The central argument in this paper is the following: if we agree that one of the aims of explanation is to provide or increase understanding, and if we assess understanding on the basis of the inferences one can draw from the knowledge of the phenomenon which is understood, then the value of an explanation, i.e. its capacity to provide or increase understanding of the explained phenomenon, should be assessed on the basis of the extra-inferences which this explanation allows for. The (...) extra-inferences which a given explanation allows for constitute its inferential content. The analysis of the explanation’s inferential content could be applied to all kinds of explanations with the aim of assessing their goodness. I show how such an analysis helps us to better understand a number of difficulties that have puzzled contemporary philosophers of explanation: the flagpole counterexample to the deductive-nomological model of explanation, the conjunction problem, the difference between good and bad circular explanations. (shrink)

I defend a new account of constitutive essence on which an entity’s constitutively essential properties are its most fundamental, nontrivial necessary properties. I argue that this account accommodates the Finean counterexamples to classic modalism about essence, provides an independently plausible account of constitutive essence, and does not run into clear counterexamples. I conclude that this theory provides a promising way forward for attempts to produce an adequate nonprimitivist, modalist account of essence. As both triviality and fundamentality in the account (...) are understood in terms of grounding, the theory also potentially has important implications for the relation between essence and grounding. (shrink)

This paper investigates the link between informational consequence and credence. I first suggest a natural constraint, namely that informational consequence should preserve certainty: on any rational credence distribution, when the premises of an informational inferences have credence 1, the conclusion also has credence 1. Then I show that the certainty‐preserving constraint leads to triviality. In particular, the following three claims are incompatible: (i) informational consequence is extensionally distinct from classical consequence; (ii) informational inferences preserve certainty; (iii) credences obey (a (...) subset of) classical Bayesian constraints. The proof is straightforward, but the theoretical implications are substantial. Informational theorists need to either give up the idea that credence applies to epistemic discourse, or develop a nonclassical theory of credence and credal update. Moreover, the result also suggests that there is a connection between informational consequence and triviality results, including classical triviality results like Lewis's. (shrink)

A triviality result for what Lewis called “the Desire by Necessity Thesis” and Broome : 265–267, 1991) called “the Desire as Expectation Thesis” is presented. The result shows that this thesis and three other reasonable conditions can be jointly satisfied only in trivial cases. Some meta-ethical implications of the result are discussed. The discussion also highlights several issues regarding Lewis ’ original triviality result for “the Desire as Belief Thesis” that have not been properly understood in the literature.

According to Stalnaker’s Thesis, the probability of a conditional is the conditional probability. Under some mild conditions, the thesis trivialises probabilities and conditionals, as initially shown by David Lewis. This article asks the following question: does still lead to triviality, if the probability function in is replaced by a probability-like function? The article considers plausibility functions, in the sense of Friedman and Halpern, which additionally mimic probabilistic additivity and conditionalisation. These quasi probabilities comprise Friedman–Halpern’s conditional plausibility spaces, as well (...) as other known representations of conditional doxastic states. The paper proves Lewis’ triviality for quasi probabilities and discusses how this has implications for three other prominent strategies to avoid Lewis’ triviality: Adams’ thesis, where the probability function on the left in is replaced by a probability-like function, abandoning conditionalisation, where probability conditionalisation on the right in is replaced by another propositional update procedure and the approximation thesis, where equality in is replaced by approximation. The paper also shows that Lewis’ triviality result is really about ‘additiveness’ and ‘conditionality’. (shrink)

"THE central problem in moral philosophy is commonly known as the is-ought problem." So runs the opening sentence of the introduction to a recent volume of readings on this issue. [1] Taken as a statement about the preoccupations of moral philosophers of the present century, we can accept this assertion. The problem of how statements of fact are related to moral judgments has dominated recent moral philosophy. Associated with this problem is another, which has also been given considerable attention - (...) the question of how morality is to be defined. The two issues are linked, since some definitions of morality allow us to move from statements of fact to moral judgments, while others do not. In this article I shall take the two issues together, and try to show that they do not merit the amount of attention they have been given. I shall argue that the differences between the contending parties are terminological, and that there are various possible terminologies, none of which has, on balance, any great advantage over any other terminology. So instead of continuing to regard these issues as central, moral philosophers could, I believe, "agree to disagree" about the "is-ought" problem, and about the definition of morality, provided only that everyone was careful to stipulate how he was using the term "moral" and was aware of the implications and limitations of the definition he was using. Moral philosophers could then move on to consider more important issues. (shrink)

In Rogerson and Restall’s, the “class of implication formulas known to trivialize ” is recorded. The aim of this paper is to show how to invalidate any member in this class by using “weak relevant model structures”. Weak relevant model structures verify deep relevant logics only.

