Why are conditional degrees of belief in an observation E, given a statistical hypothesis H, aligned with the objective probabilities expressed by H? After showing that standard replies are not satisfactory, I develop a suppositional analysis of conditional degree of belief, transferring Ramsey’s classical proposal to statistical inference. The analysis saves the alignment, explains the role of chance-credence coordination, and rebuts the charge of arbitrary assessment of evidence in Bayesian inference. Finally, I explore the implications of (...) this analysis for Bayesian reasoning with idealized models in science. (shrink)

What is involved in making an inference? This chapter argues against what Paul Boghossian calls the Taking Condition: "Inferring necessarily involves the thinker taking his premises to support his conclusion and drawing his conclusion because of that fact" (2014: 5). I won’t argue that the Taking Condition is incoherent: that nothing can coherently play the role that takings are supposed to play in inference. Instead, I’ll argue that it cannot plausibly explain all the inferential knowledge that we ordinarily (...) take ourselves to have. Moreover, I’ll argue that we don’t need it to understand the nature of inference. (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)

I prove that the Boolean Prime Ideal Theorem is equivalent, under some weak set-theoretic assumptions, to what I will call the Cut-for-Formulas to Cut-for-Sets Theorem: for a set F and a binary relation |- on Power(F), if |- is finitary, monotonic, and satisfies cut for formulas, then it also satisfies cut for sets. I deduce the CF/CS Theorem from the Ultrafilter Theorem twice; each proof uses a different order-theoretic variant of the Tukey- Teichmüller Lemma. I then discuss relationships between various (...) cut-conditions in the absence of finitariness or of monotonicity. (shrink)

This paper develops a trivalent semantics for the truth conditions and the probability of the natural language indicative conditional. Our framework rests on trivalent truth conditions first proposed by Cooper (1968) and Belnap (1973) and it yields two logics of conditional reasoning: (i) a logic C of certainty-preserving inference; and (ii) a logic U for uncertain reasoning that preserves the probability of the premises. We show systematic correspondences between trivalent and probabilistic representations of inferences in either framework, (...) and we use the distinction between the two systems to cast light on the validity of inferences such as Modus Ponens, Or-To-If, and Conditional Excluded Middle. Specifically, the conditional behaves monotonically in C, but non-monotonically in U; Modus Ponens is valid in C, but valid in U only for non-nested conditionals. The result is a unified account of the semantics and epistemology of indicative conditionals that can be fruitfully applied to analyzing the validity of conditional inferences. (shrink)

According to the view of conditionals named 'inferentialism', a conditional holds when its consequent can be inferred from its antecedent. This paper identifies some major challenges that inferentialism has to face, and uses them to assess three accounts of conditionals: one is the classical strict account, the other two have recently been proposed by Douven and Rott. As will be shown, none of the three proposals meets all challenges in a fully satisfactory way. We argue through novel formal results (...) that a variation of the evidential account of conditionals suggested by Crupi and Iacona is the most promising candidate to develop inferentialism in a coherent formal framework. (shrink)

Consider the following three claims. (i) There are no truths of the form ‘p and ~p’. (ii) No one holds a belief of the form ‘p and ~p’. (iii) No one holds any pairs of beliefs of the form {p, ~p}. Irad Kimhi has recently argued, in effect, that each of these claims holds and holds with metaphysical necessity. Furthermore, he maintains that they are ultimately not distinct claims at all, but the same claim formulated in different ways. I find (...) his argument suggestive, if not entirely transparent. I do think there is at least an important kernel of truth even in (iii), and that (i) ultimately explains what’s right about the other two. Consciousness of an impossibility makes belief in the obtaining of the corresponding state of affairs an impossibility. Interestingly, an appreciation of this fact brings into view a novel conception of inference, according to which it consists in the consciousness of necessity. This essay outlines and defends this position. A central element of the defense is that it reveals how reasoners satisfy what Paul Boghossian calls the Taking Condition and do so without engendering regress. (shrink)

