Online research in philosophy

The Logics of Deontic (In)Consistency (LDI's) can be considered as the deontic counterpart of the paraconsistent logics known as Logics of Formal (In)Consistency. This paper introduces and studies new LDI's and other paraconsistent deontic logics with different properties: systems tolerant to contradictory obligations; systems in which contradictory obligations trivialize; and a bimodal paraconsistent deontic logic combining the features of previous systems. These logics are used to analyze the well-known Chisholm's paradox, taking profit of the fact that, besides contradictory obligations do not trivialize in LDI's, several logical dependencies of classical logic are blocked in the context of LDI's, allowing to dissolve the paradox.

It is quite standard, even banal, to describe Kant's project in the Critique of Pure Reason [KrV] as a critical reconciliation of rationalism and empiricism, most directly expressed in Kant's claim that intuitions and concepts are two distinct, yet equally necessary, and necessarily interdependent sources of cognition. Similarly, though Kant rejects both the rationalist foundation of morality in the concept of perfection and that of the empiricists in feeling or in the moral sense, one might broadly characterize Kant's moral philosophy as an attempt to reconcile the apriori universality and necessity of rationalist ethics with empiricist (Humean) or sentimentalist (Rousseauean) strictures concerning the distinction between the ‘ought’ and the ‘is’, between third personal knowledge of the good and first personal motivation.

The Successor Axiom asserts that every number has a successor, or in other words, that the number series goes on and on ad infinitum. The present work investigates a particular subsystem of Frege Arithmetic, called F, which turns out to be equivalent to second-order Peano Arithmetic minus the Successor Axiom, and shows how this system can develop arithmetic up through Gauss' Quadratic Reciprocity Law. It then goes on to represent questions of provability in F, and shows that F can prove its own consistency and indeed the consistency of stronger systems. So, arithmetic without the Successor Axiom has an exceptional combination of three chracteristics: it is natural, it is strong, and it proves its own, as well as stronger systems’, consistency.

Philosophical and empirical moral psychologists claim that emotions are both necessary and sufficient for moral judgment. The aim of this paper is to assess the evidence in favor of both claims and to show how a moderate rationalist position about moral judgment can be defended nonetheless. The experimental evidence for both the necessity- and the sufficiency-thesis concerning the connection between emotional reactions and moral judgment is presented. I argue that a rationalist about moral judgment can be happy to accept the necessity-thesis. My argument draws on the idea that emotions play the same role for moral judgment that perceptions play for ordinary judgments about the external world. I develop a rationalist interpretation of the sufficiency-thesis and show that it can successfully account for the available empirical evidence. The general idea is that the rationalist can accept the claim that emotional reactions are sufficient for moral judgment just in case a subject’s emotional reaction towards an action in question causes the judgment in a way that can be reflectively endorsed under conditions of full information and rationality. This idea is spelled out in some detail and it is argued that a moral agent is entitled to her endorsement if the way she arrives at her judgment reliably leads to correct moral beliefs, and that this reliability can be established if the subject’s emotional reaction picks up on the morally relevant aspects of the situation.

The paper presents a proof of the consistency of Peano Arithmetic (PA) that does not lie in deducing its consistency as a theorem in an axiomatic system. PA’s consistency cannot be proved in PA, and to deduce its consistency in some stronger system PA+ is self-defeating, since the stronger system may itself be inconsistent. Instead, a semantic proof is constructed which demonstrates consistency not relative to the consistency of some other system but in an absolute sense.

The paper provides a formal representation of goal systems. The focus is on three properties: consistency, conflict, and coherence. An aim is to attain conceptual clarity of these properties. It is argued that consistency is adequately regarded as a property relative to the decision situation or, more specifically, the set of alternatives that the agent faces. Moreover, as a condition of rationality, consistency is stronger than some writers have claimed. Conflict is adequately regarded as a relation over subsets of a given goal system and should likewise be regarded as relative to the set of alternatives that the agent faces. Coherence is given a probabilistic interpretation, based on a support relation over subsets of goal systems.

Using an axiomatization of second-order arithmetic (essentially second-order Peano Arithmetic without the Successor Axiom), arithmetic's basic operations are defined and its fundamental laws, up to unique prime factorization, are proven. Two manners of expressing a system's consistency are presented - the "Godel" consistency, where a wff is represented by a natural number, and the "real" consistency, where a wff is represented as a second-order sequence, which is a stronger notion. It is shown that the system can prove at least its Godel consistency and that closely allied systems can prove their real consistency.

What should individuals do when their firmly held moral beliefs are prima facie inconsistent with their religious beliefs? In this article weoutline several ways of posing such consistency challenges and offer a detailed taxonomy of the various responses available to someone facing a consistency challenge of this sort. Throughout the paper, our concerns are primarily pedagogical: how best to pose consistency challenges in the classroom, how to stimulate discussion of the various responses to them, and how to relate such consistency challenges to larger issues, such as whether scripture is, in general, a reliable guide to truth.

This paper investigates consistency in applied moral philosophy with regard to the recent controversy over Makah whaling in the state of Washington. The first part presents both sides of the controversy. The second part examines the meaning of 'tradition' and distinguishes between 'new' and 'old' traditions. The third part explores what might constitute moral consistency for the Makah and what might constitute moral consistency for the larger community.

What should individuals do when their firmly held moral beliefs are prima facie inconsistent with their religious beliefs? In this article we outline several ways of posing such consistency challenges and offer a detailed taxonomy of the various responses available to someone facing a consistency challenge of this sort. Throughout the paper, our concerns are primarily pedagogical: how best to pose consistency challenges in the classroom, how to stimulate discussion of the various responses to them, and how to relate such consistency challenges to larger issues, such as whether Scripture is, in general, a reliable guide to truth.