Proponents of Veritism believe that truth is the sole non-instrumental epistemic good. This view is often taken to entail that all truths should be of equal epistemic value. Hence, it is put under stress by the presence of trivial truths: truths to which we attach relatively little or no epistemic value. Pritchard, in the defense of Veritism, has tried to argue that the best way to understand the implications of Veritism is to think in terms of how an intellectually virtuous (...) inquirer would pursue truth. Furthermore, he thinks that such an inquirer would prefer weighty truths and set aside trivial ones. As such, he thinks that our epistemic disregard for trivial truths is just to be expected given Veritism. We argue that Pritchard’s defense of Veritism fails, and the problem of trivial truths remains a significant challenge for Veritism. (shrink)

Recent work in formal semantics suggests that the language system includes not only a structure building device, as standardly assumed, but also a natural deductive system which can determine when expressions have trivial truth-conditions (e.g., are logically true/false) and mark them as unacceptable. This hypothesis, called the `logicality of language', accounts for many acceptability patterns, including systematic restrictions on the distribution of quantifiers. To deal with apparent counter-examples consisting of acceptable tautologies and contradictions, the logicality of language is often paired (...) with an additional assumption according to which logical forms are radically underspecified: i.e., the language system can see functional terms but is `blind' to open class terms to the extent that different tokens of the same term are treated as if independent. This conception of logical form has profound implications: it suggests an extreme version of the modularity of language, and can only be paired with non-classical---indeed quite exotic---kinds of deductive systems. The aim of this paper is to show that we can pair the logicality of language with a different and ultimately more traditional account of logical form. This framework accounts for the basic acceptability patterns which motivated the logicality of language, can explain why some tautologies and contradictions are acceptable, and makes better predictions in key cases. As a result, we can pursue versions of the logicality of language in frameworks compatible with the view that the language system is not radically modular vis-a-vis its open class terms and employs a deductive system that is basically classical. (shrink)

Recent work in formal semantics suggests that the language system includes not only a structure building device, as standardly assumed, but also a natural deductive system which can determine when expressions have trivial truth‐conditions (e.g., are logically true/false) and mark them as unacceptable. This hypothesis, called the ‘logicality of language’, accounts for many acceptability patterns, including systematic restrictions on the distribution of quantifiers. To deal with apparent counter‐examples consisting of acceptable tautologies and contradictions, the logicality of language is often paired (...) with an additional assumption according to which logical forms are radically underspecified: i.e., the language system can see functional terms but is ‘blind’ to open class terms to the extent that different tokens of the same term are treated as if independent. This conception of logical form has profound implications: it suggests an extreme version of the modularity of language, and can only be paired with non‐classical—indeed quite exotic—kinds of deductive systems. The aim of this paper is to show that we can pair the logicality of language with a different and ultimately more traditional account of logical form. This framework accounts for the basic acceptability patterns which motivated the logicality of language, can explain why some tautologies and contradictions are acceptable, and makes better predictions in key cases. As a result, we can pursue versions of the logicality of language in frameworks compatible with the view that the language system is not radically modular vis‐á‐vis its open class terms and employs a deductive system that is basically classical. (shrink)

It is a well-known fact that although the poset of open sets of a topological space is a Heyting algebra, its Heyting implication is not necessarily stable under the inverse image of continuous functions and hence is not a geometric concept. This leaves us wondering if there is any stable family of implications that can be safely called geometric. In this paper, we will first recall the abstract notion of implication as a binary modality introduced in Akbar Tabatabai (Implication via (...) spacetime. In: Mathematics, logic, and their philosophies: essays in honour of Mohammad Ardeshir, pp 161–216, 2021). Then, we will use a weaker version of categorical fibrations to define the geometricity of a category of pairs of spaces and implications over a given category of spaces. We will identify the greatest geometric category over the subcategories of open-irreducible (closed-irreducible) maps as a generalization of the usual injective open (closed) maps. Using this identification, we will then characterize all geometric categories over a given category $${\mathcal {S}}$$ S, provided that $${\mathcal {S}}$$ S has some basic closure properties. Specially, we will show that there is no non-trivial geometric category over the full category of spaces. Finally, as the implications we identified are also interesting in their own right, we will spend some time to investigate their algebraic properties. We will first use a Yoneda-type argument to provide a representation theorem, making the implications a part of an adjunction-style pair. Then, we will use this result to provide a Kripke-style representation for any arbitrary implication. (shrink)

The present article discusses shared epistemological characteristics of two distinct areas of research: the field of first-person inquiry and the field of quantum mechanics. We outline certain philosophical challenges that arise in each of the two lines of inquiry, and point towards the central similarity of their observational situation: the impossibility of disregarding the interrelatedness of the observed phenomena with the act of observation. We argue that this observational feature delineates a specific category of research that we call the non-trivial (...) domain. Unlike the trivial domain, non-trivial research cannot assume the view from nowhere on which the observed phenomena could be regarded as existing independently of the process of observation. Presenting first-person inquiry and quantum mechanics as two of its examples, we show that non-trivial research violates several fundamental observational presuppositions of the trivial domain, exemplified in the principles of classical physics. Drawing on Niels Bohr’s philosophy of quantum mechanics and the constructivist notion of enaction, we stress the constructive, participatory, and irreversible nature of observation in the non-trivial domain. We discuss the possibility of developing a non-representationalist epistemology of the non-trivial, and consider the implications of our discussion for research in the non-trivial domain, as well as for the general understanding of the scientific inquiry. (shrink)

In his paper [6], Greg Restall conjectured that a logic supports a naïve comprehension scheme if and only if it is robustly contraction free, that is, if and only if no contracting connective is definable in terms of the primitive connectives of the logic. In this paper, we present infinitely many counterexamples to Restall''s conjecture, in the form of purely implicational logics which are robustly contraction free, but which trivialize naïve comprehension.

