If the theory advanced below is correct, then what is the difference (I know she [Philippa Foot]] will ask) between the moral must/must not and the must/must not of etiquette or the clubhouse? Looking forward to the conclusion I shall reach, let me reply, roughly and readily, that the difference will reside not in anything formal but in the depth, spread, and felt authority of the attachments to which the moral must/must not appeals-and categorically appeals.

This paper defends the doctrine that moral requirements are categorical in nature. My point of departure is John McDowell’s 1978 essay, “Are Moral Requirements Hypothetical Imperatives?”, in which McDowell argues, against Philippa Foot, that moral reasons are not conditional upon agents’ desires and are, in a certain sense, inescapable. After expounding McDowell’s view, exploring his idea that moral requirements “silence” other considerations and discussing its particularist ethos, I address an objection that moral reasons, as McDowell conceives them, are fundamentally (...) incomplete in ways only a full-bloodedly Kantian appeal to pure practical reason can remedy. I conclude that the objection fails: ordinary moral reasons do not stand in need of a grounding in Reason. There is no prospect of deriving them from a supreme principle of morality or other canons of rationality. Ordinary reasons are sufficient in themselves, though their significance can be elucidated and illuminated by various strategies — some broadly Aristotelian, some drawing inspiration from Kant’s formula of humanity — in ways that can strengthen and vindicate them. Notwithstanding the failure of the objection, I conclude by reflecting on how Kantian insights can yet play a significant role in a McDowellian view of moral deliberation and moral education. (shrink)

Kant has argued that moral requirements are categorical. Kant's claim has been challenged by some contemporary philosophers; this article defends Kant's doctrine. I argue that Kant's claim captures the unique feature of moral requirements. The main arguments against Kant's claim focus on one condition that a categorical imperative must meet: to be independent of desires. I argue that there is another important, but often ignored, condition that a categorical imperative must meet, and this second condition is crucial (...) to understanding why moral requirements are not hypothetical. I also argue that the claim that moral requirements are not categorical because they depend on desires for motivation is beside the point. The issue of whether moral requirements are categorical is not an issue about whether moral desires or feelings are necessary for moral motivation but are rather an issue about the ground of moral desires or moral feelings. Moral requirements are categorical because they are requirements of reason, and reason makes moral desires or feelings possible. (shrink)

Abstract:Recently, the idea that every hypothetical imperative must somehow be ‘backed up’ by a prior categorical imperative has gained a certain influence among Kant interpreters and ethicists influenced by Kant. Since instrumentalism is the position that holds that hypothetical imperatives can by themselves and without the aid of categorical imperatives explain all valid forms of practical reasoning, the influential idea amounts to a rejection of instrumentalism as internally incoherent. This paper argues against this prevailing view both as an (...) interpretation of Kant and as philosophical understanding of practical reason. In particular, it will be argued that many of the arguments that claim to show that hypothetical imperatives must be backed up by categorical imperatives mistakenly assume that the form of practical reasoning must itself occur as a premise within the reasoning. An alternative to this assumption will be offered. I will conclude that while instrumentalism may well be false, there is no reason to believe it is incoherent. (shrink)

Due to Gӧdel’s incompleteness results, the categoricity of a sufficiently rich mathematical theory and the semantic completeness of its underlying logic are two mutually exclusive ideals. For first- and second-order logics we obtain one of them with the cost of losing the other. In addition, in both these logics the rules of deduction for their quantifiers are non-categorical. In this paper I examine two recent arguments –Warren (2020), Murzi and Topey (2021)– for the idea that the natural deduction rules (...) for the first-order universal quantifier are categorical, i.e., they uniquely determine its semantic intended meaning. Both of them make use of McGee’s open-endedness requirement and the second one uses in addition Garson’s (2013) local models for defining the validity of these rules. I argue that the success of both these arguments is relative to their semantic or infinitary assumptions, which could be easily discharged if the introduction rule for the universal quantifier is taken to be an infinitary rule, i.e. non-compact. Consequently, I reconsider the use of the ω-rule and I show that the addition of the ω-rule to the standard formalizations of first-order logic is categorical. In addition, I argue that the open-endedness requirement does not make the first-order Peano Arithmetic categorical and I advance an argument for its categoricity based on the inferential conservativity requirement. (shrink)

David Gauthier suggested that all genuine moral problems are Prisoners Dilemmas (PDs), and that the morally and rationally required solution to a PD is to co-operate. I say there are four other forms of moral problem, each a different way of agents failing to be in PDs because of the agents’ preferences. This occurs when agents have preferences that are malevolent, self-enslaving, stingy, or bullying. I then analyze preferences as reasons for action, claiming that this means they must not target (...) the impossible, they must be able to be acted on in the circumstances, their targets must be attainable, and having the preferences must make their targets more likely. For groups of agents to have a distribution of preferences, their preferences must jointly have those four features, this imposing a kind of universalizability requirement on possible preferences. I then claim that, if all agents began with preferences satisfying these requirements, their preferences would not be of the morally problematic sort (on pain, variously, of circularity or contradiction in the specification of their targets). Instead, they would be either morally innocent preferences, or ones which put the agents in PDs. And it would then be instrumentally rational for the agents to prefer mutual co-operation. Thus if all agents initially had rationally permissible preferences and made rational choices of actions and preferences thereafter, they would never acquire immoral preferences, and so never be rationally moved to immoral actions. Further, the states of affairs such agents would be moved to bring about would be compatible with what Rawls’ agents would chose behind a veil of ignorance. Morality therefore reduces to rationality; necessarily, the actions categorically required by morality are also categorically required by rationality. (shrink)

