We present the inconsistency-adaptive deontic logic DP r , a nonmonotonic logic for dealing with conflicts between normative statements. On the one hand, this logic does not lead to explosion in view of normative conflicts such as O A ∧ O ∼A, O A ∧ P ∼A or even O A ∧ ∼O A. On the other hand, DP r still verifies all intuitively reliable inferences valid in Standard Deontic Logic (SDL). DP r interprets a given premise set ‘as (...) normally as possible’ with respect to SDL. Whereas some SDL-rules are verified unconditionally by DP r , others are verified conditionally. The latter are applicable unless they rely on formulas that turn out to behave inconsistently in view of the premises. This dynamic process is mirrored by the proof theory of DP r. (shrink)
In this paper my purpose is to examine whether the case of inconsistent believers can offer a reason to object to theories of belief ascription that rely on a rationality constraint. I shall first illustrate how the possibility of inconsistent believers might be a challenge for the rationality constraint and then assess Davidson's influential reply to that challenge.
Whereas a number of recent articles have focussed upon whether the thesis of content externalism is compatible with a certain sort of knowledge that is gained via first-person authority,1 far less attention has been given to the relationship that this thesis bears to the possession of knowledge in general and, in particular, its relation to internalist and externalist epistemologies. Nevertheless, although very few actual arguments have been presented to this end, there does seem to be a shared suspicion that content (...) externalism must be incompatible with epistemic internalism. In a recent and influential paper, however, James Chase has challenged this conventional wisdom by offering a subtle defence of the view that content externalism and epistemic internalism are, in fact, compatible after all.2 Our aim here is twofold. First, to show that Chase is only able to achieve this result because he focuses upon the internalist conception of justification, rather than knowledge. Second, to formulate one prima facie argument which shows that an internalist conception of knowledge is incompatible with an externalist conception of content, an argument which, moreover, is not touched by Chase. (shrink)
The paper examines philosophical issues that arise in contexts where one has many different models for treating the same system. I show why in some cases this appears relatively unproblematic (models of turbulence) while others represent genuine difficulties when attempting to interpret the information that models provide (nuclear models). What the examples show is that while complementary models needn’t be a hindrance to knowledge acquisition, the kind of inconsistency present in nuclear cases is, since it is indicative of a (...) lack of genuine theoretical understanding. It is important to note that the differences in modeling do not result directly from the status of our knowledge of turbulent flows as opposed to nuclear dynamics—both face fundamental theoretical problems in the construction and application of models. However, as we shall, the ‘problem context(s)’ in which the modeling takes plays a decisive role in evaluating the epistemic merit of the models themselves. Moreover, the theoretical difficulties that give rise to inconsistent as opposed to complementary models (in the cases I discuss) impose epistemic and methodological burdens that cannot be overcome by invoking philosophical strategies like perspectivism, paraconsistency or partial structures. (shrink)
In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes. In this paper I show that a number of logics are susceptible to a strengthened version of Curry's paradox. This can be adapted to provide a proof theoretic analysis of the omega-inconsistency in Lukasiewicz's continuum valued logic, allowing us to better evaluate which logics are suitable for a naïve truth theory. On this basis I identify two natural subsystems of Lukasiewicz logic which individually, (...) but not jointly, lack the problematic feature. (shrink)
Emotivists hold that moral opinions are wishes and desires, and that the function of moral language is to “express” such states. But if moral opinions were but wishes or desires, why would we see certain opinions as inconsistent with, or following from other opinions? And why should our reasoning include complex opinions such as the opinion that a person ought to be blamed only if he has done something wrong? Indeed, why would we think that anything is conditional on his (...) doing something wrong unless “doing something wrong” signifies a real kind of action? -/- Many have believed, and seemingly on good grounds, that these questions lack good answers, and that emotivism is doomed for that very reason. What I will argue, however, is that once emotivism is recognized for what it is, namely an empirical theory about the psychological nature of moral opinions, and once we relate it to a general theory of human reasoning, moral reasoning and intuitions of inconsistency and consequence are only to be expected. Recent objections to earlier emotivist or “expressivist” accounts can thus be met, and the phenomena of inconsistency and consequence fully embraced by emotivists. (shrink)
I elaborate and defend the inconsistency view on vagueness I have earlier argued for in my (2002) and (forthcoming). In rough outline, the view is that the sorites paradox arises because tolerance principles, despite their inconsistency, are meaning-constitutive for vague expressions. Toward the end of the paper I discuss other inconsistency views on vagueness that have been proposed, and compare them to the view I favor.
