I discuss the design of the method of entropic inference as a general framework for reasoning under conditions of uncertainty. The main contribution of this discussion is to emphasize the pragmatic elements in the derivation. More specifically: (1) Probability theory is designed as the uniquely natural tool for representing states of incomplete information. (2) An epistemic notion of information is defined in terms of its relation to the Bayesian beliefs of ideally rational agents. (3) The method of updating (...) from a prior to a posterior probability distribution is designed through an eliminative induction process that singles out the logarithmic relative entropy as the unique tool for inference. The resulting framework includes as special cases both MaxEnt and Bayes’ rule. It therefore unifies entropic and Bayesian methods into a single general inference scheme. I find that similar pragmatic elements are an integral part of Putnam’s internal realism, of Floridi’s informational structural realism, and also of van Fraasen’s empiricist structuralism. I conclude with the conjecture that their valuable insights can be incorporated into a single coherent doctrine—an informational pragmatic realism. (shrink)

The idea that perceptual and cognitive systems must incorporate knowledge about the structure of the environment has become a central dogma of cognitive theory. In a Bayesian context, this idea is often realized in terms of “tuning the prior”—widely assumed to mean adjusting prior probabilities so that they match the frequencies of events in the world. This kind of “ecological” tuning has often been held up as an ideal of inference, in fact defining an “ideal observer.” But widespread as (...) this viewpoint is, it directly contradicts Bayesian philosophy of probability, which views probabilities as degrees of belief rather than relative frequencies, and explicitly denies that they are objective characteristics of the world. Moreover, tuning the prior to observed environmental frequencies is subject to overfitting, meaning in this context overtuning to the environment, which leads (ironically) to poor performance in future encounters with the same environment. Whenever there is uncertainty about the environment—which there almost always is—an agent's prior should be biased away from ecological relative frequencies and toward simpler and more entropic priors. (shrink)

It has become something of a dogma in the philosophy of science that modern cosmology has completed Boltzmann's program for explaining the statistical validity of the Second Law of thermodynamics by providing the low entropy initial state needed to ground the asymmetry in entropic behavior that underwrites our inference about the past. This dogma is challenged on several grounds. In particular, it is argued that it is likely that the Boltzmann entropy of the initial state of the universe (...) is an ill-defined or severely hobbled concept. It is also argued that even if the entropy of the initial state of the universe had a well-defined, low value, this would not suffice to explain why thermodynamics works as well as it does for the kinds of systems we care about. Because the role of Boltzmann entropy in our inferences to the past has been vastly overrated, the failure of the Boltzmann program does not pose a serious problem for our knowledge of the past. But it does call a different explanation of why thermodynamics works as well as it does. A suggestion is offered for a different approach. (shrink)

The debate about the passage of time is usually confined to Minkowski‟s geometric interpretation of space-time. It infers the block universe from the notion of relative simultaneity. But there are alternative interpretations of space-time – so-called axiomatic approaches –, based on the existence of „optical facts‟, which have thermodynamic properties. It may therefore be interesting to approach the afore-mentioned debate from the point of view of relativistic thermodynamics, in which invariant parameters exist, which may serve to indicate the passage of (...) time. Of particular interest is the use of entropic clocks, gas clocks and statistical thermometers, which suggest that two observers in Minkowski space-time could agree on an objective passing of time. (shrink)

The essay revisits the puzzle of the ‘passage’ of time in relation to EPR-type measurements and asks what philosophical consequences can be drawn from them. Some argue that the lack of invariance of temporal order in the measurement of a space-like related EPR pair, under relativistic motion, casts serious doubts on the ‘reality’ of the lapse of time. Others argue thatcertain features of quantum mechanics establisha tensed theory of time – understood here as Possibilism or the growing block universe. The (...) paper analyzes the employment of frame-invariant entropic clocks in a relativistic setting and argues that tenselessness does not imply timelessness. But this conclusion does not support a tensed theory of time, which requires a preferred foliation. It is argued that the only reliable inference from the EPR example and the use of entropic clocks is an inference not just to a Leibnizian order of the succession of events but a frame-invariant order according to some selected clocks. (shrink)