On a widespread naturalist view, the meanings of mathematical terms are determined, and can only be determined, by the way we use mathematical language—in particular, by the basic mathematical principles we’re disposed to accept. But it’s mysterious how this can be so, since, as is well known, minimally strong first-order theories are non-categorical and so are compatible with countless non-isomorphic interpretations. As for second-order theories: though they typically enjoy categoricity results—for instance, Dedekind’s categoricity theorem for second-order and Zermelo’s quasi-categoricity (...) theorem for second-order —these results require full second-order logic. So appealing to these results seems only to push the problem back, since the principles of second-order logic are themselves non-categorical: those principles are compatible with restricted interpretations of the second-order quantifiers on which Dedekind’s and Zermelo’s results are no longer available. In this paper, we provide a naturalist-friendly, non-revisionary solution to an analogous but seemingly more basic problem—Carnap’s Categoricity Problem for propositional and first-order logic—and show that our solution generalizes, giving us full second-order logic and thereby securing the categoricity or quasi-categoricity of second-order mathematical theories. Briefly, the first-order quantifiers have their intended interpretation, we claim, because we’re disposed to follow the quantifier rules in an open-ended way. As we show, given this open-endedness, the interpretation of the quantifiers must be permutation-invariant and so, by a theorem recently proved by Bonnay and Westerståhl, must be the standard interpretation. Analogously for the second-order case: we prove, by generalizing Bonnay and Westerståhl’s theorem, that the permutation invariance of the interpretation of the second-order quantifiers, guaranteed once again by the open-endedness of our inferential dispositions, suffices to yield full second-order logic. (shrink)

Many recent writers in the philosophy of mathematics have put great weight on the relative categoricity of the traditional axiomatizations of our foundational theories of arithmetic and set theory. Another great enterprise in contemporary philosophy of mathematics has been Wright's and Hale's project of founding mathematics on abstraction principles. In earlier work, it was noted that one traditional abstraction principle, namely Hume's Principle, had a certain relative categoricity property, which here we term natural relative categoricity. In this paper, we show (...) that most other abstraction principles are not naturally relatively categorical, so that there is in fact a large amount of incompatibility between these two recent trends in contemporary philosophy of mathematics. To better understand the precise demands of relative categoricity in the context of abstraction principles, we compare and contrast these constraints to stability-like acceptability criteria on abstraction principles, the Tarski-Sher logicality requirements on abstraction principles studied by Antonelli and Fine, and supervaluational ideas coming out of Hodes' work. (shrink)

In Germany, Otfried Höffe has been a leading contributor to debates in moral, legal, political, and social philosophy for close to three decades. Höffe's work, brings into relief the relevance of these German discussions to their counterparts in English-language circles. In this book, originally published in Germany in 1990 and expanded since, Höffe proposes an extended and original interpretation of Kant‚ philosophy of law, and social morality. Höffe articulates his reading of Kant in the context of an account of modernity (...) as a "polyphonous project," in which the dominant themes of pluralism and empiricism are countered by the theme of categorically binding moral principles, such as human rights. Paying equal attention to the nuances of Kant's texts and the character of the philosophical issues in their own right, Höffe ends up with a Kantianism that requires, rather than precludes, a moral anthropology and that questions the fashionable juxtaposition of Kant and Aristotle as exemplars of incompatible approaches to ethical and political thought. (shrink)

This study investigated whether and how a person's varied series of lexical categories corresponding to different discriminatory characteristics of the same colors affect his or her perception of colors. In three experiments, Chinese participants were primed to categorize four graduated colors—specifically dark green, light green, light blue, and dark blue—into green and blue; light color and dark color; and dark green, light green, light blue, and dark blue. The participants were then required to complete a visual search task. Reaction times (...) in the visual search task indicated that different lateralized categorical perceptions of color corresponded to the various priming situations. These results suggest that all of the lexical categories corresponding to different discriminatory characteristics of the same colors can influence people's perceptions of colors and that color perceptions can be influenced differently by distinct types of lexical categories depending on the context. (shrink)

Categorical perception (CP) refers to how similar things look different depending on whether they are classified as the same category. Many studies demonstrate that adult humans show CP for human emotional faces. It is widely debated whether the effect can be accounted for solely by perceptual differences (structural differences among emotional faces) or whether additional perceiver-based conceptual knowledge is required. In this review, I discuss the phenomenon of CP and key studies showing CP for emotional faces. I then discuss (...) a new model of emotion which highlights how perceptual and conceptual knowledge interact to explain how people see discrete emotions in others’ faces. In doing so, I discuss how language (emotion words included in the paradigm) contribute to CP. (shrink)

During public health crises including the COVID-19 pandemic, resource scarcity and contagion risks may require health systems to shift—to some degree—from a usual clinical ethic, focused on the well-being of individual patients, to a public health ethic, focused on population health. Many triage policies exist that fall under the legal protections afforded by “crisis standards of care,” but they have key differences. We critically appraise one of the most fundamental differences among policies, namely the use of criteria to categorically exclude (...) certain patients from eligibility for otherwise standard medical services. We examine these categorical exclusion criteria from ethical, legal, disability, and implementation perspectives. Focusing our analysis on the most common type of exclusion criteria, which are disease-specific, we conclude that optimal policies for critical care resource allocation and the use of cardiopulmonary resuscitation (CPR) should not use categorical exclusions. We argue that the avoidance of categorical exclusions is often practically feasible, consistent with public health norms, and mitigates discrimination against persons with disabilities. (shrink)

