Da Ré and Szmuc argue that while there is a symmetry between ‘infectious’ and ‘immune’ logics, this symmetry fails w.r.t. extending an algebra with an immune or an infectious element. In this paper, I show that the symmetry also fails w.r.t. defining a new logical operation from a given set of primitive (Boolean) operations. I use the case of the material conditional to illustrate this point.

This article is concerned with an exploration of a family of systems—called immune logics—that arise from certain dualizations of the well-known family of infectious logics. The distinctive feature of the semantic of infectious logics is the presence of a certain “infectious” semantic value, by which two different though equivalent things are meant. On the one hand, it is meant that these values are zero elements for all the operations in the underlying algebraic structure. On the other (...) hand, it is meant that these values behave in a value-in-value-out fashion for all the operations in the underlying algebraic structure. Thus, in a rather informal manner, we will refer to immune logics as those systems whose underlying semantics count with a certain “immune” semantic value behaving in a way that is somewhat dual to that of the infectious values. In a more formal manner, carrying out this dualization will prove to be not as straightforward as one could imagine, since the two characterizations of infectiousness discussed above lead to two different outcomes when one tries to conduct them. We explore these alternatives and provide technical results regarding them, and the various logical systems defined using such semantics. (shrink)

pseudo-Master's thesis Since Jacques Derrida’s 1989 essay “Force of Law: the Mystical Foundations of Authority,” Carl Schmitt has been a perennial subject of Derrida’s political critique. I will argue that Derrida’s concept of auto-immunity is uniquely applicable to Derrida’s interpretation of Schmitt’s political philosophy. Therefore, my argument will consist of two interrelated but equally divergent parts; the digressive structure will attempt to mimic Derrida’s complex style of weaving opposed concepts into a coherent whole. First, I will demonstrate the many forms (...) of Derrida’s concept of auto-immunity. Second, I will exhibit how this schema uniquely applies to Derrida’s criticisms of Schmitt and the contemporary state of politics. (shrink)

In Voyous, Jacques Derrida develops his argument starting from the presupposition that democracy as such is the entity whose integrity and immunity are at stake and, therefore, under investigation. This gesture reflects the setting in which ten years before, in Foi et savoir, he had cast his reasoning about the logic of immunity. There, it was one of the sources of religion, the immunity of the sacred, that operated according to this logic. The hyphen between these two essays, beside Derrida’s (...) own crossed references, is the genealogical reasoning on the meaning and essence of the concept of democracy: contrary to what Derrida claims, it will be maintained that Athenian democracy had a clear immune matrix, whose constant exercise is clearly defined, in spite of himself, by Vernant, and it will be shown how modern democracy has been forced to change policy. Modern democracy is an entity characterized by an immune deficiency. In order to save Derrida’s intuition from both the collapse of different vantage points and from a quite bizarre reticence in taking into account of the immune value of rituals, our starting point will be René Girard’s œuvre and his reading of the role of immune logic in sacred systems and, more generally, in modernity. The threshold between the auto-immune reaction, immune deficiency and auto-immune disease, between the sacrifice who delimits and constitutes the self and the holocauste du peuple en détail, is the space where, constantly exposed to the risk of auto-denial, democracy lives. (shrink)

The concept of ‘immunity’ is the central notion in Roberto Esposito’s assessments of modern politics. Understanding modern politics from Esposito’s perspective is synonymous with understanding the concept of immunity. However, if one looks at modern political theory, one finds that a number of concepts such as social contract, state/sovereignty, person, property, and liberty stand out as central concepts rather than a single concept. This article argues that these concepts, which have different meanings, are part of one and the same logic, (...) and that it is possible to conceptualise this logic around ‘immunity.’ For this reason, this article proposes, first, to consider the concept of ‘immunity’ as a concept that expresses the logic to which these concepts belong. Second, it argues that the concept of immunity allows us to see the continuity between modern politics and contemporary political tendencies. Based on this argument, the article claims that Esposito increases the explanatory power of Michel Foucault’s understanding of biopolitics, which is insufficient to explain the logic of the transition from life-protective to life-hostile activities in politics. The article concludes that ‘immunity’ provides a conceptual key to understanding the possibility of totalitarianism in biopolitical times from Nazism to the COVID-19 pandemic. (shrink)