This paper is about four inferences patterns governing conditionals: Transitivity, Simplification, Contraposition, and Antecedent Strengthening. Transitivity, Simplification, and Contraposition are intuitively compelling. Although Antecedent Strengthening may seem less attractive at first, close attention to the full range of data reveals that it too has considerable appeal. An adequate theory of conditionals should account for these facts. The strict theory does so by validating them. But the variably strict theory invalidates them. So the variably strict theorist faces a question: why do (...) we find these inferences so compelling? In this paper, I suggest an answer on her behalf: that they are reasonable inferences in the sense introduced by Stalnaker (1975). -/- . (shrink)

Ranking theory is a formal epistemology that has been developed in over 600 pages in Spohn's recent book The Laws of Belief, which aims to provide a normative account of the dynamics of beliefs that presents an alternative to current probabilistic approaches. It has long been received in the AI community, but it has not yet found application in experimental psychology. The purpose of this paper is to derive clear, quantitative predictions by exploiting a parallel between ranking theory and a (...) statistical model called logistic regression. This approach is illustrated by the development of a model for the conditional inference task using Spohn's ranking theoretic approach to conditionals. (shrink)

The paper offers an account of inference. The account underwrites the idea that inference requires that the reasoner takes her premises to support her conclusion. I reject views according to which such ‘takings’ are intuitions or beliefs. I sketch an alternative view on which inferring consists in attaching what I call ‘inferential force’ to a structured collection of contents.

The paper defends a variant of the material implication approach to the meaning of conditional sentences against some arguments that are considered to be widely subscribed to and/or important in the philosophical, psychological and linguistic literature. These arguments are shown to be wrong, debatable, or to miss their aim if the truth conditions defining material implication are viewed as determining nothing but the denotation of conditional sentences and if the function of conditional sentences in deduction (logic) is (...) focused on rather than in inferencing (reasoning). It is shown that some ‘paradoxes of material implication’ are due to inconsistent premises of deductions introduced by semantic relations between clauses constituting the premises, a fact which does not invalidate the approach. Other ‘paradoxes’ are shown to arise because they are based on uninformative deductions, violating a basic pragmatic principle. In addition, the paper introduces the distinction between the set of possible states of a mental model of the actual world and of alternative worlds. It is argued that material implication determines the denotation of an indicative conditional as a subset of the former set and the denotation of a subjunctive conditional as a subset of the latter set, thus unifying these two types of conditionals. (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)

While we can judge and believe things by merely accepting testimony, we cannot make inferences by merely accepting testimony. A good theory of inference should explain this. The theories that are best suited to explain this fact seem to be theories that accept a so-called intuitional construal of Boghossian’s Taking Condition.

According to Paul Boghossian and others, inference is subject to the taking condition: it necessarily involves the thinker taking his premises to support his conclusion, and drawing the conclusion because of that fact. Boghossian argues that this condition vindicates the idea that inference is an expression of agency, and that it has several other important implications too. However, we argue in this paper that the taking condition should be rejected. The condition gives rise to several serious prima facie (...) problems and the reasons which have been offered in favour of it fail to convince. (shrink)

Despite being a milestone in the history of statistical causal inference, Sewall Wright’s 1918 invention of path analysis did not receive much immediate attention from the statistical and scientific community. Through a careful historical analysis, this paper reveals some previously overlooked philosophical issues concerning the history of causal inference. Placing the invention of path analysis in a broader historical and intellectual context, I portray the scientific community’s initial lack of interest in the method as a natural consequence of (...) relevant scientific and philosophical conditions. In addition to Karl Pearson’s positivist refutation of causation, I contend that the acceptance of path analysis faced several other challenges, including the introduction of a new formalism, conceptual barriers to causal inference, and the lack of model-based statistical thinking. The presence of these challenges shows that the delayed progress in causal inference in the early twentieth century was inevitable. (shrink)

