Sharon Street defines her constructivism about practical reasons as the view that whether something is a reason to do a certain thing for a given agent depends on that agent’s normative point of view. However, Street has also maintained that there is a judgment about practical reasons which is true relative to every possible normative point of view, namely constructivism itself. I show that the latter thesis is inconsistent with Street’s own constructivism about epistemic reasons and discuss some consequences of (...) this incompatibility. (shrink)

In order to reason in a non-trivializing way with contradictions, para- consistent logics reject some classically valid inferences. As a way of re- covering some of these inferences, Graham Priest ([Priest, 1991]) proposed to nonmonotonically strengthen the Logic of Paradox by allowing the se- lection of “less inconsistent” models via a comparison of their respective inconsistent parts. This move recaptures a good portion of classical logic in that it does not block, e.g., disjunctive syllogism, unless it is applied to contradictory (...) assumptions. In Priest’s approach the inconsistent parts of models are compared in an extensional way by considering their inconsis- tent objects. This distinguishes his system from the standard format of (inconsistency-)adaptive logics pioneered by Diderik Batens, according to which (atomic) contradictions validated in models form the basis of their comparison. A well-known problem for Priest’s extensional approach is its lack of the Strong Reassurance property, i.e., for specific settings there may be infinitely descending chains of less and less inconsistent models, thus never reaching a minimally inconsistent model. In this paper, we demonstrate that Strong Reassurance holds for the extensional approach under a cardinality-based comparison of the incon- sistent parts of models. Furthermore, we introduce and investigate the metatheory of the class of first-order nonmonotonic inconsistency-tolerant construct over the extensional or quantitative comparisons of their respec- tive models. Core model-theoretic properties for these logics, such as the Löwenheim-Skolem theorems, along with other nonmonotonic properties, are further studied. (shrink)

I here present and defend what I call the Triviality Theory of Truth, to be understood in analogy with Matti Eklund’s Inconsistency Theory of Truth. A specific formulation of is defended and compared with alternatives found in the literature. A number of objections against the proposed notion of meaning-constitutivity are discussed and held inconclusive. The main focus, however, is on the problem, discussed at length by Gupta and Belnap, that speakers do not accept epistemically neutral conclusions of Curry (...) derivations. I first argue that the facts about speakers’ reactions to such Curry derivations do not constitute a problem for the Triviality Theory specifically. Rather, they follow from independent, uncontroversial facts. I then propose a solution which coheres with the theory as I understand it. Finally, I consider a normative reading of their objection and offer a response. (shrink)

In recent years, a number of theorists have claimed that beliefs about probability are transparent. To believe probably p is simply to have a high credence that p. In this paper, I prove a variety of triviality results for theses like the above. I show that such claims are inconsistent with the thesis that probabilistic modal sentences have propositions or sets of worlds as their meaning. Then I consider the extent to which a dynamic semantics for probabilistic modals can (...) capture theses connecting belief, certainty, credence, and probability. I show that although a dynamic semantics for probabilistic modals does allow one to validate such theses, it can only do so at a cost. I prove that such theses can only be valid if probabilistic modals do not satisfy the axioms of the probability calculus. (shrink)

This dissertation offers a proof of the logical possibility of testing empirical/factual theories that are inconsistent, but non-trivial. In particular, I discuss whether or not such theories can satisfy Popper's principle of falsifiablility. An inconsistent theory Ƭ closed under a classical consequence relation implies every statement of its language because in classical logic the inconsistency and triviality are coextensive. A theory Ƭ is consistent iff there is not a α such that Ƭ ⊢ α ∧ ¬α, otherwise it (...) is inconsistent. We say, instead, that Ƭ is non-trivial iff there is at least one α such that Ƭ ⊢ α, otherwise we say that it trivial. This happens because classical logic satisfies the principle of explosion, according ex contradictione sequitur quodlibet (from a contradiction anything follows). Under these conditions inconsistent classical theories would be compatible with any well-formed formula, which makes them useless for science. There are, however, so-called paraconsistent logics in which the principle of explosion does not generally hold and in which a theory can be (simply) inconsistent, but also absolutely consistent. It is in this logical framework that we can prove that some inconsistent theories can be falsifiable. (shrink)