A self-ascription is a thought or sentence in which a predicate is self-consciously ascribed to oneself. Self-ascriptions are best expressed using the first-person pronoun. Mental self-ascriptions are ascriptions to oneself of mental predicates (predicates that designate mental properties), non-mental self-ascriptions are ascriptions to oneself of non-mental predicates (predicates that designate non-mental properties). It is often claimed that there is a range of self-ascriptions that are immune to error through misidentification relative to the first-person pronoun (IEM for short). What this (...) means, and exactly which self-ascriptions are properly classed as IEM, is a topic hotly disputed. Some claim that only mental self-ascriptions are IEM, others claim that some non-mental self-ascriptions are IEM. Before this question can be decided, it needs to be judged exactly what it means to say that a self-ascription is IEM. And here we stumble across the fact that there are, at least, two non-equivalent ways of defining the phenomenon1. I will be claiming that one of these definitions should be rejected. (shrink)

We define and study a new notion called k-immunity that lies between immunity and hyperimmunity in strength. Our interest in k-immunity is justified by the result that θ does not k-tt reduce to a k-immune set, which improves a previous result by Kobzev [7]. We apply the result to show that Φ′ does not btt-reduce to MIN, the set of minimal programs. Other applications include the set of Kolmogorov random strings, and retraceable and regressive sets. We also give a (...) new characterization of effectively simple sets and show that simple sets are not btt-cuppable. (shrink)

We examine the multiplicity of complementation amongst subspaces of V ∞ . A subspace V is a complement of a subspace W if V ∩ W = {0} and (V ∪ W) * = V ∞ . A subspace is called fully co-r.e. if it is generated by a co-r.e. subset of a recursive basis of V ∞ . We observe that every r.e. subspace has a fully co-r.e. complement. Theorem. If S is any fully co-r.e. subspace then S has (...) a decidable complement. We give an analysis of other types of complements S may have. For example, if S is fully co-r.e. and nonrecursive, then S has a (nonrecursive) r.e. nowhere simple complement. We impose the condition of immunity upon our subspaces. Theorem. Suppose V is fully co-r.e. Then V is immune iff there exist M 1 , M 2 ∈ L(V ∞ ), with M 1 supermaximal and M 2 k-thin, such that $M_1 \oplus V = M_2 \oplus V = V_\infty$ . Corollary. Suppose V is any r.e. subspace with a fully co-r.e. immune complement W (e.g., V is maximal or V is h-immune). Then there exist an r.e. supermaximal subspace M and a decidable subspace D such that $V \oplus W = M \oplus W = D \oplus W = V_\infty$ . We indicate how one may obtain many further results of this type. Finally we examine a generalization of the concepts of immunity and soundness. A subspace V of V ∞ is nowhere sound if (i) for all Q ∈ L(V ∞ ) if $Q \supset V$ then Q = V ∞ , (ii) V is immune and (iii) every complement of V is immune. We analyse the existence (and ramifications of the existence) of nowhere sound spaces. (shrink)

In this article, I want to suggest a template for rereading accepted discourses of climate change management and sustainability, which, I argue, are ironically sustained by an immunitary paradigm. This paradigm is founded on a species-split—a have and have-not conception of the human in which the latter sustains the comforts of the former. Thus, I suggest, whenever we read discourses of sustainability we should acknowledge the ironic subtext that seeks to sustain an underclass to immunize an elite. This immunity is (...) a complex ontological operation: as Roberto Esposito points out in his significant work on the logic of immunity, in immune systems “the equilibrium of the whole is determined not by subtraction, but by... (shrink)

The principle of noncombatant immunity (NCI) lies at the heart of jus in bello or the moral rules governing the conduct of war. This paper takes up the status of NCI in asymmetrical wars (AW). The argument proceeds in six parts. In the first we present a skeptical or realist position about the feasibility of NCI in AW. Part two surveys the development of the idea of NCI. Part three provides an account of the logic and dynamics of AW. Part (...) four lays out a set of objections to the realist position. Part five imagines a realist rejoinder. In the final part we examine the moral and political implications of assuming that the realists are right about NCI in AW. We argue that even if they are, this does not imply the realist conclusion that “anything goes” in AW. In fact, we suggest that difficulties upholding NCI in AW may give rise to a special argument for conscientious objection. (shrink)

