This book is a specialized monograph on the development of the mathematical and computational metatheory of reductive logic and proof-search, areas of logic that are becoming important in computer science. A systematic foundational text on these emerging topics, it includes proof-theoretic, semantic/model-theoretic and algorithmic aspects. The scope ranges from the conceptual background to reductive logic, through its mathematical metatheory, to its modern applications in the computational sciences. Suitable for researchers and graduate students in mathematical, computational and philosophical logic, and in (...) theoretical computer science and artificial intelligence, this is the latest in the prestigous world-renowned Oxford Logic Guides, which contains Michael Dummet's Elements of intuitionism (2nd Edition), Dov M. Gabbay, Mark A. Reynolds, and Marcelo Finger's Temporal Logic Mathematical Foundations and Computational Aspects, J. M. Dunn and G. Hardegree's Algebraic Methods in Philosophical Logic, H. Rott's Change, Choice and Inference: A Study of Belief Revision and Nonmonotonic Reasoning, and P. T. Johnstone's Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2. (shrink)

This book is a specialized monograph on the development of the mathematical and computational metatheory of reductive logic and proof-search, areas of logic that are becoming important in computer science. A systematic foundational text on these emerging topics, it includes proof-theoretic, semantic/model-theoretic and algorithmic aspects. The scope ranges from the conceptual background to reductive logic, through its mathematical metatheory, to its modern applications in the computational sciences. Suitable for researchers and graduate students in mathematical, computational and philosophical logic, and in (...) theoretical computer science and artificial intelligence, this is the latest in the prestigous world-renowned Oxford Logic Guides, which contains Michael Dummet's Elements of intuitionism, Dov M. Gabbay, Mark A. Reynolds, and Marcelo Finger's Temporal Logic Mathematical Foundations and Computational Aspects, J. M. Dunn and G. Hardegree's Algebraic Methods in Philosophical Logic, H. Rott's Change, Choice and Inference: A Study of Belief Revision and Nonmonotonic Reasoning, and P. T. Johnstone's Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2. (shrink)

Proof-theoretic semantics (P-tS) is the paradigm of semantics in which meaning in logic is based on proof (as opposed to truth). A particular instance of P-tS for intuitionistic propositional logic (IPL) is its base-extension semantics (B-eS). This semantics is given by a relation called support, explaining the meaning of the logical constants, which is parameterized by systems of rules called bases that provide the semantics of atomic propositions. In this paper, we interpret bases as collections of definite formulae and use (...) the operational view of them as provided by uniform proof-search—the proof-theoretic foundation of logic programming (LP)—to establish the completeness of IPL for the B-eS. This perspective allows negation, a subtle issue in P-tS, to be understood in terms of the negation-as-failure protocol in LP. Specifically, while the denial of a proposition is traditionally understood as the assertion of its negation, in B-eS we may understand the denial of a proposition as the failure to find a proof of it. In this way, assertion and denial are both prime concepts in P-tS. (shrink)

In proof-theoretic semantics, meaning is based on inference. It may seen as the mathematical expression of the inferentialist interpretation of logic. Much recent work has focused on base-extension semantics, in which the validity of formulas is given by an inductive definition generated by provability in a ‘base’ of atomic rules. Base-extension semantics for classical and intuitionistic propositional logic have been explored by several authors. In this paper, we develop base-extension semantics for the classical propositional modal systems |$K$|⁠, |$KT$|⁠, |$K4$| and (...) |$S4$|⁠, with |$\square $| as the primary modal operator. We establish appropriate soundness and completeness theorems and establish the duality between |$\square $| and a natural presentation of |$\lozenge $|⁠. We also show that our semantics is in its current form not complete with respect to euclidean modal logics. Our formulation makes essential use of relational structures on bases. (shrink)

