A good argument is one whose conclusions follow from its premises; its conclusions are consequences of its premises. But in what sense do conclusions follow from premises? What is it for a conclusion to be a consequence of premises? Those questions, in many respects, are at the heart of logic (as a philosophical discipline). Consider the following argument: 1. If we charge high fees for university, only the rich will enroll. We charge high fees for university. Therefore, only the (...) rich will enroll. There are many different things one can say about this argument, but many agree that if we do not equivocate (if the terms mean the same thing in the premises and the conclusion) then the argument is valid, that is, the conclusion follows deductively from the premises. This does not mean that the conclusion is true. Perhaps the premises are not true. However, if the premises are true, then the conclusion is also true, as a matter of logic. This entry is about the relation between premises and conclusions in valid arguments. (shrink)

One of the great successes in the study of language has been the application of formal methods, including those of formal logic. Even so, this chapter argues against one way of accounting for this success, by arguing that the study of natural language semantics and of logical consequence relations are not the same. There is indeed a lot we can glean about logic from looking at our languages, and at our inferential practices, but the semantic properties of natural languages (...) do not determine genuine logical consequence relations. We can get from natural language semantics to logical consequence, but only by a significant process of identification of logical constants, abstraction, and idealization. The chapter also discusses different approaches to the nature of logical consequence, and examines which allow logic and natural language to come closer together. (shrink)

In his classic 1936 essay "On the Concept of Logical Consequence", Alfred Tarski used the notion of satisfaction to give a semantic characterization of the logical properties. Tarski is generally credited with introducing the model-theoretic characterization of the logical properties familiar to us today. However, in his book, The Concept of Logical Consequence, Etchemendy argues that Tarski's account is inadequate for quite a number of reasons, and is actually incompatible with the standard model-theoretic account. Many of his criticisms (...) are meant to apply to the model-theoretic account as well. In this paper, I discuss the following four critical charges that Etchemendy makes against Tarski and his account of the logical properties: (1) (a) Tarski's account of logical consequence diverges from the standard model-theoretic account at points where the latter account gets it right. (b) Tarski's account cannot be brought into line with the model-theoretic account, because the two are fundamentally incompatible. (2) There are simple counterexamples (enumerated by Etchemendy) which show that Tarski's account is wrong. (3) Tarski committed a modal fallacy when arguing that his account captures our pre-theoretical concept of logical consequence, and so obscured an essential weakness of the account. (4) Tarski's account depends on there being a distinction between the "logical terms" and the "non-logical terms" of a language, but (according to Etchemendy) there are very simple (even first-order) languages for which no such distinction can be made. Etchemendy's critique raises historical and philosophical questions about important foundational work. However, Etchemendy is mistaken about each of these central criticisms. In the course of justifying that claim, I give a sustained explication and defense of Tarski's account. Moreover, since I will argue that Tarski's account and the model theoretic account really do come to the same thing, my subsequent defense of Tarski's account against Etchemendy's other attacks doubles as a defense against criticisms that would apply equally to the familiar model-theoretic account of the logical properties. (shrink)

This paper contains a detailed account of the notion of admissibility in the setting of consequence relations. It is proved that the two notions of admissibility used in the literature coincide, and it provides an extension to multi–conclusion consequence relations that is more general than the one usually encountered in the literature on admissibility. The notion of a rule scheme is introduced to capture rules with side conditions, and it is shown that what is generally understood under the (...) extension of a consequence relation by a rule can be extended naturally to rule schemes, and that such extensions capture the intuitive idea of extending a logic by a rule. (shrink)

Recent work in philosophical logic has taken interesting and unexpected turns. It has seen not only a proliferation of logical systems, but new applications of a wide range of different formal theories to philosophical questions. As a result, philosophers have been forced to revisit the nature and foundation of core logical concepts, chief amongst which is the concept of logical consequence. This essay sets the contributions of the volume in context and identifies how they advance important debates within the (...) philosophy of logic. (shrink)

In this paper I ask what logical consequence is, and give an answer that is somewhat different from the usual ones. It isn’t clear why anyone would need a new approach to logical consequence, so I begin by explaining the work that I need the answer to do and why the standard conceptions aren’t adequate. Then I articulate a replacement view which is.

