ABSTRACT: A traditional objection to inferentialism states that not all inferences can be meaning-constitutive and therefore inferentialism has to comprise an analytic-synthetic distinction. As a response, Peregrin argues that meaning is a matter of inferential rules and only the subset of all the valid inferences for which there is a widely shared corrective behaviour corresponds to rules and so determines meaning. Unfortunately, Peregrin does not discuss what counts as “widely shared”. In the paper, I argue for an empirical plausibility (...) of Peregrin’s proposal. The aim of the paper is to show that we can find examples of meaning-constitutive linguistic action, which sustain Peregrin’s response. The idea is supported by examples of meaning modulation. If Peregrin is right, then we should be able to find specific meaning modulations in which a new meaning is publicly available and modulated in such a way that it has a potential to be widely shared. I believe that binding modulations – a specific type of meaning modulations – satisfy this condition. (shrink)

This paper aims to solve a potential problem for the methodology of constitutive inference offered by Harbecke. The methodology is ultimately based on Mill’s “method of difference”, which requires a complete variation of factors in a given frame. In constitutive contexts, such a complete variation is often impossible. The offered solution utilizes the notion of a “mechanism slice”. In a first step, an example of a currently accepted explanation in neuroscience is reconstructed, which serves as a reference (...) point of the subsequent discussion. The regularity theory of mechanistic constitution and the corresponding methodology of constitutive inference are then introduced. Eventually, it is argued that the proposed solution accommodates well all schematic situations in which the impossibility of varying all test factors could be expected either to lead to false inferences or to preclude the establishment of correct constitutive claims. (shrink)

This paper discusses two challenges for a Boolean method for establishing constitutive regularity statements which, according to the regularity theory of mechanistic constitution, form the core of any mechanistic explanation in neuroscience. After presenting the regularity definition for the constitution relation and a methodology for constitutive inference, the paper discusses the problem of full variation of tested mechanistic factors and the problem of informational redundancy. A solution is offered for each problem. The first requires some adjustments to (...) the original theory by introducing the technical notion of a set of types satisfying independent instantiability. The second one is resolved by demonstrating that the problem of informational redundancy is based on a confusion that fails to challenge the theory. It is concluded that the methodology of constitutive inference is consistent and plausible with respect to actual practice in neuroscience. (shrink)

This paper discusses two challenges for a Boolean method for establishing constitutive regularity statements which, according to the regularity theory of mechanistic constitution, form the core of any mechanistic explanation in neuroscience. After presenting the regularity definition for the constitution relation and a methodology for constitutive inference, the paper discusses the problem of full variation of tested mechanistic factors and the problem of informational redundancy. A solution is offered for each problem. The first requires some adjustments to (...) the original theory by introducing the technical notion of a set of types satisfying independent instantiability. The second one is resolved by demonstrating that the problem of informational redundancy is based on a confusion that fails to challenge the theory. It is concluded that the methodology of constitutive inference is consistent and plausible with respect to actual practice in neuroscience. (shrink)

This monograph proposes a new way of studying the different forms of correlational inference, known in the Islamic jurisprudence as qiyās. According to the authors’ view, qiyās represents an innovative and sophisticated form of dialectical reasoning that not only provides new epistemological insights into legal argumentation in general but also furnishes a fine-grained pattern for parallel reasoning which can be deployed in a wide range of problem-solving contexts and does not seem to reduce to the standard forms of analogical (...) reasoning studied in contemporary philosophy of science and argumentation theory. After an overview of the emergence of qiyās and of the work of al-Shīrāzī penned by Soufi Youcef, the authors discuss al-Shīrāzī’s classification of correlational inferences of the occasioning factor. The second part of the volume deliberates on the system of correlational inferences by indication and resemblance. The third part develops the main theoretical background of the authors’ work, namely, the dialogical approach to Martin-Löf's Constructive Type Theory. The authors present this in a general form and independently of adaptations deployed in parts I and II. Part III also includes an appendix on the relevant notions of Constructive Type Theory, which has been extracted from an overview written by Ansten Klev. The book concludes with some brief remarks on contemporary approaches to analogy in Common and Civil Law and also to parallel reasoning in general. (shrink)

It is impossible to hold patently contradictory beliefs in mind together at once. Why? Because we know that it is impossible for both to be true. This impossibility is a species of rational necessity, a phenomenon that uniquely characterizes the relation between one person's beliefs. Here, Eric Marcus argues that the unity of the rational mind--what makes it one mind--is what explains why, given what we already believe, we can't believe certain things and must believe certain others in this special (...) sense. What explains this is that beliefs, and the inferences by which we acquire them, are constituted by a particular kind of endorsement of those very states and acts. This, in turn, entails that belief and inference are essentially self-conscious: to hold a belief or to make an inference is at the same time to know that one does. An examination of the nature of belief and inference, in light of the phenomenon of rational necessity, reveals how the unity of the rational mind is a function of our knowledge of ourselves as bound to believe the true. Rational self-consciousness is the form of mental togetherness. (shrink)

We argue that stereotypes associated with concepts like he-said–she-said, conspiracy theory, sexual harassment, and those expressed by paradigmatic slurs provide “normative inference tickets”: conceptual permissions to automatic, largely unreflective normative conclusions. These “mental shortcuts” are underwritten by associated stereotypes. Because stereotypes admit of exceptions, normative inference tickets are highly flexible and productive, but also liable to create serious epistemic and moral harms. Epistemically, many are unreliable, yielding false beliefs which resist counterexample; morally, many perpetuate bigotry and oppression. Still, (...) some normative inference tickets, like some activated by sexual harassment, constitute genuine moral and hermeneutical advances. For example, our framework helps explain Miranda Fricker’s notion of “hermeneutical lacunae”: what early victims of “sexual harassment” — as well as their harassers — lacked before the term was coined was a communal normative inference ticket — one that could take us, collectively, from “this is happening” to “this is wrong.”. (shrink)

In this article, I will provide a critical overview of the form of non-deductive reasoning commonly known as “Inference to the Best Explanation” (IBE). Roughly speaking, according to IBE, we ought to infer the hypothesis that provides the best explanation of our evidence. In section 2, I survey some contemporary formulations of IBE and highlight some of its putative applications. In section 3, I distinguish IBE from C.S. Peirce’s notion of abduction. After underlining some of the essential elements of (...) IBE, the rest of the entry is organized around an examination of various problems that IBE confronts, along with some extant attempts to address these problems. In section 4, I consider the question of when a fact requires an explanation, since presumably IBE applies only in cases where some explanation is called for. In section 5, I consider the difficult question of how we ought to understand IBE in light of the fact that among philosophers, there is significant disagreement about what constitutes an explanation. In section 6, I consider different strategies for justifying the truth-conduciveness of the explanatory virtues, e.g., simplicity, unification, scope, etc., criteria which play an indispensable role in any given application of IBE. In section 7, I survey some of the most recent literature on IBE, much of which consists of investigations of the status of IBE from the standpoint of the Bayesian philosophy of science. (shrink)

