In their Introduction to Logic, Copi and Cohen suggest that students construct a formal proof by "working backwards from the conclusion by looking for some statement or statements from which it can be deduced and then trying to deduce those intermediate statements from the premises. What follows is an elaboration of this suggestion. I describe an almost mechanical procedure for determining from which statement(s) the conclusion can be deduced and the rules by which the required inferences can be made. (...) This method is designed to forestall the quandary in which many beginners find themselves: not knowing how to get started. (shrink)

A background assumption of this paper is that the repertoire of inference schemes available to humanity is not fixed, but subject to change as new schemes are invented or refined and as old ones are obsolesced or abandoned. This is particularly visible in areas like health and environmental sciences, where enormous societal investment has been made in finding ways to reach more dependable conclusions. Computational modeling of argumentation, at least for the discourse in expert fields, will require the possibility (...) of modeling change in a stock of schemes that may be applied to generate conclusions from data. We examine Randomized Clinical Trial, an inference scheme established within medical science in the mid-20th Century, and show that its successful defense by means of practical reasoning allowed for its black-boxing as an inference scheme that generates (and warrants belief in) conclusions about the effects of medical treatments. Modeling the use of a scheme is well-understood; here we focus on modeling how the scheme comes to be established so that it is available for use. (shrink)

In the theory of meaning, it is common to contrast truth-conditional theories of meaning with theories which identify the meaning of an expression with its use. One rather exact version of the somewhat vague use-theoretic picture is the view that the standard rules of inference determine the meanings of logical constants. Often this idea also functions as a paradigm for more general use-theoretic approaches to meaning. In particular, the idea plays a key role in the anti-realist program of (...) Dummett and his followers. In the theory of truth, a key distinction now is made between substantial theories and minimalist or deflationist views. According to the former, truth is a genuine substantial property of the truth-bearers, whereas according to the latter, truth does not have any deeper essence, but all that can be said about truth is contained in T-sentences (sentences having the form: ‘P’ is true if and only if P). There is no necessary analytic connection between the above theories of meaning and truth, but they have nevertheless some connections. Realists often favour some kind of truth-conditional theory of meaning and a substantial theory of truth (in particular, the correspondence theory). Minimalists and deflationists on truth characteristically advocate the use theory of meaning (e.g. Horwich). Semantical anti-realism (e.g. Dummett, Prawitz) forms an interesting middle case: its starting point is the use theory of meaning, but it usually accepts a substantial view on truth, namely that truth is to be equated with verifiability or warranted assertability. When truth is so understood, it is also possible to accept the idea that meaning is closely related to truth-conditions, and hence the conflict between use theories and truth-conditional theories in a sense disappears in this view. (shrink)

A certain type of inference rules in modal logics, generalizing Gabbay's Irreflexivity rule, is introduced and some general completeness results about modal logics axiomatized with such rules are proved.

In Tractatus 5.132 Wittgenstein argues that inferential justification depends solely on the understanding of the premises and conclusion, and is not mediated by any further act. On this basis he argues that Frege’s and Russell’s rules of inference are “senseless” and “superfluous”. This line of argument is puzzling, since it is unclear that there could be any viable account of inference according to which no such mediation takes place. I show that Wittgenstein’s rejection of rules of (...) inference can be motivated by taking account of his holistic construal of the relation between inference and understanding. (shrink)

The “Game of the Rule” is easy enough: I give you the beginning of a sequence of numbers (say) and you have to figure out how the sequence continues, to uncover the rule by means of which the sequence is generated. The game depends on two obvious constraints, namely (1) that the initial segment uniquely identify the sequence, and (2) that the sequence be non-random. As it turns out, neither constraint can fully be met, among other reasons because the relevant (...) notion of randomness is either vacuous or undecidable. This may not be a problem when we play for fun. It is, however, a serious problem when it comes to playing the game for real, i.e., when the player to issue the initial segment is not one of us but the world out there, the sequence consisting not of numbers (say) but of the events that make up our history. Moreover, when we play for fun we know exactly what initial segment to focus on, but when we play for real we don’t even know that. This is the core difficulty in the philosophy of the inductive sciences. (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)