The standard semantic definition of consequence with respect to a selected set X of symbols, in terms of truth preservation under replacement (Bolzano) or reinterpretation (Tarski) of symbols outside X, yields a function mapping X to a consequence relation ⇒x. We investigate a function going in the other direction, thus extracting the constants of a given consequence relation, and we show that this function (a) retrieves the usual logical constants from the usual logical consequence relations, and (...) (b) is an inverse to—more precisely, forms a Galois connection with—the Bolzano-Tarski function. (shrink)

Large language model (LLM) agents are increasingly deployed in sequential decision-making pipelines where each action irrevocably modifies the environment. Existing agentic architectures commit to action sequences generated by the LLM without systematically evaluating the downstream consequences of those sequences prior to execution - a fundamental gap that amplifies risk and limits accountability. We introduce Consequence-Aware Agentic AI (CA2I), a formal framework that augments the standard generate-then-execute paradigm with a dedicated Consequence Assessment Module (CAM). CAM evaluates every candidate action (...) sequence against a historical consequence model and selects the sequence whose predicted outcome optimally balances return and risk before any irreversible action is taken. We formalise the framework as a constrained sequential decision problem and prove that, under mild stationarity assumptions, Sharpe-ratio-based selection dominates random selection in expectation. To validate the framework empirically, we instantiate CA2I in the domain of LLM-driven financial trading strategy selection, using GPT-5.4 to generate five candidate strategies per asset and a backtesting engine as the consequence model. Experiments on ten diversified US equities over a strictly held-out three-month out-of-sample window (August--October~2025) demonstrate that CA2I achieves a mean test-period Sharpe ratio of 0.51 - a 4.25 times improvement over random strategy selection (Sharpe = 0.12, p = 0.041) - while reducing mean maximum drawdown relative to buy-and-hold by 18%. Sensitivity analysis confirms selection stability: Sharpe-ratio and Calmar-ratio selection agree on 100% of strategy choices across all ten assets. We further demonstrate that CA2I provides a concrete, computationally tractable pathway toward Responsible AI in agentic systems: by making consequence evaluation an explicit, auditable, and mathematically grounded architectural step, the framework operationalises transparency, accountability, and harm avoidance as mandated by the EU AI Act, NIST AI Risk Management Framework, and IEEE Ethically Aligned Design standards. (shrink)

We generalize the notion of consequence relation standard in abstract treatments of logic to accommodate intuitions of relevance. The guiding idea follows the use criterion, according to which in order for some premises to have some conclusion(s) as consequence(s), the premises must each be used in some way to obtain the conclusion(s). This relevance intuition turns out to require not just a failure of monotonicity, but also a move to considering consequence relations as obtaining between multisets. We (...) motivate and state basic definitions of relevant consequence relations, both in single conclusion (asymmetric) and multiple conclusion (symmetric) settings, as well as derivations and theories, guided by the use intuitions, and prove a number of results indicating that the definitions capture the desired results (at least in many cases). (shrink)

This chapter scrutinizes the Consequence Argument for the incompatibility of free will and determinism within an interventionist causal-modelling framework. Traditional discussions of the argument presuppose that causal reasoning concerns the temporal evolution of total states of the universe. By contrast, interventionism focuses on how local, small-scale systems evolve according to causal generalizations that fall short of being laws. It also assigns an important role to interventions: external influences on a system that disrupt the causal generalizations which apply to it. (...) When the Consequence Argument is recast in interventionist terms, the argument can be seen to rely on a false premise. In particular, interventionism supports at most a qualified variant of determinism, which is insufficient for the Consequence Argument to go through. Finally, the chapter compares the present response to the argument with David Lewis’s local miracle compatibilism. (shrink)

Logic, the tradition has it, is normative for reasoning. But is that really so? And if so, in what sense is logic normative for reasoning? As Gilbert Harman has reminded us, devising a logic and devising a theory of reasoning are two separate enterprises. Hence, logic's normative authority cannot reside in the fact that principles of logic just are norms of reasoning. Once we cease to identify the two, we are left with a gap. To bridge the gap one would (...) need to produce what John MacFarlane has appropriately called a bridge principle, i.e. a general principle articulating a substantive and systematic link between logical entailment and norms of reasoning. This is Harman's skeptical challenge. In this paper I argue that Harman's skeptical challenge can be met. I show how candidate bridge principles can be systematically generated and evaluated against a set of well‐motivated desiderata. Moreover, I argue that bridge principles advanced by MacFarlane himself and others, for all their merit, fail to address the problem originally set forth by Harman and so do not meet the skeptical challenge. Finally, I develop a bridge principle that meets Harman's requirements as well as being substantive. (shrink)

We characterize all finitary consequence relations over S4.3, both syntactically, by exhibiting so-called passive rules that extend the given logic, and semantically, by providing suitable strongly adequate classes of algebras. This is achieved by applying an earlier result stating that a modal logic L extending S4 has projective unification if and only if L contains S4.3. In particular, we show that these consequence relations enjoy the strong finite model property, and are finitely based. In this way, we extend (...) the known results by Bull and Fine, from logics, to consequence relations. We also show that the lattice of consequence relations over S4.3 is countable and distributive and it forms a Heyting algebra. (shrink)

Consequence rleations over sets of "judgments" are defined by using "overdetermined" as well as "underdetermined" valuations. Some of these relations are shown to be categorical. And generalized soundness and completeness results are given for both multiple and single conclusion consequence relations.