Many accept the following three theses in animal ethics. First, although animal welfare should not be—or at least, need not be—our top moral priority, it is not a trivial one either. Second, if an animal is sentient, then it is a moral patient. Third, the extinction of an animal species is a tragic outcome that we have moral reason to prevent. I argue that a traditional (i.e., pre-modern) Buddhist perspective pushes against the first thesis and that a naturalized Buddhist perspective (...) is inconsistent with the latter two. (shrink)

In a circulated but heretofore unpublished 2001 paper, I argued that Leiter’s analogy to Quine’s “naturalization of epistemology” does not do the philosophical work Leiter suggests. I revisit the issues in this new essay. I first show that Leiter’s replies to my arguments fail. Most significantly, if – contrary to the genuinely naturalistic reading of Quine that I advanced – Quine is understood as claiming that we have no vantage point from which to address whether belief in scientific theories is (...) ever justified, it would not help Leiter’s parallel. Given Leiter’s way of drawing the parallel, the analogous position in the legal case would be not the Legal Realists’ indeterminacy thesis, but the very different position that we have no vantage point from which to address whether legal decisions can ever be justified. I then go on to address the more important question of whether the indeterminacy thesis, if true, would support any replacement of important legal philosophical questions with empirical ones. Although Ronald Dworkin has argued against the indeterminacy thesis, if he were wrong on this issue, it would not in any way suggest that the questions with which Dworkin is centrally concerned cannot fruitfully be addressed. The indeterminacy thesis is a bone of contention in an ordinary philosophical debate between its proponents and Dworkin. Of course, if the determinacy thesis were true, no one should try to show that it is false, but this triviality lends no support to the kind of replacement proposal that Leiter proposes. I conclude with some general reflections on naturalism and philosophical methodology. (shrink)

It is shown that in a linearly ordered MV-algebra A , the implication is unique if and only if the identity function is the unique De Morgan automorphism on A . Modulo categorical equivalence, our uniqueness criterion recalls Ohkuma's rigidness condition for totally ordered abelian groups. We also show that, if A is an Archimedean totally ordered MV-algebra, then each non-trivial De Morgan automorphism of the underlying involutive lattice of A yields a new implication on A , which is not (...) isomorphic to the original implication. (shrink)

Consideration of the experimental activities carried out in one discipline, through the lens of another, can lead to novel insights. Here, we comment from a biological perspective upon experiments in quantum mechanics proposed by physicists that are likely to feasible in the near future. In these experiments, an entire living organism would be knowingly placed into a coherent quantum state for the first time, i.e. would be coerced into demonstrating quantum phenomena. The implications of the proposed experiment for a biologist (...) depend to an extent upon the outcomes. If successful, then the organism will have been temporarily in a state where it has an unmeasurable metabolism—not because a metabolic rate is undetectable, but because any attempt to measure it would automatically bring the organism out of the state. We argue that this would in essence represent a new category of cryptobiosis. Further, the organism would not necessarily retain all of the characteristics commonly attributed to living systems, unlike the currently known categories of cryptobiosis. If organisms can survive having previously been in a coherent state, then we must accept that living systems do not necessarily need to remain in a decoherent state at all times. This would be something new to biologists, even if it might seem trivial to physicists. It would have implications concerning the physical extremes organisms can tolerate, the search for extraterrestrial life, and our philosophical view of animation. (shrink)

In a circulated but heretofore unpublished 2001 paper, I argued that Leiter's analogy to Quine's 'naturalization of epistemology' does not do the philosophical work Leiter suggests. I revisit the issues in this new essay. I first show that Leiter's replies to my arguments fail. Most significantly, if — contrary to the genuinely naturalistic reading of Quine that I advanced — Quine is understood as claiming that we have no vantage point from which to address whether belief in scientific theories is (...) ever justified, it would not help Leiter's parallel. Given Leiter's way of drawing the parallel, the analogous position in the legal case would be not the Legal Realists' indeterminacy thesis, but the very different position that we have no vantage point from which to address whether legal decisions can ever be justified. I then go on to address the more important question of whether the indeterminacy thesis, if true, would support any replacement of important legal philosophical questions with empirical ones. Although Ronald Dworkin has argued against the indeterminacy thesis, if he were wrong on this issue, it would not in any way suggest that the questions with which Dworkin is centrally concerned cannot fruitfully be addressed. The indeterminacy thesis is a bone of contention in an ordinary philosophical debate between its proponents and Dworkin. Of course, if the determinacy thesis were true, no one should try to show that it is false, but this triviality lends no support to the kind of replacement proposal that Leiter proposes. I conclude with some general reflections on naturalism and philosophical methodology. (shrink)

In everyday conversations, professional codes, policy debates, and academic literature, the concept of respect is referred to frequently. Bioethical arguments in recent decades equate the idea of respect for persons with individuals who are capable of autonomous decision-making, with the focus being explicitly on ‘autonomy,’ ‘capacity,’ or ‘capability.’ In much of bioethics literature, respect for persons is replaced by respect for autonomy. Though the unconditional respect for persons and their autonomy (irrespective of actual decision-making capacity) is established in Kantian bioethics, (...) current argument and debates often revolve around a thin concept of autonomy, focusing on capacity and capability: persons are owed respect because they are ‘rational beings’ or with a focus on ‘agency’ and ‘decision-making abilities.’ However, these aspects alone are insufficient while engaging the concept of respect for persons, particularly in healthcare settings. This paper sets out to explore if the concept of respect for persons—as opposed to a thin concept of autonomy—could help us engage better in healthcare practices. We shall probe the practical value of the experiential aspect of respect—understood as the recognition of persons as respect-worthy through certain dispositions and deliberative acts—by reflecting on instances in clinical practice that tend to be dismissed as negligible or even unavoidable in a stressful environment such as a busy hospital. We shall argue that these instances are far from trivial but carry moral significance and express an unacceptable—disrespectful—attitude that can compromise the moral habitus in hospital settings. In our conclusion, we call for practicing recognition respect in the health professional–patient encounter by focussing on manners, attitudes, and behaviors. Furthermore, we call for continuous medical ethics education programs to address the moral significance of disrespectful behaviors and their manifestations in particular socio-cultural contexts. (shrink)