We extend Meyer's 1972 investigation of sets of minimal indices. Blum showed that minimal index sets are immune, and we show that they are also immune against high levels of the arithmetic hierarchy. We give optimal immunity results for sets of minimal indices with respect to the arithmetic hierarchy, and we illustrate with an intuitive example that immunity is not simply a refinement of arithmetic complexity. Of particular note here are the fact that there are three minimal index (...) sets located in Π3 − Σ3 with distinct levels of immunity and that certain immunity properties depend on the choice of underlying acceptable numbering. We show that minimal index sets are never hyperimmune; however, they can be immune against the arithmetic sets. Lastly, we investigate Turing degrees for sets of random strings defined with respect to Bagchi's size-function s. (shrink)

The thesis addresses the issues of error through misidentification and immunity to error through misidentification in relation to the problem of the first person. First, it provides an explanation of error through misidentification. Secondly, it shows that there are two possible ways of understanding immunity to error through misidentification. It is then argued that the first understanding of immunity to error through misidentification leads to what is labelled "the trilemma about the self". That is to say, either we provide an (...) explanation of immunity to error through misidentification, but we subscribe to two contentious metaphysical views about the self-the Cartesian and the Idealist; or else we hold the view that the self is identical with a human being, but we have no explanation of immunity to error through misidentification. It is then shown that in order to solve the trilemma, a different understanding of immunity to error through misidentification must be offered. After discussing various possible understandings of immunity to error through misidentification, a sound account of it is finally provided. Moreover, it is shown how non-inferential, introspection-based mental self-ascriptions can comply with it, in such a way that they turn out to be logically immune to error through misidentification. Finally, by drawing on Evans' and Peacocke's accounts of the possession conditions of the first person concept-in which IEM I-judgements play a central role-, it is shown that it is a concept of a human being who thinks of herself as such. Hence, our first person concept is firmly anti-Cartesian and anti-Idealist. As a consequence, it is maintained that not only is there no need to hold the Cartesian and the Idealist metaphysics of the self in order to explain why some I-judgements can be immune to error through misidentification, but it is also argued that one can no longer be either Cartesian or Idealist. For that would expose one to conceptual incoherence. (shrink)

Trust has been widely investigated both theoretically and empirically. Whether thought of as the result of a calculation of costs/benefits, a shared identity, or a leap of faith, there always seems to be an ‘as if’ rhetorical gesture which is ultimately needed to explain how actors move from the base of trust to expectations of trust via suspending judgment on uncertainty and fear of vulnerability to betrayal and exploitation — the actors ultimately act ‘as if’ they do not fear uncertainty (...) and vulnerability to betrayal. Yet this ‘as if’ element has remained seriously under-theorised. Drawing on Derrida's deconstruction, I propose a way of thinking this ‘as if’ element of trust. I thus argue that the decision to trust occurs in a terrain of structural undecidability. The latter is thought of as the possibility condition of trust as well as the subject of trust and a sense of responsibility for this trust. The aporiatic nature of undecidability makes this trust an auto-immune trust which obeys the tripartite logic of ‘without’ which both negates and affirms trust. (shrink)

This article analyses the biochemical object of tnf inhibitors from the perspective of living with an autoimmune disease. The author tries to tease out how the concept of immune inhibition is used in tandem with the biochemical object of tnf inhibitors to dominate in defining and narrating what health and disease, normal and pathological, cure and healing can mean in the context of autoimmune bodies. Specifically, and within the ‘pathological’ framework of autoimmune diseases, the pharmacological treatment of tnf inhibition (...) is designed to suppress the ‘overly’ active immune system, thus acting as a negative or suppressing biochemical agent aimed at putting the ‘malfunctioning’ immune system back in balance. As can be seen in the current conjuncture, tnf inhibitors officially —and governmentally— place those taking them in a risk group, as they 'lower' their overall bodily immunity and make them more vulnerable to infectious diseases, while stabilizing their patho-logical, ‘over’-immune uninhibited condition. Part personal narrative of being diagnosed with an autoimmune condition, part speculative autoimmune theory inspired by such a diagnosis, the article ultimately calls for a different form of embodiment that is neither negative nor affirmative, and yet is resistant even to itself. (shrink)