The literature on indicative conditionals contains two appealing views. The first is the selectional view: on this view, conditionals operate by selecting a single possibility, which is used to evaluate the consequent. The second is the informational view: on this view, conditionals don’t express propositions, but rather impose constraints on information states of speakers. Both views are supported by strong arguments, but they are incompatible on their standard formulations. Hence it appears that we have to choose between mutually exclusive options. (...) But the options are not exclusive. This paper develops a theory of the semantics and assertability of conditionals that is both selectional and informational. The theory vindicates the signature inferences of both selectional and informational theories, including so-called Conditionals Excluded Middle and principles about the interplay between conditionals and ‘might’. It also predicts some interesting and puzzling facts about the assertion of conditionals. (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)

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)

This paper argues that two widely accepted principles about the indicative conditional jointly presuppose the falsity of one of the most prominent arguments against epistemological iteration principles. The first principle about the indicative conditional, which has close ties both to the Ramsey test and the “or‐to‐if” inference, says that knowing a material conditional suffices for knowing the corresponding indicative. The second principle says that conditional contradictions cannot be true when their antecedents are epistemically possible. Taken (...) together, these principles entail that it is impossible to be in a certain kind of epistemic state: namely, a state of ignorance about which of two partially overlapping bodies of knowledge corresponds to one's actual one. However, some of the more popular “margin for error” style arguments against epistemological iteration principles suggest that such states are not only possible, but commonplace. I argue that the tension between these views runs deep, arising just as much for non‐factive attitudes like belief, presupposition, and certainty. I also argue that this is worse news for those who accept the principles about the indicative conditional than it is for those who reject epistemological iteration principles. (shrink)

This paper presents a unified theory of the truth conditions and probability of indicative conditionals and their compounds in a trivalent framework. The semantics validates a Reduction Theorem: any compound of conditionals is semantically equivalent to a simple conditional. This allows us to validate Stalnaker's Thesis in full generality and to use Adams's notion of $p$-validity as a criterion for valid inference. Finally, this gives us an elegant account of Bayesian update with indicative conditionals, establishing that despite differences (...) in meaning, it is tantamount to learning a material conditional. (shrink)

I argue that the accounts of inference recently presented (in this journal) by Paul Boghossian, John Broome, and Crispin Wright are unsatisfactory. I proceed in two steps: First, in Sects. 1 and 2, I argue that we should not accept what Boghossian calls the “Taking Condition on inference” as a condition of adequacy for accounts of inference. I present a different condition of adequacy and argue that it is superior to the one offered by Boghossian. More precisely, (...) I point out that there is an analog of Moore’s Paradox for inference; and I suggest that explaining this phenomenon is a condition of adequacy for accounts of inference. Boghossian’s Taking Condition derives its plausibility from the fact that it apparently explains the analog of Moore’s Paradox. Second, in Sect. 3, I show that neither Boghossian’s, nor Broome’s, nor Wright’s account of inference meets my condition of adequacy. I distinguish two kinds of mistake one is likely to make if one does not focus on my condition of adequacy; and I argue that all three—Boghossian, Broome, and Wright—make at least one of these mistakes. (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)

Most inferentialists hope to bypass givenness by tracking the conditionals claimants are implicitly committed to. I argue that this approach is underdetermined because one can always construct parallel trees of conditionals. I illustrate this using the Müller-Lyer illusion and touching a table. In the former case, the lines are either even or uneven; in the latter case, a moving hand will either sweep through or be halted. For each possibility, we can rationally foresee consequents. However, I argue that, until and (...) unless we benefit from what is given in experience, we cannot know whether to affirm the antecedents of those conditionals. (shrink)

In this manuscript we study individual variation in the interpretation of conditionals by establishing individual profiles of the participants based on their behavioral responses and reflective attitudes. To investigate the participants’ reflective attitudes we introduce a new experimental paradigm called the Scorekeeping Task, and a Bayesian mixture model tailored to analyze the data. The goal is thereby to identify the participants who follow the Suppositional Theory of conditionals and Inferentialism and to investigate their performance on the uncertain and-to-if inference (...) task. (shrink)