The logics of formal inconsistency (LFIs, for short) are paraconsistent logics (that is, logics containing contradictory but non-trivial theories) having a consistency connective which allows to recover the ex falso quodlibet principle in a controlled way. The aim of this paper is considering a novel semantical approach to first-order LFIs based on Tarskian structures defined over swap structures, a special class of multialgebras. The proposed semantical framework generalizes previous aproaches to quantified LFIs presented in the literature. The case of (...) QmbC, the simpler quantified LFI expanding classical logic, will be analyzed in detail. An axiomatic extension of QmbC called QLFI1o is also studied, which is equivalent to the quantified version of da Costa and D'Ottaviano 3-valued logic J3. The semantical structures for this logic turn out to be Tarkian structures based on twist structures. The expansion of QmbC and QLFI1o with a standard equality predicate is also considered. (shrink)

This is a thesis in support of the conceptual yoking of analytic truth to a priori knowledge. My approach is a semantic one; the primary subject matter throughout the thesis is linguistic objects, such as propositions or sentences. I evaluate arguments, and also forward my own, about how such linguistic objects’ truth is determined, how their meaning is fixed and how we, respectively, know the conditions under which their truth and meaning are obtained. The strategy is to make explicit what (...) is distinctive about analytic truths. The objective is to show that truths, known a priori, are trivial in a highly circumscribed way. My arguments are premised on a language-relative account of analytic truth. The language relative account which underwrites much of what I do has two central tenets: 1. Conventionalism about truth and, 2. Non-factualism about meaning. I argue that one decisive way of establishing conventionalism and non-factualism is to prioritise epistemological questions. Once it is established that some truths are not known empirically an account of truth must follow which precludes factual truths being known non-empirically. The function of Part 1 is, chiefly, to render Carnap’s language-relative account of analytic truth. I do not offer arguments in support of Carnap at this stage, but throughout Parts 2 and 3, by looking at more current literature on a priori knowledge and analytic truth, it becomes quickly evident that I take Carnap to be correct, and why. In order to illustrate the extent to which Carnap’s account is conventionalist and non-factualist I pose his arguments against those of his predecessors, Kant and Frege. Part 1 is a lightly retrospective background to the concepts of ‘analytic’ and ‘a priori’. The strategy therein is more mercenary than exegetical: I select the parts from Kant and Frege most relevant to Carnap’s eventual reaction to them. Hereby I give the reasons why Carnap foregoes a factual and objective basis for logical truth. The upshot of this is an account of analytic truth (i.e. logical truth, to him) which ensures its trivial nature. In opposition to accounts of a priori knowledge, which describe it as knowledge gained from rational apprehension, I argue that it is either knowledge from logical deduction or knowledge of stipulations. I therefore reject, in Part 2, three epistemologies for knowing linguistic conventions (e.g. implicit definitions): 1. intuition, 2. inferential a priori knowledge and, 3. a posteriori knowledge. At base, all three epistemologies are rejected because they are incompatible with conventionalism and non-factualism. I argue this point by signalling that such accounts of knowledge yield unsubstantiated second-order claims and/or they render the relevant linguistic conventions epistemically arrogant. For a convention to be arrogant it must be stipulated to be true. The stipulation is then considered arrogant when its meaning cannot be fixed, and its truth cannot be determined without empirical ‘work’. Once a working explication of ‘a priori’ has been given, partially in Part 1 (as inferential) and then in Part 2 (as non-inferential) I look, in Part 3, at an apriorist account of analytic truth, which, I argue, renders analytic truth non-trivial. The particular subject matter here is the implicit definitions of logical terms. The opposition’s argument holds that logical truths are known a priori (this is part of their identification criteria) and that their meaning is factually based. From here it follows that analytic truth, being determined