Purpose: To consider the implications of the operation of the nervous system -- and of the constitution of cultures as closed networks of languaging and emotioning -- for how we understand and generate so-called "virtual realities." Findings: The nervous system is a detector of configurations within itself and thus cannot represent reality. The distinction between virtual and non-virtual realities does not apply to the operation of the nervous system; rather it pertains to the operation of the observer as a languaging (...) being. Our human existence has changed as virtual realities have become non-virtual through their systemic cultural inclusion in the realization of our biological human manner of living. Implications: Virtual realities are never trivial, because we always become transformed as we live them according to the emotioning of the psychic space that they bring about in our living, and this is so regardless of whether we like it or not. (shrink)

Corporations, and the environments in which they operate, are complex, with changing multiple dimensions, and an inherent capacity to evolve qualitatively. A central premise of this study is that a postmodern reading of ethics represents an expression of, and an engagement with, the ethical complexities that define the business landscape. In particular, the deconstructive philosophy of Jacques Derrida offers a non-trivial reading of a complex notion of ethics, and thereby helps us to develop the skills necessary to critique and intervene (...) in our practices, and to develop robust strategies for living in the absence of prescriptive ethical frameworks. Although a central premise of this study is that substantive ethical claims can only be generated within a given context, the study nevertheless presents readers with a meta-position that illustrates the type of considerations that should inform ethical reflection from a complexity perspective. In order to illustrate the value that this meta-position holds for business ethics, these considerations are explored in terms of the implications that they hold for our understanding of corporate social responsibility, for the practice of responsible management and leadership practices, and for teaching business ethics. (shrink)

The authors of [MOC 00] conjectured that intuitionistic and classical logics are asymptotically identical. Their conjecture concerns the implicational parts of these logics over k variables and is trivially true for k = 1, because implicational parts of intuitionistic and classical logics over one variable are identical. So, it seems to be interesting to investigate the appropriate fragments of these logics for k = 2. The result is obtained by reducing the problem to the same one of Dummett's intermediate linear (...) logic of two variables. Actually, this paper shows the existence of the density of this logic and demonstrates that the linear calculus covers a substantial part of classical propositional one. (shrink)

A minimal theorem in a logic L is an L-theorem which is not a non-trivial substitution instance of another L-theorem. Komori (1987) raised the question whether every minimal implicational theorem in intuitionistic logic has a unique normal proof in the natural deduction system NJ. The answer has been known to be partially positive and generally negative. It is shown here that a minimal implicational theorem A in intuitionistic logic has a unique -normal proof in NJ whenever A is provable without (...) non-prime contraction. The non-prime contraction rule in NJ is the implication introduction rule whose cancelled assumption differs from a propositional variable and appears more than once in the proof. Our result improves the known partial positive solutions to Komori's problem. Also, we present another simple example of a minimal implicational theorem in intuitionistic logic which does not have a unique -normal proof in NJ. (shrink)

It is well-known that intuitionistic logics can be formalized by means of Heyting algebras, i.e. relatively pseudocomplemented semilattices. Within such algebras the logical connectives implication and conjunction are formalized as the relative pseudocomplement and the semilattice operation meet, respectively. If the Heyting algebra has a bottom element |$0$|⁠, then the relative pseudocomplement with respect to |$0$| is called the pseudocomplement and it is considered as the connective negation in this logic. Our idea is to consider an arbitrary meet-semilattice with |$0$| (...) satisfying only the Ascending Chain Condition (these assumptions are trivially satisfied in finite meet-semilattices) and introduce the operators formalizing the connectives negation |$x^{0}$| and implication |$x\rightarrow y$| as the set of all maximal elements |$z$| satisfying |$x\wedge z=0$| and as the set of all maximal elements |$z$| satisfying |$x\wedge z\leq y$|⁠, respectively. Such a negation and implication is ‘unsharp’ since it assigns to one entry |$x$| or to two entries |$x$| and |$y$| belonging to the semilattice, respectively, a subset instead of an element of the semilattice. Surprisingly, this kind of negation and implication still shares a number of properties of these connectives in intuitionistic logic, in particular the derivation rule Modus Ponens. Moreover, unsharp negation and unsharp implication can be characterized by means of five, respectively seven simple axioms. We present several examples. The concepts of a deductive system and of a filter are introduced as well as the congruence determined by such a filter. We finally describe certain relationships between these concepts. (shrink)

A promising strategy for better understanding space and time at the Planck scale, is outlined and further pursued. It is explained in detail, how black hole unitarity demands the existence of transformations that can remove firewalls. This must then be combined with a continuity condition on the horizon, with antipodal identification as an inevitable consequence. The antipodal identification comes with a \ inversion. We claim to have arrived at ‘new physics’, but rather than string theory, our ‘new physics’ concerns new (...) constraints on the topology and the boundary conditions of general coordinate transformations. The resulting theory is conceptually quite non trivial, and more analysis is needed. A strong entanglement between Hawking particles at opposite sides of the black hole is suspected, but questions remain. A few misconceptions concerning black holes, originating from older investigations, are discussed. (shrink)

Motivated by H. Curry’s well-known objection and by a proposal of L. Henkin, this article introduces the positive tableaux, a form of tableau calculus without refutation based upon the idea of implicational triviality. The completeness of the method is proven, which establishes a new decision procedure for the (classical) positive propositional logic. We also introduce the concept of paratriviality in order to contribute to the question of paradoxes and limitations imposed by the behavior of classical implication.