This paper discusses the account of alethic modality as presented by Wilfrid Sellars in his earlier work from 1947 to 1958. Its aim is twofold. First, I discuss Sellars' analysis by exploring its historical relationship to Carnap's account of modality. I argue that Carnap's early syntactic treatment of modality profoundly influenced Sellars' own so-called ‘regulist' account of modality in terms of rules of inference. Furthermore, it is suggested that Sellars' lesser-known possible worlds analysis was influenced by Carnap's later (...) semantic account of modality. The second aim of the paper is a critical one. I raise a number of objections to Sellars’ account of modality and argue that his account confronts some serious limitations. I also argue that Sellars does not provide a satisfying explanation of the relationship between his regulist account and his possible worlds analysis. I offer such an explanation by arguing that his regulist account should be understood as a pragmatic account of what is conveyed by the use of modal sentences, whereas his possible worlds analysis is a semantic account of the asserted content of modal statements. That is, the regulist account and the possible worlds analysis have different explanatory targets. (shrink)

Defenders of Inference to the Best Explanation claim that explanatory factors should play an important role in empirical inference. They disagree, however, about how exactly to formulate this role. In particular, they disagree about whether to formulate IBE as an inference rule for full beliefs or for degrees of belief, as well as how a rule for degrees of belief should relate to Bayesianism. In this essay I advance a new argument against non-Bayesian versions of IBE. My (...) argument focuses on cases in which we are concerned with multiple levels of explanation of some phenomenon. I show that in many such cases, following IBE as an inference rule for full beliefs leads to deductively inconsistent beliefs, and following IBE as a non-Bayesian updating rule for degrees of belief leads to probabilistically incoherent degrees of belief. (shrink)

Many classically valid meta-inferences fail in a standard supervaluationist framework. This allegedly prevents supervaluationism from offering an account of good deductive reasoning. We provide a proof system for supervaluationist logic which includes supervaluationistically acceptable versions of the classical meta-inferences. The proof system emerges naturally by thinking of truth as licensing assertion, falsity as licensing negative assertion and lack of truth-value as licensing rejection and weak assertion. Moreover, the proof system respects well-known criteria for the admissibility of inference rules. (...) Thus, supervaluationists can provide an account of good deductive reasoning. Our proof system moreover brings to light how one can revise the standard supervaluationist framework to make room for higher-order vagueness. We prove that the resulting logic is sound and complete with respect to the consequence relation that preserves truth in a model of the non-normal modal logic _NT_. Finally, we extend our approach to a first-order setting and show that supervaluationism can treat vagueness in the same way at every order. The failure of conditional proof and other meta-inferences is a crucial ingredient in this treatment and hence should be embraced, not lamented. (shrink)

This essay advances and develops a dynamic conception of inference rules and uses it to reexamine a long-standing problem about logical inference raised by Lewis Carroll’s regress.

Elizabeth Karger has suggested an interpretation of Ockham's theory of the modes of common personal supposition ("TM") according to which the purpose of TM is to provide certain distinctions that Ockham will use in formulating a unified theory of immediate inference among certain kinds of sentences. Karger presents a single, powerful rule of inference that incorporates TM distinctions and that is meant to codify Ockham's theory of immediate inference. I raise an objection to Karger's rule, thereby calling (...) into doubt the interpretation of Ockham that is based on attributing that rule to him. (shrink)

I discuss a neglected solution to the skeptical problem introduced by Lewis Carroll’s “What the Tortoise Said to Achilles” (1895) in terms of a self-citational inferential license. I then consider some responses to this solution. The most significant response on behalf of the skeptic utilizes the familiar distinction between two ways of accepting a rule: as action-guiding and as a mere truth. I argue that this is ultimately unsatisfactory and conclude by opting for an alternative conception of rules as (...) representations of behavior deployed for various purposes, some theoretical and others practical. This alternative conception does not allow the skeptical problem to get off the ground. (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)

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)

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)

There is wide support in logic, philosophy, and psychology for the hypothesis that the probability of the indicative conditional of natural language, $P(\textit{if } A \textit{ then } B)$, is the conditional probability of $B$ given $A$, $P(B|A)$. We identify a conditional which is such that $P(\textit{if } A \textit{ then } B)= P(B|A)$ with de Finetti's conditional event, $B|A$. An objection to making this identification in the past was that it appeared unclear how to form compounds and iterations of (...) conditional events. In this paper, we illustrate how to overcome this objection with a probabilistic analysis, based on coherence, of these compounds and iterations. We interpret the compounds and iterations as conditional random quantities which, given some logical dependencies, may reduce to conditional events. We show how the inference to $B|A$ from $A$ and $B$ can be extended to compounds and iterations of both conditional events and biconditional events. Moreover, we determine the respective uncertainty propagation rules. Finally, we make some comments on extending our analysis to counterfactuals. (shrink)

