Strict Conditional Research Articles

Credences for strict conditionals

AbstractLess‐than‐certain conditional judgments pose notorious problems for strict analyses of conditionals: across their various incarnations, these analyses have trouble making sense of how conditionals could have non‐trivial probabilities in the first place; minimal constraints on how such probabilities are to be assigned, moreover, lead to results that seem at odds with a strict outlook on the semantics of conditionals, most notably the validity of Conditional Excluded Middle. I demonstrate that a strict analysis can overcome the trouble if couched in a bilateral dynamic setting that properly extends the familiar Ramsey test for accepting conditionals to other iffy attitudes, most importantly the one of rejecting a conditional. The resulting framework accommodates the appeal of Stalnaker's thesis as well as of Conditional Excluded Middle in a strict setting. A discussion of how to handle the probability of epistemically modalized conditionals and of compounds of conditionals is provided.

Strict conditionals

Both Lowe and Tsai have presented their own versions of the theory that both indicative and subjunctive conditionals are strict conditionals. We critically discuss both versions and we find each version wanting.

Definable Conditionals

The variably strict analysis of conditionals does not only largely dominate the philosophical literature, since its invention by Stalnaker and Lewis, it also found its way into linguistics and psychology. Yet, the shortcomings of Lewis–Stalnaker’s account initiated a plethora of modifications, such as non-vacuist conditionals, presuppositional indicatives, perfect conditionals, or other conditional constructions, for example: reason relations, difference-making conditionals, counterfactual dependency, or probabilistic relevance. Many of these new connectives can be treated as strengthened or weakened conditionals. They are definable conditionals. This article develops a technique to infer the logic for such definable conditionals from the known logic of the underlying defining conditional. The technique is applied to central examples. The results show that a large part of the zoo of conditionals arises from a basic conditional—a constant nucleus of the different contextual and conceptual variations of variably strict conditionals.

Relative Necessity and Propositional Quantification

Following Smiley’s (The Journal of Symbolic Logic, 28, 113–134 1963) influential proposal, it has become standard practice to characterise notions of relative necessity in terms of simple strict conditionals. However, Humberstone (Reports on Mathematical Logic, 13, 33–42 1981) and others have highlighted various flaws with Smiley’s now standard account of relative necessity. In their recent article, Hale and Leech (Journal of Philosophical Logic, 46, 1–26 2017) propose a novel account of relative necessity designed to overcome the problems facing the standard account. Nevertheless, the current article argues that Hale & Leech’s account suffers from its own defects, some of which Hale & Leech are aware of but underplay. To supplement this criticism, the article offers an alternative account of relative necessity which overcomes these defects. This alternative account is developed in a quantified modal propositional logic and is shown model-theoretically to meet several desiderata of an account of relative necessity.

Strictness and connexivity

ABSTRACT This paper discusses Aristotle's thesis and Boethius' thesis, the most distinctive theorems of connexive logic. Its aim is to show that, although there is something plausible in Aristotle's thesis and Boethius' thesis, the intuitions that may be invoked to motivate them are consistent with any account of indicative conditionals that validates a suitably restricted version of them. In particular, these intuitions are consistent with the view that indicative conditionals are adequately formalized as strict conditionals.

The counterfactual direct argument

Many have accepted that ordinary counterfactuals and might counterfactuals are duals. In this paper, I show that this thesis leads to paradoxical results when combined with a few different unorthodox yet increasingly popular theses, including the thesis that counterfactuals are strict conditionals. Given Duality and several other theses, we can quickly infer the validity of another paradoxical principle, ‘The Counterfactual Direct Argument’, which says that ‘A> (B or C)’ entails ‘A> (not B> C)’. First, I provide a collapse theorem for the ‘counterfactual direct argument’ (CDA). The counterfactual direct argument entails the logical equivalence of the subjunctive and material conditional, given a variety of assumptions. Second, I provide a semantics that validates the counterfactual direct argument without collapse. This theory further develops extant dynamic accounts of conditionals. I give a new semantics for disjunction, on which A or B is only true in a context when A and B are both unsettled. The resulting framework validates CDA while invalidating other commonly accepted principles concerning the conditional and disjunction.