In Lehrer’s case of the superstitious lawyer, a lawyer possesses conclusive evidence for his client’s innocence, and he appreciates that the evidence is conclusive, but the evidence is causally inert with respect to his belief in his client’s innocence. This case has divided epistemologists ever since Lehrer originally proposed it in his argument against causal analyses of knowledge. Some have taken the claim that the lawyer bases his belief on the evidence as a data point for our theories to accommodate, (...) while others have denied that the lawyer has knowledge, or that he bases his belief on the evidence. In this paper, we move the dialectic forward by way of arguing that the superstitious lawyer genuinely infers his client’s innocence from the evidence. To show that the lawyer’s inference is genuine, we argue in defense of a version of a doxastic construal of the ‘taking’ condition on inference. We also provide a pared-down superstitious lawyer-style case, which displays the key features of the original case without including its complicated and distracting features. But interestingly, although we argue that the lawyer’s belief is based on his good evidence, and is also plausibly doxastically justified, we do not argue that the lawyer knows that his client is innocent. (shrink)

This paper is about two controversial inference-patterns involving counterfactual or subjunctive conditionals. Given a plausible assumption about the truth-conditions of counterfactuals, it is shown that one can't go wrong in applying hypothetical syllogism (i.e., transitivity) so long as the set of worlds relevant for the conclusion is a subset of the sets of worlds relevant for the premises. It is also shown that one can't go wrong in applying antecedent strengthening so long as the set of worlds relevant for (...) the conclusion is a subset of that for the premise. These results are then adapted to Lewis's theory of counterfactuals. (shrink)

Curry's paradox for "if.. then.." concerns the paradoxical features of sentences of the form "If this very sentence is true, then 2+2=5". Standard inference principles lead us to the conclusion that such conditionals have true consequents: so, for example, 2+2=5 after all. There has been a lot of technical work done on formal options for blocking Curry paradoxes while only compromising a little on the various central principles of logic and meaning that are under threat. -/- Once we have (...) a sense of the technical options, though, a philosophical choice remains. When dealing with puzzles in the logic of conditionals, a natural place to turn is independently motivated semantic theories of the behaviour of "if... then...". This paper argues that the closest-worlds approach outlined in Nolan 1997 offers a philosophically satisfying reason to deny conditional proof and so block the paradoxical Curry reasoning, and can give the verdict that standard Curry conditionals are false, along with related "contraction conditionals". (shrink)

We present a puzzle about knowledge, probability and conditionals. We show that in certain cases some basic and plausible principles governing our reasoning come into conflict. In particular, we show that there is a simple argument that a person may be in a position to know a conditional the consequent of which has a low probability conditional on its antecedent, contra Adams’ Thesis. We suggest that the puzzle motivates a very strong restriction on the inference of a (...) conditional from a disjunction. (shrink)

Transcranial magnetic stimulation is used to make inferences about relationships between brain areas and their functions because, in contrast to neuroimaging tools, it modulates neuronal activity. The central aim of this article is to critically evaluate to what extent it is possible to draw causal inferences from repetitive TMS data. To that end, we describe the logical limitations of inferences based on rTMS experiments. The presented analysis suggests that rTMS alone does not provide the sort of premises that are sufficient (...) to warrant strong inferences about the direct causal properties of targeted brain structures. Overcoming these limitations demands a close look at the designs of rTMS studies, especially the methodological and theoretical conditions which are necessary for the functional decomposition of the relations between brain areas and cognitive functions. The main points of this article are that TMS-based inferences are limited in that stimulation-related causal effects are not equivalent to structure-related causal effects due to TMS side effects, the electric field distribution, and the sensitivity of neuroimaging and behavioral methods in detecting structure-related effects and disentangling them from confounds. Moreover, the postulated causal effects can be based on indirect effects. A few suggestions on how to manage some of these limitations are presented. We discuss the benefits of combining rTMS with neuroimaging in experimental reasoning and we address the restrictions and requirements of rTMS control conditions. The use of neuroimaging and control conditions allows stronger inferences to be gained, but the strength of the inferences that can be drawn depends on the individual experiment’s designs. Moreover, in some cases, TMS might not be an appropriate method of answering causality-related questions or the hypotheses have to account for the limitations of this technique. We hope this summary and formalization of the reasoning behind rTMS research can be of use not only for scientists and clinicians who intend to interpret rTMS results causally but also for philosophers interested in causal inferences based on brain stimulation research. (shrink)

In this paper, I explore a question about deductive reasoning: why am I in a position to immediately infer some deductive consequences of what I know, but not others? I show why the question cannot be answered in the most natural ways of answering it, in particular in Descartes’s way of answering it. I then go on to introduce a new approach to answering the question, an approach inspired by Hume’s view of inductive reasoning.