Some believe that all arguments make an implicit “inference claim” that the conclusion is inferable from the premises (e.g., Bermejo-Luque, Grennan, the Groarkes, Hitchcock, Scriven). I try to show that this is confused. An act of arguing arises because an inference can be attributed to us, not a meta-level “inference claim” that would make the argument self-referential and regressive. I develop six (other) possible explanations of the popularity of the doctrine that similarly identify confusions.

In his essay ‘Transparency, Belief, Intention’, Alex Byrne (2011) argues that transparency—our ability to form beliefs about some of our intentional mental states by considering their subject matter, rather than on the basis of special psychological evidence—involves inferring ‘from world to mind’. In this reply I argue that this cannot be correct. I articulate an intuitive necessary condition for a pattern of belief to count as a rule of inference, and I show that the pattern involved in transparency does (...) not meet that condition. As a result, I conclude that transparency does not involve inference. (shrink)

Lewis Carroll’s 1895 paper “Achilles and the Tortoise” showed that we need a distinction between rules of inference and premises. We cannot, on pain of regress, treat all rules simply as further premises in an argument. But Carroll’s paper doesn’t say very much about what rules there must be. Indeed, it is consistent with what Carroll says there to think that the only rule is -elimination. You might think that modern Bayesians, who seem to think that (...) the only rule of inference they need is conditionalisation, have taken just this lesson from Carroll. But obviously nothing in Carroll’s argument rules out there being other rules as well. (shrink)

In a series of papers over the past twenty years, and in a new book, Igor Douven has argued that Bayesians are too quick to reject versions of inference to the best explanation that cannot be accommodated within their framework. In this paper, I survey their worries and attempt to answer them using a series of pragmatic and purely epistemic arguments that I take to show that Bayes’ Rule really is the only rational way to respond to your evidence.

Logical inferentialism maintains that the formal rules of inference fix the meanings of the logical terms. The categoricity problem points out to the fact that the standard formalizations of classical logic do not uniquely determine the intended meanings of its logical terms, i.e., these formalizations are not categorical. This means that there are different interpretations of the logical terms that are consistent with the relation of logical derivability in a logical calculus. In the case of the quantificational logic, (...) the categoricity problem is generated by the finite nature of the standard calculi and one direction in which it can be solved is to strengthen the deductive systems by adding infinite rules (such as the ω-rule), i.e., to construct a full formalization. Another main direction is to provide a natural semantics for the standard rules of inference, i.e., a semantics for which these rules are categorical. My aim in this paper is to analyze some recent approaches for solving the categoricity problem and to argue that a logical inferentialist should accept the infinite rules of inference for the first order quantifiers, since our use of the expressions “all” and “there is” leads us beyond the concrete and finite reasoning, and human beings do sometimes employ infinite rules of inference in their reasoning. (shrink)

In our thought, we employ rules of inference and belief-forming methods more generally. For instance, we (plausibly) employ deductive rules such as Modus Ponens, ampliative rules such as Inference to the Best Explanation, and perceptual methods that tell us to believe what perceptually appears to be the case. What explains our entitlement to employ these rules and methods? This chapter considers the motivations for broadly internalist answers to this question. It considers three such motivations—one (...) based on simple cases, one based on a general conception of epistemic responsibility, and one based on skeptical scenarios. The chapter argues that none of these motivations is successful. The first two motivations lead to forms of internalism—Extreme Method Internalism and Defense Internalism—that are too strong to be tenable. The third motivation motivates Mental Internalism (Mentalism), which does not fit with plausible accounts of entitlement. (shrink)