John Campbell (1999) has recently maintained that the phenomenon of thought insertion as it is manifested in schizophrenic patients should be described as a case in which the subject is introspectively aware of a certain thought and yet she is wrong in identifying whose thought it is. Hence, according to Campbell, the phenomenon of thought insertion might be taken as a counterexample to the view that introspection-based mental selfascriptions are logically immune to error through misidentification (IEM, hereafter). Thus, if (...) Campbell is right, it would not be true that when the subject makes a mental self-ascription on the basis of introspective awareness of a given mental state, there is no possible world in which she could be wrong as to whether it is really she who has that mental state. Notice the interesting interdisciplinary implications of Campbell’s project: on the one hand, a fairly precise notion elaborated in philosophy such as IEM (and the related notion of error through misidentification, EM hereafter) is used to describe a characteristic symptom of schizophrenia.1 On the other hand, such a phenomenon, described in the way proposed, is taken to be a possible counterexample to a sort of “philosophical dogma” such as IEM of introspection-based non-inferential mental self-ascriptions. In the first section of the paper I will point out the characteristic features of EM and explain logical immunity to error through misidentification of introspection-based mental self-ascriptions; in the second section I will consider the case of thought insertion in more detail and show why, after all, it is not a counterexample to the view that introspectionbased mental self-ascriptions are logically IEM. Finally, I will offer a re-description of the phenomenon of thought insertion. (shrink)

In The Blue Book, Wittgenstein defined a category of uses of “I” which he termed “I”-as-subject, contrasting them with “I”-as-object uses. The hallmark of this category is immunity to error through misidentification (IEM). This article extends Wittgenstein’s characterisation to the case of memory-judgments, discusses the significance of IEM for self-consciousness—developing the idea that having a first-person thought involves thinking about oneself in a distinctive way in which one cannot think of anyone or anything else—and refutes a common objection to the (...) claim that memory-judgments exhibit IEM. (shrink)

The paper offers a solution to the semantic paradoxes, one in which (1) we keep the unrestricted truth schema “True(A)↔A”, and (2) the object language can include its own metalanguage. Because of the first feature, classical logic must be restricted, but full classical reasoning applies in “ordinary” contexts, including standard set theory. The more general logic that replaces classical logic includes a principle of substitutivity of equivalents, which with the truth schema leads to the general intersubstitutivity of True(A) with A (...) within the language.The logic is also shown to have the resources required to represent the way in which sentences (like the Liar sentence and the Curry sentence) that lead to paradox in classical logic are “defective”. We can in fact define a hierarchy of “defectiveness” predicates within the language. Contrary to claims that any solution to the paradoxes just breeds further paradoxes (“revenge problems”) involving defectiveness predicates, there is a general consistency/conservativeness proof that shows that talk of truth and the various “levels of defectiveness” can all be made coherent together within a single object language. (shrink)

We analyze the degree spectra of structures in which different types of immunity conditions are encoded. In particular, we give an example of a structure whose degree spectrum coincides with the hyperimmune degrees. As a corollary, this shows the existence of an almost computable structure of which the complement of the degree spectrum is uncountable.

We use certain strong Q-reducibilities, and their corresponding strong positive reducibilities, to characterize the hyperimmune sets and the hyperhyperimmune sets: if A is any infinite set then A is hyperimmune (respectively, hyperhyperimmune) if and only if for every infinite subset B of A, one has \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\overline{K}\not\le_{\rm ss} B}$$\end{document} (respectively, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\overline{K}\not\le_{\overline{\rm s}} B}$$\end{document}): here \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\le_{\overline{\rm (...) s}}}$$\end{document} is the finite-branch version of s-reducibility, ≤ss is the computably bounded version of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\le_{\overline{\rm s}}}$$\end{document}, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\overline{K}}$$\end{document} is the complement of the halting set. Restriction to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Sigma^0_2}$$\end{document} sets provides a similar characterization of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Sigma^0_2}$$\end{document} hyperhyperimmune sets in terms of s-reducibility. We also show that no \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${A \geq_{\overline{\rm s}}\overline{K}}$$\end{document} is hyperhyperimmune. As a consequence, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\deg_{\rm s}(\overline{K})}$$\end{document} is hyperhyperimmune-free, showing that the hyperhyperimmune s-degrees are not upwards closed. (shrink)