Peter van Inwagen’s original formulation of the Consequence Argument employed an inference rule that was shown to be invalid given van Inwagen’s interpretation of the modal operators in the Consequence Argument. In response, van Inwagen recently suggested a revised interpretation of his modal operators. Following up on a debate between Blum and Schnieder, I analyze van Inwagen’s revised interpretation in terms of explanatory notions and I argue that van Inwagen faces a dilemma: he either has to admit that (...) beta entails fatalism, or he has to admit that a new counterexample invalidates beta. Either way, it seems reasonable to reject beta and to conclude that the Consequence Argument fails. Further, I argue that Widerker’s well-known substitute for rule beta is faced with a similar dilemma and, therefore, is bound to fail as well. I conclude that, if the modal operators are interpreted in terms of explanatory notions, neither van Inwagen’s nor Widerker’s rule of inference turns out to be valid. (shrink)

Contrastivists view ought-sentences as expressing comparisons among alternatives. Deontic actualists believe that the value of each alternative in such a comparison is determined by what would actually happen if that alternative were to be the case. One of the arguments that motivates actualism is a challenge to the principle of agglomeration over conjunction—the principle according to which if you ought to run and you ought to jump, then you ought to run and jump. I argue that there is no way (...) of developing the actualist insight into a logic that invalidates the agglomeration principle without also invalidating other desirable patterns of inference. After doing this, I extend the analysis to other contrastive views that challenge agglomeration in the way that the actualist does. This motivates skepticism about the actualist’s way of challenging agglomeration. (shrink)

The Consequence Argument has elicited various responses, ranging from acceptance as obviously right to rejection as obviously problematic in one way or another. Here we wish to focus on one specific response, according to which the Consequence Argument begs the question. This is a serious accusation that has not yet been adequately rebutted, and we aim to remedy that in what follows. We begin by giving a formulation of the Consequence Argument. We also offer some tentative proposals (...) about the nature of begging the question. Although the charge of begging the question is frequently made in philosophy, it is surprisingly difficult to pin down the precise nature of this dialectical infelicity (or family of such infelicities). Thus we offer some new proposals about the nature of begging the question with an eye to understanding what is going on in central cases in which the charge is legitimately made. We then defend the Consequence Argument against the charge that it begs the question, so construed. We contend that, whatever the other liabilities of the argument may be, it does not beg the question against the compatibilist. (shrink)

_ Source: _Volume 56, Issue 3-4, pp 292 - 319 With William of Ockham and John Buridan, Walter Burley is often listed as one of the most significant logicians of the medieval period. Nevertheless, Burley’s contributions to medieval logic have received notably less attention than those of either Ockham or Buridan. To help rectify this situation, the author here provides a comprehensive examination of Burley’s account of consequences, first recounting Burley’s enumeration, organization, and division of consequences, with particular attention to (...) the shift from natural and accidental to formal and material consequence, and then locating Burley’s contribution to the theory of consequences in the context of fourteenth-century work on the subject, detailing its relation to the earliest treatises on consequences, then to Ockham and Buridan. (shrink)

Background: Discrimination in nursing has led to the formation of some taboos that often impact the individual’s professional development. Nurses use strategies to overcome discrimination that can lead to consequences. Research objective: This study assessed nurses’ experiences to explore the consequences of Iranian nurses’ strategies to overcome intra-professional discrimination. Research design: This qualitative content analysis study employed purposive sampling to reach 25 nurses working at educational hospitals in Tehran, Tabriz, and Ilam, Iran. The data were collected using deep and unstructured (...) interviews along with notes in a period of time between April 2016 and May 2017. Interviews were simultaneously analyzed using inductive and conventional content analysis method after being transcribed. Ethical consideration: This study was approved by the Regional Committee of Medical Research Ethics. Also, voluntary participation, anonymity, and confidentiality were considered. Findings: Two themes emerged from our analysis due to consequences of nurses’ efforts to overcome intra-professional discrimination: “seeking justice” and “passivity.” Discussion: Nurses’ efforts to overcome professional discrimination have led to outcomes. These outcomes can be affect on their individual effort to achieve organizational goals, provide better care or feel disabling or nurses turnover. Conclusion: Strategies adopted by nurses to overcome intra-professional discrimination have led to consequences which vary from negative to positive and impact their performance. (shrink)