The overwhelming majority of those who theorize about implicit biases posit that these biases are caused by some sort of association. However, what exactly this claim amounts to is rarely specified. In this paper, I distinguish between different understandings of association, and I argue that the crucial senses of association for elucidating implicit bias are the cognitive structure and mental process senses. A hypothesis is subsequently derived: if associations really underpin implicit biases, then implicit biases should be modulated by counterconditioning (...) or extinction but should not be modulated by rational argumentation or logical interventions. This hypothesis is false; implicit biases are not predicated on any associative structures or associative processes but instead arise because of unconscious propositionally structured beliefs. I conclude by discussing how the case study of implicit bias illuminates problems with popular dual-process models of cognitive architecture. (shrink)

Two of the most influential theories about scientific inference are inference to the best explanation and Bayesianism. How are they related? Bas van Fraassen has claimed that IBE and Bayesianism are incompatible rival theories, as any probabilistic version of IBE would violate Bayesian conditionalization. In response, several authors have defended the view that IBE is compatible with Bayesian updating. They claim that the explanatory considerations in IBE are taken into account by the Bayesian because the Bayesian either does (...) or should make use of them in assigning probabilities to hypotheses. I argue that van Fraassen has not succeeded in establishing that IBE and Bayesianism are incompatible, but that the existing compatibilist response is also not satisfactory. I suggest that a more promising approach to the problem is to investigate whether explanatory considerations are taken into account by a Bayesian who assigns priors and likelihoods on his or her own terms. In this case, IBE would emerge from the Bayesian account, rather than being used to constrain priors and likelihoods. I provide a detailed discussion of the case of how the Copernican and Ptolemaic theories explain retrograde motion, and suggest that one of the key explanatory considerations is the extent to which the explanation a theory provides depends on its core elements rather than on auxiliary hypotheses. I then suggest that this type of consideration is reflected in the Bayesian likelihood, given priors that a Bayesian might be inclined to adopt even without explicit guidance by IBE. The aim is to show that IBE and Bayesianism may be compatible, not because they can be amalgamated, but rather because they capture substantially similar epistemic considerations. 1 Introduction2 Preliminaries3 Inference to the Best Explanation4 Bayesianism5 The Incompatibilist View : Inference to the Best Explanation Contradicts Bayesianism5. 1 Criticism of the incompatibilist view6 Constraint - Based Compatibilism6. 1 Criticism of constraint - based compatibilism7 Emergent Compatibilism7. 1 Analysis of inference to the best explanation7. 1. 1 Inference to the best explanation on specific hypotheses7. 1. 2 Inference to the best explanation on general theories7. 1. 3 Copernicus versus Ptolemy7. 1. 4 Explanatory virtues7. 1. 5 Summary7. 2 Bayesian account8 Conclusion. (shrink)

This paper considers the Cartesian theatre as a metaphor for the virtual reality models that the brain uses to make inferences about the world. This treatment derives from our attempts to understand dreaming and waking consciousness in terms of free energy minimization. The idea here is that the Cartesian theatre is not observed by an internal audience but furnishes a theatre in which fictive narratives and fantasies can be rehearsed and tested against sensory evidence. We suppose the brain is driven (...) by the imperative to infer the causes of its sensory samples; in much the same way as scientists are compelled to test hypotheses about experimental data. This recapitulates Helmholtz's notion of unconscious inference and Gregory's treatment of perception as hypothesis testing. However, we take this further and consider the active sampling of the world as the gathering of confirmatory evidence for hypotheses based on our virtual reality. The ensuing picture of consciousness resolves a number of seemingly hard problems in consciousness research and is internally consistent with current thinking in systems neuroscience and theoretical neurobiology. In this formalism, there is a dualism that distinguishes between the process of inference and the process that entails inference. This separation is reflected by the distinction between beliefs and the physical brain states that encode them. This formal approach allows us to appeal to simple but fundamental theorems in information theory and statistical thermodynamics that dissolve some of the mysterious aspects of consciousness. (shrink)

