Mark Schroeder has argued that all reasonable forms of inconsistency of attitude consist of having the same attitude type towards a pair of inconsistent contents (A-type inconsistency). We suggest that he is mistaken in this, offering a number of intuitive examples of pairs of distinct attitudes types with consistent contents which are intuitively inconsistent (B-type inconsistency). We further argue that, despite the virtues of Schroeder's elegant A-type expressivist semantics, B-type inconsistency is in many ways the more (...) natural choice in developing an expressivist account of moral discourse. We close by showing how to adapt ordinary formality-based accounts of logicality to define a B-type account of logical inconsistency and distinguish it from both semantic and pragmatic inconsistency. In sum, we provide a roadmap of how to develop a successful B-type expressivism. (shrink)
In this paper we present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language in such a way that consistency may be logically independent of non-contradiction. We defend the view according to which logics of formal inconsistency may be interpreted as theories of logical consequence of an epistemological character. We also argue that in order to (...) philosophically justify paraconsistency there is no need to endorse dialetheism, the thesis that there are true contradictions. Furthermore, we show that mbC, a logic of formal inconsistency based on classical logic, may be enhanced in order to express the basic ideas of an intuitive interpretation of contradictions as conflicting evidence. (shrink)
We present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language. We shall defend the view according to which logics of formal inconsistency are theories of logical consequence of normative and epistemic character. This approach not only allows us to make inferences in the presence of contradictions, but offers a philosophically acceptable account of paraconsistency.
The present paper is devoted to computational aspects of propositional inconsistency-adaptive logics. In particular, we prove (relativized versions of) some principal results on computational complexity of derivability in such logics, namely in cases of CLuN r and CLuN m , i.e., CLuN supplied with the reliability strategy and the minimal abnormality strategy, respectively.
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, I will characterize a new class of inconsistency-adaptive logics, namely inconsistency-adaptive modal logics. These logics cope with inconsistencies in a modal context. More specifically, when faced with inconsistencies, inconsistency-adaptive modal logics avoid explosion, but still allow the derivation of sufficient consequences to adequately explicate the part of human reasoning they are intended for.
For several decades now philosophers have discussed apparent examples of internally inconsistent scientific theories. However, there is still much controversy over how exactly we should conceive of scientific theories in the first place. Here I argue for a new approach, whereby all of the truly important questions about inconsistency in science can be asked and answered without disagreements about theories and theory-content getting in the way. Three examples commonly described as ‘internally inconsistent theories’ are analysed in the light of (...) this approach. In the process, the question ‘Is the theory inconsistent or not?’ is identified as a bad, or at least unimportant, question. (shrink)
I erect a framework within the semantic view of theories for explaining the empirical success of internally inconsistent models and theories, with scientific realism in mind. The framework is an instance of the ‘content-driven’ approach to inconsistency, advocated by both Norton (Philos Sci 54:327–350, 1987) and Smith (Stud Hist Philos Sci 19:429–445, 1988a, In: Fine A, Leplin J (eds) PSA1988, 1988b), whose ideas my analysis aims to clarify and substantiate.
