Vann McGee has recently argued that Belnap’s criteria constrain the formal rules of classical natural deduction to uniquely determine the semantic values of the propositional logical connectives and quantifiers if the rules are taken to be open-ended, i.e., if they are truth-preserving within any mathematically possible extension of the original language. The main assumption of his argument is that for any class of models there is a mathematically possible language in which there is a sentence true in just those models. (...) I show that this assumption does not hold for the class of models of classical propositional logic. In particular, I show that the existence of non-normal models for negation undermines McGee’s argument. (shrink)
The concern of deductive logic is generally viewed as the systematic recognition of logical principles, i.e., of logical truths. This paper presents and analyzes different instantiations of the three main interpretations of logical principles, viz. as ontological principles, as empirical hypotheses, and as true propositions in virtue of meanings. I argue in this paper that logical principles are true propositions in virtue of the meanings of the logical terms within a certain linguistic framework. Since these principles also regulate and control (...) the process of deduction in inquiry, i.e., they are prescriptive for the use of language and thought in inquiry, I argue that logic may, and should, be seen as an instrument or as a way of proceeding (modus procedendi) in inquiry. (shrink)
Starting from certain metalogical results, I argue that first-order logical truths of classical logic are a priori and necessary. Afterwards, I formulate two arguments for the idea that first-order logical truths are also analytic, namely, I first argue that there is a conceptual connection between aprioricity, necessity, and analyticity, such that aprioricity together with necessity entails analyticity; then, I argue that the structure of natural deduction systems for FOL displays the analyticity of its truths. Consequently, each philosophical approach to these (...) truths should account for this evidence, i.e., that first-order logical truths are a priori, necessary, and analytic, and it is my contention that the semantic account is a better candidate. (shrink)
This paper attempts to motivate the view that instead of rejecting modus ponens as invalid in certain situations, one could preserve its validity by associating such situations with non-normal interpretations of logical connectives.
The problem analysed in this paper is whether we can gain knowledge by using valid inferences, and how we can explain this process from a model-theoretic perspective. According to the paradox of inference (Cohen & Nagel 1936/1998, 173), it is logically impossible for an inference to be both valid and its conclusion to possess novelty with respect to the premises. I argue in this paper that valid inference has an epistemic significance, i.e., it can be used by an agent to (...) enlarge his knowledge, and this significance can be accounted in model-theoretic terms. I will argue first that the paradox is based on an equivocation, namely, it arises because logical containment, i.e., logical implication, is identified with epistemological containment, i.e., the knowledge of the premises entails the knowledge of the conclusion. Second, I will argue that a truth-conditional theory of meaning has the necessary resources to explain the epistemic significance of valid inferences. I will explain this epistemic significance starting from Carnap’s semantic theory of meaning and Tarski’s notion of satisfaction. In this way I will counter (Prawitz 2012b)’s claim that a truth-conditional theory of meaning is not able to account the legitimacy of valid inferences, i.e., their epistemic significance. (shrink)
We argue that, if taken seriously, Kripke's view that a language for science can dispense with a negation operator is to be rejected. Part of the argument is a proof that positive logic, i.e., classical propositional logic without negation, is not categorical.
As recently stakeholders complain about the use of conflict minerals in consumer products that are often invisible to them in final products, firms across industries implement conflict mineral management practices. Conflict minerals are those, whose systemic exploitation and trade contribute to human right violations in the country of extraction and surrounding areas. Particularly, supply chain managers in the Western world are challenged taking reasonable steps to identify and prevent risks associated with these resources due to the globally dispersed nature of (...) supply chains and the opacity of the origin of commodities. Supply chain due diligence represents a holistic concept to proactively manage supply chains reducing the likelihood of the use of conflict minerals effectively. Based on an exploratory study with 27 semi-structured interviews within five European industries, we provide insights into patterns of implementation, key motivational factors, barriers and enablers, and impacts of SCDD in mineral supply chains. Our results contribute to both theory and practice as we provide first insights to SCDD practices and make recommendations for an industry-wide implementation of SCDD. Altogether, this study provides the basis for future theory testing research in the context of SCDD and conflict mineral management. (shrink)
Media increasingly accuse firms of exploiting suppliers, and these allegations often result in lurid headlines that threaten the reputations and therefore business successes of these firms. Neither has the phenomenon of supplier exploitation been investigated from a rigorous, ethical standpoint, nor have answers been provided regarding why some firms pursue exploitative approaches. By systemically contrasting economic liberalism and just prices as two divergent perspectives on supplier exploitation, we introduce a distinction of common business practice and unethical supplier exploitation. Since supplier (...) exploitation is based on power, we elucidate several levels of power as antecedents and investigate the role of ethical climate as a moderator. This study extends Victor and Cullen’s ethical climate matrix according to a supply chain dimension and is summarized in an integrated, conceptual model of five propositions for future theory testing. Results provide a frame of reference for executives and scholars, who can now delineate unethical exploitation and understand important antecedents of the phenomenon better. (shrink)
We interpret solution rules on a class of simple allocation problems as data on the choices of a policy maker. We analyze conditions under which the policy maker’s choices are (i) rational (ii) transitive-rational, and (iii) representable; that is, they coincide with maximization of a (i) binary relation, (ii) transitive binary relation, and (iii) numerical function on the allocation space. Our main results are as follows: (i) a well-known property, contraction independence (a.k.a. IIA) is equivalent to rationality; (ii) every contraction (...) independent and other-c monotonic rule is transitive-rational; and (iii) every contraction independent and other-c monotonic rule, if additionally continuous, can be represented by a numerical function. (shrink)
We propose and axiomatically analyze a class of rational solutions to simple allocation problems where a policy-maker allocates an endowment $E$ among $n$ agents described by a characteristic vector c. We propose a class of recursive rules which mimic a decision process where the policy-maker initially starts with a reference allocation of $E$ in mind and then uses the data of the problem to recursively adjust his previous allocation decisions. We show that recursive rules uniquely satisfy rationality, c-continuity, and other-c (...) monotonicity. We also show that a well-known member of this class, the Equal Gains rule, uniquely satisfies rationality, c-continuity, and equal treatment of equals. (shrink)