Why do we draw the boundaries between “blue” and “green”, where we do? One proposed answer to this question is that we categorize color the way we do because we perceive color categorically. Starting in the 1950’s, the phenomenon of “categorical perception” (CP) encouraged such a response. CP refers to the fact that adjacent color patches are more easily discriminated when they straddle a category boundary than when they belong to the same category. In this paper, I make three (...) related claims. (1) Although what seems to guide discrimination performances seems to indeed be categorical information, the evidence in favor of the fact that categorical perception infl uences the way we perceive color is not convincing. (2) That CP offers a useful account of categorization is not obvious.While aiming at accounting for categorization, CP itself requires an account of categories. This being said, CP remains an interesting phenomenon. Why and how is our discrimination behavior linked to our categories? It is suggested that linguistic labels determine CP through a naming strategy to which participants resort while discriminating colors. This paper’s fi nal point is (3) that the naming strategy account is not enough. Beyond category labels, what seems to guide discrimination performance is category structure. (shrink)

Cook (1995) criticized Kosslyn, Chabris, Marsolek & Koenig's (1992) network simulation models of spatial relations encoding in part because the absolute position of a stimulus in the input array was correlated with its spatial relation to a landmark; thus, on at least some trials, the networks did not need to compute spatial relations. The network models reported here include larger input arrays, which allow stimuli to appear in a large range of locations with an equal probability of being above or (...) below a “bar,” thus eliminating the confound present in earlier models. The results confirm the original hypothesis that as the size of the network's receptive fields increases, performance on a coordinate spatial relations task (which requires computing precise, metric distance) will be relatively better than on a categorical spatial relations task (which requires computing above/below relative to a landmark). (shrink)

In Germany, Otfried Höffe has been a leading contributor to debates in moral, legal, political, and social philosophy for close to three decades. Höffe's work, brings into relief the relevance of these German discussions to their counterparts in English-language circles. In this book, originally published in Germany in 1990 and expanded since, Höffe proposes an extended and original interpretation of Kant‚ philosophy of law, and social morality. Höffe articulates his reading of Kant in the context of an account of modernity (...) as a "polyphonous project," in which the dominant themes of pluralism and empiricism are countered by the theme of categorically binding moral principles, such as human rights. Paying equal attention to the nuances of Kant's texts and the character of the philosophical issues in their own right, Höffe ends up with a Kantianism that requires, rather than precludes, a moral anthropology and that questions the fashionable juxtaposition of Kant and Aristotle as exemplars of incompatible approaches to ethical and political thought. (shrink)

We develop a general covariant categorical modeling theory of natural systems' behavior based on the fundamental functorial processes of representation and localization-globalization. In the second part of this study we analyze the semantic bidirectional process of localization-globalization. The notion of a localization system of a complex information structure bears a dual role: Firstly, it determines the appropriate categorical environment of base reference contexts for considering the operational modeling of a complex system's behavior, and secondly, it specifies the global (...) compatibility conditions of local contextual information. A localization system acts on the global information structure of a complex system, partitions it into sorts, and eventually, forces the consistent sheaf-theoretic fibering of the latter over the base category of commutative reference contexts. In this manner, the sheafification of the Spectrum functor of a complex information structure takes place by imposing on the uniform and homologous fibered structure of elements of the Spectrum presheaf the following two requirements of coherence in relation to the localization-globalization process: [i]. Compatibility of information under restriction from the global to the local level, and [ii]. Compatibility of information under extension from the local to the global level. Correspondingly, the options of local and global receive a concrete mathematical meaning with respect to a suitable notion of topology (categorical Grothendieck topology) defined on the base category of commutative reference contexts. Finally, the accurate functorial process modeling of a complex system's behavior, respecting the processes of representation and localization-globalization, is being effectuated by means of establishing a categorical dual equivalence between the category of complex information structures, and the topes of sheaves over the base category of partial or local information carriers, equipped with the categorical topology of epimorphosis families. (shrink)

A new case of Shelah's eventual categoricity conjecture is established: Let be an abstract elementary class with amalgamation. Write and. Assume that is H2‐tame and has primes over sets of the form. If is categorical in some, then is categorical in all. The result had previously been established when the stronger locality assumptions of full tameness and shortness are also required. An application of the method of proof of the mentioned result is that Shelah's categoricity conjecture holds in (...) the context of homogeneous model theory (this was known, but our proof gives new cases): If D be a homogeneous diagram in a first‐order theory T and D is categorical in a, then D is categorical in all. (shrink)

According to Bernard Williams, attempts to justify a categorically binding impartial principle fail because they can only establish categorically binding requirements on action by making them non-universalizable , and can only establish impartial requirements by rendering them inapplicable to real agents . But, an individual cannot be the particular agent the individual is without being an agent every bit as much as an individual cannot be an agent without being the particular agent that the individual is. On this basis, it (...) is argued that, when the actual Gewirthian argument for a categorically binding impartial principle is presented, which Williams does not do, his objections to it do not hold and the argument establishes that agents are categorically bound to accept a substantive impartial principle that, at the same time, permits them to live lives that respect their own personal interests. Consequently, Williams’ dilemma is false. (shrink)