This article proposes the meeting of fuzzy logic with paraconsistency in a very precise and foundational way. Specifically, in this article we introduce expansions of the fuzzy logic MTL by means of primitive operators for consistency and inconsistency in the style of the so-called Logics of Formal Inconsistency (LFIs). The main novelty of the present approach is the definition of postulates for this type of operators over MTL-algebras, leading to the definition and axiomatization of a family of logics, (...) expansions of MTL, whose degree-preserving counterpart are paraconsistent and moreover LFIs. (shrink)
This chapter argues that the distinction between ambitious and modest transcendental arguments, developed and deployed by various authors in the wake of Stroud’s influential critique of transcendental reasoning, may be pointless when applied to transcendental arguments from performative inconsistency that have moral statements as their conclusions. If moral truth is assertorically constrained, then any modest moral transcendental argument from performative inconsistency can be converted into an ambitious moral transcendental argument. The chapter provides an account of performative inconsistency (...) and suggests an alternative to the widespread reading of transcendental conditionals in terms of an ‘if-then’-sentences whose antecedents express a proposition to the effect that some x is possible and whose consequents express a statement to the effect that some y is actual. (shrink)
Scientific pluralism is the view according to which there is a plurality of scientific domains and of scientific theories, and these theories are empirically adequate relative to their own respective domains. Scientific monism is the view according to which there is a single domain to which all scientific theories apply. How are these views impacted by the presence of inconsistent scientific theories? There are consistency-preservation strategies and inconsistency-toleration strategies. Among the former, two prominent strategies can be articulated: Compartmentalization and (...) Information restriction. Among the inconsistency-toleration strategies, we have: Paraconsistent compartmentalization and Dialetheism. In this paper, I critically assess the adequacy of each of these four views. (shrink)
In this paper we present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language in such a way that consistency may be logically independent of non- contradiction. We defend the view according to which logics of formal inconsistency may be interpreted as theories of logical consequence of an epistemological character. We also argue that in order (...) to philosophically justify paraconsistency there is no need to endorse dialetheism, the thesis that there are true contradictions. Furthermore, we argue that an intuitive reading of the bivalued semantics for the logic mbC, a logic of formal inconsistency based on classical logic, fits in well with the basic ideas of an intuitive interpretation of contradictions. On this interpretation, the acceptance of a pair of propositions A and ¬A does not mean that A is simultaneously true and false, but rather that there is conflicting evidence about the truth value of A. (shrink)
Consistency is often pictured as an indispensable requisite for rationality. The paper argues that this is overly rigoristic. Inconsistency can be treated as a matter of isolable singularities rather than an all-destructive disaster. The paper, supports and illustrates a perspective on which consistency can be seen as a desideratum rather than a totaly non-negotiable demand. The argumentation of the paper casts consistency in the role of a cognitive ideal rather than a sine qua non condition of rational process.
Nicholas Rescher has argued we must tolerate inconsistency because of our cognitive limitations. He has also produced, together with R. Brandom, a serious attempt at exploring the logic of inconsistency. Inconsistency tolerance calls for a systematic rewriting of our logical doctrines: it requires a paraconsistent logic. However, having given up all aggregation of premises, Rescher's proposal for a paraconsistenl logic fails to account for the reductive reasoning Rescher appeals to in his account of inconsistency tolerance. A (...) non-adjunctive logic developed by P.K. Schotch and RE. Jennings provides just what Rescher's logic is lacking: It allows a tolerant attitude toward inconsistency while giving an account of reductive reasoning. (shrink)
In section I, I argue that the principal reason why inconsistency is a fault is that it involves having at least one false belief. In section 2, I argue that inconsistency need not be a serious epistemic fault. The argument in section 2 is based on the notion that what matters epistemically is always in the final analysis an item's effect on attaining the goal of truth. In section 3 I describe two cases in which it is best (...) from an epistemic point of view to knowingly retain inconsistent beliefs. In section 4 my goal is to put into perspective the charge that relativism ought to be rejected because it involves one in inconsistency. (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)
In this paper, two axiomatic theories T− and T′ are constructed, which are dual to Tarski’s theory T+ (1930) of deductive systems based on classical propositional calculus. While in Tarski’s theory T+ the primitive notion is the classical consequence function (entailment) Cn+, in the dual theory T− it is replaced by the notion of Słupecki’s rejection consequence Cn− and in the dual theory T′ it is replaced by the notion of the family Incons of inconsistent sets. The author has proved (...) that the theories T+, T−, and T′ are equivalent. (shrink)
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)
Several writers have argued that the state lacks the moral standing to hold socially deprived offenders responsible for their crimes because the state would be hypocritical in doing so. Yet the state is not disposed to make an unfair exception of itself for committing the same sorts of crimes as socially deprived offenders, so it is unclear that the state is truly hypocritical. Nevertheless, the state is disposed to inconsistently hold its citizens responsible, blaming or punishing socially deprived offenders more (...) often or more harshly than other offenders, even when the crimes are the same. The state’s stable disposition to inconsistently hold offenders responsible undermines its standing to hold offenders responsible for the same reasons that hypocrisy undermines standing; instead of making an unfair exception of itself, the state makes an unfair exception of others. Strikingly, this means that the state lacks the standing to hold anyone responsible for a crime for which it is unfairly disposed to hold citizens responsible inconsistently, not just socially deprived offenders. Thus, it is even more urgent that the state regain its moral standing by working toward a justice system that holds offenders responsible consistently. (shrink)
Plato’s view on pleasure in the Republic emerges in the course of developing the third proof of his central thesis that the just man is happier than the unjust. Plato presents it as the “greatest and most decisive” proof of his central thesis, so one might expect to find an abundance of scholarly work on it. Paradoxically, however, this argument has received little attention from scholars, and what has been written on it has generally been harshly critical. I believe that (...) this treatment of the argument has been unfair and that the relevant passages deserve a more careful and charitable interpretation. In this paper, I take up two serious charges that scholars have leveled against this proof, that it is inconsistent and that it involves a “fatal ambiguity”. I show that these charges result from misinterpreting Plato’s text, and I offer an alternative interpretation of the relevant passages. In doing so, I hope to shed some light on the complexities involved in Plato’s unappreciated third proof. (shrink)
An argument for Trivialism, the view that natural languages are logically inconsistent, is provided that does not rely on contentious empirical assumptions about natural language terms such as “and” or “or.” Further, the view is defended against an important objection recently mounted against it by Thomas Hofweber.
