In this paper we offer a new argument for the existence of God. We contend that the laws of logic are metaphysically dependent on the existence of God, understood as a necessarily existent, personal, spiritual being; thus anyone who grants that there are laws of logic should also accept that there is a God. We argue that if our most natural intuitions about them are correct, and if they are to play the role in our intellectual activities that we take (...) them to play, then the laws of logic are best construed as necessarily existent thoughts -- more specifically, as divine thoughts about divine thoughts. We conclude by highlighting some implications for both theistic arguments and antitheistic arguments. (shrink)

Splitting livers allows two people to receive a liver transplant from one donated adult liver, but the risks to the adult recipient are greater than if they had received the equivalent whole liver. It has been suggested, therefore, that splitting livers harms adult recipients. Without liver splitting, however, there would be few livers available for children, and paediatric waiting time and waiting list mortality would significantly increase. In this paper, we argue that although splitting livers makes adults worse off, this (...) should be considered sub-optimal benefit rather than harm. We explore justifications for sub-optimally benefitting adults in this way and consider alternatives to the current approach. We argue that splitting livers masks the more fundamental problem of low paediatric donation rates and that increasing the number of paediatric donations would improve the situation for both adult and paediatric liver patients. (shrink)

Obesity is the definitive epidemic of the modern era in the United States. Its well-documented public health impacts, especially related to children and adolescents, are horrific. Nearly one-third of American minors are overweight; over 50% of them are obese. Already, these kids suffer from multiple adverse physical and mental health conditions. Sadly, absent serious communal and individual interventions, their lives may be cut short compared to their own parents’ life expectancy. While recent surveillance suggests childhood obesity may be trending down (...) slightly in some populations, public health experts remain concerned about the threat obesity poses to the health of America's youth.The concurrent travesty underlying childhood obesity is the relative societal failure to slow and reverse its spread. (shrink)

Obesity is the definitive epidemic of the modern era in the United States. Its well-documented public health impacts, especially related to children and adolescents, are horrific. Nearly one-third of American minors are overweight; over 50% of them are obese. Already, these kids suffer from multiple adverse physical and mental health conditions. Sadly, absent serious communal and individual interventions, their lives may be cut short compared to their own parents’ life expectancy. While recent surveillance suggests childhood obesity may be trending down (...) slightly in some populations, public health experts remain concerned about the threat obesity poses to the health of America's youth.The concurrent travesty underlying childhood obesity is the relative societal failure to slow and reverse its spread. (shrink)

Confused terms appear to signify more than one entity. Carnap maintained that any putative name that is associated with more than one object in a relevant universe of discourse fails to be a genuine name. Although many philosophers have agreed with Carnap, they have not always agreed among themselves about the truth-values of atomic sentences containing such terms. Some hold that such atomic sentences are always false, and others claim they are always truth-valueless. Field maintained that confused terms can still (...) refer, albeit partially, and offered a supervaluational account of their semantic properties on which some atomic sentences with confused terms can be true. After outlining many of the most important theoretical considerations for and against various semantic theories for such terms, we report the results of a study designed to investigate which of these accounts best accords with the truth-value judgments of ordinary language users about sentences containing these terms. We found that naïve participants view confused names as capable of successfully referring to one or more objects. Thus, semantic theories that judge them to involve total reference failure do not comport well with patterns of ordinary usage. (shrink)

Michael A. Petersa and Fazal Rizvib aBeijing Normal University, Beijing, PR China; bMelbourne University, Melbourne, Australia Our minds are still racing back and forth, longing for a return to ‘no...