This paper explores an idea of Stoic descent that is largely neglected nowadays, the idea that an argument is valid when the conditional formed by the conjunction of its premises as antecedent and its conclusion as consequent is true. As it will be argued, once some basic features of our naıve understanding of validity are properly spelled out, and a suitable account of conditionals is adopted, the equivalence between valid arguments and true conditionals makes perfect sense. The account of (...) validity outlined here, which displays one coherent way to articulate the Stoic intuition, accords with standard formal treatments of deductive validity and encompasses an independently grounded characterization of inductive validity. (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.

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)

IBE ('Inference to the best explanation' or abduction) is a popular and highly plausible theory of how we should judge the evidence for claims of past events based on present evidence. It has been notably developed and supported recently by Meyer following Lipton. I believe this theory is essentially correct. This paper supports IBE from a probability perspective, and argues that the retrodictive probabilities involved in such inferences should be analysed in terms of predictive probabilities and a priori probability (...) ratios of initial events. The key point is to separate these two features. Disagreements over evidence can be traced to disagreements over either the a priori probability ratios or predictive conditional ratios. In many cases, in real science, judgements of the former are necessarily subjective. The principles of iterated evidence are also discussed. The Sceptic's position is criticised as ignoring iteration of evidence, and characteristically failing to adjust a priori probability ratios in response to empirical evidence. (shrink)

Suppose that two competing norms, N1 and N2, can be identified such that a given person’s response can be interpreted as correct according to N1 but incorrect according to N2. Which of these two norms, if any, should one use to interpret such a response? In this paper we seek to address this fundamental problem by studying individual variation in the interpretation of conditionals by establishing individual profiles of the participants based on their case judgments and reflective attitudes. To investigate (...) the participants’ reflective attitudes we introduce a new experimental paradigm called the Scorekeeping Task. As a case study, we identify the participants who follow the Suppositional Theory of conditionals (N1) versus Inferentialism (N2) and investigate to what extent internally consistent competence models can be reconstructed for the participants on this basis. After extensive empirical investigations, an apparent reasoning error with and-to-if inferences was found in one of these two groups. The implications of this case study for debates on the proper role of normative considerations in psychology are discussed. (shrink)

According to one tradition, uttering an indicative conditional involves performing a special sort of speech act: a conditional assertion. We introduce a formal framework that models this speech act. Using this framework, we show that any theory of conditional assertion validates several inferences in the logic of conditionals, including the False Antecedent inference. Next, we determine the space of truth-conditional semantics for conditionals consistent with conditional assertion. The truth value of any such conditional (...) is settled whenever the antecedent is false, and whenever the antecedent is true and the consequent is false. Then, we consider the space of dynamic meanings consistent with the theory of conditional assertion. We develop a new family of dynamic conditional-assertion operators that combine a traditional test operator with an update operation. (shrink)

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)

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)

Language theorists have recently come to have an increasing appreciation for the fact that context contributes heavily in determining our interpretation of what is said. Indeed, it now seems clear that no complete understanding of a natural language is possible without some account of the way in which context affects our interpretation of discourse. In this paper, I will attempt to explore one facet of the language – context relationship, namely, the relation between conditionals and context. The first part of (...) the paper develops an account of truth for conditionals which allows them to depend on momentary features of the context in which they are uttered. In the second half of the paper, comparisons with other recent theories of the conditional will be considered. Particular attention will be given to the problem of whether the conditional really violates classical inferences such as Hypothetical Syllogism and Contraposition as has often been claimed in recent years. (shrink)