This thesis brings together two concerns. The first is the nature of inference—what it is to infer—where inference is understood as a distinctive kind of conscious and self-conscious occurrence. The second concern is the possibility of doxastic agency. To be capable of doxastic agency is to be such that one is capable of directly exercising agency over one’s beliefs. It is to be capable of exercising agency over one’s beliefs in a way which does not amount to mere (...) self-manipulation. Subjects who can exercise doxastic agency can settle questions for themselves. A challenge to the possibility of doxastic agency stems from the fact that we cannot believe or come to believe “at will”, where this in turn seems to be so because belief “aims at truth”. It must be explained how we are capable of doxastic agency despite that we cannot believe or come to believe at will. On the orthodox ‘causalist’ conception of inference for an inference to occur is for one act of acceptance to cause another in some specifiable “right way”. This conception of inference prevents its advocates from adequately seeing how reasoning could be a means to exercise doxastic agency, as it is natural to think it is. Suppose, for instance, that one reasons and concludes by inferring where one’s inference yields belief in what one infers. Such an inference cannot be performed at will. We cannot infer at will when inference yields belief any more than we can believe or come to believe at will. When it comes to understanding the extent to which one could be exercising agency in such a case the causalist conception of inference suggests that we must look to the causal history of one’s concluding act of acceptance, the nature of the act’s being determined by the way in which it is caused. What results is a picture on which such reasoning as a whole cannot be action. We are at best capable of actions of a kind which lead causally to belief fixation through “mental ballistics”. The causalist account of inference, I argue, is in fact either inadequate or unmotivated. It either fails to accommodate the self-consciousness of inference or is not best placed to play the very explanatory role which it is put forward to play. On the alternative I develop when one infers one’s inference is the conscious event which is one’s act of accepting that which one is inferring. The act’s being an inference is determined, not by the way it is caused, but by the self-knowledge which it constitutively involves. This corrected understanding of inference renders the move from the challenge to the possibility of doxastic agency to the above ballistics picture no longer tempting. It also yields an account of how we are capable of exercising doxastic agency by reasoning despite being unable to believe or come to believe at will. In order to see how such reasoning could amount to the exercise of doxastic agency it needs to be conceived of appropriately. I suggest that paradigm reasoning which potentially amounts the exercise of doxastic agency ought to be conceived of as primarily epistemic agency—agency the aim of which is knowledge. With inference conceived as suggested, I argue, it can be seen how to engage in such reasoning can just be to successfully exercise such agency. (shrink)

The deviation of mathematical proof—proof in mathematical practice—from the ideal of formal proof—proof in formal logic—has led many philosophers of mathematics to reconsider the commonly accepted view according to which the notion of formal proof provides an accurate descriptive account of mathematical proof. This, in turn, has motivated a search for alternative accounts of mathematical proof purporting to be more faithful to the reality of mathematical practice. Yet, in order to develop and evaluate such alternative accounts, it appears as a (...) necessary prerequisite to first possess a clear picture of what the deviation of mathematical proof from formal proof consists in. The present work aims to contribute building such a picture by investigating the relation between the elementary steps of deduction constituting the two types of proofs—mathematical inference and logical inference. Many claims have been made in the literature regarding the relation between mathematical inference and logical inference, most of them stating that the former is lacking properties that are constitutive of the latter. Such differentiating claims are, however, usually put forward without a clear conception of the properties occurring in them, and are generally considered to be immediately justified by our direct acquaintance, or phenomenological experience, with the two types of inferences. The present study purports to advance our understanding of the relation between mathematical inference and logical inference by developing a detailed philosophical analysis of the differentiating claims, that is, an analysis of the meaning of the differentiating claims—through the properties that occur in them—as well as the reasons that support them. To this end, we provide at the outset a representative list of the different properties of logical inference that have occurred in the differentiating claims, and we notice that they all boil down to the three properties of formality, generality, and mechanicality. For each one of these properties, our analysis proceeds in two steps: we first provide precise conceptual characterizations of the different ways logical inference has been said to be formal, general, and mechanical, in the philosophical and logical literature on formal proof; we then examine why mathematical inference does not appear to be formal, general, and mechanical, for the different variations of these notions identified. Our study results in a precise conceptual apparatus for expressing and discussing the properties differentiating mathematical inference from logical inference, and provides a first inventory of the various reasons supporting the observations of those differences. The differentiating claims constitute thus a set of data that any philosophical account of mathematical inference and proof purporting to be more faithful to mathematical practice ought to be able to accommodate and explain. (shrink)

This paper discusses the role of levels and level-bound theoretical terms in neurobiological explanations under the presupposition of a regularity theory of constitution. After presenting the definitions for the constitution relation and the notion of a mechanistic level in the sense of the regularity theory, the paper develops a set of inference rules that allow to determine whether two mechanisms referred to by one or more accepted explanations belong to the same level, or to different levels. The rules are (...) characterized as underlying level distinctions in neuroscience research. (shrink)

Gebharter has proposed using one of the best known Bayesian network causal discovery algorithms, PC, to identify the constitutive dependencies underwriting mechanistic explanations. His proposal assumes that mechanistic constitution behaves like deterministic direct causation, such that PC is directly applicable to mixed variable sets featuring both causal and constitutive dependencies. Gebharter claims that such mixed sets, under certain restrictions, comply with PC’s background assumptions. The aim of this article is to show that Gebharter’s proposal incurs severe problems, ultimately (...) rooted in the widespread non-compliance of mechanistic systems with PC’s assumptions. This casts severe doubts on the attempt to implicitly define constitution as a form of deterministic direct causation complying with PC’s assumptions. (shrink)