Trust can be understood as a precondition for a well-functioning society or as a way to handle complexities of living in a risk society, but also as a fundamental aspect of human morality. Interactions on the Internet pose some new challenges to issues of trust, especially connected to disembodiedness. Mistrust may be an important obstacle to Internet use, which is problematic as the Internet becomes a significant arena for political, social and commercial activities necessary for full participation in a liberal (...) democracy. The Categorical Imperative lifts up trust as a fundamental component of human ethical virtues – first of all, because deception and coercion, the antitheses of trust, cannot be universalized. Mistrust is, according to Kant, a natural component of human nature, as we are social beings dependent on recognition by others but also prone to deceiving others. Only in true friendships can this tendency be overcome and give room for unconditional trust. Still we can argue that Kant must hold that trustworthy behaviour as well as trust in others is obligatory, as expressions of respect for humanity. The Kantian approach integrates political and ethical aspects of trust, showing that protecting the external activities of citizens is required in order to act morally. This means that security measures, combined with specific regulations are important preconditions for building online trust, providing an environment enabling people to act morally and for trust-based relationships. (shrink)

A system of logic usually comprises a language for which a model-theory and a proof-theory are defined. The model-theory defines the semantic notion of model-theoretic logical consequence (⊨), while the proof-theory defines the proof- theoretic notion of logical consequence (or logical derivability, ⊢). If the system in question is sound and complete, then the two notions of logical consequence are extensionally equivalent. The concept of full formalization is a more restrictive one and requires in addition the preservation of the standard (...) meanings of the logical terms in all the admissible interpretations of the logical calculus, as it is proof-theoretically defined. Although classical first-order logic is sound and complete, its standard formalizations fall short to be full formalizations since they allow non-intended interpretations. This fact poses a challenge for the logical inferentialism program, whose main tenet is that the meanings of the logical terms are uniquely determined by the formal axioms or rules of inference that govern their use in a logical calculus, i.e., logical inferentialism requires a categorical calculus. This paper is the first part of a more elaborated study which will analyze the categoricity problem from its beginning until the most recent approaches. I will first start by describing the problem of a full formalization in the general framework in which Carnap (1934/1937, 1943) formulated it for classical logic. Then, in sections IV and V, I shall discuss the way in which the mathematicians B.A. Bernstein (1932) and E.V. Huntington (1933) have previously formulated and analyzed it in algebraic terms for propositional logic and, finally, I shall discuss some critical reactions Nagel (1943), Hempel (1943), Fitch (1944), and Church (1944) formulated to these approaches. (shrink)

Categorical loudness scaling (CLS) measures provide useful information about an individual’s loudness perception across the dynamic range of hearing. A probability model of CLS categories has previously been described as a multi-category psychometric function (MCPF). In the study, a representative “catalog” of potential listener MCPFs was used in conjunction with maximum-likelihood estimation to derive CLS functions for participants with normal hearing and with hearing loss. The approach of estimating MCPFs for each listener has the potential to improve the accuracy (...) of the CLS measurements, particularly when a relatively low number of data points are available. The present study extends the MCPF approach by using Bayesian inference to select stimulus parameters that are predicted to yield maximum expected information (MEI) during data collection. The accuracy and reliability of the MCPF-MEI approach were compared to the standardized CLS measurement procedure (ISO16832:2006). A non-adaptive, fixed-level, paradigm served as a “gold-standard” for this comparison. The test time required to obtain measurements in the standard procedure is a major barrier to its clinical uptake. Test time was reduced from approximately 15 minutes to approximately 3 minutes with the MEI-adaptive procedure. Results indicated that the test-retest reliability and accuracy of the MCPF-MEI adaptive procedures were similar to the standardized CLS procedure. Computer simulations suggest that the reliability and accuracy of the MEI procedure were limited by intrinsic uncertainty of the listeners represented in the MCPF catalog. In other words, the MCPF provided insufficient predictive power to significantly improve adaptive-tracking efficiency under practical conditions. Concurrent optimization of both the MCPF catalog and the MEI-adaptive procedure have the potential to produce better results. Regardless of the adaptive-tracking method used in the CLS procedure, the MCPF catalog remains clinically useful for enabling maximum-likelihood determination of loudness categories. (shrink)

We develop a general covariant categorical modeling theory of natural systems’ behavior based on the fundamental functorial processes of representation and localization-globalization. In the first part of this study we analyze the process of representation. Representation constitutes a categorical modeling relation that signifies the semantic bidirectional process of correspondence between natural systems and formal symbolic systems. The notion of formal systems is substantiated by algebraic rings of observable attributes of natural systems. In this perspective, the distinction between simple (...) and complex systems is reflected in the appropriate qualification of their corresponding rings of observables. The crucial distinguishing requirement with respect to the coordinatizing rings of observables has to do with the property of global commutativity. The global information structure representing the behavior of a complex system is modeled functorially in terms of its Spectrum functor. Due to the fact that, the fundamental process of representation is bidirectional by construction, it admits a precise categorical formulation in terms of the syntactic language of adjoint functors, constituting thus, a categorical adjunction. The left adjoint functor of this adjunction signifies the process of encoding the information related with phenomena of natural systems in terms of coordinatizing rings of observables, whereas, the right adjoint functor signifies the inverse process of information decoding, which, can be used for making predictions about the behavior of natural systems. (shrink)

In proof-theoretic semantics, model-theoretic validity is replaced by proof-theoretic validity. Validity of formulae is defined inductively from a base giving the validity of atoms using inductive clauses derived from proof-theoretic rules. A key aim is to show completeness of the proof rules without any requirement for formal models. Establishing this for propositional intuitionistic logic raises some technical and conceptual issues. We relate Sandqvist’s (complete) base-extension semantics of intuitionistic propositional logic to categorical proof theory in presheaves, reconstructing categorically the (...) soundness and completeness arguments, thereby demonstrating the naturality of Sandqvist’s constructions. This naturality includes Sandqvist’s treatment of disjunction that is based on its second-order or elimination-rule presentation. These constructions embody not just validity, but certain forms of objects of justifications. This analysis is taken a step further by showing that from the perspective of validity, Sandqvist’s semantics can also be viewed as the natural disjunction in a category of sheaves. (shrink)