The problem analysed in this paper is whether we can gain knowledge by using valid inferences, and how we can explain this process from a model-theoretic perspective. According to the paradox of inference (Cohen & Nagel 1936/1998, 173), it is logically impossible for an inference to be both valid and its conclusion to possess novelty with respect to the premises. I argue in this paper that valid inference has an epistemic significance, i.e., it can be used by (...) an agent to enlarge his knowledge, and this significance can be accounted in model-theoretic terms. I will argue first that the paradox is based on an equivocation, namely, it arises because logical containment, i.e., logical implication, is identified with epistemological containment, i.e., the knowledge of the premises entails the knowledge of the conclusion. Second, I will argue that a truth-conditional theory of meaning has the necessary resources to explain the epistemic significance of valid inferences. I will explain this epistemic significance starting from Carnap’s semantic theory of meaning and Tarski’s notion of satisfaction. In this way I will counter (Prawitz 2012b)’s claim that a truth-conditional theory of meaning is not able to account the legitimacy of valid inferences, i.e., their epistemic significance. (shrink)

This paper provides new tools for philosophical argument analysis and fresh empirical foundations for ‘critical’ ordinary language philosophy. Language comprehension routinely involves stereotypical inferences with contextual defeaters. J.L. Austin’s Sense and Sensibilia first mooted the idea that contextually inappropriate stereotypical inferences from verbal case-descriptions drive some philosophical paradoxes; these engender philosophical problems that can be resolved by exposing the underlying fallacies. We build on psycholinguistic research on salience effects to explain when and why even perfectly competent speakers cannot help making (...) stereotypical inferences which are contextually inappropriate. We analyse a classical paradox about perception, suggest it relies on contextually inappropriate stereotypical inferences from appearance-verbs, and show that the conditions we identified as leading to contextually inappropriate stereotypical inferences are met in formulations of the paradox. Three experiments use a forced-choice plausibility-ranking task to document the predicted inappropriate inferences, in English, German, and Japanese. The cross-linguistic study allows us to assess the wider relevance of the proposed analysis. Our findings open up new perspectives for ‘evidential’ experimental philosophy. (shrink)

There are numerous formal systems that allow inference of new conditionals based on a conditional knowledge base. Many of these systems have been analysed theoretically and some have been tested against human reasoning in psychological studies, but experiments evaluating the performance of such systems are rare. In this article, we extend the experiments in [19] in order to evaluate the inferential properties of c-representations in comparison to the well-known Systems P and Z. Since it is known that System (...) Z and c-representations mainly differ in the sorts of inheritance inferences they allow, we discuss subclass inheritance and present experimental data for this type of inference in particular. (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)

It is usually accepted that deductions are non-informative and monotonic, inductions are informative and nonmonotonic, abductions create hypotheses but are epistemically irrelevant, and both deductions and inductions can’t provide new insights. In this article, I attempt to provide a more cohesive view of the subject with the following hypotheses: (1) the paradigmatic examples of deductions, such as modus ponens and hypothetical syllogism, are not inferential forms, but coherence requirements for inferences; (2) since any reasoner aims to be coherent, any (...) class='Hi'>inference must be deductive; (3) a coherent inference is an intuitive process where the premises should be taken as sufficient evidence for the conclusion, which on its turn should be viewed as necessary evidence for the premises in some modal range; (4) inductions, properly understood, are abductions, but there are no abductions beyond the fact that in any inference the conclusion should be regarded as necessary evidence for the premises; (5) monotonicity is not only compatible with the retraction of past inferences given new information, but it is a requirement for it; (6) this explanation of inferences holds true for discovery processes, predictions and trivial inferences. (shrink)

Recently several papers have reported relevance effects on the cognitive assessments of indicative conditionals, which pose an explanatory challenge to the Suppositional Theory of conditionals advanced by David Over, which is influential in the psychology of reasoning. Some of these results concern the “Equation” (P(if A, then C) = P(C|A)), others the de Finetti truth table, and yet others the uncertain and-to-inference task. The purpose of this chapter is to take a Birdseye view on the debate and investigate some (...) of the open theoretical issues posed by the empirical results. Central among these is whether to count these effects as belonging to pragmatics or semantics. (shrink)