One reason for the popularity of Craver’s mutual manipulability account of constitutive relevance is that it seems to make good sense of the experimental practices and constitutive reasoning in the life sciences. Two recent papers propose a theoretical alternative to in light of several important conceptual objections. Their alternative approach, the no de-coupling account, conceives of constitution as a dependence relation that once postulated provides the best explanation of the impossibility of breaking the common cause coupling of a (...) macro-level mechanism and its micro-level components. This entails an abductive view of constitutive inference. Proponents of the NDC or abductive account recognize that their discussion leaves open a big question concerning the practical dimension of the notion of constitutive relevanssssce: Is it possible to faithfully reconstruct constitutional reasoning in science in terms of a failure to de-couple, via interlevel experiments, phenomena from their mechanistic constituents? Focusing on the field of memory and long-term potential research, this article argues that the abductive account provides a more adequate description of interlevel experiments in neuroscience. We also suggest that the account highlights some significant practical recommendations of how to interpret the findings of interlevel experiments. 1Introduction 2Mutual Manipulability and Constitutive Relevance 2.1Constitutive relevance through an interventionist lens 2.2Mutual manipulability: A methodological application 3Trouble for the Mutual Manipulability Account 4The Abductive Account of Constitution 5The Abductive Account: A Methodological Application 5.1Long-term potential and memory experiments 5.2A comparative summary 6Conclusions. (shrink)

It is often argued that inferential role semantics (IRS) entails semantic holism as long as theorists fail to answer the question about which inferences, among the many, are meaning-constitutive. Since analyticity, as truth in virtue of meaning, is a widely dismissed notion in indicating which inferences determine meaning, it seems that holism follows. Semantic holism is often understood as facing problems with the stability of content and many usual explanations of communication. Thus, we should choose between giving up IRS, (...) to avoid these holistic entailments, and defending holism against this charge, to rescue IRS. I try to pursue the second goal by analyzing certain patterns of counterfactual reasoning. Wilfrid Sellars and Robert Brandom claim that, to defend IRS, content-constitutive inferences are those counterfactually robust. While it is difficult to assess the goodness of such a view, it nonetheless entails that counterfactually non-robust inferences (which I call “modally ruled out inferences”) are not content-constitutive. If this is true, and if we take certain remarks about the grasp of concepts on board, there is a way to restrict the scope of the holism entailed by IRS to the extent of reshaping problems with the stability of content. (shrink)

In this paper, I defend what I call the ‘Inference Principle’. This principle holds that if an agent obtains some information legitimately, then the agent can make any inference she wants based on the information, without violating anyone’s right to privacy. This principle is interesting for at least three reasons. First, it constitutes a novel answer to the timely question of whether the widespread use of ‘data analytics’ to infer personal information about individuals is morally permissible. Second, it (...) contradicts what seems to be a common view of inferences’ ability to violate privacy rights. Third, it offers an account of the theoretically underdeveloped issue of what duties are engendered by the moral right to privacy with regard to inferred information. (shrink)

This monograph is an in-depth and engaging discourse on the deeply cognitive roots of human scientific quest. The process of making scientific inferences is continuous with the day-to-day inferential activity of individuals, and is predominantly inductive in nature. Inductive inference, which is fallible, exploratory, and open-ended, is of essential relevance in our incessant efforts at making sense of a complex and uncertain world around us, and covers a vast range of cognitive activities, among which scientific exploration constitutes the pinnacle. (...) Inductive inference has a personal aspect to it, being rooted in the cognitive unconscious of individuals, which has recently been found to be of paramount importance in a wide range of complex cognitive processes. One other major aspect of the process of inference making, including the making of scientific inferences, is the role of a vast web of beliefs lodged in the human mind, as also of a huge repertoire of heuristics, that constitute an important component of ‘unconscious intelligence’. Finally, human cognitive activity is dependent in a large measure on emotions and affects, that operate mostly at an unconscious level. Of special importance in scientific inferential activity is the process of hypothesis making, which is examined in this book, along with the above aspects of inductive inference, at considerable depth. The book focuses on the inadequacy of the viewpoint of naive realism in understanding the contextual nature of scientific theories, where a cumulative progress towards an ultimate truth about Nature appears to be too simplistic a generalization. It poses a critique to the commonly perceived image of science which is seen as the last word in logic and objectivity, the latter in the double sense of being independent of individual psychological propensities and, at the same time, approaching a correct understanding of the workings of a mind-independent nature. Adopting the naturalist point of view, it examines the essential tension between the cognitive endeavours of individuals and scientific communities, immersed in belief systems and cultures, on the one hand, and the engagement with a mind-independent reality on the other. In the end, science emerges as an interpretation of nature, which is perceived by us only contextually, as successively emerging cross-sections of limited scope and extent. Successive waves of theory building in science appear as episodic and kaleidoscopic changes in perspective as certain in-built borders are crossed, rather than as a cumulative progress towards some ultimate truth. While written in an informal and conversational style, the book raises a number of deep and intriguing questions located at the interface of cognitive psychology and philosophy of science, meant for both the general lay reader and the specialist. Of particular interest is the way it explores the role of belief (aided by emotions and affects) in making the process of inductive inference possible since belief is a subtle though all-pervasive cognitive factor not adequately investigated in the current literature. (shrink)

When a speaker states an argument in arguing—in its core sense—for the conclusion, the speaker asserts, as opposed to merely implies or implicates, the associated inference claim to the effect that the conclusion follows from the premises. In defense of this, I argue that how an inference claim is conveyed when stating an argument is constrained by constitutive and normative conditions for core cases of the speech of arguing for a conclusion. The speech act of assertion better (...) reflects such conditions than does implication, conversational implicature, or conventional implicature. (shrink)

A group of philosophers led by the late John Pollock has applied a method of reasoning about probability, known as direct inference and governed by a constraint known as Reichenbach's principle, to argue in support of ‘thirdism’ concerning the Sleeping Beauty Problem. A subsequent debate has ensued about whether their argument constitutes a legitimate application of direct inference. Here I defend the argument against two extant objections charging illegitimacy. One objection can be overcome via a natural and plausible (...) definition, given here, of the binary relation ‘logically stronger than’ between two properties that can obtain even when the respective properties differ from one another in ‘arity’; given this definition, the Pollock group's argument conforms to Reichenbach's principle. Another objection prompts a certain refinement of Reichenbach's principle that is independently well-motivated. My defense of the Pollock group's argument has epistemological import beyond the Sleeping Beauty problem, because it both widens and sharpens the applicability of direct inference as a method for inferring single-case epistemic probabilities on the basis of general information of a probabilistic or statistical nature. (shrink)

