in the literature fail and that the obvious responses that could be made look to undermine the motivations for adopting nihilism in the first place.     

Where gamma fails

A major question for the relevant logics has been, “Under what conditions is Ackermann's ruleγ from -A ∨B andA to inferB, admissible for one of these logics?” For a large number of logics and theories, the question has led to an affirmative answer to theγ problem itself, so that such an answer has almost come to be expected for relevant logics worth taking seriously. We exhibit here, however, another large and interesting class of logics-roughly, the Boolean extensions of theW — free relevant logics (and, precisely, the well-behaved subsystems of the 4-valued logicBN4) — for which γ fails.     

Three-valued Logics in Modal Logic

Every truth-functional three-valued propositional logic can be conservatively translated into the modal logic S5. We prove this claim constructively in two steps. First, we define a Translation Manual that converts any propositional formula of any three-valued logic into a modal formula. Second, we show that for every S5-model there is an equivalent three-valued valuation and vice versa. In general, our Translation Manual gives rise to translations that are exponentially longer than their originals. This fact raises the question whether there are three-valued logics for which there is a shorter translation into S5. The answer is affirmative: we present an elegant linear translation of the Logic of Paradox and of Strong Three-valued Logic into S5.     

Nelson's Negation on the Base of Weaker Versions of Intuitionistic Negation

Constructive logic with Nelson negation is an extension of the intuitionistic logic with a special type of negation expressing some features of constructive falsity and refutation by counterexample. In this paper we generalize this logic weakening maximally the underlying intuitionistic negation. The resulting system, called subminimal logic with Nelson negation, is studied by means of a kind of algebras called generalized N-lattices. We show that generalized N-lattices admit representation formalizing the intuitive idea of refutation by means of counterexamples giving in this way a counterexample semantics of the logic in question and some of its natural extensions. Among the extensions which are near to the intuitionistic logic are the minimal logic with Nelson negation which is an extension of the Johansson's minimal logic with Nelson negation and its in a sense dual version — the co-minimal logic with Nelson negation. Among the extensions near to the classical logic are the well known 3-valued logic of Lukasiewicz, two 12-valued logics and one 48-valued logic. Standard questions for all these logics — decidability, Kripke-style semantics, complete axiomatizability, conservativeness are studied. At the end of the paper extensions based on a new connective of self-dual conjunction and an analog of the Lukasiewicz middle value ½ have also been considered.     

Legal Coercion,Respect & Reason-Responsive Agency

Legal coercion seems morally problematic because it is susceptible to the Hegelian objection that it fails to respect individuals in a way that is ‘due to them as men’. But in what sense does legal coercion fail to do so? And what are the grounds for this requirement to respect? This paper is an attempt to answer these questions. It argues that (a) legal coercion fails to respect individuals as reason-responsive agents; and (b) individuals ought to be respected as such in virtue of the fact that they are human beings. Thus it is in this sense that legal coercion fails to treat individuals with the kind of respect ‘due to them as men’.     

Quine on intensional entities: Modality and quantification,truth and satisfaction

In this paper, I reconstruct Quine?s arguments against quantified modal logic, from the early 1940?s to the early 1960?s. Quine?s concerns were not technical. Quine was looking for a coherent interpretation of quantified-in English modal sentences. I argue that Quine?s main thesis is that the intended objectual interpretation of the quantifiers is incompatible with any semantic reading of the modal operators, for example as expressing analytic necessity, unless the entities in the domain of quantification are intensions, i.e. definitional entities. The difficulty is that it makes no sense to say of an ordinary object that it bears a property necessarily or contingently when the necessity or contingency in question is analytic. However, starting in 1960, Quine claims that quantified-in modal sentences can be coherently interpreted only as essentialist predications. When we say about an object that it necessarily F?s, we can only coherently mean that it essentially F?s. In the paper, I argue that adequately qualified the thesis is plausible. Two important qualifications are needed. The first is the assumption that satisfaction is an irreducibly predicative notion, making any explication of satisfaction in terms of truth inadequate. The second is the ontological rejection of purely semantic, i.e. merely definitional, entities. With these qualifications in place, Quine?s rejection of the combination of objectual quantifiers and semantic modalities can be upheld. In this way, we vindicate a qualified version of Quine?s conjecture that quantified modal logic is committed to essentialism.     

What is <Emphasis Type="Italic">the</Emphasis> Logic of Inference?