We give a novel approach to proving soundness and completeness for a logic (henceforth: the object-logic) that bypasses truth-in-a-model to work directly with validity. Instead of working with specific worlds in specific models, we reason with eigenworlds (i.e., generic representatives of worlds) in an arbitrary model. This reasoning is captured by a sequent calculus for a _meta_-logic (in this case, first-order classical logic) expressive enough to capture the semantics of the object-logic. Essentially, one has a calculus of validity for the (...) object-logic. The method proceeds through the perspective of reductive logic (as opposed to the more traditional paradigm of deductive logic), using the space of reductions as a medium for showing the behavioural equivalence of reduction in the sequent calculus for the object-logic and in the validity calculus. Rather than study the technique in general, we illustrate it for the logic of Bunched Implications (BI), thus IPL and MILL (without negation) are also treated. Intuitively, BI is the free combination of intuitionistic propositional logic and multiplicative intuitionistic linear logic, which renders its meta-theory is quite complex. The literature on BI contains many similar, but ultimately different, algebraic structures and satisfaction relations that either capture only fragments of the logic (albeit large ones) or have complex clauses for certain connectives (e.g., Beth’s clause for disjunction instead of Kripke’s). It is this complexity that motivates us to use BI as a case-study for this approach to semantics. (shrink)

This book is a specialized monograph on the development of the mathematical and computational metatheory of reductive logic and proof-search including proof-theoretic, semantic/model-theoretic and algorithmic aspects. The scope ranges from the conceptual background to reductive logic, through its mathematical metatheory, to its modern applications in the computational sciences.

The lambdaPi-calculus, a theory of first-order dependent function types in Curry-Howard-de Bruijn correspondence with a fragment of minimal first-order logic, is defined as a system of (linearized) natural deduction. In this paper, we present a Gentzen-style sequent calculus for the lambdaPi-calculus and prove the cut-elimination theorem. The cut-elimination result builds upon the existence of normal forms for the natural deduction system and can be considered to be analogous to a proof provided by Prawitz for first-order logic. The type-theoretic setting considered (...) here elegantly illustrates the distinction between the processes of normalization in a natural deduction system and cut-elimination in a Gentzen-style sequent calculus. (shrink)

The reductive, as opposed to deductive, view of logic is the form of logic that is, perhaps, most widely employed in practical reasoning. In particular, it is the basis of logic programming. Here, building on the idea of uniform proof in reductive logic, we give a treatment of logic programming for BI, the logic of bunched implications, giving both operational and denotational semantics, together with soundness and completeness theorems, all couched in terms of the resource interpretation of BI’s semantics. We (...) use this set-up as a basis for exploring how coalgebraic semantics can, in contrast to the basic denotational semantics, be used to describe the concrete operational choices that are an essential part of proof-search. The overall aim, toward which this paper can be seen as an initial step, is to develop a uniform, generic, mathematical framework for understanding the relationship between the deductive structure of logics and the control structures of the corresponding reductive paradigm. (shrink)

We introduce a logic BI in which a multiplicative (or linear) and an additive (or intuitionistic) implication live side-by-side. The propositional version of BI arises from an analysis of the proof-theoretic relationship between conjunction and implication; it can be viewed as a merging of intuitionistic logic and multiplicative intuitionistic linear logic. The naturality of BI can be seen categorically: models of propositional BI's proofs are given by bicartesian doubly closed categories, i.e., categories which freely combine the semantics of propositional intuitionistic (...) logic and propositional multiplicative intuitionistic linear logic. The predicate version of BI includes, in addition to standard additive quantifiers, multiplicative (or intensional) quantifiers ∀ new and ∃ new which arise from observing restrictions on structural rules on the level of terms as well as propositions. We discuss computational interpretations, based on sharing, at both the propositional and predicate levels. (shrink)

Quantitative research studies examining the effects of literacy instruction set in social studies classrooms (grades 6-12) on students’ academic content learning and reading comprehension are synthesized using meta-analytic techniques. An extensive search of the scholarly literature between 1983 and 2013 yielded a total of twelve intervention studies that provided literacy instruction to secondary students within social studies classes and quantitatively measured content learning outcomes, reading comprehension, or both. Findings revealed that content learning outcomes were consistently improved with instruction that included (...) text-processing activities such as summarizing and generating questions. While many social studies teachers do not provide explicit reading supports, in part because they perceive that the time needed to do so is prohibitive, the findings of this synthesis suggest that sound reading practices hold promise as a means through which teachers can help students better access social studies content, thus improving student learning outcomes. More rigorous quantitative research is needed to further understand the causal effects of literacy practices in social studies settings. Highlights • Literacy instruction supports both reading comprehension and academic content • Literacy instruction does not negatively affect content knowledge acquisition. • Few studies investigate the effects of literacy instruction in social studies. • More research is needed to explore the effects of literacy instruction in social studies. (shrink)