In Of Grammatology, Derrida gave his attention to a number of philosophies of language for which writing is attributed the status of a supplemental form, with speech considered a more original form of language and the proper object of the linguist's science. A number of Derrida's remarks pointed out that the very defense of democracy, or human rights, even where they excluded children, women, workers, and colonized peoples, also provided the resources for subsequent claims by these groups for inclusion. Feminisms (...) bear witness to the historical auto‐immunity of the denial of women's rights. Historically, women's rights claims will also have their own auto‐immune logics, in their identifications with nationalist logics, in their alignment with an image of progress often disseminated at the expense of other cultures or classes, in an ethnocentrism or race blindness to which feminism has often been prone. (shrink)

Let be a countable first‐order language and be an ‐structure. “Definable set” means a subset of M which is ‐definable in with parameters. A set is said to be immune if it is infinite and does not contain any infinite definable subset. X is said to be partially immune if for some definable A, is immune. X is said to be totally non‐immune if for every definable A, and are not immune. Clearly every definable set (...) is totally non‐immune. Here we ask whether the converse is true and prove that it is false for every countable structure whose class of definable sets satisfies a mild condition. We investigate further the possibility of an alternative construction of totally non‐immune non‐definable sets with the help of a subclass of immune sets, the class of cohesive sets, as well as with the help of a generalization of definable sets, the semi‐definable ones (the latter being naturally defined in models of arithmetic). Finally connections are found between totally non‐immune sets and generic classes in nonstandard models of arithmetic. (shrink)

One of the characteristics of all somatic cells is a finite life span. Cells may proliferate until they reach a point after which, although they are metabolically active, they can no longer produce daughter cells. This observation is central to the clonal exhaustion hypothesis, a mechanism cited to explain age-associated immune dysfunction. In this hypothesis, repeated division of lymphocytes leads to a replicative limit, after which they enter the senescent phase but are not lost from the pool of T (...) cells. Advancing age would then be associated with an increase in the number of T cells that are unable to proliferate to a stimulus which induces a proliferative response in T cells from younger individuals. This hypothesis seems both logical and reasonable and is supported by data from both humans and mice with the demonstration of an age-related accumulation of senescent T cells in both species. However, there is an apparent paradox. The paradox arises because the onset of immunosenescence appears to be more closely linked to the life span of the animal rather than the life span of the lymphocyte. BioEssays 21:519–524, 1999. © 1999 John Wiley & Sons, Inc. (shrink)

Let ???? be a computable structure and let R be a new relation on its domain. We establish a necessary and sufficient condition for the existence of a copy ℬ of ???? in which the image of R (¬R, resp.) is simple (immune, resp.) relative to ℬ. We also establish, under certain effectiveness conditions on ???? and R, a necessary and sufficient condition for the existence of a computable copy ℬ of ???? in which the image of R (¬R, (...) resp.) is simple (immune, resp.). (shrink)

This article proposes that the prime ideals of the university - those of truth, knowledge, justice, and emancipation - are also those that currently produce unjust practices "outside" and "within". Using the work of Jacques Derrida and Paul Virilio, the article argues that the central problem of the university today consists not so much of a neo-liberalisation, but of the speeding-up of these ideals through their enmeshment with techniques of calculation, vision, and prediction. The current university therefore suffers from what (...) it with Derrida identifies as an "auto-immune disease," in which the acceleration of its foundational aspirations have led to a near-total subjugation of all and everything to an oppressive quest for transparency. However, the article proposes via Virilio that this totalising transparency paradoxically also produces more blindness, accidents, and unknowability. It hopes to illustrate this with some examples in the teaching scene as well by working through some of its own conceptual tensions. The other logic of the university today, the article finally proposes, consists of a "dark" or stealth functionality, opening up the promise of a radically different future and unanticipated resistance despite itself. (shrink)

An approach to explaining the nature and source of logic and its laws with a rich historical tradition takes the laws of logic to be laws of thought. This view seems intuitively compelling, after all, logic seems to be intimately related with how we think. But how exactly should we understand it? And what arguments can we give in favour? I will propose one line of argument for the claim that the laws of logic are laws of thought. I will (...) motivate the claim that there is a certain phenomenon, namely, that there are logical principles which are immune to rational doubt. I will then give an argument to the best explanation; I will argue that the best explanation of this phenomenon is to take the laws of logic to be constitutive-normative laws of thought. The proposal, and some responses to potential objections, will have a notably Kantian flavour. (shrink)