Inferentialism is a theory in the philosophy of language which claims that the meanings of expressions are constituted by inferential roles or relations. Instead of a traditional model-theoretic semantics, it naturally lends itself to a proof-theoretic semantics, where meaning is understood in terms of inference rules with a proof system. Most work in proof-theoretic semantics has focused on logical constants, with comparatively little work on the semantics of non-logical vocabulary. Drawing on Robert Brandom’s notion of material inference and (...) Greg Restall’s bilateralist interpretation of the multiple conclusion sequent calculus, I present a proof-theoretic semantics for atomic sentences and their constituent names and predicates. The resulting system has several interesting features: (1) the rules are harmonious and stable; (2) the rules create a structure analogous to familiar model-theoretic semantics; and (3) the semantics is compositional, in that the rules for atomic sentences are determined by those for their constituent names and predicates. (shrink)

Inferentialism is a theory in the philosophy of language which claims that the meanings of expressions are constituted by inferential roles or relations. Instead of a traditional model-theoretic semantics, it naturally lends itself to a proof-theoretic semantics, where meaning is understood in terms of inference rules with a proof system. Most work in proof-theoretic semantics has focused on logical constants, with comparatively little work on the semantics of non-logical vocabulary. Drawing on Robert Brandom’s notion of material inference and (...) Greg Restall’s bilateralist interpretation of the multiple conclusion sequent calculus, I present a proof-theoretic semantics for atomic sentences and their constituent names and predicates. The resulting system has several interesting features: (1) the rules are harmonious and stable; (2) the rules create a structure analogous to familiar model-theoretic semantics; and (3) the semantics is compositional, in that the rules for atomic sentences are determined by those for their constituent names and predicates. (shrink)

When a speaker states an argument in arguing—in its core sense—for the conclusion, the speaker asserts, as opposed to merely implies or implicates, the associated inference claim to the effect that the conclusion follows from the premises. In defense of this, I argue that how an inference claim is conveyed when stating an argument is constrained by constitutive and normative conditions for core cases of the speech of arguing for a conclusion. The speech act of assertion better (...) reflects such conditions than does implication, conversational implicature, or conventional implicature. (shrink)

The major competing statistical paradigms share a common remarkable but unremarked thread: in many of their inferential applications, different probability interpretations are combined. How this plays out in different theories of inference depends on the type of question asked. We distinguish four question types: confirmation, evidence, decision, and prediction. We show that Bayesian confirmation theory mixes what are intuitively “subjective” and “objective” interpretations of probability, whereas the likelihood-based account of evidence melds three conceptions of what constitutes an “objective” probability.

In lieu of an abstract, here is a brief excerpt of the content:BOOK REVIEWS The Inference That Makes Science. By ERNAN McMULLIN. The Aquinas Lecture, 1992. Milwaukee: Marquette University Press, 1992. Pp. iv +112. In this ambitious lecture Father Ernan McMullin recapitulates and refines a thesis that has guided his thought for the past forty years. In essence the thesis is this: precisely how science is made has eluded the best minds for centuries, and only in the work of (...) Charles Sanders Peirce, suitably emended by McMullin, has the puzzle finally been solved. " Retroduction " is the inference that makes science. Once this is understood, errors on what constitutes scientific method-those of Aristotle, Aquinas, Galileo, Newton, Bacon, Hume, et al.-can be rectified and one can see science for what it truly is: a complex process of theory appraisal that yields, not definitive truth, but well-established results to which assent can be given with at best "practical certainty," whatever that might be (pp. 91-96). Why McMullin should have chosen such a theme for an Aquinas Lecture is a question that defies reasonable answer. Surely one does not have to he so negative about the thought of Aristotle, Aquinas, and Galileo to advance one's ideas about science in the present day. What McMullin could easily have done, and he hints at this in the last two paragraphs of his lecture (pp. 97-98), is show how retroduction is itself simply a relaxed version of the demonstrative regress, the method actually endorsed by Aristotle, Aquinas, and Galileo. Such a retroductive version, fair enough, yields knowledge of a probable cause, the type of knowledge most typical of modern science. McMullin did not have to embark on the dangerous course of trying to prove that proof and certainty are forever beyond the grasp of science, or that never in the history of science has anyone established a definitive truth. That, in effect, is what McMullin has tried to do, and in the attempt to make the point he fumbles at almost every juncture throughout a very long lecture. To set the record straight more than a review is being re--·quested; perhaps a book, and even that might not suffice for those whose minds are made up. To understand the import of the lecture one must appreciate that it is hut a brief episode in a debate over demonstration in science that has been going on since McMullin first came to the University of Notre Dame in 1954. I myself have published many hooks and articles that engage the very point of his lecture and provide the contra evidence to 131 132 BOOK REVIEWS show elements of continuity in scientific method from Aristotle to the present. My last two volumes, in press at the same time as McMullin's Aquinas Lecture, answer in detail the aporiai he there raises.1 I need 1 Galileo's Logic of Discovery and Proof. The Backgrnund, Content, and Use of His Appropriated Treatises on Aristotle's Posterior Analytics. Boston Studies in the Philosophy of Science 137. Dordrecht-Boston-London: Kluwer Academic Publishers, 1992, xxiii + 323 pp.; Galileo's Logical Treatises. A Translation, with Notes and Commentary, of His Appropriated Questions on Aristotle's Posterior Analytics. Boston Studies in the Philosophy of Science 138. DordrechtBoston -London: Kluwer Academic Publishers, 1992, xix + 239 pp. only refer the interested reader to them for an extended and documented reply to his arguments. Some idea of the flavor of our debate, however, can be gained from the following. To support his thesis, McMullin has to maintain that Aristotle's proof that the moon is a sphere (from its having phases) and that Galileo's proofs that there are mountains on the moon, that Jupiter has satellites, and that Venus circles the sun (all based on telescopic observations) are not strictly demonstrative, that is, they do not yield true and certain conclusions. He declines to answer a query I have often tendered whether he personally is certain on the basis of pre-spacecraft evidence that the moon is a sphere, that there are mountains on it, that Jupiter has satellites, and so on. Instead he offers the categorical response "that planetary science is not an apodictic science, indeed that no natural science is... (shrink)

This essay delves into the essentialities of object-giving sources within the formulation of epistemic objectivity. It explores the relationship between objectivity and intentional states, particularly in the context of immediate and transcendent experiences. A key focus of this paradigm is the examination of inferences and how they are held in X’s intentional processes. These claims about inferences contribute to the perception of objectivity by highlighting the epistemological transitions of things that occur in the constitutive ideation. Additionally, the activity within (...) X’s episteme leads to significant articulations that reflect a structural realism of experiences. The essay also introduces a convention of the experiential-intentional process so that the causality manipulations could be avoided by the precents of sources of ideation. In this instance, the central niche is occupied by transcendental reflections of intentionality, which are fundamentally founded on experiences and objectivity, and they possess a distinct rhetorical quality. They manifest as acts, propositional forms, and constituents, all of which contribute to the understanding and justification of objectivity. To establish such a framework that upholds objectivity, certain prerequisites must be met. Firstly, the framework must possess justificational resources that prevent causality manipulations. Secondly, pre-reflective sources should not inter-define causality in epistemic circumstances, although this does not exclude the emergence of causal relations, and thus this approach offers a correlational explanation. Lastly, transcendental reflections should remain compatible with the experiential-intentional process, allowing for the accommodation of subjectivity in the justification of objectivity. (shrink)