by factually based meaning, is also factual. I oppose these arguments by exposing the internal inconsistencies; that implicit definition is premised on the arbitrary stipulation of truth which is inconsistent with saying that there are facts which determine the same truth. In doing so, I endorse the standard irrealist position about implicit definition and analytic truth (along with the “early friends of implicit definition” such as Wittgenstein and Carnap). What is it that I am trying to get at by doing all of the abovementioned? Here is a very abstracted explanation. The unmitigated realism of the rationalists of old, e.g. Plato, Descartes, Kant, have stoically borne the brunt of the allegation of yielding ‘synthetic a priori’ claims. The anti-rationalist phase of this accusation I am most interested in is that forwarded by the semantically driven empiricism of the early 20th century. It is here that the charge of the ‘synthetic a priori’ really takes hold. Since then new methods and accusatory terms are employed by, chiefly, non-realist positions. I plan to give these proper attention in due course. However, it seems to me that the reframing of the debate in these new terms has also created the illusion that current philosophical realism, whether naturalistic realism, realism in science, realism in logic and mathematics, is somehow not guilty of the same epistemological and semantic charges levelled against Plato, Descartes and Kant. It is of interest to me that in, particularly, current analytic philosophy (given its rationale) realism in many areas seems to escape the accusation of yielding synthetic priori claims. Yet yielding synthetic a priori claims is something which realism so easily falls prey to. Perhaps this is a function of the fact that the phrase, ‘synthetic a priori’, used as an allegation, is now outmoded. This thesis is nothing other than an indictment of metaphysics, or speculative philosophy (this being the crime), brought against a specific selection of realist arguments. I, therefore, ask of my reader to see my explicit, and perhaps outmoded, charge of the ‘synthetic a priori’ levelled against respective theorists as an attempt to draw a direct comparison with the speculative metaphysics so many analytic philosophers now love to hate. I think the phrase ‘synthetic a priori’ still does a lot of work in this regard, precisely because so many current theorists wrongly think they are immune to this charge. Consequently, I shall say much about what is not permitted. Such is, I suppose, the nature of arguing ‘against’ something. I’ll argue that it is not permitted to be a factualist about logical principles and say that they are known a priori. I’ll argue that it is not permitted to say linguistic conventions are a posteriori, when there is a complete failure in locating such a posteriori conventions. Both such philosophical claims are candidates for the synthetic a priori, for unmitigated rationalism. But on the positive side, we now have these two assets: Firstly, I do not ask us to abandon any of the linguistic practises discussed; merely to adopt the correct attitude towards them. For instance, where we use the laws of logic, let us remember that there are no known/knowable facts about logic. These laws are therefore, to the best of our knowledge, conventions not dissimilar to the rules of a game. And, secondly, once we pass sentence on knowing, a priori, anything but trivial truths we shall have at our disposal the sharpest of philosophical tools. A tool which can only proffer a better brand of empiricism. (shrink)

Standard accounts of counterfactuals with metaphysically impossible antecedents take them to by trivially true. But recent work shows that nontrivial countermetaphysicals are frequently appealed to in scientific modeling and are indispensable for a number of metaphysical projects. I focus on three recent discussions of counterpossible counterfactuals, which apply counterpossibles in both scientific and metaphysical modeling. I show that a sufficiently developed modal counterpart theory can provide a semantics for a wide range of counterpossibles without any inconsistent possibilities or other forms (...) of impossible worlds. But such a view faces problems: in order for the metaphysical views I discuss to bear weight, there must be a significant difference between the metaphysical possibilities and impossibilities. I will show how the counterpart-theoretic view delineates the possible from impossible, while still making room for the impossible. (shrink)