COMPLETENESS FOR COUNTER-DOXA CONDITIONALS – USING RANKING SEMANTICS

AbstractStandard conditionals $\varphi > \psi$, by which I roughly mean variably strict conditionals à la Stalnaker and Lewis, are trivially true for impossible antecedents. This article investigates three modifications in a doxastic setting. For the neutral conditional, all impossible-antecedent conditionals are false, for the doxastic conditional they are only true if the consequent is absolutely necessary, and for the metaphysical conditional only if the consequent is ‘model-implied’ by the antecedent. I motivate these conditionals logically, and also doxastically by properties of conditional belief and belief revision. For this I show that the Lewisian hierarchy of conditional logics can be reproduced within ranking semantics, provided we slightly stretch the notion of a ranking function. Given this, acceptance of a conditional can be interpreted as a conditional belief. The epistemic and the neutral conditional deviate from Lewis’ weakest system $V$, in that ID ($\varphi > \varphi$) or even CN ($\varphi > \top$) are dropped, and new axioms appear. The logic of the metaphysical conditional is completely axiomatised by $V$ to which we add the known Kripke axioms T5 for the outer modality. Related completeness results for variations of the ranking semantics are obtained as corollaries.

Difference analysis of results of disease risk assessment by using binary Logistic regression under different analysis strategies

Objective To investigate the importance of conditional control on the results of binary Logistic regression analysis. Methods 664 male patients diagnosed with CHD and 400 healthy controls who visited the Department of Cardiology at People’s Hospital of Yuxi City in Yunnan province from October 2010 to March 2013were enrolled consecutively in this case-control study, and 14 physiological and biochemical indexes [including: age, UA, TC, TG, HDL-C, LDL-C, APOA1, APOB100, Lp(a), HCY, TBIL, DBIL, IBIL, γ-GT] were collected. The correlations and differences in mathematical model results between physiological, biochemical indexes and CHD were compared by binary Logistic regression analysis under different statistical analysis strategies and then the model was analyzed by the ROC curve. Results (1) With no conditional control, all of the 14 physiological and biochemical indexes were directly inputted in the binary Logistic regression analysis, and after 11 steps regression analysis, 11 indexes [age, UA, TG, HDL-C, LDL-C, APOA1, APOB100, Lp(a), HCY, DBIL, γ-GT] were retained. Because of the self-correcting ability of the binary Logistic regression analysis, relatively satisfactory results can be obtained. However, someof the resultsarehard to explain. (2) According to the application conditions of Logistic regression analysis, after performing the normality test, difference analysis and correlation analysis of these indexes, using condition analysis and control, considering the distribution characteristics of the indexes, excluding internal confounding factors among variables, 9 more independent indexes [age, UA, TC, lnTG, lnLp(a), lnHCY, HDL-C, LDL-C and TBIL] were selected for Logistic regression analysis. After 7 steps regression analysis, 7 indexes [age, UA, HDL-C, lnTG, lnLp(a), lnHCY and lnTBIL] were finally selected, and the area under the curve is 0.927. Conclusion When the binary Logistic regression analysis was used to confirm risk factors and establish risk assessment models for complex diseases, it is better to adopt strict conditional control to improve the reliability and validity of the analysis.(Chin J Lab Med, 2018, 41: 232-236) Key words: Coronary disease; Risk factors; Logistic models; Risk assessment

Tinjauan Konstitusional terhadap Perpanjangan Program Sunset Policy

This paper provides a constitutional review of the extension of the Sunset Policy program. It tries to analyze whether or not the extension of the Sunset Policy program abuses the existing law. The paper argues that even though the extension of the program does not break the Indonesian constitutional law, the government should be more prudent to establish the next public policies based on the government regulation of the law substitute. This paper recommends to constituting a clear regulation in regard to the strict conditionals of the establishment of a government regulation of the law substitute.

Counterfactuals as Strict Conditionals

Abstract This paper defends the thesis that counterfactuals are strict conditionals. Its purpose is to show that there is a coherent view according to which counterfactuals are strict conditionals whose antecedent is stated elliptically. Section 1 introduces the view. Section 2 outlines a reply to the main argument against the thesis that counterfactuals are strict conditionals. Section 3 compares the view with a proposal due to Åqvist, which may be regarded as its direct predecessor. Section 4 explains how the view differs from contextualist strict conditional accounts of counterfactuals. Finally, section 5 addresses the thorny issue of disjunctive antecedents.