The topic of this paper is the question whether there is a logic which could be justly called the logic of inference. It may seem that at least since Prawitz, Dummett and others demonstrated the proof-theoretical prominency of intuitionistic logic, the forthcoming answer is that it is this logic that is the obvious choice for the accolade. Though there is little doubt that this choice is correct (provided that inference is construed as inherently single-conclusion and complying with the Gentzenian structural rules), I do not think that the usual justification of it is satisfactory. Therefore, I will first try to clarify what exactly is meant by the question, and then sketch a conceptual framework in which it can be reasonably handled. I will introduce the concept of ‘inferentially native’ logical operators (those which explicate inferential properties) and I will show that the axiomatization of these operators leads to the axiomatic system of intuitionistic logic. Finally, I will discuss what modifications of this answer enter the picture when more general notions of inference are considered. Presented by Hannes Leitgeb     

Normal Natural Deduction Proofs (in classical logic)

Natural deduction (for short: nd-) calculi have not been used systematically as a basis for automated theorem proving in classical logic. To remove objective obstacles to their use we describe (1) a method that allows to give semantic proofs of normal form theorems for nd-calculi and (2) a framework that allows to search directly for normal nd-proofs. Thus, one can try to answer the question: How do we bridge the gap between claims and assumptions in heuristically motivated ways? This informal question motivates the formulation of intercalation calculi. Ic-calculi are the technical underpinnings for (1) and (2), and our paper focuses on their detailed presentation and meta-mathematical investigation in the case of classical predicate logic. As a central theme emerges the connection between restricted forms of nd-proofs and (strategies for) proof search: normal forms are not obtained by removing local "detours", but rather by constructing proofs that directly reflect proof-strategic considerations. That theme warrants further investigation.

     

Is it Morally Wrong to Defend Unjust Causes as a Lawyer?

The question I address in this article is whether it is morally wrong for a lawyer to represent a client whose purpose is immoral or unjust. My answer to this question is that it is wrong, prima facie. This conclusion holds, even accepting certain traditional principles of lawyer's professional ethics, such as the right of defence and the so‐called principle of ‘adversarial’ litigation. Both the adversarial system and the right of defence are sufficient to support or justify the right of potential clients (and citizens in general) to defend their interests in the judicial system and to do so with the technical assistance of a lawyer. This right includes a right to pursue unjust or immoral purposes (within the law). However, having a right to do X does not mean that it is morally permissible to do X. We can have a right to do something morally wrong. This being so, the fundamental moral reason for a lawyer not to accept representation for a client with an immoral purpose is that it is, prima facie, morally wrong to help someone do something wrong.     

Double-Negation Elimination in Some Propositional Logics

This article answers two questions (posed in the literature), each concerning the guaranteed existence of proofs free of double negation. A proof is free of double negation if none of its deduced steps contains a term of the formn(n(t)) for some term t, where n denotes negation. The first question asks for conditions on the hypotheses that, if satisfied, guarantee the existence of a double-negation-free proof when the conclusion is free of double negation. The second question asks about the existence of an axiom system for classical propositional calculus whose use, for theorems with a conclusion free of double negation, guarantees the existence of a double-negation-free proof. After giving conditions that answer the first question, we answer the second question by focusing on the Lukasiewicz three-axiom system. We then extend our studies to infinite-valued sentential calculus and to intuitionistic logic and generalize the notion of being double-negation free. The double-negation proofs of interest rely exclusively on the inference rule condensed detachment, a rule that combines modus ponens with an appropriately general rule of substitution. The automated reasoning program Otter played an indispensable role in this study.     

Answer Sets and Qualitative Decision Making

Logic programs under answer set semantics have become popular as a knowledge representation formalism in Artificial Intelligence. In this paper we investigate the possibility of using answer sets for qualitative decision making. Our approach is based on an extension of the formalism, called logic programs with ordered disjunction (LPODs). These programs contain a new connective called ordered disjunction. The new connective allows us to represent alternative, ranked options for problem solutions in the heads of rules: A × B intuitively means: if possible A, but if A is not possible then at least B. The semantics of logic programs with ordered disjunction is based on a preference relation on answer sets. We show that LPODs can serve as a basis for qualitative decision making.     

Eta,disco, odisco,andF

Two coefficients are proposed for measuring the extent of overlap in distributions as a direct function of the variance between the arithmetic means (“disco” and “odisco”). They are designed to answer such questions as: “Given the value of a numerical variablex, to which population should an individual be assigned so that minimum error would be incurred?” This is just the reverse of the question addressed by ANOVA. These coefficients are shown to be analytic inx and they are related to Pearson's eta and Fisher'sF. Extensions of these coefficients (designed for univariate, one-way discrimination) tok-way and multivariate discriminant analysis and measurement of “interaction” are suggested.     

Discovering knowability: a semantic analysis

In this paper, we provide a semantic analysis of the well-known knowability paradox stemming from the Church–Fitch observation that the meaningful knowability principle all truths are knowable, when expressed as a bi-modal principle ${\diamondsuit}$ , yields an unacceptable omniscience property all truths are known. We offer an alternative semantic proof of this fact independent of the Church–Fitch argument. This shows that the knowability paradox is not intrinsically related to the Church–Fitch proof, nor to the Moore sentence upon which it relies, but rather to the knowability principle itself. Further, we show that, from a verifiability perspective, the knowability principle fails in the classical logic setting because it is missing the explicit incorporation of a hidden assumption of stability: ‘the proposition in question does not change from true to false in the process of discovery.’ Once stability is taken into account, the resulting stable knowability principle and its nuanced versions more accurately represent verification-based knowability and do not yield omniscience.     