"Technological balance" occurs automatically when the designer, builder, and user of a tool is the same person. "Technological imbalance" occurs when these activities become separated and in opposition to one another. Tools become menacing exoge nous objects. We see a shift in connotation of the word technology from the skill of the person to the object produced. Designers and builders create tools with the passive consent and willful ignorance of users. Curricula often contribute to this imbalance. Apprentice designers and builders (...) receive specialized instruction in creating objects, whereas users uncritically learn the procedural requirements of the resulting objects. This system of education turns "machine tending" into a pedagogical goal. The university has the potential to become a model of technological balance for the soci ety as a whole using such means as selecting tools that encourage balance, "technology audits, " and break ing down the specializations among designers, builders, and users. (shrink)

[This is an edited version of a keynote talk at the conference on Neural Information Processing Systems (NeurIPS) on November 28, 2022, with some minor additions and subtractions.] -/- There has recently been widespread discussion of whether large language models might be sentient or conscious. Should we take this idea seriously? I will break down the strongest reasons for and against. Given mainstream assumptions in the science of consciousness, there are significant obstacles to consciousness in current models: for example, their (...) lack of recurrent processing, a global workspace, and unified agency. At the same time, it is quite possible that these obstacles will be overcome in the next decade or so. I conclude that while it is somewhat unlikely that current large language models are conscious, we should take seriously the possibility that successors to large language models may be conscious in the not-too-distant future. (shrink)

Was human nature designed by natural selection in the Pleistocene epoch? The dominant view in evolutionary psychology holds that it was -- that our psychological adaptations were designed tens of thousands of years ago to solve problems faced by our hunter-gatherer ancestors. In this provocative and lively book, David Buller examines in detail the major claims of evolutionary psychology -- the paradigm popularized by Steven Pinker in The Blank Slate and by David Buss in The Evolution of Desire (...) -- and rejects them all. This does not mean that we cannot apply evolutionary theory to human psychology, says Buller, but that the conventional wisdom in evolutionary psychology is misguided.Evolutionary psychology employs a kind of reverse engineering to explain the evolved design of the mind, figuring out the adaptive problems our ancestors faced and then inferring the psychological adaptations that evolved to solve them. In the carefully argued central chapters of Adapting Minds, Buller scrutinizes several of evolutionary psychology's most highly publicized "discoveries," including "discriminative parental solicitude". Drawing on a wide range of empirical research, including his own large-scale study of child abuse, he shows that none is actually supported by the evidence.Buller argues that our minds are not adapted to the Pleistocene, but, like the immune system, are continually adapting, over both evolutionary time and individual lifetimes. We must move beyond the reigning orthodoxy of evolutionary psychology to reach an accurate understanding of how human psychology is influenced by evolution. When we do, Buller claims, we will abandon not only the quest for human nature but the very idea of human nature itself. (shrink)

Does consciousness collapse the quantum wave function? This idea was taken seriously by John von Neumann and Eugene Wigner but is now widely dismissed. We develop the idea by combining a mathematical theory of consciousness (integrated information theory) with an account of quantum collapse dynamics (continuous spontaneous localization). Simple versions of the theory are falsified by the quantum Zeno effect, but more complex versions remain compatible with empirical evidence. In principle, versions of the theory can be tested by experiments with (...) quantum computers. The upshot is not that consciousness-collapse interpretations are clearly correct, but that there is a research program here worth exploring. (shrink)

I argue that virtual reality is a sort of genuine reality. In particular, I argue for virtual digitalism, on which virtual objects are real digital objects, and against virtual fictionalism, on which virtual objects are fictional objects. I also argue that perception in virtual reality need not be illusory, and that life in virtual worlds can have roughly the same sort of value as life in non-virtual worlds.