Abstract Introduction Logically valid deductive arguments are clear examples of abstract recursive computational proce‐ dures on propositions or on probabilities. However, it is not known if the cortical time‐consuming inferential pro‐ cesses in which logical arguments are eventually realized in the brain are in fact physically different from other kinds of inferential processes. Methods In order to determine whether an electrical EEG discernible pattern of logical deduction exists or not, a new experimental paradigm is proposed contrasting logically valid and invalid (...) inferences with exactly the same content (same premises and same relational variables) and distinct logical complexity (propositional truth‐functional operators). Electroencephalographic signals from 19 subjects (24.2 ± 3.3 years) were acquired in a two‐condition para‐ digm (100 trials for each condition). After the initial general analysis, a trial‐by‐trial approach in beta‐2 band allowed to uncover not only evoked but also phase asynchronous activity between trials. Results showed that (i) deductive inferences with the same content evoked the same response pattern in logically valid and invalid conditions, (ii) mean response time in logically valid inferences is 61.54% higher, (iii) logically valid inferences are subjected to an early (400 ms) and a late reprocessing (600 ms) verified by two distinct beta‐2 activa‐ tions (p‐value < 0,01, Wilcoxon signed rank test). Conclusion We found evidence of a subtle but measurable electrical trait of logical validity. Results put forward the hypothesis that some logically valid deductions are recursive or computational cortical events. Keywords Beta‐2 band, Evoked potentials, Induced potentials, Deductive inference, Logical validity, Cortical bases of logical reasoning. (shrink)

An adequate semantics for generic sentences must stake out positions across a range of contested territory in philosophy and linguistics. For this reason the study of generic sentences is a venue for investigating different frameworks for understanding human rationality as manifested in linguistic phenomena such as quantification, classification of individuals under kinds, defeasible reasoning, and intensionality. Despite the wide variety of semantic theories developed for generic sentences, to date these theories have been almost universally model-theoretic and representational. This essay outlines (...) a range of proof-theoretic analyses for characterizing generics. Particular attention is given to an expressivist proof-theory that can be traced to 1) work on logical syntax that Carnap undertook prior to his turn toward truth-conditional model theory in the late 1930s, and 2) research on sequent calculi and natural deduction systems that originate in work from Gentzen and Prawitz.11 This essay offers a more precise exposition of some of the material discussed in the first two chapters of my dissertation (Stovall Citation2015a). These ideas developed in the context of a working group on non-monotonic logic run by Robert Brandom, and they were subsequently clarified through the work of Nissim Francez (particularly Francez Citation2015). I am indebted to many people for feedback and criticism on this essay, though I am sure none among them would agree with everything I say and do here. I would particularly like to thank Brandom, Francez, Ulf Hlobil, Daniel Kaplan, Jared Millson, Bernhard Nickel, Jaroslav Peregrin, Jeffry Pelletier, Thomas Ricketts, Mark Risjord, Shawn Standefer, and two reviewers for this journal. Work on this essay was supported by the joint Lead-Agency research grant between the Austrian Science Foundation (FWF) and the Czech Science Foundation (GAČR), Inferentialism and Collective Intentionality, GF17-33808L. It was substantially revised prior to its final submission. (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)

According to the so-called ‘standard theory’ of conditions, the conditionship relation is converse, that is, if A is a sufficient condition for B, B is a necessary condition for A. This theory faces well-known counterexamples that appeal to both causal and other asymmetric considerations. I show that these counterexamples lose their plausibility once we clarify two key components of the standard theory: that to satisfy a condition is to instantiate a property, and that what is usually called ‘conditionship relation’ is (...) an inferential relation. Throughout the paper this way of interpreting the standard theory is compared favourably over an alternative interpretation that is outlined in causal terms, since it can be applied to all counterexamples without losing its intuitive appeal. (shrink)