I revisit my earlier arguments for the (trivial) inconsistency of natural languages, and take up the objection that no such argument can be established on the basis of surface usage. I respond with the evidential centrality of surface usage: the ways it can and can't be undercut by linguistic science. Then some important ramifications of having an inconsistent natural language are explored: (1) the temptation to engage in illegitimate reductio reasoning, (2) the breakdown of the knowledge idiom (because its (...) facticity isn't comfortable with every sentence being true and false). Restoring the utility of the knowledge idiom motivates regimentation - the consistentist reinterpretation of natural language inferences (as they occur in real time). It's then sketched how to give the semantics of a natural language despite its inconsistency: Necessary and sufficient truth conditions are dropped in favor of necessary truth conditions and sufficient truth conditions. (shrink)
Is there anything irrational, or self-undermining, about having "inconsistent" attitudes of caring or valuing? In this paper, I argue that, contra suggestions of Harry Frankfurt and Charles Taylor, the answer is "No." Here I focus on "valuations," which are endorsed desires or attitudes. The proper characterization of what I call "valuational inconsistency" I claim, involves not logical form (valuing A and not-A), but rather the co-possibility of what is valued; valuations are inconsistent when there is no possible world in (...) which what is valued can co-exist. Essentially conflicting valuations, I show, are no worse for an agent than contingently conflicting ones, which are common and no threat to rationality or well-being. Partly based on reflections about a conflicted mother, who values staying at home and also having a career, I argue that valuational inconsistency does not render a person unable to act, does not make a person's actions ineffective because of vacillation, does not undermine a person's autonomy, and need not make a person dissatisfied with himself. I defend my characterization of inconsistency as an apt one; I offer some reasons to value inconsistency itself; and I draw out some implications for coherence thinking in moral philosophy. (shrink)
It is argued that Yablo’s Paradox is not strictly paradoxical, but rather ‘ω-paradoxical’. Under a natural formalization, the list of Yablo sentences may be constructed using a diagonalization argument and can be shown to be ω-inconsistent, but nonetheless consistent. The derivation of an inconsistency requires a uniform fixed-point construction. Moreover, the truth-theoretic disquotational principle required is also uniform, rather than the local disquotational T-scheme. The theory with the local disquotation T-scheme applied to individual sentences from the Yablo list is (...) also consistent. (shrink)
I argue for an alternative to invariantist, contextualist, and relativist semantics for ‘know’. This is that our use of ‘know’ is inconsistent; it is governed by several mutually inconsistent inference principles. Yet this inconsistency does not prevent us from assigning an effective content to most individual knowledge ascriptions, and it leads to trouble only in exceptional circumstances. Accordingly, we have no reason to abandon our inconsistent knowledge-talk.
I provide a method of measuring the inconsistency of a set of sentences – from 1-consistency, corresponding to complete consistency, to 0-consistency, corresponding to the explicit presence of a contradiction. Using this notion to analyze the lottery paradox, one can see that the set of sentences capturing the paradox has a high degree of consistency (assuming, of course, a sufficiently large lottery). The measure of consistency, however, is not limited to paradoxes. I also provide results for general sets of (...) sentences. (shrink)
The paper discusses the Inconsistency Theory of Truth (IT), the view that “true” is inconsistent in the sense that its meaning-constitutive principles include all instances of the truth-schema (T). It argues that (IT) entails that anyone using “true” in its ordinary sense is committed to all the (T)-instances and that any theory in which “true” is used in that sense entails the (T)-instances (which, given classical logic, entail contradictions). More specifically, I argue that theorists are committed to the meaning-constitutive (...) principles of logical constants, relative to the interpretation they intend thereof (e.g., classical), and that theories containing logical constants entail those principles. Further, I argue, since there is no relevant difference from the case of “true”, inconsistency theorists’ uses of “true” commit them to the (T)-instances. Adherents of (IT) are recommended, as a consequence, to eschew the truth-predicate. I also criticise Matti Eklund’s account of how the semantic value of “true” is determined, which can be taken as an attempt to show how “true” can be consistently used, despite being inconsistent. (shrink)
This book is a stimulating and engaging discussion of philosophical issues in the foundations of classical electromagnetism. In the rst half, Frisch argues against the standard conception of the theory as consistent and local. The second half is devoted to the puzzle of the arrow of radiation: the fact that waves behave asymmetrically in time, though the laws governing their evolution are temporally symmetric. The book is worthwhile for anyone interested in understanding the physical theory of electromagnetism, as well for (...) the views it presents on philosophical issues such as causation, counterfactuals, laws, scienti c theories, models, and explanation. While philosophers of physics tend to focus on quantum mechanics and relativity, Frisch’s book shows that there are deep foundational issues in classical physics, equally worthy of attention. That said, let me lodge disagreement on some key points. Frisch argues from an alleged inconsistency in classical electromagnetism— that Maxwell’s equations, the Lorentz force law, and the conservation of energy cannot be jointly true—to the conclusion that the standard view of scienti c theories as a formalism plus an interpretation is incorrect. Consistency is a necessary condition of any view on which scienti c theories give us an account of “ways the world could be” (Frisch, , ). Since classical electromagnetism is successfully used by practicing physicists, consistency must be just one criterion of theory choice weighed equally among others. This is an intriguing idea, but I am not sure that consistency can be given up so easily. That road leads dangerously close to accepting orthodox ‘Copenhagen’ quantum mechanics. Surely the inconsistency of.. (shrink)
Yujin Nagasawa has recently defended Frank Jackson’s knowledge argument from the “inconsistency objection.” The objection claims that the premises of the knowledge argument are inconsistent with qualia epiphenomenalism. Nagasawa defends Jackson by showing that the objection mistakenly assumes a causal theory of phenomenal knowledge. I argue that although this defense might succeed against two versions of the inconsistency objection, mine is unaffected by Nagasawa’s argument, in which case the inconsistency in the knowledge argument remains.
In this paper I critically evaluate a number of current "consistent inconsistency theories" and then briefly motivate a rival position. The rival position challenges a consistent inconsistency theory, by sharing many of its basic commitments without suffering the problems that such a theory appears to face.