Adams’ thesis is generally agreed to be linguistically compelling for simple conditionals with factual antecedent and consequent. We propose a derivation of Adams’ thesis from the Lewis- Kratzer analysis of if-clauses as domain restrictors, applied to probability operators. We argue that Lewis’s triviality result may be seen as a result of inexpressibility of the kind familiar in generalized quantifier theory. Some implications of the Lewis- Kratzer analysis are presented concerning the assignment of probabilities to compounds of conditionals.

Various connexive FDE-based modal logics are studied. Some of these logics contain a conditional that is both connexive and strict, thereby highlighting that strictness and connexivity of a conditional do not exclude each other. In particular, the connexive modal logics cBK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-}$$\end{document}, cKN4, scBK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-}$$\end{document}, scKN4, cMBL, and scMBL are introduced semantically by means of classes of Kripke models. The logics cBK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} (...) \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-}$$\end{document} and cKN4 are connexive variants of the FDE-based modal logics BK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-}$$\end{document} and KN4 with a weak and a strong implication, respectively. The system cMBL is a connexive variant of the modal bilattice logic MBL. The latter is a modal extension of Arieli and Avron’s logic of logical bilattices and is characterized by a class of Kripke models with a four-valued accessibility relation. In the systems scBK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-}$$\end{document}, scKN4, and scMBL, the conditional is both connexive and strict. Sound and complete tableau calculi for all these logics are presented and used to show that the entailment relations of the systems under consideration are decidable for finite premise set. Moreover, the logics cBK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {cBK}^-$$\end{document} and cMBL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {cMBL}$$\end{document} are shown to be algebraizable. The algebraizability of cMBL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {cMBL}$$\end{document} is derived from proving cMBL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {cMBL}$$\end{document} to be definitionally equivalent to MBL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {MBL}$$\end{document}. All connexive modal logics studied in this paper are decidable, paraconsistent, and inconsistent but non-trivial logics. (shrink)

Information processing in neural systems can be described and analysed at multiple spatiotemporal scales. Generally, information at lower levels is more fine-grained but can be coarse-grained at higher levels. However, only information processed at specific scales of coarse-graining appears to be available for conscious awareness. We do not have direct experience of information available at the scale of individual neurons, which is noisy and highly stochastic. Neither do we have experience of more macro-scale interactions, such as interpersonal communications. Neurophysiological evidence (...) suggests that conscious experiences co-vary with information encoded in coarse-grained neural states such as the firing pattern of a population of neurons. In this article, we introduce a new informational theory of consciousness: Information Closure Theory of Consciousness (ICT). We hypothesise that conscious processes are processes which form non-trivial informational closure (NTIC) with respect to the environment at certain coarse-grained scales. This hypothesis implies that conscious experience is confined due to informational closure from conscious processing to other coarse-grained scales. ICT proposes new quantitative definitions of both conscious content and conscious level. With the parsimonious definitions and a hypothesise, ICT provides explanations and predictions of various phenomena associated with consciousness. The implications of ICT naturally reconcile issues in many existing theories of consciousness and provides explanations for many of our intuitions about consciousness. Most importantly, ICT demonstrates that information can be the common language between consciousness and physical reality. (shrink)

This work studies some problems connected to the role of negation in logic, treating the positive fragments of propositional calculus in order to deal with two main questions: the proof of the completeness theorems in systems lacking negation, and the puzzle raised by positive paradoxes like the well-known argument of Haskel Curry. We study the constructive com- pleteness method proposed by Leon Henkin for classical fragments endowed with implication, and advance some reasons explaining what makes difficult to extend this constructive (...) method to non-classical fragments equipped with weaker implications (that avoid Curry's objection). This is the case, for example, of Jan Lukasiewicz's n-valued logics and Wilhelm Ackermann's logic of restricted implication. Besides such problems, both Henkin's method and the triviality phenomenon enable us to propose a new positive tableau proof system which uses only positive meta-linguistic resources, and to mo- tivate a new discussion concerning the role of negation in logic proposing the concept of paratriviality. In this way, some relations between positive reasoning and infinity, the possibilities to obtain a ¯first-order positive logic as well as the philosophical connection between truth and meaning are dis- cussed from a conceptual point of view. (shrink)

Contemporary culture trivializes the "seven deadly sins," or vices, as if they have no serious moral or spiritual implications. Glittering Vices clears this misconception by exploring the traditional meanings of gluttony, sloth, lust, and others. It offers a brief history of how the vices were compiled and an eye opening explication of how each sin manifests itself in various destructive behaviors. Readers gain practical understanding of how the vices shape our culture today and how to correctly identify and eliminate the (...) deeply rooted patterns of sin that are work in their own lives. This accessible book is essential for any reader interested in spiritual disciplines and character formation. Excerpt Very simply, a virtue (or vice) is acquired through practice repeated activity that increases our proficiency at the activity and gradually forms our character. . . . We often need external incentives and sanctions to get us through the initial stages of the process, when our old, entrenched desires still pull us toward the opposite behavior. But with encouragement, discipline, and often a role model or mentor, practice can make things feel more natural and enjoyable as we gradually develop the internal values and desires corresponding to our outward behavior. Virtue often develops, that is, from the outside in. This is why, when we want to reform our character from vice to virtue, we often need to practice and persevere in regular spiritual disciplines and formational practices for a lengthy period of time. (shrink)