Discussions about the nature of essence and about the inference problem for non-Humean theories of nomic modality have largely proceeded independently of each other. In this article I argue that the right conclusions to draw about the inference problem actually depend significantly on how best to understand the nature of essence. In particular, I argue that this conclusion holds for the version of the inference problem developed and defended by Alexander Bird. I argue that Bird’s own argument (...) that this problem is fatal for David Armstrong’s influential theory of the laws of nature but not for dispositional essentialism is seriously flawed. In place of this argument, I develop an argument that whether Bird’s inference problem raises serious difficulties for Armstrong’s theory depends on the answers to substantial questions about how best to understand essence. The key consequence is that considerations about the nature of essence have significant, underappreciated implications for Armstrong’s theory. (shrink)

The following quotation from Rosenbaum (1995) expresses a commonly held view about the problem of potential confounders, and how they can be dealt with. (We will take a “confounder” of treatment and response to be a variable that is a cause of both treatment and response.).

The emerging neurocomputational vision of humans as embodied, ecologically embedded, social agents—who shape and are shaped by their environment—offers a golden opportunity to revisit and revise ideas about the physical and information-theoretic underpinnings of life, mind, and consciousness itself. In particular, the active inference framework makes it possible to bridge connections from computational neuroscience and robotics/AI to ecological psychology and phenomenology, revealing common underpinnings and overcoming key limitations. AIF opposes the mechanistic to the reductive, while staying fully grounded in (...) a naturalistic and information-theoretic foundation, using the principle of free energy minimization. The latter provides a theoretical basis for a unified treatment of particles, organisms, and interactive machines, spanning from the inorganic to organic, non-life to life, and natural to artificial agents. We provide a brief introduction to AIF, then explore its implications for evolutionary theory, ecological psychology, embodied phenomenology, and robotics/AI research. We conclude the paper by considering implications for machine consciousness. (shrink)

In this paper I adduce a new argument in support of the claim that IBE is an autonomous form of inference, based on a familiar, yet surprisingly, under-discussed, problem for Hume’s theory of induction. I then use some insights thereby gleaned to argue for the claim that induction is really IBE, and draw some normative conclusions.

The aim of this book is to present the fundamental theoretical results concerning inference rules in deductive formal systems. Primary attention is focused on: admissible or permissible inference rules the derivability of the admissible inference rules the structural completeness of logics the bases for admissible and valid inference rules. There is particular emphasis on propositional non-standard logics (primary, superintuitionistic and modal logics) but general logical consequence relations and classical first-order theories are also considered. The book is (...) basically self-contained and special attention has been made to present the material in a convenient manner for the reader. Proofs of results, many of which are not readily available elsewhere, are also included. The book is written at a level appropriate for first-year graduate students in mathematics or computer science. Although some knowledge of elementary logic and universal algebra are necessary, the first chapter includes all the results from universal algebra and logic that the reader needs. For graduate students in mathematics and computer science the book is an excellent textbook. (shrink)

The aim here is to investigate assertion and inference as notions of logic. Assertion will be explained in terms of its purpose, which is to give interlocutors the right to request the assertor to do a certain task. The assertion is correct if, and only if, the assertor knows how to do this task. Inference will be explained as an assertion equipped with what I shall call a justification profile, a strategy for making good on the assertion. The (...) inference is valid if, and only if, correctness is preserved from the premiss assertions to the conclusion assertion. Most of this is a spelling out of views on assertion and inference presented by Per Martin-Löf in lectures since 2015. (shrink)

True beliefs and truth-preserving inferences are, in some sense, good beliefs and good inferences. When an inference is valid though, it is not merely truth-preserving, but truth-preserving in all cases. This motivates my question: I consider a Modus Ponens inference, and I ask what its validity in particular contributes to the explanation of why the inference is, in any sense, a good inference. I consider the question under three different definitions of ‘case’, and hence of ‘validity’: (...) the orthodox definition given in terms of interpretations or models, a metaphysical definition given in terms of possible worlds, and a substitutional definition defended by Quine. I argue that the orthodox notion is poorly suited to explain what's good about a Modus Ponens inference. I argue that there is something good that is explained by a certain kind of truth across possible worlds, but the explanation is not provided by metaphysical validity in particular; nothing of value is explained by truth across all possible worlds. Finally, I argue that the substitutional notion of validity allows us to correctly explain what is good about a valid inference. (shrink)