Moral requirements apply to rational agents as such. But it is a conceptual truth that if agents are morally required to act in a certain way then we expect them to act in that way. Being rational, as such, must therefore suffice to ground our expectation that rational agents will do what they are morally required to do. But how could this be so? It could only be so if we think of the moral requirements that apply to agents as (...) themselves categorical requirements of rationality or reason. For the only thing we can legitimately expect of rational agents as such is that they do what they are rationally required to do (Smith 1994: 85). (shrink)

Regulations implemented by World Athletics (WA) require female athletes with differences of sexual development to suppress their blood testosterone levels in order to participate in certain women’s sporting competitions. These regulations have been justified by reference to fairness. In this paper, we reconstruct WA’s understanding of fairness, which requires a “level playing field” where no athlete should have a significant performance advantage based on factors other than talent, dedication, and hard work over an average athlete in their category. We demonstrate (...) that by placing regulations only on testosterone levels, while ignoring physical as well as socioeconomic advantages, WA consistently fails to meet its own definition of fairness. We then discuss several ways in which this definition could be met. Our analysis shows that a categorical system, in which athletes are divided into categories based on properties leading to significant performance advantages, is best suited for meeting WA’s definition of fairness. (shrink)

This paper explores the relevance of Kant's categorical imperative to military ethics and the solution it suggests for improving the treatment of women in the military. The second formulation of the categorical imperative makes universal respect for humanity a moral requirement by asserting that one must always treat other people as means in themselves and never as merely means to an end. This principle is a promising guide for military ethics and can be reconciled with the acts (...) of violence required by war. This paper argues that it can also regulate soldiers? relations to each other and that it may contribute to reorienting military culture in a way that overcomes the biases against female military personnel. (shrink)

The paper addresses the capabilities and limitations of extrafoveal processing during a categorical visual search. Previous research has established that a target could be identified from the very first or without any saccade, suggesting that extrafoveal perception is necessarily involved. However, the limits in complexity defining the processed information are still not clear. We performed four experiments with a gradual increase of stimuli complexity to determine the role of extrafoveal processing in searching for the categorically defined geometric shape. The (...) series of experiments demonstrated a significant role of extrafoveal processing while searching for simple two‐dimensional shapes and its gradual decrease in a condition with more complicated three‐dimensional shapes. The factors of objects’ spatial orientation and distractor homogeneity significantly influenced both reaction time and the number of saccades required to identify a categorically defined target. An analysis of the individual p‐value distributions revealed pronounced individual differences in using extrafoveal analysis and allowed examination of the performance of each particular participant. The condition with the forced prohibition of eye movements enabled us to investigate the efficacy of covert attention in the condition with complicated shapes. Our results indicate that both foveal and extrafoveal processing are simultaneously involved during a categorical search, and the specificity of their interaction is determined by the spatial orientation of objects, type of distractors, the prohibition to use overt attention, and individual characteristics of the participants. (shrink)

In this book the authors reconcile two different viewpoints of the foundations of mathematics, namely mathematical logic and category theory. In Part I, they show that typed lambda-calculi, a formulation of higher order logic, and cartesian closed categories are essentially the same. In Part II, it is demonstrated that another formulation of higher order logic is closely related to topos theory. Part III is devoted to recursive functions. Numerous applications of the close relationship between traditional logic and the algebraic language (...) of category theory are given. The authors have included an introduction to category theory and develop the necessary logic as required, making the book essentially self-contained. Detailed historical references are provided throughout, and each section concludes with a set of exercises. Thus it is well-suited for graduate courses and research in mathematics and logic. Researchers in theoretical computer science, artificial intelligence and mathematical linguistics will also find this an accessible introduction to a subject of increasing application to these disciplines. (shrink)

Is logical consistency required for a set of beliefs or propositions to be categorically coherent? An affirmative answer is often assumed by mainstream epistemologists, and yet it is unclear why. Cases like the lottery and the preface call into question the assumption that beliefs must be consistent in order to be epistemically rational. And thus it is natural to wonder why all inconsistent sets of propositions are incoherent. On the other hand, Easwaran and Fitelson have shown that particular kinds of (...) inconsistency entail the epistemically ‘irrationality’ of holding certain sets of beliefs. In cases of the latter kind of inconsistency, it seems more reasonable to insist that such sets of beliefs or propositions are categorically incoherent. What the precise relationship is between coherence and consistency depends on the nature of the coherence relation. We shall examine recent attempts to explicate the coherence relation in terms of probabilistic measures of confirmation or agreement to see what they can teach us about the relationship between coherence and consistency. We shall show that some probabilistic measures of coherence allow for inconsistent sets to be categorically coherent, while satisfying plausible epistemic rationality constraints. Other probabilistic measures of coherence impose very strong logical consistency requirements, and some measures are tolerant of most forms of inconsistency. As we try to understand what distinguishes coherence measures in this respect, we will also draw some important lessons about Bayesian confirmation measures and differences in the way that they treat contradictory propositions. (shrink)