Legal systems often rule that people own objects in their territory. We propose that an early-developing ability to make territory-based inferences of ownership helps children address informational demands presented by ownership. Across 6 experiments (N = 504), we show that these inferences develop between ages 3 and 5 and stem from two aspects of the psychology of ownership. First, we find that a basic ability to infer that people own objects in their territory is already present at age 3 (Experiment (...) 1). Children even make these inferences when the territory owner unintentionally acquired the objects and was unaware of them (Experiments 2 and 3). Second, we find that between ages 3 and 5, children come to consider past events in these judgments. They move from solely considering the current location of an object in territory-based inferences, to also considering and possibly inferring where it originated (Experiments 4 to 6). Together, these findings suggest that territory-based inferences of ownership are unlikely to be constructions of the law. Instead, they may reflect basic intuitions about ownership that operate from early in development. (shrink)

It has been common wisdom for centuries that scientific inference cannot be deductive; if it is inference at all, it must be a distinctive kind of inductive inference. According to demonstrative theories of induction, however, important scientific inferences are not inductive in the sense of requiring ampliative inference rules at all. Rather, they are deductive inferences with sufficiently strong premises. General considerations about inferences suffice to show that there is no difference in justification between an (...) inference construed demonstratively or ampliatively. The inductive risk may be shouldered by premises or rules, but it cannot be shirked. Demonstrative theories of induction might, nevertheless, better describe scientific practice. And there may be good methodological reasons for constructing our inferences one way rather than the other. By exploring the limits of these possible advantages, I argue that scientific inference is neither of essence deductive nor of essence inductive. (shrink)

The present PhD thesis is concerned with the question whether good reasoning requires that the subject has some cognitive grip on the relation between premises and conclusion. One consideration in favor of such a requirement goes as follows: In order for my belief-formation to be an instance of reasoning, and not merely a causally related sequence of beliefs, the process must be guided by my endorsement of a rule of reasoning. Therefore I must have justified beliefs about the relation between (...) my premises and my conclusion. -/- The rationality of a belief often depends on whether it is rightly connected to other beliefs, or more generally to other mental states —the states capable of providing a reason to holding the belief in question. For instance, some rational beliefs are connected to other beliefs by being inferred from them. It is often accepted that the connection implies that the subject in some sense ‘takes the mental states in question to be reason-providing’. But views on how exactly this is to be understood differ widely. They range from interpretations according to which ‘taking a mental state to be reason-providing’ imposes a mere causal sustaining relation between belief and reason-providing state to interpretations according to which one ‘takes a mental state to be reason-providing’ only if one believes that the state is reason-providing. The most common worry about the latter view is that it faces a vicious regress. In this thesis a different but in some respects similar interpretation of ‘taking something as reason-providing’ is given. It is argued to consist of a disposition to react in certain ways to information that challenges the reason-providing capacity of the allegedly reason-providing state. For instance, that one has inferred A from B partly consists in being disposed to suspend judgment about A if one obtains a reason to believe that B does not render A probable. The account is defended against regress-objections and the suspicion of explanatory circularity. (shrink)

A priori theories of justification of logic based on meaning often lead to trouble, in particular to issues concerning circularity. First, I present Boghossian’s a prioriview. Boghossian maintains the rule-circular justifications from a conceptual role semantics. However, rule-circular justifications are problematic. Recently, Boghossian (Boghossian, 2015) has claimed that rules should be thought of as contents and contents as abstract objects. In this paper, I discuss Boghossian’s view. My argumentation consists of three main parts. First, I analyse several arguments to (...) show that in fact, Boghossian’s inferentialist solution is not fully satisfying. Second, I discuss the matter further, if one accepts that basic logical rules are constitutive of meaning, that is, they constitute the logical concepts and the content of a rule is an abstract object, then abstract objects — like, for example, rules — could be constitutive of meaning. The question is whether conceptual priority is in the judgment or in the object and what theory of content is pursued. Grasping content as a matter of knowing how a word or concept behaves in inferences is not completely explicative. Finally, I contend that rules come to exist as a result of certain kinds of mental action. These actions function as constitutive norms. Logical rules are not abstract objects but ideal. What one construes as norms or rules of content may involve idealization, but this is because we share a language. (shrink)

We are justified in employing the rule of inference Modus Ponens (or one much like it) as basic in our reasoning. By contrast, we are not justified in employing a rule of inference that permits inferring to some difficult mathematical theorem from the relevant axioms in a single step. Such an inferential step is intuitively “too large” to count as justified. What accounts for this difference? In this paper, I canvass several possible explanations. I argue that the most (...) promising approach is to appeal to features like usefulness or indispensability to important or required cognitive projects. On the resulting view, whether an inferential step counts as large or small depends on the importance of the relevant rule of inference in our thought. (shrink)

