Truth-Conditional Accounts of Indicative Conditionals

We will look at several theories of indicative conditionals grouped into three categories: those that base its semantics on its logical counterpart (the material conditional); intensional analyses, which bring in alternative possible worlds; and a third subgroup which denies that indicative conditionals express propositions at all. We will also look at some problems for each kind of approach.

In the 1960’s, both Montague (e.g. 1970, 222) and Grice (1975, 24) famously declared that natural languages were not so different from the formal languages of logic as people had thought. Montague sought to comprehend the grammars of both within a single theory, and Grice sought to explain away apparent divergences as due to the fact that the former, but not the latter, were used for conversation. But, if we confine our concept of logic to first order predicate logic (or (...) FOPL) with identity (that is, omitting everything which is not required for the pursuit of mathematical truth), then there are of course many other aspects, in addition to its use in conversation, which distinguish natural language from logic. Conventional implicature, information structure (including presupposition), tense and time reference, and the expression of causation and inference are several of these, which combine as well with syntactic complexities which are unnecessary in first order predicate logic. In this paper I will argue that such distinguishing aspects should be more fully exploited to explain the differences between the material conditional of logic and the indicative conditional of one natural language (English). (shrink)

Grice's arguments that ordinary language indicative conditionals are logically equivalent to material conditionals are criticized. It is agreed that 'indirectness conditions' going beyond the material conditional can "sometimes" be detached' from ordinary language conditionals, but it is argued that this is not always possible. An example in which a speaker who knows that some mushrooms are non-poisonous tells a hearer "if you eat those mushrooms you will be poisoned", causing the hearer not to eat the mushrooms, is discussed, and it (...) is argued that this utterance should be regarded as factually unsatisfactory', and therefore, by Grice's own standards, false. (shrink)

The material interpretation of conditionals is commonly recognized as involving some paradoxical results. I here argue that the truth functional approach to natural language is the reason for the inadequacy of this material interpretation, since the truth or falsity of some pair of statements ‘p’ and ‘q’ cannot per se be decisive for the truth or falsity of a conditional relation ‘if p then q’. This inadequacy also affects the ability of the overall formal system to establish whether or not (...) arguments involving conditionals are valid. I also demonstrate that the Paradox of Indicative Conditionals does not actually involve a paradox, but instead contains some paralogistic elements that make it appear to be a paradox. The discussion of the paradox in this paper further reveals that the material interpretation of conditionals adversely affects the treatment of disjunctions. -/- Much has been said about these matters in the literature that point in the same direction. However, there seems to be some reluctance against fully complying with the arguments against the truth functional account of conditionals, since many of the alternative accounts rely on the material conditional, or at least on an understanding of the conditional as a function of antecedent and consequent in a similar sense as the material conditional. My argument against truth functionality indicates that it may in general involve similar problems to treat conditionals as such functions, whether one deals with theories of truth, assertability or probability. (shrink)

Grice argues that indicative conditionals ‘if p then q’ have conventional, truth conditional meaning according to the material conditional ‘p  q’. In order to explain away the known paradoxes with this interpretation, he distinguishes between truth conditions and assertion conditions, attempting to demonstrate that the assumed connection between ‘p’ and ‘q’ (the Indirectness Condition) is a conversational implicature; hence a matter only relevant for the assertion conditions of a conditional. This paper argues that Grice fails to demonstrate i) that (...) the Indirectness Condition is cancellable, hence a conversational implicature, ii) that the Indirectness Condition is not part of the conventional, truth-relevant meaning of ‘if’, and accordingly, iii) semantic or logical equivalence between indicative and material conditionals. (shrink)

The truth functional account of conditional statements ‘if A then B’ is not only inadequate; it eliminates the very conditionality expressed by ‘if’. Focusing only on the truth-values of the statements ‘A’ and ‘B’ and different combinations of these, one is bound to miss out on the conditional relation expressed between them. All approaches that treat conditionals as functions of their antecedents and consequents will end up in some sort of logical atomism where causal matters simply are reduced to the (...) joint occurrence of A and B. (shrink)

This paper falls into two parts. In the first part, I argue that consideration of general indicative conditionals, e.g., sentences like If a donkey brays it is beaten, provides a powerful argument that a pure material implication analysis of indicative if p, q is correct. In the second part I argue, opposing writers like Jackson, that a Gricean style theory of pragmatics can explain the manifest assertability conditions of if p, q in terms of its conventional content – assumed to (...) be merely (p⊃q) – and the conversational implicature contents which utterance of if p, q may gain in certain contexts. I also defend the pragmatic approach against a recent objection by Edgington that appeal to pragmatics cannot explain what we are inclined to say about the believability conditions, as opposed to the assertability conditions, of indicative if p, q. (shrink)

This paper is concerned with Sir Peter Strawson’s critical discussion of Paul Grice’s defence of the material implication analysis of conditionals. It argues that although Strawson’s own ‘consequentialist’ suggestion concerning the meaning of conditionals cannot be correct, a related and radically contextualist account is able to both account for the phenomena that motivated Strawson’s consequentialism, and to undermine the material implication analysis by providing a simpler account of the processes that we go through when interpreting conditionals.