The argument from inductive risk (AIR) states that scientists should consider the consequences of hypotheses and methodological choices in the course of ongoing research. It has played a central role in the widespread retreat from the ideal of value-free science. The argument is motivated, to a significant extent, by the laudable concern to use science to better society. I argue that this concern, when taken seriously, tells against the idea that individual working scientists should consider social consequences. First, I show (...) that the AIR assigns scientists a striking task: to frame social decisions and assess their full spectrum of consequences. Then, I argue that scientists should not be assigned such a task. For one thing, if both scientists and policy makers take social consequences into account, we are liable to end up with skewed and biased decisions. For another, scientists are not well-placed to carry out social decision making. I then discuss and diffuse some objections and potential misapprehensions. The paper concludes by noting contexts in which the inductive risk line has more force, and by highlighting the importance, in discussing values in science, of attending to units and levels of analysis. (shrink)

From the beginning, the implications of quantum theory for our most general understanding of the world have been a matter of intense debate. Einstein argues that the theory had to be regarded as fundamentally incomplete. Its inability, for example, to predict the exact time of decay of a single radioactive atom had to be due to a failure of the theory and not due to a permanent inability on our part or a fundamental indeterminism in nature itself. In 1964, John (...) Bell derived a theorem which showed that any deterministic theory which preserved locality would have certain consequences for measurements performed at a distance from one another. An experimental check seems to show that these consequences are not, in fact, realized. The correlation between the sets of events is much stronger than any local deterministic theory could allow. What is more, this stronger correlation is precisely that which is predicted by quantum theory. The astonishing result is that local deterministic theories of the classical sort seem to be permanently excluded. Not only can the individual decay not be predicted, but no future theory can ever predict it. The contributors in this volume wrestle with this conclusion. Some welcome it; others leave open a return to at lease some kind of deterministic world, one which must however allow something like action-at-a distance. How much lit it? And how can one avoid violating relativity theory, which excludes action-at-a-distance? How can a clash between the two fundamental theories of modern physics, relativity and quantum theory, be avoided? What are the consequences for the traditional philosophic issue of causality explanation and objectivity? One thing is certain; we can never return to the comfortable Newtonian world where everything that happened was, in principle, predictable and where what happened at one measurement site could not affect another set of measurements being performed light-years away, at a distance that a light-signal could not bridge. Contributors: James T. Cushing, Abner Shimony, N. David Mermin, Jon P. Jarrett, Linda Wessels, Bas C. van Fraassen, Jeremy Butterfield, Michael L. G. Redhead, Henry P. Stapp, Arthur Fine, R. I. G. Hughes, Paul Teller, Don Howard, Henry J. Folse, and Ernan McMullin. (shrink)

The consequence argument is among the most influential arguments for the conclusion that free will and determinism are incompatible. Recently, however, it has become increasingly clear that the argument fails to establish that particular incompatibilist conclusion. Even so, a version of the argument can be formulated that supports a different incompatibilist conclusion, according to which free will is incompatible with our behavior being predetermined by factors beyond our control. This conclusion, though not equivalent to the traditional incompatibilist thesis that (...) determinism strictly precludes free will, is something many incompatibilists have had in mind all along and, indeed, is arguably the more central incompatibilist position. The consequence argument thus remains philosophically important, even if, as several of its critics have argued, it can't be used to establish the strict incompatibility of free will and determinism. (shrink)

Reasoning over our knowledge bases and theories often requires non-deductive inferences, especially – but by no means only – when commonsense reasoning is the case, i.e. when practical agency is called for. This kind of reasoning can be adequately formalized via the notion of supraclassical consequence, a non-deductive consequence tightly associated with default and non-monotonic reasoning and featuring centrally in abductive, inductive, and probabilistic logical systems. In this paper, we analyze core concepts and problems of these systems in (...) the light of supraclassical consequence. (shrink)