A handful of well-known arguments (the 'diachronic Dutch book arguments') rely upon theorems establishing that, in certain circumstances, you are immune from sure monetary loss (you are not 'diachronically Dutch bookable') if and only if you adopt the strategy of conditionalizing (or Jeffrey conditionalizing) on whatever evidence you happen to receive. These theorems require non-trivial assumptions about which evidence you might acquire---in the case of conditionalization, the assumption is that, if you might learn that e, then it is not the (...) case that you might learn something else that is consistent with e. These assumptions may not be relaxed. When they are, not only will non-(Jeffrey) conditionalizers be immune from diachronic Dutch bookability, but (Jeffrey) conditionalizers will themselves be diachronically Dutch bookable. I argue: 1) that there are epistemic situations in which these assumptions are violated; 2) that this reveals a conflict between the premise that susceptibility to sure monetary loss is irrational, on the one hand, and the view that rational belief revision is a function of your prior beliefs and the acquired evidence alone, on the other; and 3) that this inconsistency demonstrates that diachronic Dutch book arguments for (Jeffrey) conditionalization are invalid. (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)

In this paper I formalise the falsificationist proposal omitting Popper’s requirement of consistency. This omission results in (i) trivial theories being falsifiable in an inappropriate sense of the term, but also in (ii) some inconsistent non-trivial theories being so in an appropriate one. This justifies a slight alteration of the definition of falsifiability that excludes (i) but allows (ii). Instead of requiring that a falsifiable theory be consistent, my proposal only requires that the intersection of its classes of potential corroborators (...) and falsifiers be empty. (shrink)

The 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.

Suppose that you're certain that a certain sentence, e.g. "Frida is tall", lacks a determinate truth value. What cognitive attitude should you take towards it—reject it, suspend judgment, or what else? We show that, by adopting a seemingly plausible principle connecting credence in A and Determinately A, we can prove a very implausible answer to this question: i.e., all indeterminate claims should be assigned credence zero. The result is striking similar to so-called triviality results in the literature on modals (...) and conditionals. (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)

The paper examines Derek Parfit’s claim that naturalism trivializes the agent’s practical argument and therefore abolishes the normativity of its conclusion. In the first section, I present Parfit’s charge in detail. After this I discuss three possible responses to the objection. I show that the first two responses either fail or are inconclusive. Trying to avoid Parfit’s charge by endorsing irreductionist naturalism is not a solution because this form of naturalism is metaphysically untenable. Non- descriptive naturalism, on the other hand, (...) does not answer the pressing concern behind Parfit’s charge. I conclude that we had better turn to the third response: Peter Railton’s vindicatory reductionism. However, I also argue that naturalism can only avoid triviality in this way if it is able to respond to further challenges concerning the vindication of the reduction it proposes. Hence, though not a knockdown argument as it is intended to be, Parfit’s charge can still pose a threat to naturalist accounts of normativity. (shrink)

The badness of having conflicting emotions is a familiar theme in academic ethics, clinical psychology, and commercial self-help, where emotional harmony is often put forward as an ideal. Many philosophers give emotional harmony pride of place in their theories of practical reason.1 Here we offer a defense of a particular species of emotional conflict, namely, ambivalence. We articulate an conception of ambivalence, on which ambivalence is unresolved inconsistent desire (§1) and present a case of appropriate ambivalence (§2), before considering two (...) alternative defenses of emotional conflict (§3). We then argue that inconsistent desires can be fitting (§4) and that it can be reasonable not to resolve inconsistent desires (§5), before considering an objection (§6) and concluding the discussion (§7). (shrink)

I present a possible worlds semantics for a hyperintensional belief revision operator, which reduces the logical idealization of cognitive agents affecting similar operators in doxastic and epistemic logics, as well as in standard AGM belief revision theory. (Revised) belief states are not closed under classical logical consequence; revising by inconsistent information does not perforce lead to trivialization; and revision can be subject to ‘framing effects’: logically or necessarily equivalent contents can lead to different revisions. Such results are obtained without resorting (...) to non-classical logics, or to non-normal or impossible worlds semantics. The framework combines, instead, a standard semantics for propositional S5 with a simple mereology of contents. (shrink)