Bentham's dictum, ‘everybody to count for one, nobody for more than one’, is frequently noted but seldom discussed by commentators. Perhaps it is not thought contentious or exciting because interpreted as merely reminding the utilitarian legislator to make certain that each person's interests are included, that no one is missed, in working the felicific calculus. Since no interests are secure against the maximizing directive of the utility principle, which allows them to be overridden or sacrificed, the dictum is not usually (...) taken to be asserting fundamental rights that afford individuals normative protection against the actions of others or against legislative policies deemed socially expedient. Such non-conventional moral rights seem denied a place in a utilitarian theory so long as the maximization of aggregate happiness remains the ultimate standard and moral goal. (shrink)

This essay addresses the other side of the robot ethics debate, taking up and investigating the question “Can and should robots have rights?” The examination of this subject proceeds by way of three steps or movements. We begin by looking at and analyzing the form of the question itself. There is an important philosophical difference between the two modal verbs that organize the inquiry—can and should. This difference has considerable history behind it that influences what is asked about and how. (...) Second, capitalizing on this verbal distinction, it is possible to identify four modalities concerning social robots and the question of rights. The second section will identify and critically assess these four modalities as they have been deployed and developed in the current literature. Finally, we will conclude by proposing another alternative, a way of thinking otherwise that effectively challenges the existing rules of the game and provides for other ways of theorizing moral standing that can scale to the unique challenges and opportunities that are confronted in the face of social robots. (shrink)

Is there progress in philosophy? A glass-half-full view is that there is some progress in philosophy. A glass-half-empty view is that there is not as much as we would like. I articulate a version of the glass-half-empty view, argue for it, and then address the crucial question of what explains it.

In this book, David Stump traces alternative conceptions of the a priori in the philosophy of science and defends a unique position in the current debates over conceptual change and the constitutive elements in science. Stump emphasizes the unique epistemological status of the constitutive elements of scientific theories, constitutive elements being the necessary preconditions that must be assumed in order to conduct a particular scientific inquiry. These constitutive elements, such as logic, mathematics, and even some fundamental laws of nature, (...) were once taken to be a priori knowledge but can change, thus leading to a dynamic or relative a priori. Stump critically examines developments in thinking about constitutive elements in science as a priori knowledge, from Kant’s fixed and absolute a priori to Quine’s holistic empiricism. By examining the relationship between conceptual change and the epistemological status of constitutive elements in science, Stump puts forward an argument that scientific revolutions can be explained and relativism can be avoided without resorting to universals or absolutes. (shrink)

The book is an extended study of the problem of consciousness. After setting up the problem, I argue that reductive explanation of consciousness is impossible , and that if one takes consciousness seriously, one has to go beyond a strict materialist framework. In the second half of the book, I move toward a positive theory of consciousness with fundamental laws linking the physical and the experiential in a systematic way. Finally, I use the ideas and arguments developed earlier to defend (...) a form of strong artificial intelligence and to analyze some problems in the foundations of quantum mechanics. (shrink)

Cartesian arguments for global skepticism about the external world start from the premise that we cannot know that we are not in a Cartesian scenario such as an evil-demon scenario, and infer that because most of our empirical beliefs are false in such a scenario, these beliefs do not constitute knowledge. Veridicalist responses to global skepticism respond that arguments fail because in Cartesian scenarios, many or most of our empirical beliefs are true. Some veridicalist responses have been motivated using verificationism, (...) externalism, and coherentism. I argue that a more powerful veridicalist response to global skepticism can be motivated by structuralism, on which physical entities are understood as those that play a certain structural role. I develop the structuralist response and address objections. (shrink)

There are two versions of the language-of-thought hypothesis (LOT): Representational LOT (roughly, structured representation), introduced by Ockham, and computational LOT (roughly, symbolic computation) introduced by Fodor. Like many others, I oppose the latter but not the former. Quilty-Dunn et al. defend representational LOT, but they do not defend the strong computational LOT thesis central to the classical-connectionist debate.

Does the capacity to think require the capacity to sense? A lively debate on this topic runs throughout the history of philosophy and now animates discussions of artificial intelligence. Many have argued that AI systems such as large language models cannot think and understand if they lack sensory grounding. I argue that thought does not require sensory grounding: there can be pure thinkers who can think without any sensory capacities. As a result, the absence of sensory grounding does not entail (...) that large language models cannot think or understand. I also consider to what extent quasi-sensory grounding can at least boost the performance of a language model. (shrink)

In response to a recent argument by David Bloor, I argue that denying absolutes does not necessarily lead to relativism, that one can be a fallibilist without being a relativist. At issue are the empirical natural sciences and what might be called “framework relativism”, that is, the idea that there is always a conceptual scheme or set of practices in use, and all observations are theory-laden relative to the framework. My strategy is to look at the elements that define (...) a relativist stance and show where the pragmatic fallibilist disagrees. Defending the pragmatic notion of experience will be central, given that relativists reject the idea that experience can play a role in objectively justifying belief. We can reject all absolutes and start from the premise that everything is historical, contingent, and situated. One of the lessons of pragmatism is that universal and fixed principles are not necessary for objective knowledge. (shrink)