An influential way of distinguishing inferential from non-inferential processes appeals to representational states: an agent infers a conclusion from some premises only if she represents those premises as supporting that conclusion. By contrast, when some premises merely cause an agent to believe the conclusion, there is no relevant representational state. While promising, the appeal to representational states invites a regress problem, first famously articulated by Lewis Carroll. This paper develops a novel account of inference that invokes representational states without (...) succumbing to regress. The key move is to reject the tempting idea that the relevant representational states are causally prior to inferences. I argue, instead, that an inference constitutes the relevant representational state. To infer is thus—in the very drawing of the conclusion—to represent the premises as supporting the conclusion, and thereby to commit to that support relation. (shrink)

Samuel Coleridge once noted that very short works of art ease the cognitive burden on poet and reader alike. Limiting the number of lines in a poem, he contends, allows the work 'to acquire, as it were, a Totality' which allows the reader's mind to 'rest satisfied'. Anyone who has strained to grasp the overall pattern of some massive novel, film, or musical work can readily appreciate Coleridge's point. And yet insofar as a film or poem is a temporal work (...) of art, the parts of which are manifested only consecutively, its Totality - be it an ever so small one - is never directly presented to us all at once, and its acquisition, as well as the satisfaction such an acquisition can provide, requires a feat of memory. A film, like a life, may have a brilliant, simple order and a deep and powerful unity, but the presentation and realization of such a totality is something that takes place in time, something that requires an experience of temporal unfolding - something that requires the work of a mind capable of thinking through and recollecting the temporal relations between the parts of the whole. So that while Marianne Olsen Ulrichsen's Come is a perfectly unified gem, a satisfying totality that presents itself to us in just four and a half minutes, we must nonetheless live through its unfolding to discover the coherence of its parts. One of this film's central themes is precisely this kind of process, namely, the constitution of personal identity and togetherness, in and through time and memory. What follows is just one story that may be told about an elusive process that no doubt takes very different forms for different viewers. (shrink)

In this paper, we introduce an ecological account of communication according to which acts of communication are active inferences achieved by affecting the behavior of a target organism via the modification of its field of affordances. Constraining a target organism’s behavior constitutes a mechanism of socially extended active inference, allowing organisms to proactively regulate their inner states through the behavior of other organisms. In this general conception of communication, the type of cooperative communication characteristic of human communicative interaction is (...) a way of constraining interaction dynamics toward the goals of a given joint action by constructing and altering shared fields of affordances. This account embraces a pragmatist view according to which communication is a form of action aiming to influence the behavior of a target, and stands against the traditional transmission view according to which communication fundamentally serves to convey information. Understanding acts of communication as active inference under an ecological interpretation allows us to link communicative and ultimately linguistic behavior to the biological imperative of minimizing free energy and to emphasize the action-oriented nature of communicative interaction. (shrink)

Accounts of analogical inference are usually categorized into four broad groups: abductive, deductive, inductive and sui generis. The purpose of this paper is to defend a sui generis model of analogical inference. It focuses on the sui generis account, as developed by Juthe [2005, 2009, 2015, 2016] and Botting’s [2017] criticism of it. This paper uses the pragmadialectical theory of argumentation as the methodological framework for analyzing and reconstructing argumentation. The paper has two main points. First, that Juthe’s (...) arguments against a deductive interpretation of prima facie analogy argumentation remain unaffected by Botting’s criticism, which means that many of the reasons against deductive reformulation of analogy argumentation still stand. The additional argument, which Botting himself brings up, that a deductive interpretation cannot account for the cumulative effect of analogies, just provides further reason to reject deductivism. The second main point of this paper is that an inductive interpretation of analogical inference also fails. There are constitutional differences between inductive and analogical inference that cannot be bridged. The result is a firm defense of the sui generis view of analogical inference. (shrink)

What does the Chilean Constitution say about euthanasia? When we read the Chilean Constitution we cannot find the word “euthanasia” in the text, and there is no such thing as a right to die, therefore the answer should apparently be that the Constitution does not say anything about euthanasia and, in short, euthanasia is not allowed. However, on a second reading we can find out some statements from which we can infer another answer. My aim is to show that there (...) is room for the acceptance of euthanasia in the Chilean Constitution, and in other similar Constitutions and international regulations in which freedom of conscience is granted. (shrink)

As social beings, people need to be able to interact intelligently with others in their social environment. Accordingly, people spend much time conversing with one another in order to understand the broad and fine aspects of the relations that link them. They are especially interested in the interactive behaviors that constitute social relations, such as mutual aid, gift giving and exchange, sharing, informal socializing, or deception. The evaluations of these behaviors are embedded in social relationships and charged with values and (...) emotions. We developed tasks to probe how people in an unfamiliar socio-cultural setting understand and account for the behavior of others conditional upon their category membership – by trying to elicit the basic categories, stereotypes, and models that inform the causal perceptions, inferences and reasoning people use in understanding others’ interactive behaviors – and we tested these tasks among the Wampar in Papua New Guinea. The results show changes in the relevance of social categories among the Wampar but also, and perhaps more important, limitations in the translation and applicability of cognitive tasks. (shrink)

This paper argues that three plausible principles are mutually inconsistent: One ought to assert only what one knows; If it is proper to assert some proposition q, then it is, barring special and not very common circumstances, proper to assert any proposition p from which q has been competently inferred; and Some propositions are both properly assertible and known by competent inference from propositions which one does not know. Each pair of two principles constitutes an argument against the remaining (...) principle, but which principle should one drop? (shrink)

One’s constitution—whether one is generous or miserly, temperate or intemperate, kind or mean, etc.—is beyond one’s control in significant respects. Yet one’s constitution affects how one acts. And how one acts affects one’s moral standing. The counterintuitive inference—the so-called problem of constitutive moral luck—is that one’s moral standing is, to some significant extent, beyond one’s control. This article grants the premises but resists the inference. It argues that one’s constitution should have no net impact on one’s moral (...) standing. While a bad constitution lowers the chance that one will act morally, it offers significant gains to moral standing should that chance materialize. A good constitution increases one’s chance of performing good acts but for correspondingly more modest gains. This effect should smooth out, and possibly eliminate, the expected impact of constitution on moral standing. (shrink)