K. R. Popper distinguished between two main uses of logic, the demonstrational one, in mathematical proofs, and the derivational one, in the empirical sciences. These two uses are governed by the following methodological constraints: in mathematical proofs one ought to use minimal logical means (logical minimalism), while in the empirical sciences one ought to use the strongest available logic (logical maximalism). In this paper I discuss whether Popper’s critical rationalism is compatible with a revision of logic in the empirical sciences, (...) given the condition of logical maximalism. Apparently, if one ought to use the strongest logic in the empirical sciences, logic would remain immune to criticism and, thus, non-revisable. I will show that critical rationalism is theoretically compatible with a revision of logic in the empirical sciences. However, a question that remains to be clarified by the critical rationalists is what kind of evidence would lead them to revise the system of logic that underlies a physical theory, such as quantum mechanics? Popper’s falsificationist methodology will be compared with the recently advocated extension of the abductive methodology from the empirical sciences to logic by T. Williamson, since both of them arrive at the same conclusion concerning the status of classical logic. (shrink)

This paper seeks to defend the following conclusions: The program advanced by Carnap and other necessarians for probability logic has little to recommend it except for one important point. Credal probability judgments ought to be adapted to changes in evidence or states of full belief in a principled manner in conformity with the inquirer’s confirmational commitments—except when the inquirer has good reason to modify his or her confirmational commitment. Probability logic ought to spell out the constraints on rationally coherent confirmational (...) commitments. In the case where credal judgments are numerically determinate confirmational commitments correspond to Carnap’s credibility functions mathematically represented by so—called confirmation functions. Serious investigation of the conditions under which confirmational commitments should be changed ought to be a prime target for critical reflection. The necessarians were mistaken in thinking that confirmational commitments are immune to legitimate modification altogether. But their personalist or subjectivist critics went too far in suggesting that we might dispense with confirmational commitments. There is room for serious reflection on conditions under which changes in confirmational commitments may be brought under critical control. Undertaking such reflection need not become embroiled in the anti inductivism that has characterized the work of Popper, Carnap and Jeffrey and narrowed the focus of students of logical and methodological issues pertaining to inquiry. (shrink)

This article examines an argument which may negatively influence measles vaccination uptake. According to the argument, an individual child in a highly vaccinated society may be better off by being non-vaccinated; the child does not risk vaccine adverse effects and is protected against measles through herd immunity. Firstly, the conclusion of the argument is challenged by showing that herd immunity’s protection is unreliable and inferior to vaccination. Secondly, the logic of the argument is challenged by showing that the argument is (...) inherently self-defeating and therefore logically inconsistent. In practice the argument cannot be used to protect children against measles. Measles vaccination is undoubtedly best for children, even in highly vaccinated societies. Only if a medical contraindication to vaccination exists should vaccination be waived in favour of reliance on herd immunity. This places obligations on those who stand in care relationships with the child: parents, healthcare providers, and the state. (shrink)

This article examines an argument which may negatively influence measles vaccination uptake. According to the argument, an individual child in a highly vaccinated society may be better off by being non-vaccinated; the child does not risk vaccine adverse effects and is protected against measles through herd immunity. Firstly, the conclusion of the argument is challenged by showing that herd immunity’s protection is unreliable and inferior to vaccination. Secondly, the logic of the argument is challenged by showing that the argument is (...) inherently self-defeating and therefore logically inconsistent. In practice the argument cannot be used to protect children against measles. Measles vaccination is undoubtedly best for children, even in highly vaccinated societies. Only if a medical contraindication to vaccination exists should vaccination be waived in favour of reliance on herd immunity. This places obligations on those who stand in care relationships with the child: parents, healthcare providers, and the state. (shrink)

This paper outlines a formal recursive wager resolution calculus (WRC) that provides a novel conceptual framework for sentential logic via bridge rules that link wager resolution with truth values. When paired with a traditional truth-centric criterion of logical soundness WRC generates a sentential logic that is broadly truth-conditional but not truth-functional, supports the rules of proof employed in standard mathematics, and is immune to the most vexing features of their traditional implementation. WRC also supports a novel probabilistic criterion of (...) logical soundness, the fair betting probability criterion (FBP). It guarantees that the conclusion of an FBP-valid argument is at least as credible as a conjunction of premises, and also that the conclusion is true if the premises are. In addition, WRC provides a platform for a novel non-probabilistic, computationally simpler criterion of logical soundness – the criterion of Super-validity - that issues the same logical appraisals as FBP, and hence the same guarantees. (shrink)