The idea that knowledge can be extended by inference from what is known seems highly plausible. Yet, as shown by familiar preface paradox and lottery-type cases, the possibility of aggregating uncertainty casts doubt on its tenability. We show that these considerations go much further than previously recognized and significantly restrict the kinds of closure ordinary theories of knowledge can endorse. Meeting the challenge of uncertainty aggregation requires either the restriction of knowledge-extending inferences to single premises, or eliminating epistemic uncertainty (...) in known premises. The first strategy, while effective, retains little of the original idea—conclusions even of modus ponens inferences from known premises are not always known. We then look at the second strategy, inspecting the most elaborate and promising attempt to secure the epistemic role of basic inferences, namely Timothy Williamson’s safety theory of knowledge. We argue that while it indeed has the merit of allowing basic inferences such as modus ponens to extend knowledge, Williamson’s theory faces formidable difficulties. These difficulties, moreover, arise from the very feature responsible for its virtue- the infallibilism of knowledge. (shrink)

Conceptual change and its connection to the development of new seien tific theories has reeently beeome an intensively discussed topic in philo sophieal literature. Even if the inductive aspects related to conceptual change have already been discussed to some extent, there has so far existed no systematic treatment of inductive change due to conceptual enrichment. This is what we attempt to accomplish in this work, al though most of our technical results are restricted to the framework of monadic languages. We (...) extend Hintikka's system of inductive logic to apply to situations in which new concepts are introduced to the original language. By interpreting them as theoretica1 concepts, it is possible to discuss a number of currently debated philosophical and methodological problems which have previously escaped systematic and exact treatment. For instance, the role which seientific theories employing theoretical con cepts may play within inductive inference can be studied within this framework. From the viewpoint of seientific realism, sueh a study gives outlines for a theory of what we call hypothetico-induetive inference. Some parts of this work which are based on Hintikka's system of in ductive logic are fairly technical. However, no previous knowledge of this system is required, but, in general, acquaintance with the basic ideas of elementary logic and probability theory is suffieient. This work is part of a project, originated by Professors Jaakko Hintikka and Raimo Tuomela, concerning the role of theoretical concepts in science. (shrink)

This paper is a sequel to an earlier result of the authors that in making inferences from certain probabilistic knowledge bases the maximum entropy inference process, ME, is the only inference process respecting “common sense.” This result was criticized on the grounds that the probabilistic knowledge bases considered are unnatural and that ignorance of dependence should not be identified with statistical independence. We argue against these criticisms and also against the more general criticism that ME is representation dependent. (...) In a final section, however, we provide a criticism of our own of ME, and of inference processes in general, namely that they fail to satisfy compactness. (shrink)

An empirical procedure is suggested for testing a model that postulates variables that intervene between observed causes and abserved effects against a model that includes no such postulate. The procedure is applied to two experiments in psychology. One involves a conditioning regimen that leads to response generalization; the other concerns the question of whether chimpanzees have a theory of mind.

Some theorists, ranging from W. James to contemporary psychologists, have argued that forgetting is the key to proper functioning of memory. The authors elaborate on the notion of beneficial forgetting by proposing that loss of information aids inference heuristics that exploit mnemonic information. To this end, the authors bring together 2 research programs that take an ecological approach to studying cognition. Specifically, they implement fast and frugal heuristics within the ACT-R cognitive architecture. Simulations of the recognition heuristic, which relies (...) on systematic failures of recognition to infer which of 2 objects scores higher on a criterion value, demonstrate that forgetting can boost accuracy by increasing the chances that only 1 object is recognized. Simulations of the fluency heuristic, which arrives at the same inference on the basis of the speed with which objects are recognized, indicate that forgetting aids the discrimination between the objects' recognition speeds. (shrink)

Does not the theory of a general tendency of entropy to diminish [sic] take too much for granted? To a certain extent it is supported by experimental evidence. We must accept such evidence as far as it goes and no further. We have no right to supplement it by a large draft of the scientific imagination.