If a subject’s belief system is inconsistent, does it follow that the subject’s beliefs (all of them) are unjustified? It seems not. But, coherentist theories of justification (at least some of them) imply otherwise, and so, it seems, are open to counterexample. This is the “Problem of Justified Inconsistent Beliefs”. I examine two main versions of the Problem of Justified Inconsistent Beliefs, and argue that coherentists can give at least a promising line of response to each of them.
Abstract In this paper I discuss one apparent counterexample to the rationality constraint on belief ascription. The fact that there are inconsistent believers does not seem compatible with the idea that only rational creatures can be ascribed beliefs. I consider Davidson's explanation of the possibility of inconsistent believers and claim that it involves a reformulation of the rationality constraint in terms of the believers' subscription to norms of rationality. I shall argue that Davidson's strategy is partially successful, but that the (...) emphasis on the notion of subscription badly fits with the motivations behind his theory of interpretation. (shrink)
I argue that if we make explicit the role of the user of scientific representations not only in the application but also in the construction of a model or representation, then inconsistent modeling assumptions do not pose an insurmountable obstacle to our representational practices.
A critic may attack an arguer personally by pointing out that the arguer’s position is pragmatically inconsistent: the arguer does not practice what he preaches. A number of authors hold that such attacks can be part of a good argumentative discussion. However, there is a difficulty in accepting this kind of contribution as potentially legitimate, for the reason that there is nothing wrong for a protagonist to have an inconsistent position, in the sense of committing himself to mutually inconsistent propositions. (...) If so, any such charge seems to be irrelevant. The questions to be answered in this essay are: what, if any, is the dialectical rationale for this type of criticism, and in what situations, if any, is this kind of charge dialectically legitimate? It will be shown that these attacks can be dialectically legitimate, in special circumstances, and that they can be seen as strategic␣manoeuvres where a party attempts to reconcile his dialectical and his rhetorical objectives. (shrink)
This paper discusses a conception of physics as a collection of theories that, from a logical point of view, is inconsistent. It is argued that this logical conception of the relations between physical theories is too crude. Mathematical subtleties allow for a much more nuanced and sophisticated understanding of the relations between different physical theories.
In this paper, we analyze an intra-personal game where a decision-maker is summarized by a succession of selves. Selves may (or may not) have conflicting interests, and earlier selves may have imperfect knowledge of the preferences of future selves. At date 1, self-1 chooses a menu, at date 2, the preferences of self-2 realize and self-2 chooses an item from the menu. We show that equilibrium choice is consistent with either a preference for flexibility, a preference for betweenness or a (...) preference for systematic restriction. Overall, the analysis reconciles the decision–theoretic approach of choice over time with the game–theoretic multiple-selves approach. (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)
Camus’ early philosophy has been subject to various kinds of criticism. In this paper I address a problem that has not been noticed so far, namely that it appears to be essentially inconsistent. On the one hand, Camus explicitly denies the existence of moral values, and construes his central notion of the absurd in a way that presupposes this denial. On the other hand, he is also committed to the existence of certain values. Both in his literary and philosophical works (...) Camus is not so much interested in the absurd per se, but rather in how we ought to respond to it. In justifying his supposed normative conclusions, he tacitly, but crucially, relies on evaluative judgements. If all this is true, then prospects for defenders of absurdism seem bleak. In whichever way the inconsistency is resolved, they will have to give up or significantly modify central parts of Camus’ early philosophy. But things may not stand quite as bad. As I try to show, there is a route to consistency that preserves much of Camus’ early philosophy, and leaves it prima facie plausible. The key is to re-interpret its normative aspects. Stated a bit provocatively, we need to put Camus in the self-help genre. (shrink)
ABSTRACTThe article is an extended critical discussion of Kevin Scharp’s Replacing Truth. Scharp’s case for the claim that the concept of truth is inconsistent is criticized, and so is his case for the claim that the concept of truth must be replaced because of its inconsistency.