In recent years, the e ffort to formalize erotetic inferences (i.e., inferences to and from questions) has become a central concern for those working in erotetic logic. However, few have sought to formulate a proof theory for these inferences. To fill this lacuna, we construct a calculus for (classes of) sequents that are sound and complete for two species of erotetic inferences studied by Inferential Erotetic Logic (IEL): erotetic evocation and regular erotetic implication. While an attempt has been made to (...) axiomatize the former in a sequent system, there is currently no proof theory for the latter. Moreover, the extant axiomatization of erotetic evocation fails to capture its defeasible character and provides no rules for introducing or eliminating question-forming operators. In contrast, our calculus encodes defeasibility conditions on sequents and provides rules governing the introduction and elimination of erotetic formulas. We demonstrate that an elimination theorem holds for a version of the cut rule that applies to both declarative and erotetic formulas and that the rules for the axiomatic account of question evocation in IEL are admissible in our system. (shrink)

Research into the neural correlates of consciousness (NCC) aims to identify not just those brain areas that are NCC, but also those that are not. In the received method for ruling out a brain area from being an NCC, this is accomplished by showing a brain area’s content to be consistently absent from subjects’ reports about what they are experiencing. This paper points out how this same absence can be used to infer that the brain area’s content is cognitively inaccessible, (...) in which case we would expect its content to be absent from subjects’ reports whether its content is (phenomenally) conscious or not. If so, such reports cannot count as evidence against that brain area being an NCC, and the received method fails. An alternative method (one suggested in Block, 2007) is considered. (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)

In this paper I discuss the rule of inference proposed by Kuipers under the name of Inference to the Best Theory. In particular, I argue that the rule needs to be strengthened if it is to serve realist purposes. I further describe a method for testing, and perhaps eventually justifying, a suitably strengthened version of it.

Probability updating via Bayes' rule often entails extensive informational and computational requirements. In consequence, relatively few practical applications of Bayesian adaptive control techniques have been attempted. This paper discusses an alternative approach to adaptive control, Bayesian in spirit, which shifts attention from the updating of probability distributions via transitional probability assessments to the direct updating of the criterion function, itself, via transitional utility assessments. Results are illustrated in terms of an adaptive reinvestment two-armed bandit problem.

It is quite plausible to say that you may read or write implies that you may read and you may write (though possibly not both at once). This so-called free choice principle is well-known in deontic logic. Sadly, despite being so intuitive and seemingly innocent, this principle causes a lot of worries. The paper briefly but critically examines leading accounts of free choice permission present in the literature. Subsequently, the paper suggests to accept the free choice principle, but only as (...) a default (or defeasible) rule, issuing to it a ticket-of-leave, granting it some freedom, until it commits an undesired inference. (shrink)

We argue against some of Reichenbach's claims about causal forks are incorrect. We do not see why the Second Law of Thermodynamics rules out the existence of conjunctive forks open to the past. In addition, we argue that a common effect rarely forms a conjunctive fork with its joint causes, but it sometimes does. Nevertheless, we think there is something to be said for Reichenbach's idea that forks of various kinds are relevant to explaining why we know more about (...) the past than about the future. And entropy turns out to play a role in the explanation, though not the determining role that Reichenbach envisions. (shrink)

Nickles (2017) advocates scientific antirealism by appealing to the pessimistic induction over scientific theories, the illusion hypothesis (Quoidbach, Gilbert, and Wilson, 2013), and Darwin’s evolutionary theory. He rejects Putnam’s (1975: 73) no-miracles argument on the grounds that it uses inference to the best explanation. I object that both the illusion hypothesis and evolutionary theory clash with the pessimistic induction and with his negative attitude towards inference to the best explanation. I also argue that Nickles’s positive philosophical theories are (...) subject to Park’s (2017a) pessimistic induction over antirealists. (shrink)

Lewis Carroll’s 1895 paper, 'What the Tortoise Said to Achilles' is widely regarded as a classic text in the philosophy of logic. This special issue of 'The Carrollian' publishes five newly commissioned articles by experts in the field. The original paper is reproduced, together with contemporary correspondence relating to the paper and an extensive bibliography.