Some assertions give rise to the acquaintance inference: the inference that the speaker is acquainted with some individual. Discussion of the acquaintance inference has previously focused on assertions about aesthetic matters and personal tastes (e.g. 'The cake is tasty'), but it also arises with reports about how things seem (e.g. 'Tom seems like he's cooking'). 'Seem'-reports give rise to puzzling acquaintance behavior, with no analogue in the previously-discussed domains. In particular, these reports call for a distinction between (...) the specific acquaintance inference (that the speaker is acquainted with a specific individual) and the general acquaintance inference (that the speaker is acquainted with something or other of relevance). We frame a novel empirical generalization -- the specific with stage-level generalization -- that systematizes the observed behavior, in terms of the semantics of the embedded 'like'-clause. We present supporting experimental work, and explain why the generalization makes sense given the evidential role of 'seem'-reports. Finally, we discuss the relevance of this result for extant proposals about the semantics of 'seem'-reports. More modestly, it fills a gap in previous theories by identifying which reports get which of two possible interpretations; more radically, it suggests a revision of the kind of explanation that should be given for the acquaintance behavior in question. (shrink)

Suppose we think in a language of thought. Then Paul Boghossian' is prepared to argue, first, that there may be ambiguous Mentalese expression types that have unambiguous tokens, and, second, that the way in which this is possible allows for otherwise valid theoretical or practical reasoning to be rendered invalid owing to equivocation of a sort that may be undetectable to the reasoner. Paul sees this as a possible basis from which to launch an argument for what some might call (...) "narrow content", and this is a question I'll take up later. (shrink)

Reverse inference is the most commonly used inferential strategy for bringing images of brain activation to bear on psychological hypotheses, but its inductive validity has recently been questioned. In this article, I show that, when it is analyzed in likelihoodist terms, reverse inference does not suffer from the problems highlighted in the recent literature, and I defend the appropriateness of treating reverse inference in these terms. 1 Introduction2 Reverse Inference3 Reverse Inference Defended3.1 Typical reverse inferences are (...) fallacious3.2 No quick and easy fix3.3 A likelihoodist defense of reverse inference3.4 An example4 Appropriateness of the Likelihoodist Approach4.1 Likelihoodist reverse inference is not applicable4.2 Cognitive neuroscientists are not interested in comparative conclusions4.3 Reverse inference and negative hypotheses4.4 Likelihoodist reverse inference may confuse cognitive neuroscientists4.5 Bayesian reverse inferences should be preferred to likelihoodist reverse inferences5 Conclusion. (shrink)

An algorithm recognizing admissibility of inference rules in generalized form (rules of inference with parameters or metavariables) in the intuitionistic calculus H and, in particular, also in the usual form without parameters, is presented. This algorithm is obtained by means of special intuitionistic Kripke models, which are constructed for a given inference rule. Thus, in particular, the direct solution by intuitionistic techniques of Friedman's problem is found. As a corollary an algorithm for the recognition of the solvability (...) of logical equations in H and for constructing some solutions for solvable equations is obtained. A semantic criterion for admissibility in H is constructed. (shrink)

I examine and resolve an exegetical dichotomy between two main interpretations of Peirce’s theory of abduction, namely, the Generative Interpretation and the Pursuitworthiness Interpretation. According to the former, abduction is the instinctive process of generating explanatory hypotheses through a mental faculty called insight. According to the latter, abduction is a rule-governed procedure for determining the relative pursuitworthiness of available hypotheses and adopting the worthiest one for further investigation—such as empirical tests—based on economic considerations. It is shown that the Generative Interpretation (...) is inconsistent with a fundamental fact of logic for Peirce—i.e., abduction is a kind of inference—and the Pursuitworthiness Interpretation is flawed and inconsistent with Peirce’s naturalistic explanation for the possibility of science and his view about the limitations of classical scientific method. Changing the exegetical locus classicus from the logical form of abduction to insight and economy of research, I argue for the Unified Interpretation according to which abduction includes both instinctive hypotheses-generation and rule-governed hypotheses-ranking. I show that the Unified Interpretation is immune to the objections raised successfully against the Generative and the Pursuitworthiness interpretations. (shrink)