SUMMARYDue to his famous conflict with John Stuart Mill, James Fitzjames Stephen is often assumed to have been an opponent of toleration and intellectual freedom and a defender of authoritarian or reactionary principles. These assumptions are misleading. Stephen was, and was known in his time to have been, a champion of toleration. This essay provides a comprehensive overview of his writing on these themes, drawing from a wider array of texts than is usually considered in the study of the (...) Stephen-Mill controversy. Contrary to popular belief, Stephen had a deep and multi-faceted argument in favor of toleration. As a critic of contending theories of toleration and freedom of discussion, Stephen was concerned to defeat what he saw as the resurgence of a priori principles in Victorian political philosophy and to combat the expansion of a proper notion of toleration to include a cluster of beliefs and attitudes of which he disapproved. In his approach to these issues Stephen was, arguably, as representative of Victorian thinking as the author of On Liberty. (shrink)

We estimate that 208,000 deep brain stimulation (DBS) devices have been implanted to address neurological and neuropsychiatric disorders worldwide. DBS Think Tank presenters pooled data and determined that DBS expanded in its scope and has been applied to multiple brain disorders in an effort to modulate neural circuitry. The DBS Think Tank was founded in 2012 providing a space where clinicians, engineers, researchers from industry and academia discuss current and emerging DBS technologies and logistical and ethical issues facing the field. (...) The emphasis is on cutting edge research and collaboration aimed to advance the DBS field. The Eighth Annual DBS Think Tank was held virtually on September 1 and 2, 2020 (Zoom Video Communications) due to restrictions related to the COVID-19 pandemic. The meeting focused on advances in: (1) optogenetics as a tool for comprehending neurobiology of diseases and on optogenetically-inspired DBS, (2) cutting edge of emerging DBS technologies, (3) ethical issues affecting DBS research and access to care, (4) neuromodulatory approaches for depression, (5) advancing novel hardware, software and imaging methodologies, (6) use of neurophysiological signals in adaptive neurostimulation, and (7) use of more advanced technologies to improve DBS clinical outcomes. There were 178 attendees who participated in a DBS Think Tank survey, which revealed the expansion of DBS into several indications such as obesity, post-traumatic stress disorder, addiction and Alzheimer’s disease. This proceedings summarizes the advances discussed at the Eighth Annual DBS Think Tank. (shrink)

Three decades ago, James Bogen and James Woodward argued against the possibility and usefulness of scientific explanations of data. They developed a picture of scientific reasoning where stable phenomena were identified via data without much input from theory. Rather than explain data, theories ‘save the phenomena’. In contrast, I argue that there are good reasons to explain data, and the practice of science reveals attempts to do so. I demonstrate that algorithms employed to address inverse problems in remote-sensing (...) applications should be understood as attempts to identify phenomena by explaining the data. Thus, this paper furthers understanding of data-to-phenomena reasoning in science, and demonstrates theory may play a more central role in phenomena identification than previously recognized. (shrink)

In James Campbell's new book on William James, the greatest hits are covered: stream of consciousness, radical empiricism, will to believe, moral equivalent of war, varieties of religious experience, pluralism, and an open universe. Seven great concepts and maybe another seventy lesser relatives are skillfully presented in an organized, patient, and scholarly style. Campbell's wit comes through, repeatedly referring to James as a psycholopher, neither quite psychologist nor philosopher. At times we find Campbell defending James, for (...) example against so many simplistic critiques of "The Will to Believe." Bertrand Russell doesn't get it, which still confirms why "The Will to Believe" is so badly needed. At other... (shrink)

When we read On the Origin of Species, we cannot help but hear echoes of the Wealth of Nations. Darwin’s “economy of nature” features a “division of labour” that leads to complexity and productivity. We should not, however, analyze Darwin’s ethics through this lens. Darwin did not draw his economic ideas from Smith, nor did he base his ethics on an economic foundation. Darwin’s ethics rest on Smith’s notion—from the Theory of Moral Sentiments—of an innate human faculty of sympathy. Darwin (...) gave this notion an evolutionary interpretation, concluding that any species of social animals that develops a high enough level of intelligence will evolve moral principles. But the specific moral principles evolved by any particular species will vary, depending on that species’ particular evolutionary history. Darwin’s theory of moral sentiments thus diverged profoundly from Smith’s, while remaining in the same intellectual lineage. Although my reading of Darwin’s ethics departs from the dominant trend, it is not without precedent. A century ago, William James propounded a similar interpretation of Darwin. James’s interpretation has been largely forgotten, but he had Darwin right. It seems that James then developed his own moral philosophy on what he saw as a Darwinian foundation. It may be that James read Darwin’s evolutionary ethics through a pragmatic lens and so refashioned it, in his turn, into something again profoundly different from what Darwin had conceived, but again remaining in the same intellectual lineage. (shrink)

