According to the Disjunction Problem, teleological theories of perceptual content are unable to explain why it is that a subject represents an F when an F causes the perception and not the disjunction F v G, given that the subject has mistaken G’s for F’s in the past. Without an adequate explanation these theories are stuck without an account of how non-veridical representation is possible, which would be an unsettling result. In this paper I defend Burge’s teleological (...) theory of perception against the Disjunction Problem, arguing that a perceptual state’s representing what I call an error-prohibiting disjunctive property is incompatible with the truth of perceptual anti-individualism. And because perceptual anti-individualism is at the heart of Burge’s theory, I conclude that Burgeans need not be concerned with the Disjunction Problem. (shrink)

In this paper, I focus on the so-called "tacking by disjunction problem". Namely, the problem to the effect that, if a hypothesis H is confirmed by a statement E, H is confirmed by the disjunction E v F, for whatever statement F. I show that the attempt to settle this difficulty made by Grimes 1990, in a paper apparently forgotten by today methodologists, is irremediably faulty.

The disjunction problem and the distality problem each presents a challenge that any theory of mental content must address. Here we consider their bearing on purely probabilistic causal theories. In addition to considering these problems separately, we consider a third challenge—that a theory must solve both. We call this “the hard problem.” We consider 8 basic ppc theories along with 240 hybrids of them, and show that some can handle the disjunction problem and some (...) can handle the distality problem, but none can handle the hard problem. This is our main result. We then discuss three possible responses to that result, and argue that though the first two fail, the third has some promise. (shrink)

Humean promotionalists about reasons think that whether there is a reason for an agent to ϕ depends on whether her ϕ-ing promotes the satisfaction of at least one of her desires. Several authors have recently defended probabilistic accounts of promotion, according to which an agent’s ϕ-ing promotes the satisfaction of one of her desires just in case her ϕ-ing makes the satisfaction of that desire more probable relative to some baseline. In this paper I do three things. First, I formalize (...) an argument, due to Jeff Behrends and Joshua DiPaolo, to the effect that Mark Schroeder’s and Stephen Finlay’s probabilistic accounts of promotion cannot be correct. Next, I extend this argument to a recent alternative offered by D. Justin Coates and show how Coates’ attempt to avoid the argument by introducing a distinction between ‘intrinsic’ and ‘extrinsic’ probability doesn’t help. Finally, I suggest an alternative way of understanding promotion in terms of increase in degree of fit between the causal upshot of an action and the content of a desire. I show how this view, disjunctively paired with probabilism about promotion, solves the problems with previous accounts. (shrink)

The problem of the difficulties created by disjunctive concepts is shown to be a spurious one. It is due in part to a confusion between concept formation and concept identification, in part to unfortunate terminological moves, in part to confusions between logical and methodological matters. Behind this pseudo-problem there are a number of real problems: how to work efficiently with partially interpreted concepts? are there differences in comprehension of various logical connectives? how does this comprehension change with age (...) and linguistic exposure? (shrink)

I present a problem for theories of explanation, concerning explanations involving disjunctive properties. The problem is particular acute for the explanatory non-fundamentalist, according to whom non-fundamental scientific explanations are sometimes superior to fundamental physical explanations. I criticise solutions to the problem due to Woodward, Strevens and Sober, and Lewis, and then defend a solution inspired by an account of non-fundamental laws recently defended by Callender and Cohen.

In this paper I present the double disjunction task as introduced by Johnson-Laird. This experiment is meant to show how mental model theory explains the discrepancy between logical competence and logical performance of individuals in deductive reasoning. I review the results of the task and identify three problems in the way the task is designed, that all fall under a lack of coordination between the subject and the experimenter, and an insufficient representation of the semantic/pragmatic interface. I then propose (...) a reformulation of the task, that makes explicit the underlying semantic reasoning and emphasizes the difference of interpretation of the DDT between the experimenter and the subjects. (shrink)