We generalize, by a progressive procedure, the notions of conjunction and disjunction of two conditional events to the case of n conditional events. In our coherence-based approach, conjunctions and disjunctions are suitable conditional random quantities. We define the notion of negation, by verifying De Morgan’s Laws. We also show that conjunction and disjunction satisfy the associative and commutative properties, and a monotonicity property. Then, we give some results on coherence of prevision assessments for some families of compounded conditionals; in particular (...) we examine the Fréchet-Hoeffding bounds. Moreover, we study the reverse probabilistic inference from the conjunction Cn+1 of n + 1 conditional events to the family {Cn,En+1|Hn+1}. We consider the relation with the notion of quasi-conjunction and we examine in detail the coherence of the prevision assessments related with the conjunction of three conditional events. Based on conjunction, we also give a characterization of p-consistency and of p-entailment, with applications to several inference rules in probabilistic nonmonotonic reasoning. Finally, we examine some non p-valid inference rules; then, we illustrate by an example two methods which allow to suitably modify non p-valid inference rules in order to get inferences which are p-valid. (shrink)

ABSTRACTThis paper provides a naturalistic account of inference. We posit that the core of inference is constituted by bare inferential transitions, transitions between discursive mental representations guided by rules built into the architecture of cognitive systems. In further developing the concept of BITs, we provide an account of what Boghossian [2014] calls ‘taking’—that is, the appreciation of the rule that guides an inferential transition. We argue that BITs are sufficient for implicit taking, and then, to analyse explicit (...) taking, we posit rich inferential transitions, which are transitions that the subject is disposed to endorse. (shrink)

Once upon a time, logical conventionalism was the most popular philosophical theory of logic. It was heavily favored by empiricists, logical positivists, and naturalists. According to logical conventionalism, linguistic conventions explain logical truth, validity, and modality. And conventions themselves are merely syntactic rules of language use, including inference rules. Logical conventionalism promised to eliminate mystery from the philosophy of logic by showing that both the metaphysics and epistemology of logic fit into a scientific picture of reality. For (...) naturalists of all stripes, this was paradise. Alas, paradise was lost. By the end of the twentieth century, logical conventionalism had been almost universally abandoned. But more recently, it has been revitalized. This chapter provides an overview of logical conventionalism and its history, clears away misunderstandings, and briefly responds to both the canonical objections to conventionalism (from Quine, Dummett, Boghossian, and many others) as well as new objections (from Field and Golan). From paradise lost, to paradise regained: logical conventionalism is back. (shrink)

For deductive reasoning to be justified, it must be guaranteed to preserve truth from premises to conclusion; and for it to be useful to us, it must be capable of informing us of something. How can we capture this notion of information content, whilst respecting the fact that the content of the premises, if true, already secures the truth of the conclusion? This is the problem I address here. I begin by considering and rejecting several accounts of informational content. I (...) then develop an account on which informational contents are indeterminate in their membership. This allows there to be cases in which it is indeterminate whether a given deduction is informative. Nevertheless, on the picture I present, there are determinate cases of informative (and determinate cases of uninformative) inferences. I argue that the model I offer is the best way for an account of content to respect the meaning of the logical constants and the inference rules associated with them without collapsing into a classical picture of content, unable to account for informative deductive inferences. (shrink)

Universal Generalization, if it is not the most poorly understood inference rule in natural deduction, then it is the least well explained or justified. The inference rule is, prima facie, quite ambitious: on the basis of a fact established of one thing, I may infer that the fact holds of every thing in the class to which the one belongs—a class which may contain indefinitely many things. How can such an inference be made with any confidence as (...) to its validity or ability to preserve truth from premise to conclusion? My goal in this paper is to explain how Universal Generalization works in a way that makes sense of its ability to preserve truth. In doing so, I shall review common accounts of Universal Generalization and explain why they are inadequate or are explanatorily unsatisfying. Happily, my account makes no ontological or epistemological presumptions and therefore should be compatible with whichever ontological or epistemological schemes the reader prefers. (shrink)