Idempotency requires any phonotactically licit forms to be faithfully realized. Output-drivenness requires any discrepancies between underlying and output forms to be driven exclusively by phonotactics. These formal notions are relevant for phonological theory and play a crucial role in learnability. Tesar and Magri provide tight guarantees for OT output-drivenness and idempotency through conditions on the faithfulness constraints. This paper derives analogous faithfulness conditions for HG idempotency and output-drivenness and develops an intuitive interpretation of the various OT and HG faithfulness conditions (...) thus obtained. The intuition is that faithfulness constraints measure the phonological distance between underlying and output forms. They should thus comply with a crucial axiom of the definition of distance, namely that any side of a triangle is shorter than the sum of the other two sides. This intuition leads to a faithfulness triangle inequality which is shown to be equivalent to the faithfulness conditions for idempotency and output-drivenness. These equivalences hold under various assumptions, crucially including McCarthy’s :75–138, 2003b) generalization that constraints are all categorical. (shrink)

Claims about what justice “requires” and the “requirements” of justice are pervasive in political philosophy. However, there is a highly significant ambiguity in such claims that appears to have gone unnoticed. Such claims may pick out either one of two categorically distinct and noncoextensive kinds of requirement that we call 1) requirements-as-necessary-conditions for justice and 2) requirements-as-demands of justice. This is an especially compelling instance of an ambiguity that John Broome has famously observed in the context of claims about (...) other requirements (notably the requirements of rationality and morality). But it appears to have been overlooked by political philosophers in the case of claims about the requirements of justice. The ambiguity is highly significant inasmuch as failing to notice it is liable to distort our normative thinking about politics and make us vulnerable to certain kinds of normatively consequential errors: both mistakenly drawing inferences about what justice demands of us from claims that certain states or societies are not just; and mistakenly drawing inferences about what states or societies are or would be just from claims that justice does not demand of states or societies that they do certain things. Paying greater attention to the distinction between these two different kinds of requirements and the ways in which they come apart is helpful, not merely in avoiding these distortions and errors, but also in resolving, or at least clarifying, a number of other notoriously murky meta-normative debates, especially various important debates about realism and idealism in political philosophy. (shrink)

Tae Wan Kim, John Hooker, and Thomas Donaldson make an attempt, in recent articles, to solve the alignment problem. As they define the alignment problem, it is the issue of how to give AI systems moral intelligence. They contend that one might program machines with a version of Kantian ethics cast in deontic modal logic. On their view, machines can be aligned with human values if such machines obey principles of universalization and autonomy, as well as a deontic utilitarian principle. (...) Programming machines to do so might be useful, in their view, for applications such as future autonomous vehicles. Their proposal draws both on traditional logic-based and contemporary connectionist approaches, to fuse factual information with normative principles. I will argue that this approach makes demands of machines that go beyond what is currently feasible, and may extend past the limits of the possible for AI. I also argue that a deontological ethics for machines should place greater stress on the formula of humanity of the Kantian categorical imperative. On this principle, one ought never treat a person as a mere means. Recognition of what makes a person a person requires ethical insight. Similar insight is needed to tell treatment as a means from treatment as a mere means. The resources in Kim, Hooker, and Donaldson’s approach is insufficient for this reason. Hesitation regarding deployment of autonomous machines is warranted in light of these alignment concerns. (shrink)

I offer and develop an original answer to the question of whether emotion plays an important role in the formation of moral thought. In a nutshell, my answer will be that if motivational internalism provides us with a correct description of the nature of moral thought, then emotion plays an important role because emotion is required to explain or ground the behavioral dispositions that are involved in moral thought.

A new book by Stephen Engstrom repeats a criticism of Bruce Aune's of Kant's derivation of the universalizability formula of the categorical imperative. The criticism is that Kant omitted at least one substantive premise in the derivation of the formula: ‘Act only on that maxim through which you can at the same time will that it become a universal law.’ The grounds for the formula that are given in the Groundwork of the Metaphysics of Morals, however, are said to (...) support only a weaker requirement, namely, that a maxim conform to a universal law. Hence, Kant omits at least one necessary substantive premise of the derivation. This paper attempts to show that nothing substantive is omitted from the argument. It only needs two principles of inference that it is assumed add nothing substantive to the premises. (shrink)

The motivation of this paper is to contribute to the project of finding new ways to use "utopia" in philosophy again. Since philosophers as well as poets can look to their forbears for inspiration in re-inventing terms, it would be nice if those of us trying to rehabilitate the term could lean a bit on our own disciplinary heavies, especially in the current climate of philosophical skepticism, even cynicism, about the very idea of utopia. My contribution to that task here (...) will be to present a vision of utopian commitment that I see taking shape in the interface between Kant's ethics and aesthetics. This vision is broadly speaking a moral one, insofar as it describe the barriers to, but also the necessary conditions of, human motivation to strive for the creation of a just society in the real world. But turning to Kant's ethics as a model for a theory of utopia requires some explanation. After all, his moral theory, when it takes into account the really existing conditions of human existence, appears to do so only to dismiss them as obstacles or diversions in the path of correct moral judgment. When he discusses human community, it is often to dismiss it as driven by self-interest and and an "each against all" struggle that can be responsibly regulated but never eliminated. At best this "unsocial sociability" might be evidence for a hypothetical natural purpose: human strife and misery is a mechanical force driving the progress of our talents and capacities in the long evolutionary run.1 But this is hardly a utopian vision in the sense in which we would wish to see a well-regulated society be.. (shrink)