In a friendly interdisciplinary debate, we interrogate from several vantage points the question of “personhood” in light of contemporary and near-future forms of social AI. David J. Gunkel approaches the matter from a philosophical and legal standpoint, while Jordan Wales offers reflections theological and psychological. Attending to metaphysical, moral, social, and legal understandings of personhood, we ask about the position of apparently personal artificial intelligences in our society and individual lives. Re-examining the “person” and questioning prominent construals of that (...) category, we hope to open new views upon urgent and much-discussed questions that, quite soon, may confront us in our daily lives. (shrink)

In the Garden of Eden, we had unmediated contact with the world. We were directly acquainted with objects in the world and with their properties. Objects were simply presented to us without causal mediation, and properties were revealed to us in their true intrinsic glory.

This chapter contains sections titled: Introduction1 The Problem Arguments Against Materialism Type‐A Materialism Type‐B Materialism15 The Two‐Dimensional Argument Against Type‐B Materialism Type‐C Materialism Interlude Type‐D Dualism Type‐E Dualism Type‐F Monism Conclusions.

In response to a recent argument by David Bloor, I argue that denying absolutes does not necessarily lead to relativism, that one can be a fallibilist without being a relativist. At issue are the empirical natural sciences and what might be called “framework relativism”, that is, the idea that there is always a conceptual scheme or set of practices in use, and all observations are theory-laden relative to the framework. My strategy is to look at the elements that define (...) a relativist stance and show where the pragmatic fallibilist disagrees. Defending the pragmatic notion of experience will be central, given that relativists reject the idea that experience can play a role in objectively justifying belief. We can reject all absolutes and start from the premise that everything is historical, contingent, and situated. One of the lessons of pragmatism is that universal and fixed principles are not necessary for objective knowledge. (shrink)

Experiences and beliefs are different sorts of mental states, and are often taken to belong to very different domains. Experiences are paradigmatically phenomenal, characterized by what it is like to have them. Beliefs are paradigmatically intentional, characterized by their propositional content. But there are a number of crucial points where these domains intersect. One central locus of intersection arises from the existence of phenomenal beliefs: beliefs that are about experiences.

Aristotle's claims that 'man is a political animal' and that political community 'exists for the sake of living well' have frequently been celebrated by thinkers of divergent political persuasions. The details of his political philosophy, however, have often been regarded as outmoded, contradictory, or pernicious. This book takes on the major problems that arise in attempting to understand how the central pieces of Aristotle's political thought fit together: can a conception of politics that seems fundamentally inclusive and egalitarian be reconciled (...) with a vision of justice that seems uncompromisingly hierarchical and authoritarian? Riesbeck argues that Aristotle's ideas about the distinctive nature and value of political community, political authority, and political participation are coherent and consistent with his aristocratic standards of justice. The result is a theory that, while not free of problems, remains a potentially fruitful resource for contemporary thinking about the persistent problems of political life. (shrink)

This paper argues that higher-order doubt generates an epistemic dilemma. One has a higher-order doubt with regards to P insofar as one justifiably withholds belief as to what attitude towards P is justified. That is, one justifiably withholds belief as to whether one is justified in believing, disbelieving, or withholding belief in P. Using the resources provided by Richard Feldman’s recent discussion of how to respect one’s evidence, I argue that if one has a higher-order doubt with regards to P, (...) then one is not justified in having any attitude towards P. Otherwise put: No attitude towards the doubted proposition respects one’s higher-order doubt. I argue that the most promising response to this problem is to hold that when one has a higher-order doubt about P, the best one can do to respect such a doubt is to simply have no attitude towards P. Higher-order doubt is thus much more rationally corrosive than non-higher-order doubt, as it undermines the possibility of justifiably having any attitude towards the doubted proposition. (shrink)