This paper concerns the relationship between transitivity of entailment, omega-inconsistency and nonstandard models of arithmetic. First, it provides a cut-free sequent calculus for non-transitive logic of truth STT based on Robinson Arithmetic and shows that this logic is omega-inconsistent. It then identifies the conditions in McGee for an omega-inconsistent logic as quantified standard deontic logic, presents a cut-free labelled sequent calculus for quantified standard deontic logic based on Robinson Arithmetic where the deontic modality is treated as a predicate, proves (...) omega-inconsistency and shows thus, pace Cobreros et al., that the result in McGee does not rely on transitivity. Finally, it also explains why the omega-inconsistent logics of truth in question do not require nonstandard models of arithmetic. (shrink)
This paper follows up a debate as to whether classical electrodynamics is inconsistent. Mathias Frisch makes the claim in Inconsistency, Asymmetry and Non-Locality (), but this has been quickly countered by F. A. Muller () and Gordon Belot (). 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)
This paper introduces new logical systems which axiomatize a formal representation of inconsistency (here taken to be equivalent to contradictoriness) in classical logic. We start from an intuitive semantical account of inconsistent data, fixing some basic requirements, and provide two distinct sound and complete axiomatics for such semantics, LFI1 and LFI2, as well as their first-order extensions, LFI1* and LFI2*, depending on which additional requirements are considered. These formal systems are examples of what we dub Logics of Formal (...) class='Hi'>Inconsistency (LFI) and form part of a much larger family of similar logics. We also show that there are translations from classical and paraconsistent first-order logics into LFI1* and LFI2*, and back. Hence, despite their status as subsystems of classical logic, LFI1* and LFI2* can codify any classical or paraconsistent reasoning. (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)
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)
Background The review of human participant research by Research Ethics Committees or Institutional Review Boards is a complex multi-faceted process that cannot be reduced to an algorithm. However, this does not give RECs/ IRBs permission to be inconsistent in their specific requirements to researchers or in their final opinions. In England the Health Research Authority coordinates 67 committees, and has adopted a consistency improvement plan including a process called “Shared Ethical Debate” where multiple committees review the same project. Committee reviews (...) are compared for consistency by analysing the resulting minutes. Methods We present a description of the ShED process. We report an analysis of minutes created by research ethics committees participating in two ShED exercises, and compare them to minutes produced in a published “mystery shopper” exercise. We propose a consistency score by defining top themes for each exercise, and calculating the ratio between top themes and total themes identified by each committee for each ShED exercise. Results Our analysis highlights qualitative differences between the ShED 19, ShED 20 and “mystery shopper” exercises. The quantitative measure of consistency showed only one committee across the three exercises with more than half its total themes as top themes. The average consistency scores for the three exercises were 0.23, 0.35 and 0.32. There is a statistically significant difference between the ShED 19 exercise, and the ShED 20 and mystery shopper exercises. Conclusions ShED exercises are effective in identifying inconsistency between ethics committees and we describe a scoring method that could be used to quantify this. However, whilst a level of inconsistency is probably inevitable in research ethics committee reviews, studies must move beyond the ShED methodology to understand why inconsistency occurs, and what an acceptable level of inconsistency might be. (shrink)
The review of human participant research by Research Ethics Committees or Institutional Review Boards is a complex multi-faceted process that cannot be reduced to an algorithm. However, this does not give RECs/ IRBs permission to be inconsistent in their specific requirements to researchers or in their final opinions. In England the Health Research Authority coordinates 67 committees, and has adopted a consistency improvement plan including a process called “Shared Ethical Debate” where multiple committees review the same project. Committee reviews are (...) compared for consistency by analysing the resulting minutes. We present a description of the ShED process. We report an analysis of minutes created by research ethics committees participating in two ShED exercises, and compare them to minutes produced in a published “mystery shopper” exercise. We propose a consistency score by defining top themes for each exercise, and calculating the ratio between top themes and total themes