The aim of the Consequence Argument is to show that, if determinism is true, no one has, or ever had, any choice about anything. In the stock version of the argument, its two premisses state that no one is, or ever was, able to act so that the past would have been different and no one is, or ever was, able to act so that the laws of nature would have been different. This stock version fails, however, because it (...) requires an invalid inference rule. The standard response is to strengthen both premisses by replacing ‘would’ with ‘might’. While this response ensures validity, it weakens the argument, since it strengthens the premisses. I show that we can do better: We can keep the weak reading of one premiss and just strengthen the other. This provides two versions of the Consequence Argument which are stronger than the standard revision. (shrink)

We group the existing variants of the familiar set-theoretical and truth-theoretical paradoxes into two classes: connective paradoxes, which can in principle be ascribed to the presence of a contracting connective of some sort, and structural paradoxes, where at most the faulty use of a structural inference rule can possibly be blamed. We impute the former to an equivocation over the meaning of logical constants, and the latter to an equivocation over the notion of consequence. Both equivocation sources are tightly (...) related, and can be cleared up by adopting a particular substructural logic in place of classical logic. We then argue that our perspective can be justified via an informational semantics of contraction-free substructural logics. (shrink)

It is widely accepted among medical ethicists that competence is a necessary condition for informed consent. In this view, if a patient is incompetent to make a particular treatment decision, the decision must be based on an advance directive or made by a substitute decision-maker on behalf of the patient. We call this the competence model. According to a recent report of the United Nations (UN) High Commissioner for Human Rights, article 12 of the UN Convention on the Rights of (...) Persons with Disabilities (CRPD) presents a wholesale rejection of the competence model. The High Commissioner here adopts the interpretation of article 12 proposed by the Committee on the Rights of Persons with Disabilities. On this interpretation, CRPD article 12 renders it impermissible to deny persons with mental disabilities the right to make treatment decisions on the basis of impaired decision-making capacity and demands the replacement of all regimes of substitute decision-making by supported decision-making. In this paper, we explicate six adverse consequences of CRPD article 12 for persons with mental disabilities and propose an alternative way forward. The proposed model combines the strengths of the competence model and supported decision-making. (shrink)

_ Source: _Volume 56, Issue 3-4, pp 201 - 221 This paper summarizes medieval definitions and divisions of consequences and explains the import of the medieval development of the theory of consequence for logic today. It then introduces the various contributions to this special issue of _Vivarium_ on consequences in medieval logic.

This chapter provides broad coverage of the notion of logical consequence, exploring its modal, semantic, and epistemic aspects. It develops the contrast between proof-theoretic notion of consequence, in terms of deduction, and a model-theoretic approach, in terms of truth-conditions. The main purpose is to relate the formal, technical work in logic to the philosophical concepts that underlie reasoning.

Frege puzzles exploit cognitive differences between co-referential terms. Traditionally, they were handled by some version of Frege’s distinction between sense and reference, which avoided disruptive consequences for epistemology. However, the Fregean programme did not live up to its original promise, and was undermined by the development of theories of direct reference; for semantic purposes, its prospects now look dim. In particular, well-known analogues of Frege puzzles concern pairs of uncontentious synonyms; attempts to deal with them by distinguishing idiolects or postulating (...) ‘narrow contents’ or elaborate forms of context-sensitivity are inadequate or semantically implausible. Although ascriptions of knowledge, belief, and other attitudes are ubiquitous in epistemology, epistemologists have not properly come to terms with the surprising consequences of anti-Fregean semantic accounts of attitude ascriptions. In ‘A Puzzle about Belief ’, Saul Kripke shows that natural-seeming disquotational principles for ascribing belief lead to apparently unacceptable consequences, including outright contradictions, in problem cases. Such disquotation principles, I argue, are best regarded not as conceptual connections but just as heuristics in the psychological sense, quick and easy ways of assessing belief ascriptions, usually accurate under normal conditions but far from 100% reliable. I discuss similar heuristics for ascribing knowledge and other attitudes. That the principles have a merely heuristic status need not be pre-theoretically manifest to their users. This view vindicates Kripke’s conclusion that it would be wrong-headed to draw semantic conclusions from Frege puzzles. I discuss the epistemological consequences of an anti-Fregean approach to Frege puzzles, including for Kripke’s cases of the contingent a priori and the necessary a posteriori, but also for evidence, for epistemic modalities, and for epistemic and subjective conceptions of probability. Anna Mahtani’s recent identification of Frege puzzles for the ex ante Pareto Principle as used in welfare economics provides an interesting example. I suggest a model-building methodology as the most promising way of handling at least some of the difficulties. A final issue is the choice between different anti-Fregean approaches to semantics, from very coarse-grained intensional approaches on which sentences express functions from possible worlds to truth-values to more fine-grained hyperintensional approaches on which sentences express functions from possible or impossible worlds to truth-values or else Russellian structured propositions. Some of the hyperintensional theories violate semantic compositionality. More generally, since our attitude ascriptions rely on heuristics, they should be expected to exhibit some level of error; although hyperintensional approaches may be able slightly to reduce the level of postulated error, they do so at the cost of vastly increased theoretical complexity, and so have weak explanatory power. Methodologically, a simple intensional approach does better. (shrink)