The purpose of this paper is to formulate first-order Peano arithmetic within the resources of relevant logic, and to demonstrate certain properties of the system thus formulated. Striking among these properties are the facts that it is trivial that relevant arithmetic is absolutely consistent, but classical first-order Peano arithmetic is straightforwardly contained in relevant arithmetic. Under, I shall show in particular that 0 = 1 is a non-theorem of relevant arithmetic; this, of course, is exactly the formula whose unprovability was (...) sought in the Hilbert program for proving arithmetic consistent. Under, I shall exhibit the requisite translation, drawing some Goedelian conclusions therefrom. Left open, however, is the critical problem whether Ackermann’s rule γ is admissible for theories of relevant arithmetic. The particular system of relevant Peano arithmetic featured in this paper shall be called R♯. Its logical base shall be the system R of relevant implication, taken in its first-order form RQ. Among other Peano arithmetics we shall consider here in particular the systems C♯, J♯, and RM3♯; these are based respectively on the classical logic C, the intuitionistic logic J, and the Sobocinski-Dunn semi-relevant logic RM3. And another feature of the paper will be the presentation of a system of natural deduction for R♯, along lines valid for first-order relevant theories in general. This formulation of R♯ makes it possible to construct relevantly valid arithmetical deductions in an easy and natural way; it is based on, but is in some respects more convenient than, the natural deduction formulations for relevant logics developed by Anderson and Belnap in Entailment. (shrink)

The paper investigates and refines the proportionalist solution to the causal exclusion problem developed by Menzies and List. First and foremost, it explores the implications of their inter-level compatibility result. It is highlighted that in theory the inter-level causal compatibility of realizer and realized properties allows for scenarios where the higher-level property is multiply realized. By developing concrete illustrations, the paper proves this to be an empirically plausible option. Further non-trivial implications of the framework are unpacked to show that the (...) sensitivity of causal relations to background conditions is as important in deciding on the existence and the direction of exclusion as sensitivity to the realization of the cause. This insight also opens the way to further refinements: a richer reconceptualization of upwards exclusion and a plausible answer to a critic of the Menzies and List project. (shrink)

The logicality of language is the hypothesis that the language system has access to a ‘natural’ logic that can identify and filter out as unacceptable expressions that have trivial meanings—that is, that are true/false in all possible worlds or situations in which they are defined. This hypothesis helps explain otherwise puzzling patterns concerning the distribution of various functional terms and phrases. Despite its promise, logicality vastly over-generates unacceptability assignments. Most solutions to this problem rest on specific stipulations about the properties (...) of logical form—roughly, the level of linguistic representation which feeds into the interpretation procedures—and have substantial implications for traditional philosophical disputes about the nature of language. Specifically, contextualism and semantic minimalism, construed as competing hypotheses about the nature and degree of context-sensitivity at the level of logical form, suggest different approaches to the over-generation problem. In this paper, I explore the implications of pairing logicality with various forms of contextualism and semantic minimalism. I argue that to adequately solve the over-generation problem, logicality should be implemented in a constrained contextualist framework. (shrink)

We show that the implicational fragment of intuitionism is the weakest logic with a non-trivial probabilistic semantics which satisfies the thesis that the probabilities of conditionals are conditional probabilities. We also show that several logics between intuitionism and classical logic also admit non-trivial probability functions which satisfy that thesis. On the other hand, we also prove that very weak assumptions concerning negation added to the core probability conditions with the restriction that probabilities of conditionals are conditional probabilities are sufficient to (...) trivialize the semantics. (shrink)

I shall begin with the assumption that there are, among our mental acts. some which stand in direct contact with ohjects in the material world. The aim of this paper will he to clarify and to draw out certain implications of this somewhat trivial assumption, and ultimately to say something about the ontological structure of those of our acts which effect the function of bringing us into contact with material acts which serve. as we might say, as the most external (...) points of consciousness which touch the objects consciousness is trying to grasp. Amongst material objects I shall include not only material things such as tables. (shrink)