identified by each committee for each ShED exercise. Our analysis highlights qualitative differences between the ShED 19, ShED 20 and “mystery shopper” exercises. The quantitative measure of consistency showed only one committee across the three exercises with more than half its total themes as top themes. The average consistency scores for the three exercises were 0.23, 0.35 and 0.32. There is a statistically significant difference between the ShED 19 exercise, and the ShED 20 and mystery shopper exercises. ShED exercises are effective in identifying inconsistency between ethics committees and we describe a scoring method that could be used to quantify this. However, whilst a level of inconsistency is probably inevitable in research ethics committee reviews, studies must move beyond the ShED methodology to understand why inconsistency occurs, and what an acceptable level of inconsistency might be. (shrink)
The debate on probabilistic measures of coherence has focused on evaluating sets of consistent propositions. In this paper we draw attention to the largely neglected question of whether such measures concur with intuitions on test cases involving inconsistent propositions and whether they satisfy general adequacy constraints on coherence and inconsistency. While it turns out that, for the vast majority of measures in their original shape, this question must be answered in the negative, we show that it is possible to (...) adapt many of them in order to improve their performance. (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 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)
It is shown that the consequence relations deﬁned from theRescher-Manor Mechanism are all inconsistency-adaptive logics combined with a speciﬁc interpretation schema for the premises. Each of the adaptive logics isobtained by applying a suitable adaptive strategy to the paraconsistent logicCLuN.This result provides all those consequence relations with a proof theory and with a static semantics.
We present several generalizations of the well-known Kunen inconsistency that there is no nontrivial elementary embedding from the set-theoretic universe V to itself. For example, there is no elementary embedding from the universe V to a set-forcing extension V[G], or conversely from V[G] to V, or more generally from one set-forcing ground model of the universe to another, or between any two models that are eventually stationary correct, or from V to HOD, or conversely from HOD to V, or (...) indeed from any definable class to V, among many other possibilities we consider, including generic embeddings, definable embeddings and results not requiring the axiom of choice. We have aimed in this article for a unified presentation that weaves together some previously known unpublished or folklore results, several due to Woodin and others, along with our new contributions. (shrink)
This paper demonstrates that there is an inconsistency in functionalism in psychology and philosophy of mind. Analogous inconsistencies can be expected in functionalisms in biology and social theory. (edited).
This paper investigates the question of characterizing first-order LFIs (logics of formal inconsistency) by means of two-valued semantics. LFIs are powerful paraconsistent logics that encode classical logic and permit a finer distinction between contradictions and inconsistencies, with a deep involvement in philosophical and foundational questions. Although focused on just one particular case, namely, the quantified logic QmbC, the method proposed here is completely general for this kind of logics, and can be easily extended to a large family of quantified (...) paraconsistent logics, supplying a sound and complete semantical interpretation for such logics. However, certain subtleties involving term substitution and replacement, that are hidden in classical structures, have to be taken into account when one ventures into the realm of nonclassical reasoning. This paper shows how such difficulties can be overcome, and offers detailed proofs showing that a smooth treatment of semantical characterization can be given to all such logics. Although the paper is well-endowed in technical details and results, it has a significant philosophical aside: it shows how slight extensions of classical methods can be used to construct the basic model theory of logics that are weaker than traditional logic due to the absence of certain rules present in classical logic. Several such logics, however, as in the case of the LFIs treated here, are notorious for their wealth of models precisely because they do not make indiscriminate use of certain rules; these models thus require new methods. In the case of this paper, by just appealing to a refined version of the Principle of Explosion, or Pseudo-Scotus, some new constructions and crafty solutions to certain non-obvious subtleties are proposed. The result is that a richer extension of model theory can be inaugurated, with interest not only for paraconsistency, but hopefully to other enlargements of traditional logic. (shrink)