Direct Informational Semantics, according to which [X]s represent X if ‘Xs cause [X]s’ is a law, and Fodorian naturalistic semantics both suffer from double disjunctivitis. I argue that robustness, properly construed, characterizes both represented properties and representing symbols: two or more properties normally regarded as non-disjunctive may each be nomologically connected to a non-disjunctive symbol, and two or more non-disjunctive symbols may each be nomologically connected to a property. This kind of robustness bifurcates the so-called disjunction problem into (...) a Represented-Disjunction Problem, of which Fodor was aware, and a Representer-Disjunction Problem, of which he was on the whole oblivious. Fodor fails to solve these problems: his solution to the former, the Asymmetric Dependence Condition, presupposes a successful solution to the latter, while possible responses that Fodor might make to the latter either beg the former or cannot be met or else flout the Naturalistic Requirement and the Atomistic Requirement. Even setting the Representer-Disjunction Problem aside, the Represented-Disjunction Problem does not get solved, because the robustness involving phonological/orthographic sequences guarantees that nothing can meet the Asymmetrical Dependence Condition. Indeed there is a serious problem of individuating phonological/orthographic tokens and types in a manner that satisfies Fodor’s expectations. This is made manifest by the presence of orthographic tokens embedded in larger tokens. (shrink)

The paper explores the disjunctive riddle for induction: If we know the sample Ks to be P, we also know that they are P or F. Assuming that we also know that the future Ks are non-P, we can conclude that they are F, if only we can inductively infer the evidentially supported P-or-F hypothesis. Yet this is absurd. We cannot predict that future Ks are F based on the knowledge that the samples, and only they, are P. The ensuing (...) challenge is to account for the unprojectibility of the disjunctive hypothesis. I provide an explanation in terms of epistemic dependence. The P-or-F hypothesis is unprojectible because the evidence supporting it depends epistemically on the evidence for the defeated P-hypothesis. The paper also shows that the disjunctive riddle covers the essence of Goodman's infamous grue-problem, which, therefore, can be resolved by the same means: In contrast to the green-hypothesis, the grue-hypothesis is unprojectible because the grue-evidence depends on the evidence for a defeated hypothesis. (shrink)

Perception can’t have disjunctive content. Whereas you can think that a box is blue or red, you can’t see a box as being blue or red. Based on this fact, I develop a new problem for the ambitious predictive processing theory, on which the brain is a machine for minimizing prediction error, which approximately implements Bayesian inference. I describe a simple case of updating a disjunctive belief given perceptual experience of one of the disjuncts, in which Bayesian inference and (...) predictive coding pull in opposite directions, with the former implying that one’s confidence in the belief should increase, and the latter implying that it should decrease. Thus, predictive coding fails to approximately implement Bayesian inference across the interface between belief and perception. (shrink)

Fodor (1990) argues that the theory of evolution by natural selection will not help to save naturalistic accounts of representation from the disjunction problem. This is because, he claims, the context 'was selected for representing things as F' is transparent to the substitution of predicates coextensive with F. But, I respond, from an evolutionary perspective representational contexts cannot be transparent: only under particular descriptions will a representational state appear as a "solution" to a selection "problem" and so (...) be adaptive. Only when we construe representational states as opaque in this manner are the generalizations of branches of evolutionary theory, like foraging theory, possible. (shrink)

We consider the problem of moral disjunction in professional and business activities from a virtue-ethical perspective. Moral disjunction arises when the behavioral demands of a role conflict with personal morality; it is an important problem because most people in modern societies occupy several complex roles that can cause this clash to occur. We argue that moral disjunction, and the psychological mechanisms that people use to cope with it, are problematic because they make it hard to (...) pursue virtue and to live with integrity. We present role coadunation as a process with epistemic and behavioral aspects that people can use to resolve moral disjunction with integrity. When role coadunation is successful, it enables people to live virtuous lives of appropriate narrative disunity and to honor their identity-conferring commitments. We show how role coadunation can be facilitated by interpretive communities and discuss the emergence and ideal features of those communities. (shrink)