his paper provides a sound and complete axiomatisation for constant domain modal logics without Boolean negation. This is a simpler case of the difficult problem of providing a sound and complete axiomatisation for constant-domain quantified relevant logics, which can be seen as a kind of modal logic with a two-place modal operator, the relevant conditional. The completeness proof is adapted from a proof for classical modal predicate logic (I follow James Garson’s 1984 presentation of the completeness proof quite closely), (...) but with an important twist, to do with the absence of Boolean negation. (shrink)

This essay is my review of Colleen Dyble’s book, Taming Leviathan: Waging a War of Ideas around the World. Dyble is affiliated with the legendary classical liberal British think tank, the Institute of Economic Affairs. Her anthology is a collection of essays by people around the world who have been involved with similar free-market think tanks in countries with historically statist economic systems. These writers include Greg Lindsay, founder of the Center for Independent Studies in Australia; Margaret Tse, of (...) the Instituto Liberdade in Brazil; Michael Walker, co-founder of the Fraser Institute in Canada; Cristian Larroulet, of Libertad y Desarrollo in Chile; Giancarlo Ibarguen, of the Center for Economic and Social Studies in Guatemala (which actually founded a free-market-oriented university); Parth Shah, founder of the Center for Civil Society in India; Daniel Doron, co-founder of the Israeli Center for Social and Economic Progress; Alberto Mingardi, of the Instituto Bruno Leoni in Italy; Masaru Uchigama, founder of the Japanese for Tax Reform; Elena Leontjeva, co-founder of the Lithuanian Free Market Institute; Alexander Magno, co-founder of the Foundation for Economic Freedom in the Philippines; and last, Leon Louw, of the Free Market Foundation of South Africa. I then discuss seven important reasons why classical liberal think tanks are so important in modern societies. (shrink)

James Anderson and Greg Welty have resurrected an argument for God’s existence, which we will call the argument from logic. We present three lines of response against the argument, involving the notion of necessity involved, the notion of intentionality involved, and then we pose a dilemma for divine conceptualism. We conclude that the argument faces substantial problems.

Our topic is the notion of logical consequence: the link between premises and conclusions, the glue that holds together deductively valid argument. How can we understand this relation between premises and conclusions? It seems that any account begs questions. Painting with very broad brushtrokes, we can sketch the landscape of disagreement like this: “Realists” prefer an analysis of logical consequence in terms of the preservation of truth [29]. “Anti-realists” take this to be unhelpful and o:er alternative analyses. Some, like Dummett, (...) look to preservation of warrant to assert [9, 36]. Others, like Brandom [5], take inference as primitive, and analyse other notions in terms of it. There is plenty of disagreement on the “realist” side of the fence too. It is one thing to argue that logical consequence involves preservation of truth. It is another to explain how far truth must be preserved. Is the preservation essentially modal (in all circumstances [25]) or analytic (vouchsafed by.. (shrink)

In this paper I urge friends of truth-value gaps and truth-value gluts – proponents of paracomplete and paraconsistent logics – to consider theories not merely as sets of sentences, but as pairs of sets of sentences, or what I call ‘bitheories,’ which keep track not only of what holds according to the theory, but also what fails to hold according to the theory. I explain the connection between bitheories, sequents, and the speech acts of assertion and denial. I illustrate the (...) usefulness of bitheories by showing how they make available a technique for characterising different theories while abstracting away from logical vocabulary such as connectives or quanti- fiers, thereby making theoretical commitments independent of the choice of this or that particular non-classical logic. (shrink)