This paper follows up a debate as to whether classical electrodynamics is inconsistent. Mathias Frisch makes the claim in Inconsistency, Asymmetry and Non-Locality ([2005]), but this has been quickly countered by F. A. Muller ([2007]) and Gordon Belot ([2007]). Here I argue that both Muller and Belot fail to connect with the background assumptions that support Frisch's claim. Responding to Belot I explicate Frisch's position in more detail, before providing my own criticisms. Correcting Frisch's position, I find that I (...) can present the theory in a way both authors can agree upon. Differences then manifest themselves purely within the reasoning methods employed. Introduction Features of the Theory Frisch's Inconsistency Claim Defending Frisch 4.1 Muller 4.2 Belot Difficulties for Frisch and a Compromise Conclusion CiteULike Connotea Del.icio.us What's this? (shrink)
Nonmonotonic consequence is the subject of a vast literature, but the idea of a nonmonotonic counterpart of logical inconsistency—the idea of a defeasible property representing internal conflict of an inductive or evidential nature—has been entirely neglected. After considering and dismissing two possible analyses relating nonmonotonic consequence and a nonmonotonic counterpart of logical inconsistency, this paper offers a set of postulates for nonmonotonic inconsistency, an analysis of nonmonotonic inconsistency in terms of nonmonotonic consequence, and a series of (...) results showing that nonmonotonic inconsistency conforms to these postulates given the analysis of nonmonotonic inconsistency presented here and certain postulates for nonmonotonic consequence. The results presented here establish the interest of certain previously undiscussed postulates of nonmonotonic consequence. These results also show that nonmonotonicity, which has never seemed useful in the formulation of general principles governing nonmonotonic reasoning, is relevant to the positive characterization of nonmonotonic inference after all. (shrink)
Incommensurable theories are said to be both incompatible and incomparable. This is paradoxical, because, being incompatible, these theories must have the same subject-matter, yet incomparability implies that their subject-matter is different. This paper's proposed resolution of the paradox makes use of the distinction between internal subject-matter and external subject-matter for languages (frameworks) as outlined by W. Sellars. Incommensurability arises when two languages share the same external subject-matter but differ in internal subject-matter. When they share the same external subject-matter, they can (...) be inconsistent (hence incompatible), and yet incomparable (because they are about distinct internal subject-matter). A substantial part of the paper is devoted to the technical development of the notion of inconsistency as a relationship between languages in contrast to the traditional notion of inconsistency between statements. (shrink)
All the standard and some esoteric objections to pacifism are refuted, either directly or (as with the charge of impracticality) in outline. Familiar arguments to the inconsistency and irresponsibility of pacifism are shown to turn upon illegitimately construing pacifist activities such as resisting, preventing, and defending as involving violence. Several arguments against pacifism from violence as a lesser evil turn out to be fallacious; some involve the erroneous assumption that violence is the only evil, but some lead into what (...) pacifism can simply concede, moral dilemmas. It is argued that pacifism is not a form of fanaticism, is not morally insensitive, does not imply anarchism, or vegetarianism, is not completely impractical, and can be positively underpinned. In the course of the arguments various types of pacifism are classified, pacifism is distinguished from nonviolent action, and pacifism and, differently, pacificity are disassociated from passivity: The question of a more general characterization of violence (which is different from force) emerges as a crucial issue, along with the problem of integrating pacifism into a more comprehensive moral position. (shrink)
Martin-Löf's constructive type theory forms the basis of this paper. His central notions of category and set, and their relations with Russell's type theories, are discussed. It is shown that addition of an axiom — treating the category of propositions as a set and thereby enabling higher order quantification — leads to inconsistency. This theorem is a variant of Girard's paradox, which is a translation into type theory of Mirimanoff's paradox (concerning the set of all well-founded sets). The occurrence (...) of the contradiction is explained in set theoretical terms. Crucial here is the way a proof-object of an existential proposition is understood. It is shown that also Russell's paradox can be translated into type theory. The type theory extended with the axiom mentioned above contains constructive higher order logic, but even if one only adds constructive second order logic to type theory the contradictions arise. (shrink)
An agent may abandon an initiated action plan, although he doesnot acquire new information or encounter unforeseen obstacles.Such dynamic inconsistency can be to the agent'';s guaranteeddisadvantage, and there is a debate on how it should rationallybe avoided. The main contenders are the sophisticated andthe resolute approaches. I argue that this debate is misconceived,since both approaches rely on false assumptions about theperformability of action plans. The debate can be reformulated,so as to avoid these mistaken assumptions. I try to show that (...) sucha reformulation must rely on certain implausible claims. (shrink)
This note corrects an error in the statement and proof of Propositions 9 and 10 of [C. Cross, Nonmonotonic inconsistency, Artificial Intelligence 149 (2) (2003) 161–178]. Both results turn out to depend on the postulate of Consistency Preservation.
Inconsistency of attitudes and behavior is due to the probabilistic connection between responses or actions and the (not directly observable) dispositions on which they depend. Latent variable models provide criteria for recognizing when attitude and behavior depend on the same disposition. Statistical tests of such models and techniques of parameter estimation are described. The viewpoint proposed here and illustrated with empirical examples contrasts with the prevalent reliance on correlational models and methods.