This article examines the idea of disjunctive rights—an idea first suggested by Joel Feinberg and more recently advocated by Richard Arneson. Using a hypothetical scenario to bring forward a conflict between two rights that cannot be simultaneously fulfilled, the suggestion that the conflict can be solved by describing the right-holders as holding disjunctive rights—rights that involve, in a significant way, a disjunction—is scrutinized. Several interpretations of the idea of disjunctive rights are examined from the perspectives of the interest theory (...) and will theory of rights. Ultimately, the idea of disjunctive rights fails to provide an acceptable solution to the problem at hand, as each interpretation has unacceptable implications. This conclusion challenges the compossibilist thesis, according to which moral rights do not, ultimately, conflict. Alternatively, if one wishes to keep the possibility of compossibility and disjunctive rights, the mainstream theories of rights must be revised or rejected. (shrink)

We provide a new link between deductive and probabilistic reasoning fallacies. Illusory inferences from disjunction are a broad class of deductive fallacies traditionally explained by recourse to a matching procedure that looks for content overlap between premises. In two behavioral experiments, we show that this phenomenon is instead sensitive to real-world causal dependencies and not to exact content overlap. A group of participants rated the strength of the causal dependence between pairs of sentences. This measure is a near perfect (...) predictor of fallacious reasoning by an independent group of participants in illusory inference tasks with the same materials. In light of these results, we argue that all extant accounts of these deductive fallacies require non-trivial adjustments. Crucially, these novel _indirect_ illusory inferences from disjunction bear a structural similarity to seemingly unrelated _probabilistic reasoning_ problems, in particular the conjunction fallacy from the heuristics and biases literature. This structural connection was entirely obscure in previous work on these deductive problems, due to the theoretical and empirical focus on content overlap. We argue that this structural parallelism provides arguments against the need for rich descriptions and individuating information in the conjunction fallacy, and we outline a unified theory of deductive illusory inferences from disjunction and the conjunction fallacy, in terms of Bayesian confirmation theory. (shrink)

I develop a ‘duty-plus’ approach to supererogation based on a simple intuition: if I am required to do x or y, doing x and y is a candidate for, though not necessarily, supererogation. This is an appealing view to take, located midway between two extreme positions, supererogationism and rigorism. I give a precise statement of the view through the notion of disjunctive duties, and discuss the commitments a duty-plus theorist should make, independent from the Kantian context in which this position (...) is often discussed. I also advocate the novel claim that we should take supererogation as a property of sets of actions, rather than single actions. The latter view suffers from problems in cases of concurrent acts and accumulative supererogation. (shrink)

The disjunction effect (Tversky and Shafir in Psychol Sci 3:305–309, 1992) occurs when decision makers prefer option x (versus y) when knowing that event A occurs and also when knowing that event A does not occur, but they refuse x (or prefer y) when not knowing whether or not A occurs. This form of incoherence violates Savage’s (Cognition 57:31–95, 1954) sure-thing principle, one of the basic axioms of the rational theory of decision-making. The phenomenon was attributed to a lack (...) of clear reasons for accepting an option (x) when the subjects are under uncertainty. Through a pragmatic analysis of the task and a consequent reformulation of it, we show that the effect does not depend on the presence of uncertainty, but on the introduction into the text-problem of a non-relevant goal. (shrink)

In [5, 6], Belnap proposed a number of amendments to Rescher’s strategy for reasoning with maximal consistent subsets. More recently in [18], Horty explicitly endorsed Belnap’s amendment to address a related problem in handling inconsistent instructions and commands. In this paper, we’ll examine Belnap’s amendment and point out that Belnap’s suggestion in the use of conjunctive containment is open to the very objection he raised. We’ll propose a way out. The strategy turns on the use of First Degree Entailment (...) in combination with Quine’s notion of prime implicate. (shrink)