I discuss an argument given by Dorothy Edgington for the conclusion that indicative conditionals cannot express propositions. The argument is not effective against Robert Stalnaker's context-dependent propositional theory. I isolate and defend the feature of Stalnaker's theory that allows it to evade the argument.

Most instantiations of the inference ‘y; so if x, y’ seem intuitively odd, a phenomenon known as one of the paradoxes of the material conditional. A common explanation of the oddity, endorsed by Mental Model theory, is based on the intuition that the conclusion of the inference throws away semantic information. We build on this explanation to identify two joint conditions under which the inference becomes acceptable: (a) the truth of x has bearings on the relevance of asserting y; and (...) (b) the speaker can reasonably be expected not to be in a position to assume that x is false. We show that this dual pragmatic criterion makes accurate predictions, and contrast it with the criterion defined by the mental model theory of conditionals, which we show to be inadequate. (shrink)

Adams Thesis has much evidence in its favour, but David Lewis famously showed that it cannot be true, in all but the most trivial of cases, if conditionals are proprositions and their probabilities are classical probabilities of truth. In this paper I show thatsimilar results can be constructed for a much wider class of conditionals. The fact that these results presuppose that the logic of conditionals is Boolean motivates a search for a non-Boolean alternative. It is argued that the exact (...) proposition expressed by a conditional depends on the context in which it is uttered. Consequentlyits probability of truth will depend not only on the probabilities of the various propositions it might express, but also on the probabilities of the contexts determining which proposition it does in fact express.The semantic theory developed from this is then shown to explain why agents degrees of belief satisfyAdams Thesis. Finally the theory is compared with proposals for a three-valued logic of conditionals. (shrink)

Reasoning with indicative conditionals, i.e., with statements such as 'If the weather is bad, then the plane will be late', constitutes a significant part of ordinary reasoning. How are we to proceed in the logical treatment of ordinary language arguments involving indicative conditionals? In particular, is standard formal truth-functional sentential logic applicable to these conditionals, and if so, under what circumstances? This dissertation first examines two sharply contrasting theories proposed in response to these questions. One of them is the dominant (...) view, primarily identified with H. P. Grice and Frank Jackson, which defends the traditional truth-functional treatment of indicative conditionals and also endorses the application of formal logic to them. The other theory, upheld primarily by Ernest Adams, claims that the formal truth-functional logic is inapplicable to indicative conditionals and that their proper treatment requires a special probabilistic logic. Through a critique of both of these theories, I show that these extreme approaches are defective and unsatisfactory. I argue that the main benefit of having such philosophical theories of indicative conditionals can be achieved at a much lower cost by what may be called a common sense account of indicative conditionals. The common-sense account rejects the idea that indicative conditionals in their 'true logical form' are truth-functional material conditionals. It nonetheless endorses the applicability of formal truth-functional logic to ordinary conditional reasoning. On behalf of common-sense account, I argue that the two issues, the assumption of truth-functionality of indicative conditionals and applicability of formal truth-functional logic to them, do not rise or fall together. (shrink)

I present two Triviality results for Kratzer's standard “restrictor” analysis of indicative conditionals. I both refine and undermine the common claim that problems of Triviality do not arise for Kratzer conditionals since they are not strictly conditionals at all.

I argue that taking the Practical Conditionals Thesis seriously demands a new understanding of the semantics of such conditionals. Practical Conditionals Thesis: A practical conditional [if A][ought] expresses B’s conditional preferability given A Paul Weirich has argued that the conditional utility of a state of affairs B on A is to be identified as the degree to which it is desired under indicative supposition that A. Similarly, exploiting the PCT, I will argue that the proper analysis of indicative practical conditionals (...) is in terms of what is planned, desired, or preferred, given suppositional changes to an agent’s information. Implementing such a conception of conditional preference in a semantic analysis of indicative practical conditionals turns out to be incompatible with any approach which treats the indicative conditional as expressing non-vacuous universal quantification over some domain of relevant antecedent-possibilities. Such analyses, I argue, encode a fundamental misunderstanding of what it is to be best, given some condition. The analysis that does the best vis-à-vis the PCT is, instead, one that blends a Context-Shifty account of indicative antecedents with an Expressivistic, or non-propositional, treatment of their practical consequents. (shrink)

In a series of articles, David Barnett (2006, 2009, 2010) has developed a general theory of conditionals. The grand aim is to reconcile the two main rivals: a suppositional and a truth-conditional view (Barnett 2006, 521). While I confine my critical discussion to counterfactuals, I will give some hints how they might spell trouble for his suppositional view in general.