In order to become aware of inconsistencies, one must first construe of the world in a way that reflects its consistencies. This paper begins with a tentative model for how a set of discrete memories transforms into an interconnected worldview, wherein relationships between memories are forged by way of abstractions. Inconsistencies prompt the invention of new abstractions. In regions of the conceptual network where inconsistencies abound, a cognitive analog of simulated annealing is in order; there is a willingness to question (...) previous assumptions - to ‘loosen’ conceptual relationships - so as to let new concepts percolate through the worldview and exert the needed revolutionary effect. In so doing there is a risk of assimilating dangerous concepts. Repression arrests the process by which dangerous thoughts infiltrate the conceptual network, and deception blocks thoughts that have already been assimilated. These forms of self-initiated worldview inconsistency may evoke feelings of fragmentation at the level of the individual or the society. (shrink)
In order to become aware of inconsistencies, one must first construe of the world in a way that reflects its consistencies. This paper begins with a tentative model for how a set of discrete memories transforms into an interconnected worldview wherein relationships between memories are forged by way of abstractions. Inconsistencies prompt the invention of new abstractions. In regions of the conceptual network where inconsistencies abound, a cognitive analog of simulated annealing is in order; there is a willingness to question (...) previous assumptionsto loosen conceptual relationshipsso as to let new concepts thoroughly percolate through the worldview and exert the needed revolutionary effect. In so doing there is a risk of assimilating dangerous concepts. Repression arrests the process by which dangerous thoughts infiltrate the conceptual network, and deception blocks thoughts that have already been assimilated. These forms of self-initiated worldview inconsistency may evoke feelings of fragmentation at the level of the individual or the society. (shrink)
The DSM-III-R definition of mental disorder is inconsistent with the DSM-III-R definition of paraphilias. The former requires the suffering or increased risk of suffering some harm while the latter allows that deviance, by itself, is sufficient to classify a behavioral syndrome as a paraphilia. This inconsistency is particularly clear when examining the DSM-III-R account of a specific paraphilia, Transvestic Fetishism. The author defends the DSM-III-R definition of mental disorder and argues that the DSM-III-R definition of paraphilias should be changed. (...) He recommends that the diagnostic criteria for specific paraphilias, particularly that for Transvestic Fetishism, be changed to make them consistent with the DSM-III-R definition of mental disorder. Keywords: diagnoses, disease, paraphilia, philosophy, psychiatry CiteULike Connotea Del.icio.us What's this? (shrink)
The old quantum theory of black body radiation was manifestly logically inconsistent. It required the energies of electric resonators to be both quantized and continuous. To show that this manifest inconsistency was inessential to the theory's recovery of the Planck distribution law, I extract a subtheory free of this manifest inconsistency but from which Planck's law still follows.
Isaac Levi has claimed that our reliance on the testimony of others, and on the testimony of the senses, commonly produces inconsistency in our set of full beliefs. This happens if what is reported is inconsistent with what we believe to be the case. Drawing on a conception of the role of beliefs in inquiry going back to Dewey, Levi has maintained that the inconsistent belief corpus is a state of ``epistemic hell'': it is useless as a basis for (...) inquiry and deliberation. As he has also noticed, the compatibility of these two elements of his pragmatist epistemology could be called into question. For if inconsistency means hell, how can it ever be rational to enter that state, and on what basis could we attempt to regain consistency? Levi, nonetheless, has tried to show that the conflict is only apparent and that no changes of his theory are necessary. In the main part of the paper I argue, by contrast, that his attempts to reconcile these components of his view are unsuccessful.The conflict is real andthus presents a genuine threat to Deweyan pragmatism, as understood by Levi. After an attempt to pinpoint exactly where the source of the problem lies, I explore some possibilities for how to come to grips with it. I conclude that Levi can keep his fundamental thesis concerning the role of beliefs in inquiry and deliberation, provided that he (i) gives up the view that the agent can legitimately escape from inconsistency, and (ii) modifies his account of prediction alias deliberate expansion by acknowledging a third desideratum, besides probability and informational value, namely, not to cause permanent breakdown further down the line of inquiry. The result is a position which is more similar to Peter Gärdenfors's than is Levi's original theory, while retaining the basic insights of the latter. (shrink)
The relationship between inconsistency and Lehrerian coherence is scrutinized. Like most coherence theorists of epistemic justification, Lehrer contends that consistency is necessary for coherence. Despite this contention, minimally inconsistent belief-sets prove coherent and rationally acceptable on Lehrer's account of coherence. Lehrer is left with the following dilemma: If consistency is necessary for coherence, then (i) he must revise his account of coherence accordingly and, more importantly, (ii) such coherence is nof necessary for justification, since intuitively we are justified in (...) accepting such minimally inconsistent belief-sets. If, on the other hand, minimally inconsistent acceptance systems can be coherent, then to prevent pairwise inconsistent statements form readily cohering with such systems, Lehrer must deny that rational acceptance is closed under deduction. (shrink)
No início do século XIV, Raimundo Lúlio, contrapondo-se aos mestres em Artes por ele identificados como averroistae, desenvolveria não menos que dois métodos resolutivos de inconsistência, a fim de refutar aquelas teses filosóficas que divergem da fé cristã. Um deles serve-se de silogismos contraditórios capazes de expressar a estrutura de um argumento ad hominem, ao passo que o outro nada mais é do que uma reductio ad impossibile elaborada com base em suposições contraditórias. In the early fourteenth century, Ramond Lully, (...) opposed to university philosophers whom he identified as averroistae, developed no less than two methods for the resolution of inconsistency, in order to refute philosophical theses which diverge from the Christian faith. The first of these uses contradictory syllogisms expressing the structure of an ad hominem argument, while the other is a reductio ad impossibile produced with contradictory suppositions. (shrink)
This paper presents a new argument against A-theories of time. A-theorists hold that there is an objective now (present moment) and an objective flow of time, the latter constituted by the movement of the objective now through time. A-theorists therefore want to draw different pictures of reality—showing the objective now in different positions—depending upon the time at which the picture is drawn. In this paper it is argued that the times at which the different pictures are drawn may be taken (...) to be normal times or hypertimes. If they are normal times then the A-theory is inconsistent, or else collapses to the B-theory—and appealing to primitive tense operators will not help A-theorists avoid this conclusion. If the times are hypertimes then the A-theory is consistent, but deeply problematic none the less. (shrink)
It is argued that a certain form of the view that the semantic paradoxes show that natural languages are “inconsistent” provides the best response to the semantic paradoxes. After extended discussions of the views of Kirk Ludwig and Matti Eklund, it is argued that in its strongest formulation the view maintains that understanding a natural language is sharing cognition of an inconsistent semantic theory for that language with other speakers. A number of aspects of this approach are discussed and a (...) few objections are entertained. (shrink)
He argues that the intuitively provable arithmetic sentences constitute a recursively enumerable set, which has a Gödel sentence which is itself intuitively provable. The incompleteness theorem does not apply, since the set of provable arithmetic sentences is not consistent. The purpose of this article is to sharpen Priest's argument, avoiding reference to informal notions, consensus, or Church's thesis. We add Priest's dialetheic semantics to ordinary Peano arithmetic PA, to produce a recursively axiomatized formal system PA that contains its own truth (...) predicate. Whether one is a dialetheist or not, PA is a legitimate, rigorously defined formal system, and one can explore its proof-theoretic properties. The system is inconsistent (but presumably non-trivial), and it proves its own Gödel sentence as well as its own soundness. Although this much is perhaps welcome to the dialetheist, it has some untoward consequences. There are purely arithmetic (indeed, 0) sentences that are both provable and refutable in PA. So if the dialetheist maintains that PA is sound, then he must hold that there are true contradictions in the most elementary language of arithmetic. Moreover, the thorough dialetheist must hold that there is a number g which both is and is not the code of a derivation of the indicated Gödel sentence of PA. For the thorough dialetheist, it follows ordinary PA and even Robinson arithmetic are themselves inconsistent theories. I argue that this is a bitter pill for the dialetheist to swallow. (shrink)
Douglas Patterson argues that the best way to respond to the semantic paradoxes that arise in natural language is to take natural language semantics to be (explosively) inconsistent. According to Patterson, to understand a natural language is to share with others cognition of a false semantic theory. Patterson’s main argument runs as follows. English is expressively rich. So, the first sentence occurring in this review could be.