The natural interpretation of counterfactuals with disjunctive antecedents involves selecting from each of the disjuncts the worlds that come closest to the world of evaluation. It has been long noticed that capturing this interpretation poses a problem for a minimal change semantics for counterfactuals, because selecting the closest worlds from each disjunct requires accessing the denotation of the disjuncts from the denotation of the disjunctive antecedent, which the standard boolean analysis of or does not allow (Creary and Hill, Philosophy (...) of Science 43:341–344, 1975; Nute, Journal of Philosophy 72:773–778, 1975; Fine, Mind 84(335):451–458, 1975; Ellis et al. Journal of Philosophical Logic 6:335–357, 1977). This paper argues that the failure to capture the natural interpretation of disjunctive counterfactuals provides no reason to abandon a minimal change semantics. It shows that the natural interpretation of disjunctive counterfactuals is expected once we refine our assumptions about the semantics of or and the logical form of conditionals, and (i) we assume that disjunctions introduce propositional alternatives in the semantic derivation, in line with independently motivated proposals about the semantics of or (Aloni, 2003a; Simons, Natural Language Semantics 13:271–316, 2005; Alonso-Ovalle, Disjunction in Alternative Semantics. PhD thesis, 2006); and (ii) we treat conditionals as correlative constructions, as advocated in von Fintel (1994), Izvorski (Proceedings of NELS 26, 1996), Bhatt and Pancheva (2006), and Schlenker (2004). (shrink)

Since the appearance of Prior’s tonk, inferentialists tried to formulate conditions that a collection of inference rules for a logical constant has to satisfy in order to succeed in conferring an acceptable meaning to it. Dummett proposed a pair of conditions, dubbed ‘harmony’ and ‘stability’ that have been cashed out in terms of the existence of certain transformations on natural deduction derivations called reductions and expansions. A long standing open problem for this proposal is posed by quantum disjunction: (...) although its rules are intuitively unstable, they pass the test of existence of expansions. Although most authors view instabilities of this kind as too subtle to be detected by the requirement of existence of expansions, we first discuss a case showing that this requirement can indeed detect instabilities of this kind, and then show how the expansions for disjunction-like connectives have to be reformulated to rule out quantum disjunction. We show how the alternative pattern for expansions can be formulated for connectives and quantifiers whose rules satisfy a scheme originally developed by Prawitz and Schroeder-Heister. Finally we compare our proposal with a recent one due to Jacinto and Read. (shrink)

Automated theorem proving amounts to solving search problems in usually tremendous search spaces. A lot of research therefore focuses on search space reductions. Our approach reduces the search space which arises when using so-called connection tableau calculi for first-order automated theorem proving. It uses disjunctive constraints over first-order equations to compress certain parts of this search space. We present the basics of our constrained-connection-tableau calculi, a constraint extension of connection tableau calculi, and deal with the efficient handling of constraints during (...) the search process. The new techniques are integrated into the automated connection tableau prover Setheo. (shrink)

The logician Kurt Godel in 1951 established a disjunctive thesis about the scope and limits of mathematical knowledge: either the mathematical mind is equivalent to a Turing machine (i.e., a computer), or there are absolutely undecidable mathematical problems. In the second half of the twentieth century, attempts have been made to arrive at a stronger conclusion. In particular, arguments have been produced by the philosopher J.R. Lucas and by the physicist and mathematician Roger Penrose that intend to show that the (...) mathematical mind is more powerful than any computer. These arguments, and counterarguments to them, have not convinced the logical and philosophical community. The reason for this is an insufficiency if rigour in the debate. The contributions in this volume move the debate forward by formulating rigorous frameworks and formally spelling out and evaluating arguments that bear on Godel's disjunction in these frameworks. The contributions in this volume have been written by world leading experts in the field. (shrink)

This paper considers the computational complexity of the disjunction and existential properties of intuitionistic logic. We prove that the disjunction property holds feasibly for intuitionistic propositional logic; i.e., from a proof of A v B, a proof either of A or of B can be found in polynomial time. For intuitionistic predicate logic, we prove superexponential lower bounds for the disjunction property, namely, there is a superexponential lower bound on the time required, given a proof of A (...) v B, to produce one of A and B which is true. In addition, there is superexponential lower bound on the size of terms which fulfill the existential property of intuitionistic predicate logic. There are superexponential upper bounds for these problems, so the lower bounds are essentially optimal. (shrink)