This paper discusses and relates two puzzles for indicative conditionals: a puzzle about indeterminacy and a puzzle about triviality. Both puzzles arise because of Ramsey's Observation, which states that the probability of a conditional is equal to the conditional probability of its consequent given its antecedent. The puzzle of indeterminacy is the problem of reconciling this fact about conditionals with the fact that they seem to lack truth values at worlds where their antecedents are false. The puzzle of (...) class='Hi'>triviality is the problem of reconciling Ramsey's Observation with various triviality proofs which establish that Ramsey's Observation cannot hold in full generality. In the paper, I argue for a solution to the indeterminacy puzzle and then apply the resulting theory to the triviality puzzle. On the theory I defend, the truth conditions of indicative conditionals are highly context dependent and such that an indicative conditional may be indeterminate in truth value at each possible world throughout some region of logical space and yet still have a nonzero probability throughout that region. (shrink)

On Hume’s account of motivation, beliefs and desires are very different kinds of propositional attitudes. Beliefs are cognitive attitudes, desires emotive ones. An agent’s belief in a proposition captures the weight he or she assigns to this proposition in his or her cognitive representation of the world. An agent’s desire for a proposition captures the degree to which he or she prefers its truth, motivating him or her to act accordingly. Although beliefs and desires are sometimes entangled, they play very (...) different roles in rational agency. In two classic papers (Lewis 1988, 1996), David Lewis discusses several challenges to this Humean picture, but ultimately rejects them. We think that his discussion of a central anti-Humean alternative – the desire-as-belief thesis – is in need of refinnement. On this thesis, the desire for proposition p is given by the belief that p is desirable. Lewis claims that ‘[e]xcept in trivial cases, [this thesis] collapses into contradiction’(Lewis 1996, p. 308). The problem, he argues, is that the thesis is inconsistent with the purportedly plausible requirement that one’s desire for a proposition should not change upon learning that the proposition is true; call this the invariance requirement. In this paper, we revisit Lewis’s argument. We show that, if one carefully distinguishes between non-evaluative and evaluative propositions, the desire-asbelief thesis can be rendered consistent with the invariance requirement. Lewis’s conclusion holds only under certain conditions: the desire-as-belief thesis conflicts with the invariance requirement if and only if there are certain correlations between non-evaluative and evaluative propositions. But when there are such correlations, we suggest, the invariance requirement loses its plausibility. Thus Lewis’s argument against the desire-as-belief thesis appears to be valid only in cases in which it is unsound. (shrink)

A viable theory of literary humanism must do justice to the idea that literature offers cognitive rewards to the careful reader. There are, however, powerful arguments to the effect that literature is at best only capable of offering idle visions of a world already well known. In this essay I argue that there is a form of cognitive awareness left unmentioned in the traditional vocabulary of knowledge acquisition, a form of awareness literature is particularly capable of offering. Thus even if (...) it is the case that literature has nothing interesting to give us in the way of knowledge, the literary humanist can consistently maintain that literary experience is thoroughly cognitive. (shrink)