In attempting to form rational personal probabilities by direct inference, it is usually assumed that one should prefer frequency information concerning more specific reference classes. While the preceding assumption is intuitively plausible, little energy has been expended in explaining why it should be accepted. In the present article, I address this omission by showing that, among the principled policies that may be used in setting one’s personal probabilities, the policy of making direct inferences with a preference for frequency information (...) for more specific reference classes yields personal probabilities whose accuracy is optimal, according to all proper scoring rules, in situations where all of the relevant frequency information is point-valued. Assuming that frequency information for narrower reference classes is preferred, when the relevant frequency statements are point-valued, a dilemma arises when choosing whether to make a direct inference based upon relatively precise-valued frequency information for a broad reference class, R, or upon relatively imprecise-valued frequency information for a more specific reference class, R*. I address such cases, by showing that it is often possible to make a precise-valued frequency judgment regarding R* based on precise-valued frequency information for R, using standard principles of direct inference. Having made such a frequency judgment, the dilemma of choosing between and is removed, and one may proceed by using the precise-valued frequency estimate for the more specific reference class as a premise for direct inference. (shrink)

My goal is to illuminate truth-making by way of illuminating the relation of making. My strategy is not to ask what making is, in the hope of a metaphysical theory about is nature. It's rather to look first to the language of making. The metaphor behind making refers to agency. It would be absurd to suggest that claims about making are claims about agency. It is not absurd, however, to propose that the concept of making somehow emerges from some feature (...) to do with agency. That's the contention to be explore in this paper. The way to do this is through expressivism,. Truth-making claims, and making-claims generfally, are claims in which we express mental states linked to our maipulation of concepts, like truth. In particular, they express disposition to undertake derivations using inference rules, in which introduction rules have a specific role. I then show how this theory explains our intuitions about truth's asymmetric dependence on being. (shrink)

ABSTRACT: A detailed presentation of Stoic theory of arguments, including truth-value changes of arguments, Stoic syllogistic, Stoic indemonstrable arguments, Stoic inference rules (themata), including cut rules and antilogism, argumental deduction, elements of relevance logic in Stoic syllogistic, the question of completeness of Stoic logic, Stoic arguments valid in the specific sense, e.g. "Dio says it is day. But Dio speaks truly. Therefore it is day." A more formal and more detailed account of the Stoic theory of deduction (...) can be found in S. Bobzien, Stoic Syllogistic, OSAP 1996. (shrink)

In a 2002 article Stewart Cohen advances the “bootstrapping problem” for what he calls “basic justification theories,” and in a 2010 followup he offers a solution to the problem, exploiting the idea that suppositional reasoning may be used with defeasible as well as with deductive inference rules. To curtail the form of bootstrapping permitted by basic justification theories, Cohen insists that subjects must know their perceptual faculties are reliable before perception can give them knowledge. But how is such (...) knowledge of reliability to be acquired if not through perception itself? Cohen proposes that such knowledge may be acquired a priori through suppositional reasoning. I argue that his strategy runs afoul of a plausible view about how epistemic principles function; in brief, I argue that one must actually satisfy the antecedent of an epistemic principle, not merely suppose that one does, to acquire any justification by its means – even justification for a merely conditional proposition. (shrink)

Of the dozens of purported solutions to the liar paradox published in the past fifty years, the vast majority are "traditional" in the sense that they reject one of the premises or inference rules that are used to derive the paradoxical conclusion. Over the years, however, several philosophers have developed an alternative to the traditional approaches; according to them, our very competence with the concept of truth leads us to accept that the reasoning used to derive the paradox (...) is sound. That is, our conceptual competence leads us into inconsistency. I call this alternative the inconsistency approach to the liar. Although this approach has many positive features, I argue that several of the well-developed versions of it that have appeared recently are unacceptable. In particular, they do not recognize that if truth is an inconsistent concept, then we should replace it with new concepts that do the work of truth without giving rise to paradoxes. I outline an inconsistency approach to the liar paradox that satisfies this condition. (shrink)

According to epistemic two-dimensionalism, every expression is associated with two kinds of meaning: a primary intension (a “Fregean” component) and a secondary intension (a “Russellian” component). While the rst kind of meaning lines up with the speaker’s abilities to pick out referents of correctly employed expressions in hypothetical scenarios, the second kind of meaning is a version of what standard semanticists call “semantic content”—a kind of content which does not pivot on speaker abilities. Despite its conciliatory temperament, epistemic two-dimensionalism has (...) come under recent attack. It has been alleged that it is bound to attribute to speakers a priori identifying knowledge of the referents of correctly employed terms, and bound also to reject valid rules of inference such as exportation: P(a) → λx[P(x)](a) (see, e.g., Soames 2005. (shrink)