Causal theories of content, a popular family of approaches to defining the content of mental states, commonly run afoul of two related and serious problems that prevent them from providing an adequate theory of mental content—the misrepresentation problem and the disjunction problem. In this paper, I present a causal theory of content, built on information theoretic tools, that solves these problems and provides a viable model of mental content. This is the greatest surprise reduction theory of content, (...) which identifies the content of a signal as the event the surprisal of which is most reduced by that signal. Conceptually, this amounts to the claim that the content of a signal is the event the probability of which has increased by the largest proportion, or the event that the signal makes the most less surprising to us. I develop the greatest surprise reduction theory of content in four stages. First, I introduce the general project of causal theories of content, and the challenges presented to this project by the misrepresentation and disjunction problems. Next, I review two recent and prominent causal theories of content and demonstrate the serious challenges faced by these approaches, both clarifying the need for a solution to the misrepresentation and disjunction problems and providing a conceptual background for the greatest surprise reduction theory. Then, I develop the greatest surprise reduction theory of content, demonstrate its ability to resolve the misrepresentation and disjunction problems, and explore some additional applications it may have. Finally, I conclude with a discussion of a particularly difficult challenge that remains to be addressed—the partition problem—and sketch a path to a potential solution. (shrink)

The disjunction effect (Tversky & Shafir, 1992) occurs when decision makers prefer option x (versus y) when knowing that event A occurs and also when knowing that event A does not occur, but they refuse x (or prefer y) when not knowing whether or not A occurs. This form of incoherence violates Savage's (1954) sure-thing principle, one of the basic axioms of the rational theory of decision making. The phenomenon was attributed to a lack of clear reasons for accepting (...) an option (x) when subjects are under uncertainty. Through a pragmatic analysis of the task and a consequent reformulation of it, we show that the effect does not depend on the presence of uncertainty, but on the introduction of non-relevant goals into the text problem, in both the well-known Gamble problem and the Hawaii problem. (shrink)

The quantum logical `or' is analyzed from a physical perspective. We show that it is the existence of EPR-like correlation states for the quantum mechanical entity under consideration that make it nonequivalent to the classical situation. Specifically, the presence of potentiality in these correlation states gives rise to the quantum deviation from the classical logical `or'. We show how this arises not only in the microworld, but also in macroscopic situations where EPR-like correlation states are present. We investigate how application (...) of this analysis to concepts could alleviate some well known problems in cognitive science. (shrink)

In this paper we address some central problems of combination of logics through the study of a very simple but highly informative case, the combination of the logics of disjunction and conjunction. At first it seems that it would be very easy to combine such logics, but the following problem arises: if we combine these logics in a straightforward way, distributivity holds. On the other hand, distributivity does not arise if we use the usual notion of extension between (...) consequence relations. A detailed discussion about this phenomenon, as well as some possible solutions for it, are given. (shrink)

A partial solution to Ono’s problem P54 is given. Here Ono’s problem P54 is whether Harrop disjunction property is equivalent to disjunction property or not in intermediate predicate logics. As an application of this result it is shown that some intermediate predicate logics satisfy Harrop disjunction property.

In the paper we discuss criticisms against David Armstrong’s general theory of truthmaking by Gonzalo Rodriguez-Pereyra, Peter Schulte and Benjamin Schnieder, and conclude that Armstrong’s theory survives these criticisms. Special attention is given to the problems concerning Entailment Principle, Conjunction Thesis, Disjunction Thesis and to the notion of explanation.

For intermediate logics, there is obtained in the paper an algebraic equivalent of the disjunction propertyDP. It is proved that the logic of finite binary trees is not maximal among intermediate logics withDP. Introduced is a logicND, which has the only maximal extension withDP, namely, the logicML of finite problems.

Girotto and Legrenzi's 1993 facilitation effect for their SARS version of Wason s THOG problem a disjunctive reasoning task was examined. The effect was not replicated when the standard THOG problem instructions were used in Experiments 1 and 2. However, in Experiment 3 when Girotto and Legrenzi's precise instructions were used, facilitation was observed. Experiment 4 further investigated the role of the type of instructions in the observed facilitation. The results suggest that such facilitation may result from attentional (...) factors rather than the use of a combinatorial analysis in the problem. (shrink)