The traditional Lewis–Stalnaker semantics treats all counterfactuals with an impossible antecedent as trivially or vacuously true. Many have regarded this as a serious defect of the semantics. For intuitively, it seems, counterfactuals with impossible antecedents—counterpossibles—can be non-trivially true and non-trivially false. Whereas the counterpossible "If Hobbes had squared the circle, then the mathematical community at the time would have been surprised" seems true, "If Hobbes had squared the circle, then sick children in the mountains of Afghanistan at the time would (...) have been thrilled" seems false. Many have proposed to extend the Lewis–Stalnaker semantics with impossible worlds to make room for a non-trivial or non-vacuous treatment of counterpossibles. Roughly, on the extended Lewis–Stalnaker semantics, we evaluate a counterfactual of the form "If A had been true, then C would have been true" by going to closest world—whether possible or impossible—in which A is true and check whether C is also true in that world. If the answer is "yes", the counterfactual is true; otherwise it is false. Since there are impossible worlds in which the mathematically impossible happens, there are impossible worlds in which Hobbes manages to square the circle. And intuitively, in the closest such impossible worlds, sick children in the mountains of Afghanistan are not thrilled—they remain sick and unmoved by the mathematical developments in Europe. If so, the counterpossible "If Hobbes had squared the circle, then sick children in the mountains of Afghanistan at the time would have been thrilled" comes out false, as desired. In this paper, I will critically investigate the extended Lewis–Stalnaker semantics for counterpossibles. I will argue that the standard version of the extended semantics, in which impossible worlds correspond to maximal, logically inconsistent entities, fails to give the correct semantic verdicts for many counterpossibles. In light of the negative arguments, I will then outline a new version of the extended Lewis–Stalnaker semantics that can avoid these problems. (shrink)

Both Heidegger and Wittgenstein consider the possibility of a philosophical inquiry of an absolutely universal scope—an inquiry into the being of all beings, in Heidegger’s case, and into the logical form of everything that can be meaningfully said, in Wittgenstein’s. Moreover, they both raise the worry that the theoretical language by means of which we speak of particular beings and assert particular facts is not suited to this task. And yet their own philosophical work seems to include many assertions of (...) ordinary, theoretical language. Are they being inconsistent? Or are they hoping to use theoretical language in a way that conveys what cannot be said in that language? Much of the scholarship on each of these thinkers takes the form of one of the two horns of this dilemma. In the context of Wittgenstein scholarship, however, a third alternative has been proposed: the Resolute Reading of the Tractatus. My aim is to establish the availability of a similar solution to Heidegger’s predicament. It will emerge that Heidegger rejects the possibility of a theoretical account of being and pursues a project of a radically different sort, whose goal is to bring about a transformation of our fundamental relation to being. (shrink)

A pervasive and influential argument appeals to trivial truths to demonstrate that the aim of inquiry is not the acquisition of truth. But the argument fails, for it neglects to distinguish between the complexity of the sentence used to express a truth and the complexity of the truth expressed by a sentence.

Fallacious reasoning can stem from interacting with purported advocates and/or critics who are not competent to fulfil their respective roles relative to the topic under discussion. The notions of the “incompetent advocate” and the “incompetent critic” are introduced and described, and they are then invoked in the descriptions of three new fallacies. I conclude with some recommendations as to how one can avoid these fallacious traps.

Inquiry into the meaning of logical terms in natural language (‘and’, ‘or’, ‘not’, ‘if’) has generally proceeded along two dimensions. On the one hand, semantic theories aim to predict native speaker intuitions about the natural language sentences involving those logical terms. On the other hand, logical theories explore the formal properties of the translations of those terms into formal languages. Sometimes, these two lines of inquiry appear to be in tension: for instance, our best logical investigation into conditional connectives may (...) show that there is no conditional operator that has all the properties native speaker intuitions suggest if has. Indicative conditionals have famously been the source of one such tension, ever since the triviality proofs of both Lewis (1976) and Gibbard (1981) established conclusions which are in prima facie tension with ordinary judgments about natural language indicative conditionals. In a recent series of papers, Branden Fitelson has strengthened both triviality results (Fitelson 2013, 2015, 2016), revealing a common culprit: a logical schema known as IMPORT-EXPORT. Fitelson’s results focus the tension between the logical results and ordinary judgments, since IMPORT-EXPORT seems to be supported by intuitions about natural language. In this paper, we argue that the intuitions which have been taken to support IMPORT-EXPORT are really evidence for a closely related, but subtly different, principle. We show that the two principles are independent by showing how, given a standard assumption about the conditional operator in the formal language in which IMPORT-EXPORT is stated, many existing theories of indicative conditionals validate one, but not the other. Moreover, we argue that once we clearly distinguish these principles, we can use propositional anaphora to show that IMPORT-EXPORT is in fact not valid for natural language indicative conditionals (given this assumption about the formal conditional operator). This gives us a principled and independently motivated way of rejecting a crucial premise in many triviality results, while still making sense of the speaker intuitions which appeared to motivate that premise. We suggest that this strategy has broad application and an important lesson: in theorizing about the logic of natural language, we must pay careful attention to the translation between the formal languages in which logical results are typically proved, and natural languages which are the subject matter of semantic theory. (shrink)