Order of information plays a crucial role in the process of updating beliefs across time. In fact, the presence of order effects makes a classical or Bayesian approach to inference difficult. As a result, the existing models of inference, such as the belief-adjustment model, merely provide an ad hoc explanation for these effects. We postulate a quantum inference model for order effects based on the axiomatic principles of quantum probability theory. The quantum inference model explains order (...) effects by transforming a state vector with different sequences of operators for different orderings of information. We demonstrate this process by fitting the quantum model to data collected in a medical diagnostic task and a jury decision-making task. To further test the quantum inference model, a new jury decision-making experiment is developed. Using the results of this experiment, we compare the quantum inference model with two versions of the belief-adjustment model, the adding model and the averaging model. We show that both the quantum model and the adding model provide good fits to the data. To distinguish the quantum model from the adding model, we develop a new experiment involving extreme evidence. The results from this new experiment suggest that the adding model faces limitations when accounting for tasks involving extreme evidence, whereas the quantum inference model does not. Ultimately, we argue that the quantum model provides a more coherent account for order effects that was not possible before. (shrink)

Arguing for mathematical realism on the basis of Field’s explanationist version of the Quine–Putnam Indispensability argument, Alan Baker has recently claimed to have found an instance of a genuine mathematical explanation of a physical phenomenon. While I agree that Baker presents a very interesting example in which mathematics plays an essential explanatory role, I show that this example, and the argument built upon it, begs the question against the mathematical nominalist.

By a valid inference is here understood an inference that succeeds in its aim to justify its conclusion given that its premisses are already justified. For an inference to be valid it is thus not enough that the sentence asserted in the conclusion is a logical consequence of the sentences asserted in the premisses. A proof is understood as a succession of valid inferences that is closed (i.e. all its assumptions are discharged and all its free variables (...) are bound by some of the inferences). On the other hand, in mathematics the justification of an assertion has traditionally been taken to consist in a proof of it, which gives rise to an explanatory circle.In an attempt to avoid this circle, I have in previous works tried to explain the notion of ground for an assertion without referring to valid inferences. However, it turns out that the resulting notion of ground has unwanted consequences like the notion of proof in the so-called BHK-interpretation of intuitionistic logic. For instance, one is guaranteed a ground or a proof of an implication A → B as soon as there is in fact no ground or proof of A, regardless of whether one really knows this fact, and hence without having a real justification of the assertion of the implication.In the absence of a non-circular explanation of the notions of valid inference and proof, I suggest that we should try to formulate a number of principles of how these two epistemic notions depend on each other. A more careful explanation of the validity of an inference results in what I call a heuristic idea about the validity of inference, which is used as a guide to formulate precise principles. One such principle generalizes Gentzen’s idea that his introduction rules define the meaning of the logical constants. Another principle generalizes a previously noted property of Gentzen’s elimination rules that I have called that of satisfying the inversion principle. It results in a notion that I call non-creativity, which implies validity. (shrink)

Shin and DuBrow propose that a key principle driving event segmentation relates to causal analyses: specifically, that experiences that are attributed as having the same underlying cause are grouped together into an event. This offers an alternative to accounts of segmentation based on prediction error.

An inference can be seen as a speech act, in which one passes from a number of assertions called premisses to another assertion, the conclusion, which is presented as supported or justified by the premisses. To justify the assertion that appears as conclusion is the characteristic aim of an inference. Here, we confine ourselves to deductive inferences where the justification is taken to be conclusive. A short, natural explanation of what it is for a (deductive) inference to (...) be valid is to say that it is valid if it succeeds in its aim, that is, if its premisses do (conclusively) justify the conclusion, given that premisses are justified. The paper is concerned with developing this explanation further. (shrink)