The task of this essay is to respond to the question concerning robots and responsibility—to answer for the way that we understand, debate, and decide who or what is able to answer for decisions and actions undertaken by increasingly interactive, autonomous, and sociable mechanisms. The analysis proceeds through three steps or movements. It begins by critically examining the instrumental theory of technology, which determines the way one typically deals with and responds to the question of responsibility when it involves technology. (...) It then considers three instances where recent innovations in robotics challenge this standard operating procedure by opening gaps in the usual way of assigning responsibility. The innovations considered in this section include: autonomous technology, machine learning, and social robots. The essay concludes by evaluating the three different responses—instrumentalism 2.0, machine ethics, and hybrid responsibility—that have been made in face of these difficulties in an effort to map out the opportunities and challenges of and for responsible robotics. (shrink)

‘‘Undone science’’ refers to areas of research that are left unfunded, incomplete, or generally ignored but that social movements or civil society organizations often identify as worthy of more research. This study mobilizes four recent studies to further elaborate the concept of undone science as it relates to the political construction of research agendas. Using these cases, we develop the argument that undone science is part of a broader politics of knowledge, wherein multiple and competing groups struggle over the construction (...) and implementation of alternative research agendas. Overall, the study demonstrates the analytic potential of the concept of undone science to deepen understanding of the systematic nonproduction of knowledge in the institutional matrix of state, industry, and social movements that is characteristic of recent calls for a ‘‘new political sociology of science.’’. (shrink)

Although A-consciousness and P-consciousness are conceptually distinct, a refined notion of A-consciousness makes it plausible that the two are empirically inseparable. I suggest that the notion of direct availability for global control can play a central role here, and draw out some consequences.

Do we control what we believe? Are we responsible for what we believe? In a series of ten essays David Owens explores various different forms of control we might have over belief, and the different forms of responsibility these forms of control generate.

In this chapter, the author says that the standard view of brain‐in‐a‐vat scenario is endorsed by the people who created The Matrix. The author argues that the hypothesis that he is envatted is not a skeptical hypothesis, but a metaphysical hypothesis. That is, it is a hypothesis about the underlying nature of reality. According to the author, the Matrix Hypothesis is equivalent to a version of the following three‐part Metaphysical Hypothesis. First, physical processes are fundamentally computational. Second, our cognitive systems (...) are separate from physical processes, but interact with these processes. Third, physical reality was created by beings outside physical space‐time. The Metaphysical Hypothesis combines the Creation Hypothesis, the Computational Hypothesis, and the Mind‐Body Hypothesis. It also adds a more specific claim: the computational processes underlying physical space‐time were designed by the creators as a computer simulation of a world. (shrink)

Relationships between the behavioral integrity of managers as perceived by employees and employee attitudes (job satisfaction and life satisfaction), well-being (stress and health), and behaviors (absenteeism) were tested using data from the 2002 National Study of the Changing Workforce (n = 2,820). Using multivariate and univariate analysis, perceived behavioral integrity (PBI) was positively related to job and life satisfaction and negatively related to stress, poor health, and absenteeism. The effect size for the relationship with job satisfaction was medium-to-large while the (...) effect sizes with respect to the other variables were small-to-medium. There was no support for the hypotheses that women would perceive lower levels of behavioral integrity and that the strength of the relationships between PBI and the outcomes variables would be stronger among women than among men. (shrink)

Taking a social identity approach to health behaviors, this research examines whether experimentally “activating” the human identity is an effective public-health strategy to curb the spread of COVID-19. Three goals of the research include examining: whether the human identity can be situationally activated using an experimental manipulation, whether activating the human identity causally increases behavioral intentions to protect the self and others from COVID-19, and whether activating the human identity causally increases behaviors that help protect vulnerable communities from COVID-19. Across (...) two preregistered experiments, results suggest the manipulation of identification with humanity had a significant but small effect on participants’ psychological bond with all humanity, but not their concern for all humanity. However, the manipulation had no causal effect on health-related behavioral intentions or helping behaviors that reduce the spread of COVID-19. Limitations, future directions, and direct benefits of the research are discussed. (shrink)

The book examines one of the most contested topics in linguistics and cognitive science: the role of recursion in language. It offers a precise account of what recursion is, what role it should play in cognitive theories of human knowledge, and how it manifests itself in the mental representations of language and other cognitive domains.

There is a long tradition in philosophy of using a priori methods to draw conclusions about what is possible and what is necessary, and often in turn to draw conclusions about matters of substantive metaphysics. Arguments like this typically have three steps: first an epistemic claim , from there to a modal claim , and from there to a metaphysical claim.