The aim of this study is to justify the belief that there are biological normative mechanisms that fulfill non-trivial causal roles in the explanations (as formulated by researchers) of actions and behaviors present in specific systems. One example of such mechanisms is the predictive mechanisms described and explained by predictive processing (hereinafter PP), which (1) guide actions and (2) shape causal transitions between states that have specific content and fulfillment conditions (e.g. mental states). Therefore, I am guided by a specific (...) theoretical goal associated with the need to indicate those conditions that should be met by the non-trivial theory of normative mechanisms and the specific models proposed by PP supporters. In this work, I use classical philosophical methods, such as conceptual analysis and critical reflection. I also analyze selected studies in the field of cognitive science, cognitive psychology, neurology, information theory and biology in terms of the methodology, argumentation and language used, in accordance with their theoretical importance for the issues discussed in this study. In this sense, the research presented here is interdisciplinary. My research framework is informed by the mechanistic model of explanation, which defines the necessary and sufficient conditions for explaining a given phenomenon. The research methods I chose are therefore related to the problems that I intend to solve. In the introductory chapter, “The concept of predictive processing”, I discuss the nature of PP as well as its main assumptions and theses. I also highlight the key concepts and distinctions for this research framework. Many authors argue that PP is a contemporary version of Kantianism and is exposed to objections similar to those made against the approach of Immanuel Kant. I discuss this thesis and show that it is only in a very general sense that the PP framework is neo-Kantian. Here we are not dealing with transcendental deduction nor with the application of transcendental arguments. I argue that PP is based on reverse engineering and abduction inferences. In the second part of this chapter, I respond to the objection formulated by Dan Zahavi, who directly accuses this research framework of anti-realistic consequences. I demonstrate that the position of internalism, present in the so-called conservative PP, does not imply anti-realism, and that, due to the explanatory role played in it by structural representations directed at real patterns, it is justified to claim that PP is realistic. In this way, I show that PP is a non-trivial research framework, having its subject, specific methods and its own epistemic status. Finally, I discuss positions classified as the socalled radical PP. In the chapter “Predictive processing as a Bayesian explanatory model” I justify the thesis according to which PP offers Bayesian modeling. Many researchers claim that the brain is an implemented statistical probabilistic network that is an approximation of the Bayesian 7 rule. In practice, this means that all cognitive processes are to apply Bayes' rule and can be described in terms of probability distributions. Such a solution arouses objections among many researchers and is the subject of wide criticism. The purpose of this chapter is to justify the thesis that Bayesian PP is a non-trivial research framework. For this purpose, I argue that it explains certain phenomena not only at the computational level described by David Marr, but also at the level of algorithms and implementation. Later in this chapter I demonstrate that PP is normative modeling. Proponents of the use of Bayesian models in psychology or decision theory argue that they are normative because they allow the formulation of formal rules of action that show what needs to be done to make a given action optimal. Critics of this approach emphasize that such thinking about the normativity of Bayesian modeling is unjustified and that science should shift from prescriptive to descriptive positions. In a polemic with Shira Elqayam and Jonathan Evans (2011), I show that the division they propose into prescriptivism and Bayesian descriptivism is apparent, because, as I argue, there are two forms of prescriptivism, i.e. the weak and the strong. I argue that the weak version is epistemic and can lead to anti-realism, while the strong version is ontic and allows one to justify realism in relation to Bayesian models. I argue that a weak version of prescriptivism is valid for PP. It allows us to adopt anti-realism in relation to PP. In practice, this means that you can explain phenomena using Bayes' rule. This does not, however, imply that they are Bayesian in nature. However, the full justification of realism in relation to the Bayesian PP presupposes the adoption of strong prescriptivism. This position assumes that phenomena are explained by Bayesian rule because they are Bayesian as such. If they are Bayesian in nature, then they should be explained using Bayesian modeling. This thesis will be substantiated in the chapters “Normative functions and mechanisms in the context of predictive processing” and “Normative mechanisms and actions in predictive processing”. In the chapter “The Free Energy Principle in predictive processing”, I discuss the Free Energy Principle (hereinafter FEP) formulated by Karl Friston and some of its implications. According to this principle, all biological systems (defined in terms of Markov blankets) minimize the free energy of their internal states in order to maintain homeostasis. Some researchers believe that PP is a special case of applying this principle to cognition, and that predictive mechanisms are homeostatic mechanisms that minimize free energy. The discussion of FEP is important due to the fact that some authors consider it to be important for explanatory purposes and normative. If this is the case, then FEP turns out to be crucial in explaining normative predictive mechanisms and, in general, any normative biological mechanisms. To define the explanatory possibilities of this principle, I refer to the discussion of its supporters on the issue they define as the problem of continuity and discontinuity between life and mind. A critical analysis of this discussion and the additional arguments I have formulated have allowed me to revise the explanatory ambitions of FEP. I also reject the belief that this principle is necessary to explain the nature of predictive mechanisms. I argue that the principle formulated and defended by Friston is an important research heuristic for PP analysis. 8 In the chapter “Normative functions and mechanisms in predictive processing”, I start my analyzes by formulating an answer to the question about the normative nature of homeostatic mechanisms. I demonstrate that predictive mechanisms are not homeostatic. I defend the view that a full explanation of normative mechanisms presupposes an explanation of normative functions. I discuss the most important proposals for understanding the normativity of a function, both from a systemic and teleosemantic perspective. I conclude that the non-trivial concept of a function must meet two requirements which I define as explanatory and normative. I show that none of the theories I have invoked satisfactorily meets both of these requirements. Instead, I propose a model of normativity based on Bickhard's account, but supplemented by a mechanistic perspective. I argue that a function is normative when: (1) it allows one to explain the dysfunction of a given mechanism; (2) it contributes to the maintenance of the organism's stability by shaping and limiting possible relations, processes and behaviors of a given system; and when (3) (according to the representational and predictive functions) it enables explaining the attribution of logical values of certain representations / predictions. In such an approach, a mechanism is normative when it performs certain normative functions and when it is constitutive for a specific action or behavior, despite the fact that for some reason it cannot realize it either currently or in the long-term. Such an understanding of the normativity of mechanisms presupposes the acceptance of the epistemic hypothesis. I argue that this hypothesis is not cognitively satisfactory, and therefore the ontic hypothesis should be justified, which is directly related to adopting the position of ontic prescriptivism. For this reason, referring to the mechanistic theory of scientific explanations, I formulate an ontical interpretation of the concept of a normative mechanism. According to this approach, a mechanism or a function is normative when they perform such and such causal roles in explaining certain actions and behaviors. With regard to the normative properties of predictive mechanisms and functions, this means that they are the causes of specific actions an organism carries out in the environment. In this way, I justify the necessity of accepting the ontic hypothesis and rejecting the epistemic hypothesis. The fifth chapter, “Normative mechanisms and actions in predictive processing”, is devoted to the dark room problem and the related exploration-exploitation trade-off. A dark room is the state that an agent could be in if it minimized the sum of all potential prediction errors. I demonstrate that, in accordance with the basic assumption of PP about the need for continuous and long-term minimization of prediction errors, such a state should be desirable for the agent. Is it really so? Many authors believe it is not. I argue that the test of the value of PP is the possibility of a non-trivial solution of this problem, which can be reduced to the choice between active and uncertainty-increasing exploration and safe and easily predictable exploitation. I show that the solution proposed by PP supporters present in the literature does not enable a fully satisfactory explanation of this dilemma. Then I defend the position according to which the full explanation of the normative mechanisms, and, subsequently, the solution to the dilemma of exploration and exploitation, involves reference to the existence of constraints present in the environment. The constraints 9 include elements of the environment that make a given mechanism not only causal but also normative. They are therefore key to explaining the predictive mechanisms. They do not only play the role of the context in which the mechanism is implemented, but, above all, are its constitutive component. I argue that the full explanation of the role of constraints in normative predictive mechanisms presupposes the integration of individual models of specific cognitive phenomena, because only the mechanistic integration of PP with other models allows for a non-trivial explanation of the nature of normative predictive mechanisms that would have a strong explanatory value. The explanatory monism present in many approaches to PP makes it impossible to solve the problem of the dark room. Later in this chapter, I argue that the Bayesian PP is normative not because it enables the formulation of such and such rules of action, but because the predictive mechanisms themselves are normative. They are normative because they condition the choice of such and such actions by agents. In this way, I justify the hypothesis that normative mechanisms make it possible to explain the phenomenon of agent motivation, which is crucial for solving the dark room problem. In the last part of the chapter, I formulate the hypothesis of distributed normativity, which assumes that the normative nature of certain mechanisms, functions or objects is determined by the relations into which these mechanisms, functions or objects enter. This means that what is normative (in the primary sense) is the relational structure that constitutes the normativity of specific items included in it. I suggest that this hypothesis opens up many areas of research and makes it possible to rethink many problems. In the “Conclusion”, I summarize the results of my research and indicate further research perspectives. (shrink)