Forty years ago, Niels Green-Pedersen listed five different accounts of valid consequence, variously promoted by logicians in the early fourteenth century and discussed by Niels Drukken of Denmark in his commentary on Aristotle’s Prior Analytics, written in Paris in the late 1330s. Two of these arguably fail to give defining conditions: truth preservation was shown by Buridan and others to be neither necessary nor sufficient; incompatibility of the opposite of the conclusion with the premises is merely circular if incompatibility (...) is analysed in terms of consequence. Buridan proposed to define consequence in terms of preservation of signifying as things are. John Mair pinpointed a sophism which threatens to undermine this proposal. Speaking anachronistically, Bradwardine turned it around: he suggested that a necessary condition on consequence was that the premises signify everything the conclusion signifies. Dumbleton gave counterexamples to Bradwardine’s postulates in which the conclusion arguably signifies more than, or even completely differently from the premises. Yet a long-standing tradition held that some species of validity depend on the conclusion being in some way contained in the premises. We explore the connection between signification and consequence and its role in solving the insolubles. (shrink)

Peter van Inwagen has presented a compelling argument for the incompatibility of free will and determinism, which he calls “the Consequence Argument.” This argument depends on a controversial inference rule, “rule beta,” which says.

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

Little is known about the consequences of moral distress. The purpose of this study was to identify clinical situations that caused nurses to experience moral distress, to understand the consequences of those situations, and to determine whether nurses would change their practice based on their experiences. The investigation used a descriptive approach. Open-ended surveys were distributed to a convenience sample of 204 critical care nurses employed at a university medical center. The analysis of participants’ responses used an inductive approach and (...) a thematic analysis. Each line of the data was reviewed and coded, and the codes were collapsed into themes. Methodological rigor was established. Forty-nine nurses responded to the survey. The majority of nurses had experienced moral distress, and the majority of situations that caused nurses to experience moral distress were related to end of life. The nurses described negative consequences for themselves, patients, and families. (shrink)

This chapter focuses on one of the common fallacies in Western philosophy called “adverse consequences”. The argument from adverse consequences can be seen as an argument that is intended to be pragmatic ‐ about what we should do, not about what is true ‐ but then comes to the wrong kind of conclusion. In many genuinely pragmatic arguments, however, adverse consequences are relevant to the conclusion and no fallacy is committed. So it is important to notice exactly what the conclusion (...) of the argument is. The ASCC's conclusion was that they should question the idea that diet plays a role in causing cancer; it was a conclusion about what they should do. The claim about consequences ‐ that people will probably delay going to their physician if they believe that diet plays a role in causing cancer ‐ is relevant to that conclusion. (shrink)

When ordinary people - mathematicians among them - take something to follow (deductively) from something else, they are exposing the backbone of our self-ascribed ability to reason. Jody Azzouni investigates the connection between that ordinary notion of consequence and the formal analogues invented by logicians. One claim of the book is that, despite our apparent intuitive grasp of consequence, we do not introspect rules by which we reason, nor do we grasp the scope and range of the domain, (...) as it were, of our reasoning. This point is illustrated with a close analysis of a paradigmatic case of ordinary reasoning: mathematical proof. (shrink)

In the first section, I consider what several logicians say informally about the notion of logical consequence. There is significant variation among these accounts, they are sometimes poorly explained, and some of them are clearly at odds with the usual technical definition. In the second section, I first argue that a certain kind of informal account—one that includes elements of necessity, generality, and apriority—is approximately correct. Next I refine this account and consider several important questions about it, including the (...) appropriate characterization of necessity, the criterion for selecting logical constants, and the exact role of apriority. I argue, among other things, that there is no need to recognize a special logical sense of necessity and that the selection of terms to serve as logical constants is ultimately a pragmatic matter. In the third section, I consider whether the informal account I have presented and defended is adequately represented by the usual technical definition. I show that it is, and provably so, for certain limited ways of selecting logical constants. In the general case, however, there seems to be no way to be sure that the technical and informal accounts coincide. (shrink)