We present a new frame semantics for positive relevant and substructural propositional logics. This frame semantics is both a generalisation of Routley–Meyer ternary frames and a simplification of them. The key innovation of this semantics is the use of a single accessibility relation to relate collections of points to points. Different logics are modeled by varying the kinds of collections used: they can be sets, multisets, lists or trees. We show that collection frames on trees are sound and complete for (...) the basic positive distributive substructural logic $\mathsf {B}^+$, that collection frames on multisets are sound and complete for $\mathsf {RW}^+$ (the relevant logic $\mathsf {R}^+$, without contraction, or equivalently, positive multiplicative and additive linear logic with distribution for the additive connectives), and that collection frames on sets are sound for the positive relevant logic $\mathsf {R}^+$. The completeness of set frames for $\mathsf {R}^+$ is, currently, an open question. (shrink)

The two-dimensional modal logic of Davies and Humberstone [3] is an important aid to our understanding the relationship between actuality, necessity and a priori knowability. I show how a cut-free hypersequent calculus for 2D modal logic not only captures the logic precisely, but may be used to address issues in the epistemology and metaphysics of our modal concepts. I will explain how the use of our concepts motivates the inference rules of the sequent calculus, and then show that the completeness (...) of the calculus for Davies–Humberstone models explains why those concepts have the structure described by those models. The result is yet another application of the completeness theorem. (shrink)

An advanced-level logic textbook that presents proof construction on equal footing with model building. Potentially relevant to students of mathematics and computer science as well.

I present an account of truth values for classical logic, intuitionistic logic, and the modal logic S5, in which truth values are not a fundamental category from which the logic is defined, but rather, an idealisation of more fundamental logical features in the proof theory for each system. The result is not a new set of semantic structures, but a new understanding of how the existing semantic structures may be understood in terms of a more fundamental notion of logical consequence.

Different natural deduction proof systems for intuitionistic and classical logic —and related logical systems—differ in fundamental properties while sharing significant family resemblances. These differences become quite stark when it comes to the structural rules of contraction and weakening. In this paper, I show how Gentzen and Jaśkowski’s natural deduction systems differ in fine structure. I also motivate directed proof nets as another natural deduction system which shares some of the design features of Genzen and Jaśkowski’s systems, but which differs again (...) in its treatment of the structural rules, and has a range of virtues absent from traditional natural deduction systems. (shrink)

An text for introducing both formal and philosophical logic.

Once the Kripke semantics for normal modal logics were introduced, a whole family of modal logics other than the Lewis systems S1 to S5 were discovered. These logics were obtained by changing the semantics in natural ways. The same can be said of the Kripke-style semantics for relevant logics: a whole range of logics other than the standard systems R, E and T were unearthed once a semantics was given (cf. Priest and Sylvan [6], Restall [7], and Routley et al. (...) [8]). In a similar way, weakening the structural rules of the Gentzen formulation of classical logic gives rise to other ‘substructural’ logics such as linear logic (as in Girard [4]). This process of ‘strategic weakening’ is becoming popular today, with the discovery of applications of these logics to areas such as linguistics and the theory of computation (cf. van Benthem [1]). Until now no-one has (to my knowledge) examined what the process of weakening does to the Kripke-style semantics of intuitionistic logic. This paper remedies the deficiency, introducing the family of subintuitionistic logics. These systems have some appealing features. Unlike other substructural logics such as linear logic (which lack distribution of extensional disjunction over conjunction) they have a very natural Kripke-style worlds semantics. Also, the difficulties with regard to modelling quantification in these systems may be able to shed some light on the difficulties in naturally modelling quantification in relevant logics, as it must be admitted that the semantics currently available for quantified relevant logics are rather baroque (cf. Fine [3]). But most importantly, delving in the undergrowth of logics such as intuitionistic logic gives us a ‘feel’ for how such systems are put together, and what job is being done by each aspect of the modelling conditions in.. (shrink)