Kirchhoff’s diffraction theory is introduced as a new case study in the realism debate. The theory is extremely successful despite being both inconsistent and not even approximately true. Some habitual realist proclamations simply cannot be maintained in the face of Kirchhoff’s theory, as the realist is forced to acknowledge that theoretical success can in some circumstances be explained in terms other than truth. The idiosyncrasy (or otherwise) of Kirchhoff’s case is considered.
The semantic approach to scientific representation is now long established as a favourite amongst philosophers of science. One of the foremost strains of this approach-the model-theoretic approach (MTA)-is to represent scientific theories as families of models, all of which satisfy or 'make true' a given set of constraints. However some autho.rs (Brown 2002, Frisch 2005) have criticised the approach on the grounds that certain scientific theories are logically inconsistent, and there can be no models of an inconsistent set of constraints. (...) Thus it would seem that the MTA fails to represent inconsistent scientific theories at all, and this raises concerns about the way it represents in general. In a series of papers (1990, 1993, 1995) and a recent book (2003) da Costa and French have developed a variant of the MTA approach which they call 'partial structures', and which they claim can accommodate inconsistent theories. I assess this claim, looking to two theories which have been called 'inconsistent': Bohr's theory of the atom and classical electrodynamics. (shrink)
This is a discussion of different ways of working out the idea that the semantic paradoxes show that natural languages are somehow “inconsistent”. I take the workable form of the idea to be that there are expressions such that a necessary condition of understanding them is that one be inclined to accept inconsistent claims (an conception also suggested by Matti Eklund). I then distinguish “simple” from “complex” forms of such views. On a simple theory, such expressions are meaningless, while on (...) a complex theory they are not. I argue that complex theories are incompatible with truth conditional semantics and that simple theories are only coherent when the inconsistent claims are metalingusitic attributions of meaning. I close with a discussion of the version of the simple metalinguistic theory I have defended in “Understanding the Liar” and other papers. (shrink)
Summary It is here shown that the relativistic doctrine of the relativity of simultaneity is untenable and that both the special and general theories of relativity are inconsistent. It is also shown that the theories can perhaps be made consistent, but excessively weak, through the reintroduction of absolute space and a weakening of the Lorentz transformations. Non-relativistic hypotheses for some events thought to require relativity are suggested. Finally, some conjectures are made on how so wrong a theory could have been (...) accepted by so many for so long. (shrink)
We present a model for studying communities of epistemically interacting agents who update their belief states by averaging (in a specified way) the belief states of other agents in the community. The agents in our model have a rich belief state, involving multiple independent issues which are interrelated in such a way that they form a theory of the world. Our main goal is to calculate the probability for an agent to end up in an inconsistent belief state due to (...) updating (in the given way). To that end, an analytical expression is given and evaluated numerically, both exactly and using statistical sampling. It is shown that, under the assumptions of our model, an agent always has a probability of less than 2% of ending up in an inconsistent belief state. Moreover, this probability can be made arbitrarily small by increasing the number of independent issues the agents have to judge or by increasing the group size. A real-world situation to which this model applies is a group of experts participating in a Delphi-study. (shrink)
In a recent issue of this journal, M. Frisch claims to have proven that classical electrodynamics is an inconsistent physical theory. We argue that he has applied classical electrodynamics inconsistently. Frisch also claims that all other classical theories of electromagnetic phenomena, when consistent and in some sense an approximation of classical electrodynamics, are haunted by “serious conceptual problems” that defy resolution. We argue that this claim is based on a partisan if not misleading presentation of theoretical research in classical electrodynamics.