Resumo Peter van Inwagen no seu An Essay of Free Will e, no muito mais tarde, “The Consequence Argument” formula várias versões daquilo que designou por “o argumento de consequência”. van Inwagen descreveu o “argumento da consequência” como um argumento para a incompatibilidade do determinismo com o livre arbítrio. Contudo, o autor deste artigo argumenta que a mais recente formulação do argumento da consequência não é, tal como está, um argumento para a incompatibilidade do determinismo com o livre arbítrio. (...) Embora possa ser transformado em um, não parece haver nenhuma maneira simples de transformá-lo em um argumento convincente para a incompatibilidade do determinismo com o livre arbítrio. Por isso, sugere-se, para a construção de um argumento convincente para a incompatibilidade do determinismo com o livre-arbítrio, que a melhor aposta passa pela reconstrução de uma definição do determinismo substancialmente diferente da de van Inwagen. Palavras-chave : argumento da consequência, determinismo, livre arbítrio, metafísica, van InwagenIn An Essay on Free Will, and in the much later “The Consequence Argument” Peter van Inwagen formulated various versions of what he calls “the consequence argument”. van Inwagen has described the consequence argument as an argument for the incompatibility of determinism with free will. But, I argue, the latest formulation of the consequence argument is not, as it stands, an argument for the incompatibility of determinism with free will. Although it can be turned into one, there does not seem to be any straightforward way of turning it into a cogent argument for the incompatibility of determinism with free will. I suggest that if we want to construct a cogent argument for the incompatibility of determinism with free will, our best bet is to start with a definition of determinism substantially different from van Inwagen’s. Keywords : consequence argument, determinism, free will, metaphysics, van Inwagen. (shrink)

This paper examines from a historical perspective Tarski's 1936 essay, "On the concept of logical consequence." I focus on two main aims. The primary aim is to show how Tarski's definition of logical consequence satisfies two desiderata he himself sets forth for it: (1) it must declare logically correct certain formalizations of the -rule and (2) it must allow for variation of the individual domain in the test for logical consequence. My arguments provide a refutation of some (...) interpreters of Tarski, and notably John Etchemendy, who have claimed that his definition does not satisfy those desiderata. A secondary aim of the paper is to offer some basic elements for an understanding of Tarski's definition in the historical logico-philosophical context in which it was proposed. Such historical understanding provides useful insights on Tarski's informal ideas on logical consequence and their internal cohesion. (shrink)

Incompatibilism about responsibility and determinism is sometimes directly construed as the thesis that if we found out that determinism is true, we would have to give up the reactive attitudes. Call this "the consequence". I argue that this is a mistake: the strict modal thesis does not entail the consequence. First, some incompatibilists (who are also libertarians) may be what we might call *resolute responsibility theorists* (or "flip-floppers"). On this view, if we found out that determinism is true, (...) this would not be to find out that no one is responsible; instead, what this would suggest is that incompatibilism is after all false. Second, some incompatibilists may instead deny the claim that if we found out that no one deserves the reactiveattitudes, we would have to give up the reactive attitudes. Call this position *innocent incompatibilism*. I explore several different reasons why the fact that no one deserves the reactive attitudes likely does not translate into a requirement for us to give up the reactive attitudes. The upshot: incompatibilism may be practically irrelevant, even if true. (shrink)

We provide a general investigation of Logic in which the notion of a simple consequence relation is taken to be fundamental. Our notion is more general than the usual one since we give up monotonicity and use multisets rather than sets. We use our notion for characterizing several known logics (including Linear Logic and non-monotonic logics) and for a general, semantics-independent classi cation of standard connectives via equations on consequence relations (these include Girard's \multiplicatives" and \additives"). We next (...) investigate the standard methods for uniformly representing consequence relations: Hilbert type, Natural Deduction and Gentzen type. The advantages and disadvantages of using each system and what should be taken as.. (shrink)

There are passages in Fallacies suggesting a skeptical attitude to the very idea of inductive arguments, hence to the existence of inductive fallacies. Although the passages are brief and few in number, it would appear that Hamblin’s resistance stems from doubts about the existence of relations of inductive consequence. This paper attempts to find a case in which such skepticism might plausibly be grounded. The case it proposes is highly conjectural, but important if true. Its greater importance lies in (...) the threat it creates for the whole class of nonmonotonic logics. (shrink)