What is meant under the genuine title of Aristotle’s ta Analytika is rarely properly understood. Presumably, his analytics was inspired by the method of geometric analysis. For Aristotle, this was a regressive or heuristic procedure, departing from a proposed conclusion and asking which premises could be found in order to syllogize, demonstrate or explain it. The terms that form categorical and modal propositions play a fundamental role in analytics. Aristotle introduces letters in lieu of the triples of terms constitut­ing (...) the propositions and the three syllogistic figures that schematize them. His formulation of the three syllogistic figures refers to a syntacti­cal and predicative order and position of the triples of terms, arranged in some diagrammed schemata, which, regrettably, are missing from the extant text of the Prior Analytics. Considering planar and graphic arrangements, both vertical and horizontal orders as well as the posi­tion of the three terms involved, we propose a reconstruction, at least to some extent, of these probable lettered diagrams. In such reconstructed diagrams, we can appropriately capture the definition of syllogism as a predicative connexion of terms, and easier survey a synoptic account of all valid predicative relations and transpositions, and also reduce the imperfect syllogisms into the moods of the first figure. Aristotle’s syllogistic is an analytical calculation of terms, understood as predicates and subjects within the categorical propositions, and more precisely of three terms schematized in three figures in predicative links such that, by means of a middle, follows from necessity a conclusion of the extreme terms. The necessity of the consequence is not based on the implication or inference of the propositions, but on a predictive transi­tivity through the middle term within the syllogistic figures. Syllogism must draw its conclusion through the way its terms are predicated of one another. Aristotle in his Prior Analytics developed also a complex account of modal syllogisms within necessity and possibility of belonging. This account involves also such an analyti­cal reduction to the syllogistic figures. In this analytical perspective, we try to throw some light on his modal syllogisms, although this difficult and nowadays thoroughly discussed topic would require a much wider treatment. (shrink)

Rosen's modelling relations constitute a conceptual schema for the understanding of the bidirectional process of correspondence between natural systems and formal symbolic systems. The notion of formal systems used in this study refers to information structures constructed as algebraic rings of observable attributes of natural systems, in which the notion of observable signifies a physical attribute that, in principle, can be measured. Due to the fact that modelling relations are bidirectional by construction, they admit a precise categorical formulation in (...) terms of the category-theoretic syntactic language of adjoint functors, representing the inverse processes of information encoding/decoding via adjunctions. As an application, we construct a topological modelling schema of complex systems. The crucial distinguishing requirement between simple and complex systems in this schema is reflected with respect to their rings of observables by the property of global commutativity. The global information structure representing the behaviour of a complex system is modelled functorially in terms of its spectrum functor. An exact modelling relation is obtained by means of a complex encoding/decoding adjunction restricted to an equivalence between the category of complex information structures and the category of sheaves over a base category of partial or local information carriers equipped with an appropriate topology. (shrink)

According to the Lockean thesis, a proposition is believed just in case it is highly probable. While this thesis enjoys strong intuitive support, it is known to conflict with seemingly plausible logical constraints on our beliefs. One way out of this conflict is to make probability 1 a requirement for belief, but most have rejected this option for entailing what they see as an untenable skepticism. Recently, two new solutions to the conflict have been proposed that are alleged to (...) be non-skeptical. We compare these proposals with each other and with the Lockean thesis, in particular with regard to the question of how much we gain by adopting any one of them instead of the probability 1 requirement, that is, of how likely it is that one believes more than the things one is fully certain of. (shrink)

Triage situations and other occurrences in which rationing of medical care is necessary require careful distribution of medical equipment, services, or resources. However, the evolution of triage has failed to eliminate certain biases in the standards of care, particularly for groups already facing societal disenfranchisement and discrimination. This article explores the use of triage calculators and other systems of rationing care, their implicit biases, and how to avoid allowing those biases to influence care.

We address the classification of the possible finitely-additive probability measures on the Boolean algebra of definable subsets of M which are invariant under the natural action of $\operatorname{Aut}(M)$ . This pursuit requires a generalization of Shelah's forking formulas [8] to "essentially measure zero" sets and an application of Myer's "rank diagram" [5] of the Boolean algebra under consideration. The classification is completed for a large class of ℵ 0 -categorical structures without the independence property including those which are stable.

A defense of Kant’s moral philosophy. The author seeks to counteract those interpretations of Kant that restrict their focus to the Groundwork of the Metaphysics of Morals. He argues that one must look at the whole of Kant’s writings, the earlier and later ethical writings as well as the theoretical works. This makes it possible for him to challenge the popular misconceptions of Kant’s teaching: the overemphasis on the correct motive of an action, the mistaken impression that consequences are of (...) no consequence when evaluating the moral worth of an act, and the overattention paid to logical contradiction as the test of a maxim’s morality. The Groundwork is not simply a conclusion of Kant’s early reflections on morality, but it also represents a new departure whose full significance is not seen until the later works. With the Groundwork Kant realizes that morality cannot be established on the grounds set out by the Critique of Pure Reason but requires an independent foundation. His new concept of practical necessity represents a revolution in morality. It is a mistake, then, to read the practical philosophy solely in the light of the theoretical critique. Though founded on a blind "fact of reason," Kant’s teaching is yet not abstract, overly formalistic, or rigoristic. "One must go through all the different formulas [of the categorical imperative] to understand the concept of moral judgment". Rossvaer’s rethinking brings him to stress that "the categorical imperative has no validity beyond being the form of... sensuous striving". This contention that the intellectual and sensuous faculties are not to be radically divorced leads to the ultimate intent of Rossvaer’s work. He argues that the categorical imperative is a principle of execution and only assumes its fullest form in a social philosophy. Consideration of Kant’s notion of the highest good, especially as it is developed in the later works on religion and history, allows Rossvaer to argue for the social and historical relevance of Kant’s teaching. "Since the highest good cannot be justified within an individualistic perspective, but only within a philosophy which takes up society as a problem, morality is meaningless from a human point of view unless we consider ourselves obligated to realize a universal, ethical community". With this, the kingdom of ends is transformed into an historical idealism, practical philosophy becomes a theory of action, and Kant turns out to be not so different from his detractors, Fichte, Hegel, Marx, Habermas, and others. Yet the historicization of the moral agent is yet not complete in Kant. The moral agent retains his critical standpoint, that is the distinction between rationality and the social system. Yet one is brought to ask how this critical distance can be maintained. To what extent does Kant’s overstepping the bounds of theoretical reason also entail the loss of that critical validity won by the first Critique? And, if one is forced in the end to justify one’s practical philosophy only by a social philosophy which does not find its foundation in a theoretical critique, then is the original fear of the first Critique confirmed, that morality may be meaningless after all? (shrink)