This paper clarifies the relationship between the Triviality Results for the conditional and the Restrictor Theory of the conditional. On the understanding of Triviality proposed here, it is implausible—pace many proponents of the Restrictor Theory—that Triviality rests on a syntactic error. As argued here, Triviality arises from simply mistaking the feature a claim has when that claim is logically unacceptable for the feature a claim has when that claim is unsatisfiable. Triviality rests on a semantic (...) confusion—one which some semantic theories, but not others, are prone to making. On the interpretation proposed here, Triviality Results thus play a theoretically constructive role in the project of natural language semantics. (shrink)

I defend a new account of constitutive essence on which an entity’s constitutively essential properties are its most fundamental, nontrivial necessary properties. I argue that this account accommodates the Finean counterexamples to classic modalism about essence, provides an independently plausible account of constitutive essence, and does not run into clear counterexamples. I conclude that this theory provides a promising way forward for attempts to produce an adequate nonprimitivist, modalist account of essence. As both triviality and fundamentality in the account (...) are understood in terms of grounding, the theory also potentially has important implications for the relation between essence and grounding. (shrink)

Conditional probability is often used to represent the probability of the conditional. However, triviality results suggest that the thesis that the probability of the conditional always equals conditional probability leads to untenable conclusions. In this paper, I offer an interpretation of this thesis in a possible worlds framework, arguing that the triviality results make assumptions at odds with the use of conditional probability. I argue that these assumptions come from a theory called the operator theory and that the (...) rival restrictor theory can avoid these problematic assumptions. In doing so, I argue that recent extensions of the triviality arguments to restrictor conditionals fail, making assumptions which are only justified on the operator theory. (shrink)

It is often thought the relativity of simultaneity is inconsistent with presentism. This would be troubling as it conflicts with common sense and—arguably—the empirical data. This note gives a novel fragmentalist-presentist theory that allows for the (non-trivial) relativity of simultaneity. A detailed account of the canonical moving train argument is considered. Alice, standing at the train station, forms her own ontological fragment, in which Bob’s frame of reference, given by the moving train, is modified by the Lorentz transformations. On the (...) other hand, Bob, in the train, forms his own ontological fragment from which Alice’s space and time are modified by the corresponding Lorentz transformations. Each fragment accommodates a unique present moment but does not contain information about the unique present moment of another fragment. This allows for a ‘universal’ present moment that extends throughout space, but only from the perspective of each fragment. The relativity of simultaneity is, as it were, ‘relativised’ to each fragment. This is related to the idea that, roughly speaking, the time of relativity is McTaggart’s (1908) B-series (earlier times to later times) and the time of quantum mechanics is a (fragmentalist) A-series (future/present/past), where these two related series characterize one dimension of time. (shrink)

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)