Perception is typically distinguished from cognition. For example, seeing is importantly different from believing. And while what one sees clearly influences what one thinks, it is debatable whether what one believes and otherwise thinks can influence, in some direct and non-trivial way, what one sees. The latter possible relation is the cognitive penetration of perception. Cognitive penetration, if it occurs, has implications for philosophy of science, epistemology, philosophy of mind, and cognitive science. This paper offers an analysis of the phenomenon, (...) its theoretical consequences, and a variety of experimental results and possible interpretations of them. The paper concludes by proposing some constraints for analyses and definitions of cognitive penetrability. (shrink)

It may seem trivial to state that one of the major trends in biological investigation consists in an attempt to explain the structural and functional aspects of living matter in chemical terms, in an effort to obtain insight into the equivalent of macroscopic phenomena on the molecular level. I am sure you are aware of, and this meeting of the Association has brought ample additional evidence, in how many fields this tendency has become apparent. It can be recognized in genetics (...) with the molecular analysis of chromosomes and the enzymatic or metabolic interpretation of hereditary properties like the eyecolor of Drosophila. In a purely morphological branch like histology we do not ask merely for a differentiation of stained cell structure but we ask for the nature of the staining reaction; in nerve physiology we try to interpret conduction as alterations of protein lipoid layers; or in pathology where the age old syndrome of inflammation is explored with biochemical methods. I should mention molecular models of membranes and cell surfaces, the molecular interpretation of secretion and of the macroscopic phenomena of metabolism. Yet insofar as this yield of data could be designated as a trend, it would rather seem to be the natural outcome to be expected from the application of the analytic method of science. In one instance, however, this approach has been carried farther than in all the other fields, and it would seem to be worthwhile to pause for one moment to ask whether this case is important merely because of its technical implications or whether it is meaningful in a wider sense. (shrink)

Feminist research in ethics : an introduction -- Theology in fragmented time : reflections with the concept 'postmodernism' as a starting point -- On the material spirituality of housework and its political implications -- Neither trivial nor sentimental : de-trivialization as a method in women's studies -- Power that we have; power that we need -- Women's solidarity : a value with a future -- Androcentrism and where do we go from here? : perspectives for theological reflection on 'the human (...) being' -- The minor distinction between mothers and test tubes : on the concept of women in science -- Feminist ethics and the ecology question -- The debate on animal experiments -- Biotechnology and ethics -- Invitation to feminist reflection on the economy -- Femaleness as social work -- From the norm of marriage to a plurality of lifestyles. (shrink)

An adequate theory of rights ought to forbid the harming of animals to promote trivial interests of humans, as is often done in the animal-user industries. But what should the rights view say about situations in which harming some animals is necessary to prevent intolerable injustices to other animals? I develop an account of respectful treatment on which, under certain conditions, it’s justified to intentionally harm some individuals to prevent serious harm to others. This can be compatible with recognizing the (...) inherent value of the ones who are harmed. My theory has important implications for contemporary moral issues in nonhuman animal ethics, such as the development of cultured meat and animal research. (shrink)

A logic is said to be contraction free if the rule from A→(A→B) to A→B is not truth preserving. It is well known that a logic has to be contraction free for it to support a non-trivial naïve theory of sets or of truth. What is not so well known is that if there is another contracting implication expressible in the language, the logic still cannot support such a naïve theory. A logic is said to be robustly contraction free if (...) there is no such operator expressible in its language. We show that a large class of finitely valued logics are each not robustly contraction free, and demonstrate that some other contraction free logics fail to be robustly contraction free. Finally, the sublogics of Łω (with the standard connectives) are shown to be robustly contraction free. (shrink)