We propose a new formalization of legal competences, and in particular for the Hohfeldian categories of power and immunity, through a deontic reinterpretation of dynamic epistemic logic. We argue that this logic explicitly captures the norm-changing character of legal competences while providing a sophisticated reduction of the latter to static normative positions. The logic is completely axiomatizable, and we apply it to a concrete case in German contract law to illustrate that it can capture the distinction between legal ability and (...) legal permissibility. (shrink)

This study analyzes the relevance in the art world of an ethical and juridical category as the responsibility, as well as its content and limits. The acceptance of the idea of responsibility of the artists depends on the manner in which the “art world” and its frontiers are comprehended - as an autonomous and closed realm or, on the contrary, as a space open to the public control. If the modernist logic of the autonomy had led to the emergence of (...) an artist who claims to an immunity/ impunity based on the absolute artistic freedom, the other model of the art world implies legitimately ethical and juridical questions, as well as an active relation between the public and the forms of the contemporary art. Still, the idea of responsi- bility is tighten to the mode of evaluating the powers of art. As soon as the social and political utility of the art is invoked, it ceased to be not only beyond the good or evil, but also beyond desirable and undesirable, and the responsibility of the artists belongs not only to the aesthetic realm but also to the political one. (shrink)

This paper examines the politics behind algorithmic ordering in social media, focusing on the advertising logic behind them. This is explored through a practice I call rhythmedia – the way media companies render people, objects and their relations as rhythms and order them for economic purposes. As a case study I examine the way the Facebook Immune System algorithm orchestrates people’s mediated experience towards a desired rhythm while filtering out problematic rhythms. This anti-spam algorithm shows that it is important (...) for Facebook to understand people as rhythms and assemble a dynamic database from their mediated experiences, to convince advertisers that they know when and where people do things. People’s rhythms become a product that advertisers pay and bid for through Ad Auction to intervene in specific moments and shape people’s experience. Thus, the company can shape, manage, and filter specific rhythms to order sociality that brings more value. (shrink)

The paper introduces a semantics for the language of classical first order logic supplemented with the additional operators and . This semantics understands formulas as tasks. An agent , working as a slave for its master , can carry out the task αβ if it can carry out any one of the two tasks α, β, depending on which of them was requested by the master; similarly, it can carry out xα if it can carry out α for any particular (...) value for x selected by the master; an agent can carry out α→β if it can carry out β as long as it has, as a slave , an agent who carries out α; finally, carrying out P, where P is an atomic formula, simply means making P true; in particular, is a task that no agent can carry out. When restricted to the language of classical logic, the meaning of formulas is isomorphic to their classical meaning, which makes our semantics a conservative extension of classical semantics.This semantics can claim to be a formalization of the resource philosophy associated with linear logic, if resources are understood as agents carrying out tasks. The classical operators of our language correspond to the multiplicative operators of linear logic, while and correspond to the additive conjunction and universal quantifier, respectively.Our formalism may also have a potential to be used in AI as an alternative logic of planning and action. Its main appeal is that it is immune to the frame problem and the knowledge preconditions problem.The paper axiomatically defines a logic L in the above language and proves its soundness and completeness with respect to the task semantics in the following intuitive sense: L α iff α can be carried out by an agent who has nothing but its intelligence for carrying out tasks. This logic is shown to be semidecidable in the full language and decidable when the classical quantifier is forbidden in it. (shrink)

Many people regard utility theory as the only rigorous foundation for subjective probability, and even de Finetti thought the betting approach supplemented by Dutch Book arguments only good as an approximation to a utility-theoretic account. I think that there are good reasons to doubt this judgment, and I propose an alternative, in which the probability axioms are consistency constraints on distributions of fair betting quotients. The idea itself is hardly new: it is in de Finetti and also Ramsey. What is (...) new is that it is shown that probabilistic consistency and consequence can be defined in a way formally analogous to the way these notions are defined in deductive (propositional) logic. The result is a free-standing logic which does not pretend to be a theory of rationality and is therefore immune to, among other charges, that of “logical omniscience”. (shrink)