There are various contexts in which it is not pertinent to generate and attend to all the classical consequences of a given premiss—or to trace all the premisses which classically entail a given consequence. Such contexts may involve limited resources of an agent or inferential engine, contextual relevance or irrelevance of certain consequences or premisses, modelling everyday human reasoning, the search for plausible abduced hypotheses or potential causes, etc. In this paper we propose and explicate one formal framework for (...) a whole spectrum of consequence relations, flexible enough to be tailored for choices from a variety of contexts. We do so by investigating semantic constraints on classical entailment which give rise to a family of infra-classical logics with appealing properties. More specifically, our infra-classical reasoning demands (beyond ${\alpha\models\beta}$ ) that Mod(β) does not run wild, but lies within the scope (whatever that may mean in some specific context) of Mod(α), and which can be described by a sentence ${\bullet\alpha}$ with ${\beta\models\bullet\alpha}$. Besides being infra-classical, the resulting logic is also non-monotonic and allows for non-trivial reasoning in the presence of inconsistencies. (shrink)

This paper presents an experimental study of common consequence effects in binary choice, willingness-to-pay elicitation, and willingness-to-accept elicitation. We find strong evidence in favor of the fanning out hypothesis for both WTP and WTA. In contrast, the choice data do not show a clear pattern of violations in the absence of certainty effects. Our results underline the relevance of differences between pricing and choice tasks, and their implications for models of decision making under risk.

In the paper, there is presented the theory of logical consequence operators indexed with taboo functions. It describes the mechanisms of logical inference in the environment of forbidden sentences. This kind of processes take place in ideological discourses within which their participants create various narrative worlds (mental worlds). A peculiar feature of ideological discourses is their association with taboo structures of deduction which penalize speech acts. The development of discourse involves, among others, transforming its deduction structure towards the proliferation (...) of consequence operators and modifying penalty functions. The presented theory enables to define various processes of these transformations in the precise way. It may be used in analyses of conflicts between competing elm experts acting within a discourse. (shrink)

Substructural logics and their application to logical and semantic paradoxes have been extensively studied. In the paper, we study theories of naïve consequence and truth based on a non-reflexive logic. We start by investigating the semantics and the proof-theory of a system based on schematic rules for object-linguistic consequence. We then develop a fully compositional theory of truth and consequence in our non-reflexive framework.

To understand logic is, first and foremost, to understand logical consequence. This Element provides an in-depth, accessible, up-to-date account of and philosophical insight into the semantic, model-theoretic conception of logical consequence, its Tarskian roots, and its ideas, grounding, and challenges. The topics discussed include: the passage from Tarski's definition of truth to his definition of logical consequence, the need for a non-proof-theoretic definition, the idea of a semantic definition, the adequacy conditions of preservation of truth, formality, and (...) necessity, the nature, structure, and totality of models, the logicality problem that threatens the definition of logical consequence, a general solution to the logicality, formality, and necessity problems/challenges, based on the isomorphism-invariance criterion of logicality, philosophical background and justification of the isomorphism-invariance criterion, and major criticisms of the semantic definition and the isomorphism-invariance criterion. (shrink)

Equivalences and translations between consequence relations abound in logic. The notion of equivalence can be defined syntactically, in terms of translations of formulas, and order-theoretically, in terms of the associated lattices of theories. W. Blok and D. Pigozzi proved in [4] that the two definitions coincide in the case of an algebraizable sentential deductive system. A refined treatment of this equivalence was provided by W. Blok and B. Jónsson in [3]. Other authors have extended this result to the cases (...) of k-deductive systems and of consequence relations on associative, commutative, multiple conclusion sequents. Our main result subsumes all existing results in the literature and reveals their common character. The proofs are of order-theoretic and categorical nature. (shrink)

Given a consequence relation in many-valued logic, what connectives can be defined? For instance, does there always exist a conditional operator internalizing the consequence relation, and which form should it take? In this paper, we pose this question in a multi-premise multi-conclusion setting for the class of so-called intersective mixed consequence relations, which extends the class of Tarskian relations. Using computer-aided methods, we answer extensively for 3-valued and 4-valued logics, focusing not only on conditional operators, but also (...) on what we call Gentzen-regular connectives. For arbitrary N-valued logics, we state necessary and sufficient conditions for the existence of such connectives in a multi-premise multi-conclusion setting. The results show that mixed consequence relations admit all classical connectives, and among them pure consequence relations are those that admit no other Gentzen-regular connectives. Conditionals can also be found for a broader class of intersective mixed consequence relations, but with the exclusion of order-theoretic consequence relations. (shrink)