Mathias Frisch provides the first sustained philosophical discussion of conceptual problems in classical particle-field theories. Part of the book focuses on the problem of a satisfactory equation of motion for charged particles interacting with electromagnetic fields. As Frisch shows, the standard equation of motion results in a mathematically inconsistent theory, yet there is no fully consistent and conceptually unproblematic alternative theory. Frisch describes in detail how the search for a fundamental equation of motion is partly driven by pragmatic considerations (like (...) simplicity and mathematical tractability) that can override the aim for full consistency. The book also offers a comprehensive review and criticism of both the physical and philosophical literature on the temporal asymmetry exhibited by electromagnetic radiation fields, including Einstein's discussion of the asymmetry and Wheeler and Feynman's influential absorber theory of radiation. Frisch argues that attempts to derive the asymmetry from thermodynamic or cosmological considerations fail and proposes that we should understand the asymmetry as due to a fundamental causal constraint. The book's overarching philosophical thesis is that standard philosophical accounts that strictly identify scientific theories with a mathematical formalism and a mapping function specifying the theory's ontology are inadequate, since they permit neither inconsistent yet genuinely successful theories nor thick causal notions to be part of fundamental physics. (shrink)
In this essay, I argue that the deflationary view of truth is inconsistent with Davidson's theory of meaning. I take deflationism to consist of two basic theses: the linguistic thesis that truth talk is always expressive and never explanatory, and the metaphysical thesis that truth is not a property. Since Davidson construes meaning in terms of truth-conditions, it appears that Davidson regards truth talk as explanatory, and truth as a property. Michael Williams argues otherwise, suggesting that Davidson's theory of meaning (...) can be understood in terms of his theory of radical interpretation, and that radical interpretation does not require a notion of truth richer than the deflationist allows. I argue that at the level of the T-sentences Davidson's theory of meaning entails (T-sentences yielded through the practice of radical interpretation), a non-deflationary notion of truth is indeed required. This is because, first, for Davidson, to grasp the meaning of a sentence is to grasp the T-sentence associated with it, and the T-sentence predicates the property truth of that sentencesecond, because it does so, in T-sentences "true" is explanatory, not merely expressive. I then consider the objection that T-sentences can be understood in terms of a norm of assertion, rather in terms of "true" as predicating a property of sentences, and I respond that the objection confuses pragmatic issues with semantic issues. (shrink)
I show that the standard approach to modeling phenomena involving microscopic classical electrodynamics is mathematically inconsistent. I argue that there is no conceptually unproblematic and consistent theory covering the same phenomena to which this inconsistent theory can be thought of as an approximation; and I propose a set of conditions for the acceptability of inconsistent theories.
A principle of continuity due to Leibniz has recently been revived by Graham Priest in arguing for an inconsistent account of motion. This paper argues that the Leibniz Continuity Condition has a reasonable interpretation in a different, though still inconsistent, class of dynamical systems. The account is then applied to the quantum mechanical description of the hydrogen atom.
In everyday language, we can call someone ‘consistent’ to say that they’re reliable, that they don’t change over time. Someone who’s consistently on time is always on time. Similarly, we can call someone ‘inconsistent’ to say the opposite: that they’re changeable, mercurial. A student who receives inconsistent grades on her tests throughout a semester has performed better on some than on others. With our philosophy hats on, though, we mean something quite different by ‘consistent’ and ‘inconsistent’. Something consistent is simply (...) something that’s not contradictory. There’s nothing contradictory about being on time, so anyone who’s on time at all is consistently on time, in this sense of ‘consistent’. And only a student with an unusual teacher can receive inconsistent grades on her tests throughout a semester, in this sense of ‘inconsistent’. In this paper, I’ll use ‘consistent’ and ‘inconsistent’ in their usual philosophical sense: to mark the second distinction. By contrast, I’ll use ‘constant’ and ‘inconstant’ to mark the first distinction. And although we can, should, and do sharply distinguish the two distinctions, they are related. In particular, they have both been used to account for some otherwise puzzling phenomena surrounding vague language. According to some theorists, vague language is inconstant. According to others, it is inconsistent. I do not propose here to settle these differences; only to get a bit clearer about what the differences amount to, and to show what it would take to settle.. (shrink)
The pseudo-Platonic dialogue Axiochus seems irremediably confused. Its author tosses together Platonic, Epicurean and Cynic arguments against the fear of death, apparently with no regard for their consistency. Whereas in the Apology Socrates argues that death is either annihilation or a relocation of the soul, and is a blessing either way, in the Axiochus Socrates seems to assert that death is both annihilation and a release of the soul from the body into a better realm.I argue that we can acquit (...) the Axiochus from the charge of confusion if we pay attention to its genre, a consolation letter cast in dialogue form. The dialogue dramatizes a distinctive type of consolatory argumentative practice. Socrates' use of arguments with inconsistent premises, presented in propria persona, is only one of many ways in which he is willing to sacrifice argumentative hygiene for the sake of therapeutic effectiveness. These include appealing to emotion, tailoring arguments to the audience, and presenting invalid arguments so as to induce unjustified but comforting beliefs. In these respects, I think that Socrates' argumentative practice is best compared to PH III 280-1, where Sextus Empiricus says that the skeptic will deliberately use logically weak arguments as long as they work. (shrink)
Hurford’s Constraint (Hurford, Foundations of Language, 11, 409–411, 1974) states that a disjunction is infelicitous if its disjuncts stand in an entailment relation: #John was born in Paris or in France. Gazdar (Pragmatics, Academic Press, NY, 1979) observed that scalar implicatures can obviate the constraint. For instance, sentences of the form (A or B) or (Both Aand B) are felicitous due to the exclusivity implicature of the first disjunct: A or B implicates ‘not (A and B)’. Chierchia, Fox, and Spector (...) (Handbook of semantics, 2008) use the obviation of Hurford’s Constraint in these cases to argue for a theory of local implicature. I present evidence indicating that the constraint needs to be modified in two ways. First, implicatures can obviate Hurford’s Constraint only in earlier disjuncts, not later ones: #(Both A and B) or (A or B). Second, the constraint rules out not only disjuncts that stand in an entailment relation, but also disjuncts that are even mutually consistent: #John is from Russia or Asia. I propose to make sense of these facts by providing an incremental evaluation procedure which checks that each new disjunct to the right is inconsistent with the information to its left, before the disjunct can be strengthened by local implicature. (shrink)
The idea of the positive theory is to avoid the Russell's paradox by postulating an axiom scheme of comprehension for formulas without "too much" negations. In this paper, we show that the axiom of choice is inconsistent with the positive theory GPK + ∞.