Despite the tendency to think that the justification of revealed truths depends on a verifiable contact with divine reality, this essay argues that the authoritative status of revelations is due to their role in defining a distinctively religious order of judgment. Rather than being immediately apparent to everyone, this kind of authority is local to particular forms of judgment that depend on the principles that frame these ways of thinking. Revelatory claims are logically exempted from the normal demands of justification (...) because of this role they have as definitive judgments, and they share their immunity from ordinary forms of justification with other axiomatic principles. Yet their authority can in certain cases be challenged, and it is a secondary purpose of this essay to bring the various ways of challenging their truth to light. (shrink)

In the first part of this paper, I express doubts that Tarski and Carnap were guilty of some confusions about the relations between truth and meaning, attributed to them by Soames. In the second part, I consider Quine's Carrollian argument against conventionalism about logical truth, discussed only briefly and approvingly by Soames, and I explore the question whether some not obviously incorrect forms of conventionalism about logical truth, such as what I call "finitary conventionalism", are immune to Quine's argument.

We prove various results connected together by the common thread of computability theory.First, we investigate a new notion of algorithmic dimension, the inescapable dimension, which lies between the effective Hausdorff and packing dimensions. We also study its generalizations, obtaining an embedding of the Turing degrees into notions of dimension.We then investigate a new notion of computability theoretic immunity that arose in the course of the previous study, that of a set of natural numbers with no co-enumerable subsets. We demonstrate how (...) this notion of $\Pi ^0_1$ -immunity is connected to other immunity notions, and construct $\Pi ^0_1$ -immune reals throughout the high/low and Ershov hierarchies. We also study those degrees that cannot compute or cannot co-enumerate a $\Pi ^0_1$ -immune set.Finally, we discuss a recently discovered truth-table reduction for transforming a Kolmogorov–Loveland random input into a Martin-Löf random output by exploiting the fact that at least one half of such a KL-random is itself ML-random. We show that there is no better algorithm relying on this fact, in the sense that there is no positive, linear, or bounded truth-table reduction which does this. We also generalize these results to the problem of outputting randomness from infinitely many inputs, only some of which are random.Abstract prepared by David J. Webb.E-mail: [email protected]: https://arxiv.org/pdf/2209.05659.pdf. (shrink)

Jockusch and Lewis proved that every DNC function computes a bi-immune set. They asked whether every DNC function computes an effectively bi-immune set. We construct a DNC function that computes no effectively bi-immune set, thereby answering their question in the negative.

The logical connection argument claims that since the relation between a want and the supposedly resultant action is " logical " in nature, Whereas the relation between any cause and its effect must be contingent in nature, A want therefore cannot be the cause of an action. I consider four classical formulations of the lca, And review various objections that have been brought against them. Then I present my own formulation of the lca, Which is immune to such objections. (...) I conclude that we must abandon the idea that a person's wants cause his actions. (shrink)

Providing a principled characterization of the distinction between logical and non-logical expressions is a longstanding issue in the philosophy of logic. In the Logical Syntax of Language, Carnap proposes a syntactic solution to this problem, which aims at grounding the claim that logic and mathematics are analytic. Roughly speaking, his idea is that logic and mathematics correspond to the largest part of science for which it is possible to completely specify by "syntactic" means which sentences are valid and which are (...) not. Despite a renewed interest in the philosophical benefits of analyticity, both inside and outside of Carnap scholarship, Carnap's definition of logical expressions seems to have drawn too little attention. I shall argue that it is worth a second look. More precisely, my aim will be to defend this idea against some technical problems faced by Carnap's way of implementing it and against Quinean attacks on syntax-based conventionalism. Section 1 presents Carnap's definition in the context of Logical Syntax of Language, that is, how exactly the definition works, and why Carnap needs it. In section 2, I review three challenges that have been raised in the literature, and I propose to revise the definition accordingly. I argue that its modified version is immune to the previous challenges, and, to some extent, immune to new challenges as well. In the last section, I suggest that the definition has a philosophical interest of its own, because standard Quinean objections are not as conclusive as one might think when attention is paid to the fact that Carnap requires complete syntactic specification of validities. (shrink)