Sobel sequences have had a huge impact on the discussion of counterfactuals. They can be composed of conditionals and mere descriptions. What is especially puzzling about them is that they are often felicitously uttered when their reversal is not. Up to now, there is no unified explanation. I examine two strategies. We might begin with conditionals and proceed to descriptions. Or we might begin with descriptions and proceed to conditionals. I argue for the latter variant and outline a universal theory (...) of Sobel sequences in terms of presuppositional anaphora. One relevant result is that the phenomenon neither counts against nor in favour of the simplified standard account of counterfactuals à la Stalnaker-Lewis. (shrink)

Proponents of the projection strategy take an epistemic rule for the evaluation of English conditionals, the Ramsey test, as clue to the truth-conditional semantics of conditionals. They also construe English conditionals as stronger than the material conditional. Given plausible assumptions, however, the Ramsey test induces the semantics of the material conditional. The alleged link between Ramsey test and truth conditions stronger than those of the material conditional can be saved by construing conditionals as ternary, rather than binary, propositional functions with (...) a hidden contextual parameter. But such a ternary construal raises problems of its own. (shrink)

Bradley has argued that a truth-conditional semantics for conditionals is incompatible with an allegedly very weak and intuitively compelling constraint on the interpretation of conditionals. I argue that the example Bradley offers to motivate this constraint can be explained along pragmatic lines that are compatible with the correctness of at least one popular truth-conditional semantics for conditionals.

Section 1 briefly examines three theories of indicative conditionals. The Suppositional Theory is defended, and shown to be incompatible with understanding conditionals in terms of truth conditions. Section 2 discusses the psychological evidence about conditionals reported by Over and Evans (this volume). Section 3 discusses the syntactic grounds offered by Haegeman (this volume) for distinguishing two sorts of conditional.

In this paper, I discuss conditionals as illocutionary speech acts whose interpretation depends upon the whole of the social context in which they are uttered and whose purpose is to affect the opinions and actions of others. I argue for a suppositional approach to conditional statements based in what philosophers call the Ramsey test and developing the psychological theory that conditionals elicit a process of hypothetical thinking in their listeners. By reference to the experimental psychological literature on conditionals, I show (...) that in general conditionals, even ones that are basic or abstract in nature, are not treated as truth-functional or material by ordinary people. Drawing upon the suppositional nature of conditionals and the influence of pragmatic implicature, I discuss uses of conditionals as advice, inducement, persuasions and dissuasion, arguing that speakers use conditionals to try to influence the beliefs and actions of their listeners by shaping their hypothetical thought about possibilities. (shrink)

Conditionals are central to inference. Before people can draw inferences about a natural language conditional, they must interpret its meaning. We investigated interpretation of uncertain conditionals using a probabilistic truth table task, focussing on (i) conditional event, (ii) material conditional, and (iii) conjunction interpretations. The order of object (shape) and feature (color) in each conditional's antecedent and consequent was varied between participants. The conditional event was the dominant interpretation, followed by conjunction, and took longer to process than conjunction (mean di (...) erence 500 ms). Material conditional responses were rare. The proportion of conditional event responses increased from around 40% at the beginning of the task to nearly 80% at the end, with 55% of participants showing a qualitative shift of interpretation. Shifts to the conditional event occurred later in the feature-object order than in the object-feature order. We discuss the results in terms of insight and suggest implications for theories of interpretation. (shrink)

We put forth a theory of conditional elements which can be used to dismiss apparent challenges to the truth-functionality of the conditional without apparent circularity. In the process, we refine the ideas of Yoes, published in an earlier paper in this journal, broadening and deepening them.

This note addresses the problems that arise from denying conditionals in classical logic and concludes that such problems result from using propositional logic where predicate logic with quantification over cases is indicated.

This paper deals with Austinian ifs of every stripe within classical logic. It is argued that they are truth-functional and the theory of conditional elements is used. Ellipsis is key. Corrects an error in Fulda (2010) in translation and therefore scope. -/- The PDF is made available gratis by the Publisher.

This paper presents a unified, more-or-less complete, and largely pragmatic theory of indicative conditionals as they occur in natural language, which is entirely truth-functional and does not involve probability. It includes material implication as a special—and the most important—case, but not as the only case. The theory of conditional elements, as we term it, treats if-statements analogously to the more familiar and less controversial other truth-functional compounds, such as conjunction and disjunction.

Solves Vann McGee's counterexample to Modus Ponens within classical logic by disclosing the suppressed premises and bringing them /within/ the argument.

In "Material Implications" (1992), mathematical discourse was said to be different from ordinary discourse, with the discussion centering around conditionals. This paper shows how.

Solves what is sometimes, but not always, referred to as the third paradox of material implication. Readers downloading this piece should please also download the corrigendum. Note that "pragmatic" is here used in its original sense of context-sensitive, that is, adjacency. (This comment is made in response to an article in a student journal published in the western U.S. which claimed that I said that because something involves translation it must be pragmatic; that is so, in the original sense; only (...) grammaticality can ever be context-free; all meaning is context-sensitive, as "lawful" cannot meaningfully modify "whale."). (shrink)

Replies to a letter by Dan Velleman re my my 1989 American Mathematical Monthly piece.

Demonstrates that the "paradoxes of material implication" are only apparent, sticking entirely within the confines of classical logic.