In several articles, Mumma has presented a formal diagrammatic system Eu meant to give an account of one way in which Euclid's use of diagrams in the Elements could be formalized. However, largely because of the way in which it tries to limit case analysis, this system ends up being inconsistent, as shown here. Eu also suffers from several other problems: it is unable to prove several wide classes of correct geometric claims and contains a construction rule that is probably (...) computationally intractable and that may not even be decidable. (shrink)
Moulines in his "A Logical Reconstruction of Simple Equilibrium Thermodynamics" shows that Sneedian constraints play an essential role even in the purely theoretical development of the mathematical formalism of at least one actual scientific theory. However, Moulines' treatment is apparently inconsistent because of the way he represents constraints. A very simple non-Sneedian way of representing constraints is given which removes the difficulty.
This is a discussion of different ways of working out the idea that the semantic paradoxes show that natural languages are somehow “inconsistent”. I take the workable form of the idea to be that there are expressions such that a necessary condition of understanding them is that one be inclined to accept inconsistent claims (an conception also suggested by Matti Eklund). I then distinguish “simple” from “complex” forms of such views. On a simple theory, such expressions are meaningless, while on (...) a complex theory they are not. I argue that complex theories are incompatible with truth conditional semantics and that simple theories are only coherent when the inconsistent claims are metalingusitic attributions of meaning. I close with a discussion of the version of the simple metalinguistic theory I have defended in “Understanding the Liar” and other papers. (shrink)
Quantum field theory (QFT) presents a genuine example of the underdetermination of theory by empirical evidence. There are variants of QFT—for example, the standard textbook formulation and the rigorous axiomatic formulation—that are empirically indistinguishable yet support different interpretations. This case is of particular interest to philosophers of physics because, before the philosophical work of interpreting QFT can proceed, the question of which variant should be subject to interpretation must be settled. New arguments are offered for basing the interpretation of QFT (...) on a rigorous axiomatic variant of the theory. The pivotal considerations are the roles that consistency and idealization play in this case. *Received June 2009; revised August 2009. †To contact the author, please write to: Department of Philosophy, University of Waterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada; e‐mail: dlfraser@uwaterloo.ca. (shrink)
I argue that Frank Jackson's knowledge argument cannot succeed in showing that qualia are epiphenomenal. The reason for this is that there is, given the structure of the argument, an irreconcilable tension between his support for the claim that qualia are non-physical and his conclusion that they are epiphenomenal. The source of the tension is that his argument for the non-physical character of qualia is plausible only on the assumption that they have causal efficacy, while his argument for the epiphenomenal (...) character of qualia is plausible only on the assumption that they are non-physical. Since these two arguments cannot be combined coherently, the most Jackson's argument can establish is that qualia are non-physical. (shrink)
David Lewis has argued that impossible worlds are nonsense: if there were such worlds, one would have to distinguish between the truths about their contradictory goings-on and contradictory falsehoods about them; and this--Lewis argues--is preposterous. In this paper I examine a way of resisting this argument by giving up the assumption that ‘in so-and-so world’ is a restricting modifier which passes through the truth-functional connectives The outcome is a sort of subvaluational semantics which makes a contradiction ‘A & ~A’ false (...) even when both ‘A’ and ‘~A’ are true, just as supervaluational semantics makes a tautology ‘A v ~A’ true even when neither ‘A’ nor ‘~A’ are. Connections with discussive logics and complications of the account are discussed, and some general morals are drawn. (shrink)
We investigate the structure common to causal theories that attempt to explain a (part of) the world. Causality implies conservation of identity, itself a far from simple notion. It imposes strong demands on the universalizing power of the theories concerned. These demands are often met by the introduction of a metalevel which encompasses the notions of 'system' and 'lawful behaviour'. In classical mechanics, the division between universal and particular leaves its traces in the separate treatment of cinematics and dynamics. This (...) analysis is applied to the mechanical theories of Newton and Leibniz, with some surprising results. (shrink)
Two Kinds of Vagueness When signing up for insurance benefits at my job, I was asked, “Do you have children, and if so are they young enough to be included on your policy?” I replied that I had two children, both of whom were over 21. The benefits officer responded, “That’s too vague. In some circumstances children of covered employees are eligible for benefits up to their 26th birthday. I need their ages to determine whether they can be included on (...) your policy.” She was right; my remark was too vague. The information it provided was insufficiently specific to advance our common conversational purpose. However, it was not vague, or at any rate not too vague, in the sense in which philosophical logicians and philosophers of language study vagueness. Vague predicates – like ‘old’, ‘bald’, ‘rich’, and ‘red’ – are those for which there are “borderline cases” separating things to which the predicate clearly applies from those to which it clearly does not. When o is a borderline case for a predicate P, there is, in some sense, “no saying” whether or not the proposition expressed by That/he/she/it is P (said demonstrating o) is true. According to some theories of vagueness, the proposition is undefined for truth, or untruth, and so can’t correctly be characterized either way. According to others, it is true or false -- even though it is impossible, in principle, to know which. On still other theories, it is only partially true (or true to some degree). For present purposes we needn’t worry about which of these theories is correct, or which is most illuminating in discussions of the law. The present point is simpler. The problem with my remark to the benefits officer – the sense in which it was too vague – is not a matter of its susceptibility to borderline cases. What I stated, on December 10, 2009, was that my two children were both over 21 years old then. That statement is true if and only if both were born on or before.... (shrink)
I show that van Fraassen's empiricism leads to mutually incompatible claims with regard to empirical theories. He is committed to the claim that reasons for accepting a theory and believing it are always identical, insofar as the theory in question is an empirical theory. He also makes a general claim that reasons for accepting a theory are not always reasons for believing it irrespective of whether the theory is an empirical theory.