Phenomenal consciousness presents a distinctive explanatory problem. Some regard this problem as ‘hard’, which has troubling implications for the science and metaphysics of consciousness. Some regard it as ‘easy’, which ignores the special explanatory difficulties that consciousness offers. Others are unable to decide between these two uncomfortable positions. All three camps assume that the problem of consciousness is either easy or hard. I argue against this disjunction and suggest that the problem may be ‘tricky’—that is, (...) partly easy and partly hard. This possibility emerges when we recognise that consciousness raises two explanatory questions. The Consciousness Question concerns why a subject is conscious rather than unconscious. The Character Question concerns why a conscious subject’s experience has the phenomenology it has rather than some other. I explore the possibility of one or other of these explanatory challenges being hard and the other easy, and consider the dialectical ramifications this has for all sides of the debate. (shrink)

The connective or can be treated as an inclusive disjunction or else as an exclusive disjunction. Although researchers are aware of this distinction, few have examined the conditions under which each interpretation should be anticipated. Based on linguistic-pragmatic analyses, we assume that interpretations are initially inclusive before either (a) remaining so, or (b) becoming exclusive by way of an implicature ( but not both ). We point to a class of situations that ought to predispose disjunctions to inclusive (...) interpretations and to situations that encourage exclusive interpretations. A disjunction's ultimate interpretation is based on its potential informativeness, where the interpretation of the disjunctive utterance having the smallest number of true conditions is considered most informative. Our investigation leads to five experiments employing arbitrary materials. Among the problems expected to encourage inclusive interpretations are those that present disjunctions in the antecedents of conditionals and in question forms. The best candidates to produce implicatures are those disjunctions that underdetermine an expected conjunctive conclusion, although other disjunctive utterances that are more informative as exclusive are discussed and tested. (shrink)

There are two dimensions to Fine’s truthmaker semantics. One involves a claim about the nature of propositions: propositions are not structural and nothing but sets of their possible truthmakers, and the other talks about the relation between truthmaking and Boolean operations. In this paper, I show that a claim by Fine in the latter dimension—that truthmaking is distributed over “or”—faces a counterexample. I will then go on to argue that one possible way to do away with the counterexample is to (...) restrict truthmakers to fundamentals, namely entities that are not grounded in anything else. This would, nevertheless, pose a problem for the first dimension of truthmaker semantics: certain distinct propositions would fail to be distinct. (shrink)

It is sometimes held that rules of inference determine the meaning of the logical constants: the meaning of, say, conjunction is fully determined by either its introduction or its elimination rules, or both; similarly for the other connectives. In a recent paper, Panu Raatikainen (2008) argues that this view - call it logical inferentialism - is undermined by some "very little known" considerations by Carnap (1943) to the effect that "in a definite sense, it is not true that the standard (...) rules of inference" themselves suffice to "determine the meanings of [the] logical constants" (p. 2). In a nutshell, Carnap showed that the rules allow for non-normal interpretations of negation and disjunction. Raatikainen concludes that "no ordinary formalization of logic ... is sufficient to `fully formalize' all the essential properties of the logical constants" (ibid.). We suggest that this is a mistake. Pace Raatikainen, intuitionists like Dummett and Prawitz need not worry about Carnap's problem. And although bilateral solutions for classical inferentialists - as proposed by Timothy Smiley and Ian Rumfitt - seem inadequate, it is not excluded that classical inferentialists may be in a position to address the problem too. (shrink)

Suppose that Φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\it \Phi}}$$\end{document} is a consistent sentence. Then there is no Herbrand proof of ¬Φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\neg {\it \Phi}}$$\end{document}, which means that any Herbrand disjunction made from the prenex form of ¬Φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\neg {\it \Phi}}$$\end{document} is falsifiable. We show that the problem of finding such a falsifying assignment is hard in the following sense. (...) For every total polynomial search problem R, there exists a consistent Φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\it \Phi}}$$\end{document} such that finding solutions to R can be reduced to finding a falsifying assignment to an Herbrand disjunction made from ¬Φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\neg {\it \Phi}}$$\end{document}. It has been conjectured that there are no complete total polynomial search problems. If this conjecture is true, then for every consistent sentence Φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\it \Phi}}$$\end{document}, there exists a consistent sentence Ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Psi}$$\end{document}, such that the search problem associated with Ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Psi}$$\end{document} cannot be reduced to the search problem associated with Φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\it \Phi}}$$\end{document}. (shrink)