According to the “knowability thesis,” every truth is knowable. Fitch’s paradox refutes the knowability thesis by showing that if we are not omniscient, then not only are some truths not known, but there are some truths that are not knowable. In this paper, I propose a weakening of the knowability thesis (which I call the “conjunctive knowability thesis”) to the e:ect that for every truth p there is a collection of truths such that (i) each of them is knowable and (...) (ii) their conjunction is equivalent to p. I show that the conjunctive knowability thesis avoids triviality arguments against it, and that it fares very di:erently depending on another thesis connecting knowledge and possibility. If there are two propositions, inconsistent with one another, but both knowable, then the conjunctive knowability thesis is trivially true. On the other hand, if knowability entails truth, the conjunctive knowability thesis is coherent, but only if the logic of possibility is weak. (shrink)

Propositional logic -- Propositions and arguments -- Connectives and argument forms -- Truth tables -- Trees -- Vagueness and bivalence -- Conditionality -- Natural deduction -- Predicate logic -- Predicates, names, and quantifiers -- Models for predicate logic -- Trees for predicate logic -- Identity and functions -- Definite descriptions -- Some things do not exist -- What is a predicate? -- What is logic?

In this paper we introduce a new natural deduction system for the logic of lattices, and a number of extensions of lattice logic with different negation connectives. We provide the class of natural deduction proofs with both a standard inductive definition and a global graph-theoretical criterion for correctness, and we show how normalisation in this system corresponds to cut elimination in the sequent calculus for lattice logic. This natural deduction system is inspired both by Shoesmith and Smiley's multiple conclusion systems (...) for classical logic and Girard's proofnets for linear logic. (shrink)

Formal systems seem to come in two general kinds: useful and useless. This is painting things starkly, but the point is important. Formal structures can either be used in interesting and important ways, or they can languish unused and irrelevant. Lewis' modal logics are good examples. The systems S4 and S5 are useful in many different ways. They map out structures that are relevant to a number of different applications. S1, S2 and S3 however, are not so lucky. They are (...) little studied, and used even less. It has become dear that the structures described by S4 and S5 are important in different ways, while the structures described by S1 to S3 are not so important. In this paper, we will see another formal system with a number of different uses. We will examine a substructural logic which is important in a number of different ways. The logic of Peirce monoids, inspired by the logic of relations, is useful in the independent areas of linguistic types and information flow.In what follows I will describe the logic of Peirce monoids in its various guises, sketch out its main properties, and indicate why it is important. As proofs of theorems are readily available elsewhere in the literature, I simply sketch the relevant proofs here, and point the interested reader to where complete proofs can be found. (shrink)

Here is a puzzle, which I learned from Terence Parsons in his “True Contradictions” [8]. First Degree Entailment is a logic which allows for truth value gaps as well as truth value gluts. If you are agnostic between assigning paradoxical sentences gaps and gluts, then this looks no different, in effect, from assigning them a gap value? After all, on both views you end up with a theory that doesn’t commit you to the paradoxical sentence or its negation. How is (...) the fde theory any different from the theory with gaps alone? In this paper, I will present a clear answer to this puzzle – an answer that explains how being agnostic between gaps and gluts is a genuinely different position than admitting gaps alone, by using the formal notion of a bi-theory, and showing that while such positions might agree on what is to be accepted, they differ on what is to be rejected. (shrink)

The paradoxes of self reference have to be dealt with by anyone seeking to give a satisfactory account of the logic of truth, of properties, and even of sets of numbers. Unfortunately, there is no widespread agreement as to how to deal with these paradoxes. Some approaches block the paradoxical inferences by rejecting as invalid a move that classical logic counts as valid. In the recent literature, this deviant logic analysis of the paradoxes has been called into question.This disagreement motivates (...) a re-examination of the philosophy of formal logic and the status of logical truths and rules. In this paper I do some of this work, and I show that this gives us the means to defend the deviant approaches against such criticisms. As a result I hope to show that these analyses of the paradoxes are worthy of more serious consideration than they have so far received. (shrink)