Much of the recent work on the epistemology of causation has centered on two assumptions, known as the Causal Markov Condition and the Causal Faithfulness Condition. Philosophical discussions of the latter condition have exhibited situations in which it is likely to fail. This paper studies the Causal Faithfulness Condition as a conjunction of weaker conditions. We show that some of the weaker conjuncts can be empirically tested, and hence do not have to be assumed a priori. Our results lead to (...) two methodologically significant observations: (1) some common types of counterexamples to the Faithfulness condition constitute objections only to the empirically testable part of the condition; and (2) some common defenses of the Faithfulness condition do not provide justification or evidence for the testable parts of the condition. It is thus worthwhile to study the possibility of reliable causal inference under weaker Faithfulness conditions. As it turns out, the modification needed to make standard procedures work under a weaker version of the Faithfulness condition also has the practical effect of making them more robust when the standard Faithfulness condition actually holds. This, we argue, is related to the possibility of controlling error probabilities with finite sample size (“uniform consistency”) in causal inference. (shrink)

The paper addresses the phenomenology of inference. It proposes that the conscious character of conscious inferences is partly constituted by a sense of meaning; specifically, a sense of what Grice called ‘natural meaning’. In consciously drawing the (outright, categorical) conclusion that Q from a presumed fact that P, one senses the presumed fact that P as meaning that Q, where ‘meaning that’ expresses natural meaning. This sense of natural meaning is phenomenologically analogous, I suggest, to our sense of what (...) is said in fluently comprehending everyday utterances in our first language. The proposal that conscious inference involves a sense of natural meaning is compared with views according to which conscious inference involves taking the premises (i) to be good reasons for the conclusion (as defended by Thomson and Grice), (ii) to support it (as argued by Audi and, recently, Boghossian), or (iii) to imply it (as lately contended by Broome). I argue our proposal can explain certain phenomena handled by alternatives (i) and (ii), but that some further phenomena is handled by our account but not these alternatives. In relation to alternative (iii), I argue that, in so far as implicational and natural-meaning relations come apart, the latter are a better fit for what we sense or take to be so in conscious inference. (shrink)

The Explanatory Model of Scientific Understanding is a deflationary thesis recently advocated by Kareem Khalifa. EMU is committed to two key ideas: all understanding-relevant knowledge is propositional in nature; and the abilities we use to generate understanding are merely our usual logical reasoning skills. In this paper I provide an argument against both ideas, suggesting that scientific understanding requires a significant amount of non-propositional knowledge not captured by logical relations. I use the Inferential Model of Scientific Understanding to reveal how (...) we can better represent what constitutes understanding a scientific event. In particular, this model accounts for not only logical and probabilistic inferences, but also those conceptual associations and categorizations we must make to comprehend an explanation. (shrink)

Fodor & Lepore (2001) and Williamson (2003) attack the inferentialist account of concept possession according to which possessing or understanding a concept requires endorsing the inference patterns constitutive of its content. I show that Fodor & Lepore’s concern - that the conception places an exorbitant epistemological demands on possessors of a concept - is met by Brandom’s tolerance of materially bad nonconservative inferences. Such inferences themselves, as Williamson argues, present difficulties for the ‘understanding as endorsement’ conception. I show (...) that, properly understood, Brandom’s broad conception of inferential role, which encompasses social-perspectival inferential connections, has the resources to respond to Willianson’s challenge. (shrink)

In this paper we compare grammatical inference in the context of simple and of mixed Lambek systems. Simple Lambek systems are obtained by taking the logic of residuation for a family of multiplicative connectives /, *, \, together with a package of structural postulates characterizing the resource management properties of the * connective. Different choices for Associativity and Commutativity yield the familiar logics NL, L, NLP, LP. Semantically, a simple Lambek system is a unimodal logic: the connectives get a (...) Kripke style interpretation in terms of a single ternary accessibility relation modeling the notion of linguistic composition for each individual system.The simple systems each have their virtues in linguistic analysis. But none of them in isolation provides a basis for a full theory of grammar. In the second part of the paper, we consider two types of mixed Lambek systems.The first type is obtained by combining a number of unimodal systems into one multimodal logic. The combined multimodal logic is set up in such a way that the individual resource management properties of the constituting logics are preserved. But the inferential capacity of the mixed logic is greater than the sum of its component parts through the addition of interaction postulates, together with the corresponding interpretive constraints on frames, regulating the communication between the component logics.The second type of mixed system is obtained by generalizing the residuation scheme for binary connectives to families of n-ary connectives, and by putting together families, of different arities in one logic. We focus on residuation for unary connectives, hence on mixed frames, as these already represent the complexities in full. We prove a number of elementary logical results for unary families of residuated connectives and their combination with binary families. The existing proposals for unary ‘structural modalities’ are situated within this general framework, and a number of new linguistic applications is given. (shrink)