I defend the consistency of affirming the right to life while rejecting universal healthcare and liveable income programmes. I also defend the rationality of accepting inconsistency.
Wegner’s argument on the illusory nature of conscious will, as developed in The Illusion of Conscious Will ( 2002 ) and other publications, has had major impact. Based on empirical data, he develops a theory of apparent mental causation in order to explain the occurrence of the illusion of conscious will. Part of the evidence for his argument is derived from a specific interpretation of the phenomenon of auditory verbal hallucinations as they may occur in schizophrenia. The aim of this (...) paper is to evaluate the validity of the evidence on auditory verbal hallucinations as employed by Wegner. I conclude that auditory hallucinations do not provide solid evidence for Wegner’s theory. Moreover, the phenomena in schizophrenia provide, in fact, an argument against part of Wegner’s theory of apparent mental causation. (shrink)
Chomsky’s principle of epistemological tolerance says that in theoretical linguistics contradictions between the data and the hypotheses may be temporarily tolerated in order to protect the explanatory power of the theory. The paper raises the following problem: What kinds of contradictions may be tolerated between the data and the hypotheses in theoretical linguistics? First a model of paraconsistent logic is introduced which differentiates between week and strong contradiction. As a second step, a case study is carried out which exemplifies that (...) the principle of epistemological tolerance may be interpreted as the tolerance of week contradiction. The third step of the argumentation focuses on another case study which exemplifies that the principle of epistemological tolerance must not be interpreted as the tolerance of strong contradiction. The reason for the latter insight is the unreliability and the uncertainty of introspective data. From this finding the author draws the conclusion that it is the integration of different data types that may lead to the improvement of current theoretical linguistics and that the integration of different data types requires a novel methodology which, for the time being, is not available. (shrink)
An agent whose preferences violate the Independence Axiom or for some other reason are not representable by an expected utility function, can avoid 'dynamic inconsistency' either by foresight ('sophisticated choice') or by subsequent adjustment of preferences to the chosen plan of action ('resolute choice'). Contrary to McClennen and Machina, among others, it is argued these two seemingly conflicting approaches to 'dynamic rationality' need not be incompatible. 'Wise choice' reconciles foresight with a possibility of preference adjustment by rejecting the two (...) assumptions that create the conflict: Separability of Preferences in the case of sophisticated choice and Reduction to Normal form in the case of resolute choice.. (shrink)
This is acknowledged by moral realists and non-cognitivists alike, but, for obvious reasons, they relate differently to this resemblance. For realists, it provides arguments, and for non-cognitivists, it provides potential trouble. Realists claim that the various points of resemblance between moral and factual discourse indicate that moral discourse simply is a kind of factual discourse.1 However, in recent years a number of interesting attempts have been made in trying to show that the realist appearance of moral discourse can after all (...) be accommodated within a noncognitivist view. (shrink)
Augustine was undeniably a dogmatic thinker, but he also had an “aporetic side” which makes him more relevant to Christian philosophers today than isgenerally recognized. Augustine’s first experience of reading philosophy came from Cicero’s Hortensius, from which Augustine gained an appreciation for philosophical scepticism which he never lost. Thus, in all of his works and in all periods of his life, Augustine’s characteristic way of doing philosophy is aporetic, rather than either systematic or speculative. Paradoxically, Augustine’s faith in the truth (...) of Holy Scripture and Church Doctrine gave him a freedom to explore theological and philosophical conundra and, if he could not resolve them, admit frankly that he could not do so. Like Socrates, Augustine was wise partly because he admitted to being puzzled about things that others took for granted. Some of the perplexities which occupied him are: (a) the nature of time; (b) whether it is possible to show someone (without using words) what walking is if one is already walking; (c) whether one is responsible for what one does in one’s dreams; (d) whether one can think about sadness or pleasure by having an image of it in one’s mind, but without experiencing any sadness or pleasure in the thought, and (e) (perhaps most famously, in the Confessions) how one can want something that he does not believe to be good. (shrink)
Consistency and optimality together with converse consistency provide an illuminating and novel characterization of the equilibrium concept (Peleg and Tijs, 1996). But (together with non-emptiness) they preclude refinements of the equilibrium notion and selection of a unique equilibrium (Norde et al., 1996). We suggest two escape routes: By generalizing the concept of strict equilibrium we question the practical relevance of the existence requirement for refinements. To allow for equilibrium selection we suggest more complex reduced games which capture the inclinations of (...) ``players who already left''. (shrink)
Piccione and Rubinstein (1997) present and analyse the sequential decision problem of an “absentminded driver”. The driver's absentmindedness (imperfect recall) leads him to time-inconsistent strategy evaluations. His original evaluation gets replaced by a new one under impact of the information that the circumstances have changed, notwithstanding the fact that this change in circumstances has been expected by him all along. The time inconsistency in strategy evaluation suggests that such an agent might have reason to renege on his adopted strategy. (...) As we shall see, however, this danger is only apparent. There is no serious problem of dynamic inconsistency in this case. My diagnosis of the case under consideration is in many respects similar to the one provided by Aumann, Hart and Perry (1997), but the analysis leading to this diagnosis is not quite the same. (shrink)