Counterfactuals, the Discrimination Problem and the Limit Assumption

The aim of this paper is to identify what I take to be the main conceptual problem in Lewis’ semantics for counterfactuals when the Limit Assumption (LA) is not satisfied, what I call the Discrimination Problem (DP), and to present and discuss a modification of Lewis’ semantics that aims at solving DP. First, I outline Lewis’ semantics, highlighting the aspects that will be relevant for our discussion. Second, I present DP and discuss it with a heuristic example. Third, I present the new proposal and comment some formal consequences and the objections they give rise to. Fourth, I present an allegedly equivalent version of the proposal and discuss the difference between counterfactuals and strict conditionals. Finally, I defend that the two proposals are different and argue for the first one as the best way of capturing two intuitions that seem in conflict when the LA is not satisfied. I conclude with a dilemma: either the proposal here defended works or LA is inescapable. Thus, if the proposal doesn’t work, the paper must then be considered as an indirect defense of the Limit Assumption.

Thought experiments and the problem of deviant realizations

Descriptions of Gettier cases can be interpreted in ways that are incompatible with the standard judgment that they are cases of justified true belief without knowledge. Timothy Williamson claims that this problem cannot be avoided by adding further stipulations to the case descriptions. To the contrary, we argue that there is a fairly simple way to amend the Ford case, a standard description of a Gettier case, in such a manner that all deviant interpretations are ruled out. This removes one major objection to interpreting our judgments about Gettier cases as strict conditionals.

Conditional reasoning and the Wason selection task: Biconditional interpretation instead of reasoning bias

Two experiments were conducted to show that the IF … THEN … rules used in the different versions of Wason's (1966) selection task are not psychologically—though they are logically—equivalent. Some of these rules are considered by the participants as strict logical conditionals, whereas others are interpreted as expressing a biconditional relationship. A deductive task was used jointly with the selection task to show that the original abstract rule is quite ambiguous in this respect, contrary to deontic rules: the typical “error” made by most people may indeed be explained by the fact that they consider the abstract rule as a biconditional. Thus, there is no proper error or bias in the selection task as it is still argued, but a differential interpretation of the rule. The need for taking into account a pragmatic component in the process of reasoning is illustrated by the experiments.

Strict Conditionals: a Negative Result

Jonathan Lowe has argued that a particular variation on C.I. Lewis’ notion of strict implication avoids the paradoxes of strict implication. In this paper it is argued that Lowe’s notion of implication does not achieve this aim. More over, a general argument is given to the effect that no other variation on Lewis’ notion of constantly strict implication describes the logical behavior of natur al language conditionals in a satisfactory way. 1 Indicative conditionals and strict implication In reaction to Russell’s interpretation of conditional sen tences as classical material implications, C.I. Lewis suggested that it would be more appropriate to interpret natural language conditionals as strict implications. He claimed t hat the truth-conditions of a sentence of the form ‘if p then q’ are given by the sentence ‘Necessarily, not p or q’ Lewis (1912). Russell and Lewis were speaking at cross purposes. Russell was mainly interested in the logical meaning of conditional expressions in the restricted context of mathematical proofs, whereas C.I. Lewis wanted to express the logical meaning of indicative conditionals in natural language in general. And it is true that in mathematical proofs, the meaning of conditional assertions can be taken to be expressed by the corresponding material implications. But the so-called paradoxes of material implicationto which C.I. Lewis drew Russell’s attention do show that material im plications do not capture the truth-conditions of conditional expressions as th ey are generally used in daily speech. Attempts have been made to relegate the paradoxes of material implication to pragmatics, by classifying the paradoxes of material implication as true assertions which violate some of the Gricean conversational implicatures. But the attempts that are made so far are generally regarded as unsatisfactory. 1

Legal Reasons: Between Universalism and Particularism

AbstractThe first part of this work analyses the universalist and the particularist conceptions of reasons. The second part projects this analysis to the legal domain. The author stresses that universalism and particularism regarding reasons are mutually exclusive theories linked to incompatible conceptions of norms, i.e. norms as strict universal conditionals and norms as defeasible conditionals. In giving an account of this tenet, different meanings of universality and defeasibility are explored. A parallel debate regarding reasons can be found in the legal domain, where two contrasting categories of norms are usually distinguished: rules and principles. On this issue the author argues that the conception of legal reasons depends on the way in which this contrast between different kinds of legal norms is shaped.