In this essay we collect and put together a number of ideas relevant to the under- standing of the phenomenon of creativity, confining our considerations mostly to the domain of cognitive psychology while we will, on a few occasions, hint at neuropsy- chological underpinnings as well. In this, we will mostly focus on creativity in science, since creativity in other domains of human endeavor have common links with scientific creativity while differing in numerous other specific respects. We begin by briefly (...) introducing a few basic notions relating to cognition, among which the notion of ‘concepts’ is of basic relevance. The myriads of concepts lodged in our mind constitute a ‘conceptual space’ of an enormously complex structure, where con- cepts are correlated by beliefs that are themselves made up of concepts and are as- sociated with emotions. The conceptual space, moreover, is perpetually in a state of dynamic evolution that is once again of a complex nature. A major component of the dynamic evolution is made up of incessant acts of inference, where an inference occurs essentially by means of a succession of correlations among concepts set up with beliefs and heuristics, the latter being beliefs of a special kind, namely, ones relatively free of emotional associations and possessed of a relatively greater degree of justification. Beliefs, along with heuristics, have been described as the ‘mind’s software’, and con- stitute important cognitive components of the self-linked psychological resources of an individual. The self is the psychological engine driving all our mental and physical activity, and is in a state of ceaseless dynamics resulting from one’s most intimate ex- periences of the world accumulating in the course of one’s journey through life. Many of our psychological resources are of a dual character, having both a self-linked and a shared character, the latter being held in common with larger groups of people and imbibed from cultural inputs. We focus on the privately held self-linked beliefs of an individual, since these are presumably of central relevance in making possible inductive inferences – ones in which there arises a fundamental need of adopting a choice or making a decision. Beliefs, decisions, and inferences, all have the common link to the self of an individual and, in this, are fundamentally analogous to free will, where all of these have an aspect of non-determinism inherent in them. Creativity involves a major restructuring of the conceptual space where a sustained inferential process eventually links remote conceptual domains, thereby opening up the possibility of a large number of new correlations between remote concepts by a cascading process. Since the process of inductive inference depends crucially on de- cisions at critical junctures of the inferential chain, it becomes necessary to examine the basic mechanism underlying the making of decisions. In the framework that we attempt to build up for the understanding of scientific creativity, this role of decision making in the inferential process assumes central relevance. With this background in place, we briefly sketch the affect theory of decisions. Affect is an innate system of response to perceptual inputs received either from the exter- nal world or from the internal physiological and psychological environment whereby a positive or negative valence gets associated with a perceptual input. Almost every sit- uation faced by an individual, even one experienced tacitly, i.e., without overt aware-ness, elicits an affective response from him, carrying a positive or negative valence that underlies all sorts of decision making, including ones carried out unconsciously in inferential processes. Referring to the process of inferential exploration of the conceptual space that gener- ates the possibility of correlations being established between remote conceptual do- mains, such exploration is guided and steered at every stage by the affect system, analogous to the way a complex computer program proceeds through junctures where the program ascertains whether specified conditions are met with by way of generating appropriate numerical values – for instance, the program takes different routes, depending on whether some particular numerical value turns out to be positive or negative. The valence generated by the affect system in the process of adoption of a choice plays a similar role which therefore is of crucial relevance in inferential processes, especially in the exploration of the conceptual space where remote domains need to be linked up – the affect system produces a response along a single value dimension, resembling a number with a sign and a magnitude. While the affect system plays a guiding role in the exploration of the conceptual space, the process of exploration itself consists of the establishment of correlations between concepts by means of beliefs and heuristics, the self-linked ones among the latter having a special role in making possible the inferential journey along alternative routes whenever the shared rules of inference become inadequate. A successful access to a remote conceptual domain, necessary for the creative solution of a standing problem or anomaly – one that could not be solved within the limited domain hitherto accessed – requires a phase of relatively slow cumulative search and then, at some stage, a rapid cascading process when a solution is in sight. Representing the conceptual space in the form of a complex network, the overall process can be likened to one of self-organized criticality commonly observed in the dynamical evolution of complex systems. In order that inferential access to remote domains may actually be possible, it is necessary that restrictions on the exploration process – necessary for setting the context in ordinary instances of inductive inference – be relaxed and a relatively free exploration in a larger conceptual terrain be made possible. This is achieved by the mind going into the default mode, where external constraints – ones imposed by shared beliefs and modes of exploration – are made inoperative. While explaining all these various aspects of the creative process, we underline the supremely important role that analogy plays in it. Broadly speaking, analogy is in the nature of a heuristic, establishing correlations between concepts. However, analo- gies are very special in that these are particularly effective in establishing correlations among remote concepts, since analogy works without regard to the contiguity of the concepts in the conceptual space. In establishing links between concepts, analogies have the power to light up entire terrains in the conceptual space when a rapid cas- cading of fresh correlations becomes possible. The creative process occurs within the mind of a single individual or of a few closely collaborating individuals, but is then continued by an entire epistemic community, eventually resulting in a conceptual revolution. Such conceptual revolutions make pos- sible the radical revision of scientific theories whereby the scope of an extant theory is broadened and a new theoretical framework makes its appearance. The emerging theory is characterized by a certain degree of incommensurability when compared with the earlier one – a feature that may appear strange at first sight. But incommen- surability does not mean incompatibility and the apparently contrary features of the relation between the successive theories may be traced to the multi-layered structureof the conceptual space where concepts are correlated not by means of single links but by multiple ones, thereby generating multiple layers of correlation, among which some are retained and some created afresh in a conceptual restructuring. We conclude with the observation that creativity occurs on all scales. Analogous to correlations being set up across domains in the conceptual space and new domains being generated, processes with similar features can occur within the confines of a domain where a new layer of inferential links may be generated, connecting up sub- domains. In this context, insight can be looked upon as an instance of creativity within the confines of a domain of a relatively limited extent. (shrink)

This paper addresses Frege's discussion of illogical thought in the introduction to Basic Laws of Arithmetic. After a brief introduction, I discuss Frege's claims that logic is normative vis-à-vis thought, and not descriptive, and his opposition to the idea that logical laws express psychological necessities. I argue that these two strands of Frege's polemic against psychologism constitute two motivating factors behind his allowing for the possibility of illogical thought. I then explore a line of thought—originally advanced by Joan Weiner—according to (...) which Frege should have rejected illogical thought as not constituting a genuine possibility. I argue that, once developed, this line of thought constitutes an important correction (moreover, one that is consistent with his two aforementioned anti-psychologistic strands) to Frege's own response to the possibility of illogical thought. -/- . (shrink)

Approximately one in six top economic research papers draws an explicitly causal conclusion. But what do economists mean when they conclude that A 'causes' B? Does 'cause' say that we can influence B by intervening on A, or is it only a label for the correlation of variables? Do quantitative analyses of observational data followed by such causal inferences constitute sufficient grounds for guiding economic policymaking? The Philosophy of Causality in Economics addresses these questions by analyzing the meaning of causal (...) claims made by economists and the philosophical presuppositions underlying the research methods used. The book considers five key causal approaches: the regularity approach, probabilistic theories, counterfactual theories, mechanisms, and interventions and manipulability. Each chapter opens with a summary of literature on the relevant approach and discusses its reception amongst economists. The text details case studies, and goes on to examine papers which have adopted the approach in order to highlight the methods of causal inference used in contemporary economics. It analyses the meaning of the causal claim put forward, and finally reconstructs the philosophical presuppositions accepted implicitly by economists. The strengths and limitations of each method of causal inference are also considered in the context of using the results as evidence for policymaking. This book is essential reading to those interested in literature on the philosophy of economics, as well as the philosophy of causality and economic methodology in general. (shrink)