Information dynamics and uniform substitution

The picture of information acquisition as the elimination of possibilities has proven fruitful in many domains, serving as a foundation for formal models in philosophy, linguistics, computer science, and economics. While the picture appears simple, its formalization in dynamic epistemic logic reveals subtleties: given a valid principle of information dynamics in the language of dynamic epistemic logic, substituting complex epistemic sentences for its atomic sentences may result in an invalid principle. In this article, we explore such failures of uniform substitution. First, we give epistemic examples inspired by Moore, Fitch, and Williamson. Second, we answer affirmatively a question posed by van Benthem: can we effectively decide when every substitution instance of a given dynamic epistemic principle is valid? In technical terms, we prove the decidability of this schematic validity problem for public announcement logic (PAL and PAL-RC) over models for finitely many fully introspective agents, as well as models for infinitely many arbitrary agents. The proof of this result illuminates the reasons for the failure of uniform substitution.     

Intuitionistic Epistemic Logic,Kripke Models and Fitch’s Paradox

The present work is motivated by two questions. (1) What should an intuitionistic epistemic logic look like? (2) How should one interpret the knowledge operator in a Kripke-model for it? In what follows we outline an answer to (2) and give a model-theoretic definition of the operator K. This will shed some light also on (1), since it turns out that K, defined as we do, fulfills the properties of a necessity operator for a normal modal logic. The interest of our construction also lies in a better insight into the intuitionistic solution to Fitch’s paradox, which is discussed in the third section. In particular we examine, in the light of our definition, DeVidi and Solomon’s proposal of formulating the verification thesis as \(\phi \rightarrow \neg \neg K\phi\). We show, as our main result, that this definition excapes the paradox, though it is validated only under restrictive conditions on the models.     

What's Wrong with Exploitation?

abstract  This paper offers a new answer to an old question. Others have argued that exploitation is wrong because it is coercive, or degrading, or fails to protect the vulnerable. But these answers only work for certain cases; counter-examples are easily found. In this paper I identify a different answer to the question by placing exploitation within the larger family of wrongs to which it belongs. Exploitation is one species of wrongful gain, and exploiters always gain at the expense of others by inflicting relative losses on disadvantaged parties. They do harm to their victims, even when their interactions are mutually advantageous, by failing to benefit the disadvantaged party as fairness requires. This failure is the essential wrong in every case of wrongful exploitation. At the end of the paper I assess how wrong this failure is as a way to gain at another's expense.     

Why Do Men Benefit More from Marriage Than Do Women? Thinking More Broadly About Interpersonal Processes That Occur Within and Outside of Marriage

In this commentary we return to the original question of Wanic and Kulik??s paper, ??Why do men benefit more from marriage than do women??? We suggest that trying to understand why women suffer more than men in marriage (from conflict or for any other reason) will not, by itself, answer the question. The answers are certainly multifaceted and complex, and there is little reason to pit one possible answer against another. We highlight that when examining gender differences in health in marriage it is important to (a) consider the helpful processes in combination with hurtful ones, b) take a broad view on this question including many types of social processes, and c) consider processes that occur outside of marriage as well as those that occur inside of marriage.     

Second-order Logic and the Power Set

Ignacio Jane has argued that second-order logic presupposes some amount of set theory and hence cannot legitimately be used in axiomatizing set theory. I focus here on his claim that the second-order formulation of the Axiom of Separation presupposes the character of the power set operation, thereby preventing a thorough study of the power set of infinite sets, a central part of set theory. In reply I argue that substantive issues often cannot be separated from a logic, but rather must be presupposed. I call this the logic-metalogic link. There are two facets to the logic-metalogic link. First, when a logic is entangled with a substantive issue, the same position on that issue should be taken at the meta- level as at the object level; and second, if an expression has a clear meaning in natural language, then the corresponding concept can equally well be deployed in a formal language. The determinate nature of the power set operation is one such substantive issue in set theory. Whether there is a determinate power set of an infinite set can only be presupposed in set theory, not proved, so the use of second-order logic cannot be ruled out by virtue of presupposing one answer to this question. Moreover, the legitimacy of presupposing in the background logic that the power set of an infinite set is determinate is guaranteed by the clarity and definiteness of the notions of all and of subset. This is also exactly what is required for the same presupposition to be legitimately made in an axiomatic set theory, so the use of second-order logic in set theory rather than first-order logic does not require any new metatheoretic commitments.     

On Ensuring that Physicalism is Not a Dual Attribute Theory In Sheep’s Clothing

Physicalists are committed to the determination without remainder of the psychological by the physical, but are they committed to this determination being a priori? This paper distinguishes this question understood de dicto from this question understood de re, argues that understood de re the answer is yes in a way that leaves open the answer to the question understood de dicto.