Can we ever be fully practically justified in acting contrary to moral demands? My contention is that the answer is 'no'. I argue that by adopting a 'buck-passing' account of wrongness we can provide a philosophically satisfying answer to the familiar 'why should I be moral?'. In working my way toward the buck-passing account of wrongness, I outline the metaethical and 'metanormative' assumptions on which my theory stands. I also consider and reject the 'internalist' answer to 'why should I be (...) moral?'. The account I end up with is decidedly non-consequentialist and it is consistent with common-sense morality. It also provides a way of showing why moral considerations are overridingly normative in a way that is consistent with our best current understanding of what practical reason requires of us. (shrink)

The bulk of the literature concerning the governing role of non-Humean laws has been concentrated on the alleged incapability of higher order nomic facts to determine the regularities in the behaviour of actual objects, the so-called Inference Problem. Most recently Ioannidis, Livanios and Psillos (2021) argue that an adequate solution to the Inference Problem requires an answer to the question of how nomic relations manage to ‘tell’ properties what to do. Ioannidis et al. dub the difficulty that all extant accounts (...) of governing laws face to give such an answer, the Governing Problem and introduce a Dualist Model, according to which the specific behaviour of things in the world is the outcome of both the thin powers things have to be subjected to laws, and certain nomic features of the world. The aim of this paper is to show that the most plausible form of the Dualist Model can provide the basis for a novel version of the Powerful Qualities View about properties. To this end it presents ways of developing two aspects of the Dualist Model. It defends the view that nomic relations must be relata-specific in order to play their theoretical role within the Model and provides arguments for the view that natural properties should have the minimum (compatible with the core tenets of the Model) modal strength. (shrink)

Versions and extensions of intuitionistic and modal logic involving biHeyting and bimodal operators, the axiom of constant domains and Barcan's formula, are formulated as structured categories. Representation theorems for the resulting concepts are proved. Essentially stronger versions, requiring new methods of proof, of known completeness theorems are consequences. A new type of completeness result, with a topos theoretic character, is given for theories satisfying a condition considered by Lawvere . The completeness theorems are used to conclude results asserting that certain (...) logics are conservatively interpretable in others. (shrink)

Recent work on compositional distributional models shows that bialgebras over finite dimensional vector spaces can be applied to treat generalised quantifiersGeneralised quantifiers for natural language. That technique requires one to construct the vector space over powersets, and therefore is computationally costly. In this paper, we overcome this problem by considering fuzzy versions of quantifiers along the lines of ZadehZadeh, L. A., within the category of many valued relationsMany valued relations. We show that this category is a concrete instantiation of the (...) compositional distributional model. We show that the semantics obtained in this model is equivalent to the semantics of the fuzzy quantifiers of ZadehZadeh, L. A.. As a result, we are now able to treat fuzzy quantification without requiring a powerset construction. (shrink)

This essay argues that the necessary and sufficient evaluative condition for the justification of moral claims is a religious principle. Self-conscious choice entails a comprehensive variable in terms of which all possible human choice alternatives may be understood. This same variable must also be evaluative, such that human choices which are superior in its terms are categorically required and it is the necessary and sufficient evaluative condition for the justification of moral claims. Moreover, the comprehensive variable in question must be (...) a metaphysical variable in terms of which all conceivable instances of concrete existence are understood and evaluated. Appropriating Clifford Geertz, I stipulate that a variable or principle which identifies fact with value at the most fundamental level is religious. (shrink)

This chapter develops a theory of categorical normativity, of those principles that have authority over us regardless of our ends and interests. It argues that there is an intimate connection between these norms and the conditions of agency. In this respect, it offers a version of constitutivism. But the version of constitutivism defended is unique in a few respects. First, it is naturalistic: agency is an emergent property, like the properties of biology and economics. Second, it is social: agency (...) is something constructed by the complex interaction of agents. And third, it supports the normativity of a particular contractualist procedure: adhering to Kant’s Formula of the Realm of Ends is a condition on agency, and so a categorical requirement. (shrink)

Smith has defended the rationalist's conceptual claim that moral requirements are categorical requirements of reason, arguing that no status short of this would make sense of our taking these requirements as seriously as we do. Against this I argue that Smith has failed to show either that our moral commitments would be undermined by possessing only an internal, contextual justification or that they need presuppose any expectation that rational agents must converge on their acceptance. His claim that this rationalistic (...) understanding of metaethics is required for the intelligibility of moral disagreement is also found to be inadequately supported. It is further proposed that the rationalist's substantive claims – that therearesuch categorical requirements of reason and that our actual moral commitments are a case in point – are liable to disappointment; and that the conceptual claim is fatally undermined by reflection on how we might best respond to such disappointment. (shrink)