It is traditionally thought that metaphorical utterances constitute a special— nonliteral—kind of departure from lexical constraints on meaning. Dan Sperber and Deirdre Wilson have been forcefully arguing against this: according to them, relevance theory’s comprehension/interpretation procedure for metaphorical utterances does not require details specifi c to metaphor (or nonliteral discourse); instead, the same type of comprehension procedure as that in place for literal utterances covers metaphors as well. One of Sperber and Wilson’s central reasons for holding this is that metaphorical (...) utterances occupy one end of a continuum that includes literal, loose and hyperbolic utterances with no sharp boundaries in between them. Call this the continuum argument about interpreting metaphors. My aim is to show that this continuum argument doesn’t work. For if it were to work, it would have an unwanted consequence: it could be converted into a continuum argument about interpreting linguistic errors, including slips of the tongue, of which malaprops are a special case. In particular, based on the premise that the literal–loose–metaphorical continuum extends to malaprops also, we could conclude that the relevance-theoretic comprehension procedure for malaprops does not require details specifi c to linguistic errors, that is, details beyond those already in place for interpreting literal utterances. Given that we have good reason to reject this conclusion, we also have good reason to rethink the conclusion of the continuum argument about interpreting metaphors and consider what additional (metaphor-specifi c) details—about the role of constraints due to what is lexically encoded by the words used—might be added to relevance-theoretic comprehension procedures. (shrink)

Husserl characterizes sleep with the idea of “the relaxation of the will.” One finds a similar approach in the work of Maine de Biran, who explains sleep as “the suspension of the will.” More recently, Brian O’Shaughnessy and Matthew Soteriou have argued that mental actions constitute wakeful consciousness. In clinical practice, patients with disorders of consciousness who show “purposeful” behavior are classified as “minimally conscious,” while those in an “unresponsive wakeful state” merely behave reflexively. To what extent and how are (...) these proposals justified? This question pushes both the first- and the third-personal approaches to their limits: in an unconscious state, like a coma, one cannot reflect upon oneself; likewise, one cannot infer from physiological data whether someone is phenomenally conscious. This work offers a critical review of these proposals regarding the constitutive role for agency in phenomenal consciousness. It then presents revised versions of O’Shaughnessy’s and Soteriou’s Arguments from Synthesis and from Self-Consciousness. The argument is that everything of which one is phenomenally conscious is either a potential reason for a possible agentive power exertion, or just that power exertion itself. The “self” referred to in “self”-consciousness is either the agent or a “non-agent,” carrying out functions for the agent. Agency is therefore constitutive of phenomenal consciousness. The resulting view helps to solve the Combination Problem for panpsychism, by suggesting that agency is what raises sub-personal micro-consciousness to the personal level. The view may also justify the notion of a “Minimally Conscious State” in clinical practice. (shrink)

ArgumentThis paper argues that ancient Babylonian signs (omens) reflect a mode of inferential reasoning as a function of their syntactic and logical structure as conditionals. Taking into account the institutional context that produced a systematic written body of omens, the paper is principally interested in the cognitive disposition of such texts. Investigating what constitutes system in these works, formal aspects of the material are examined in terms of the nature of conditionals and the logic of conditional statements. It is argued (...) that conditional statements about ominous phenomena speak as much to a notion of conceivability and possibility as to empirical physical actuality. It is claimed that the epistemological character of the Babylonian compendia of signs cannot be understood without due attention to epistemic possibility and further, that the cuneiform omen texts comprise a different kind of scientific knowledge from that limited to a knowledge of physical phenomena and their laws. (shrink)

The coupling-constitution fallacy claims that arguments for extended cognition involve the inference of “x and y constitute z” from “x is coupled to y” and that such inferences are fallacious. We argue that the coupling-constitution fallacy fails in its goal to undermine the hypothesis of extended cognition: appeal to the coupling-constitution fallacy to rule out possible empirical counterexamples to intracranialism is fallacious. We demonstrate that appeals to coupling-constitution worries are problematic by constructing the fallacious argument against the hypothesis of (...) extended cognition. We consider several objections to our argument and find them insufficient to rebut our conclusion. (shrink)

Fodor & Lepore (2001) and Williamson (2003) attack the inferentialist account of concept possession according to which possessing or understanding a concept requires endorsing the inference patterns constitutive of its content. I show that Fodor & Lepore's concern – that the conception places an exorbitant epistemological demands on possessors of a concept – is met by Brandom's tolerance of materially bad nonconservative inferences. Such inferences themselves, as Williamson argues, present difficulties for the 'understanding as endorsement' conception. I show (...) that, properly understood, Brandom's broad conception of inferential role, which encompasses social-perspectival inferential connections, has the resources to respond to Willianson's challenge. (shrink)

Individual choices are commonly taken to manifest personal preferences. The present study investigated whether social and statistical cues influence young children's inferences about the generalizability of preferences. Preschoolers were exposed to either 1 or 2 demonstrators’ selections of objects. The selected objects constituted 18%, 50%, or 100% of all available objects. We found that children took a single demonstrator's choices as indicative only of his or her personal preference. However, when 2 demonstrators made the same selection, then children inferred that (...) it generalized to other agents of the same kind as the original demonstrator's, but not to agents of a different kind. Lastly, only when both demonstrators blatantly violated random selection (i.e., in the 18% condition) did children generalize the preference even to an agent of a different kind. Thus, from a young age, social and statistical cues inform children's naïve sociology. (shrink)

The issue of what constitutes a valid logical inference is a difficult question. At a minimum, we believe a permissible step in a proof must provide the reader with rational grounds to believe that the new step is a logically necessary consequence of previous assertions. However, this begs the question of what constitutes these rational grounds. Formalist accounts typically describe valid rules of inferences as those that can be found by applying one of the explicit rules of inference (...) in the formal system in which the proof is couched. However, philosophers of mathematics find such a description unhelpful because many inferences in the proofs that mathematicians actually produce cannot be expressed in a formal language, at least not without seriously distorting the semantic content of the inference (e.g., Larvor, 2012). In this chapter, we investigate mathematicians’ perceptions of a particular kind of inference in a particular setting. Specifically, we shed light on what types of graphical inferences mathematicians find permissible in a real analysis proof. Following Larvor (in press), we examine mathematicians’ reactions to metrical graphical inferences (i.e., inferences whose validity depends on the accuracy of the graph that was drawn and whose validity can be changed by minor deformations) and nonmetrical graphical inferences (i.e., inferences whose validity does not depend on a the accuracy of the graph and whose validity is not vulnerable to local deformations). The goal of this chapter is threefold. First, we demonstrate that most mathematicians reject metrical graphical inferences as impermissible in a real analysis proof. Second, we show that many mathematicians regard nonmetrical graphical inferences as permissible in a real analysis proofs. Third, we illustrate how mathematicians collectively disagree on the permissibility of nonmetrical inferences. (shrink)