An important strand in philosophy of science takes scientific explanation to consist in the conveyance of some kind of information. Here I argue that this idea is also implicit in some core arguments of mechanists, some of whom are proponents of an ontic conception of explanation that might be thought inconsistent with it. However, informational accounts seem to conflict with some lay and scientific commonsense judgments and a central goal of the theory of explanation, because information is relative to the (...) background knowledge of agents. Sometimes we make lay judgments about whether a model is an explanation simpliciter, not just an explanation relative to some particular agent. And as philosophers of explanation, we would like a philosophical account to tell us when a model is an explanation simpliciter, not just when a model is an explanation relative to some particular agent. Thus, even if one’s account of explanation is not concerned with explanation qua communicative or speech act, the account’s reliance on the concept of information generates a prima facie conflict between the claims that 1) explanation is the conveyance of information, 2) information is relative to the background knowledge of an agent, and 3) some models are explanations not relative to the background knowledge of any particular agent. I sketch a solution to this puzzle by distinguishing informationally what I call “explanation simpliciter” from what I call “explanation-to,” relativizing the latter to an individual’s background knowledge and the former to what I call “total scientific background knowledge”. (shrink)

The Uniform Determination of Death Act (UDDA) provides that “an individual who has sustained either (1) irreversible cessation of circulatory and respiratory functions or (2) irreversible cessation of all functions of the entire brain, including the brain stem, is dead.” We show that the UDDA contains two conflicting interpretations of the phrase “cessation of functions.” By one interpretation, what matters for the determination of death is the cessation of spontaneous functions only, regardless of their generation by artificial means. By the (...) other, what matters is the cessation of both spontaneous and artificially supported functions. Because each UDDA criterion uses a different interpretation, the law is conceptually inconsistent. A single consistent interpretation would lead to the conclusion that conscious individuals whose respiratory and circulatory functions are artificially supported are actually dead, or that individuals whose brain is entirely and irreversibly destroyed may be alive. We explore solutions to mitigate the inconsistency. (shrink)

How do opinion diversity and belief polarisation affect epistemic group decision-making, particularly if decisions must be made without delay and on the basis of permissive evidence? In an agent-based model, we track the consistency of group opinions aggregated through sentence-wise majority voting. Simulations on the model reveal that high opinion diversity, but not polarisation, incurs a significant inconsistency risk. These results indicate that epistemic group decisions based on permissive evidence can be particularly difficult for diverse groups. The results also (...) improve our understanding of what can reasonably be expected of expert groups, and where expert advice might have limits. (shrink)

Inferentialists about scientific representation hold that an apparatus’s representing a target system consists in the apparatus allowing “surrogative inferences” about the target. I argue that a serious problem for inferentialism arises from the fact that many scientific theories and models contain internal inconsistencies. Inferentialism, left unamended, implies that inconsistent scientific models have unlimited representational power, since an inconsistency permits any conclusion to be inferred. I consider a number of ways that inferentialists can respond to this challenge before suggesting my (...) own solution. I develop an analogy to exploitable glitches in a game. Even though inconsistent representational apparatuses may in some sense allow for contradictions to be generated within them, doing so violates the intended function of the apparatus’s parts and hence violates representational “gameplay.”. (shrink)

In the article ”Inconsistency of N from a not-finitist point of view” we have shown the inconsistency of N, going through a denial. Here we delete this indirect step and essentially repeat the same proof. Contextually we find a contradiction about natural number definition. Then we discuss around the rejection of infinity.

The most pressing difficulty coherentism faces is, I believe, the problem of justified inconsistent beliefs. In a nutshell, there are cases in which our beliefs appear to be both fully rational and justified, and yet the contents of the beliefs are inconsistent, often knowingly so. This fact contradicts the seemingly obvious idea that a minimal requirement for coherence is logical consistency. Here, I present a solution to one version of this problem.

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)

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.

Despite being very common in both public and private argumentation, accusations of selective application of general premises, also known as “whataboutisms”, have been mostly overlooked in argumentation studies, where they are, at most, taken as accusations of inconsistency. Here I will defend an account according to which allegations of this sort can express the suspicion that the argumentation put forward by one party does not reflect his or her actual standpoint and reasons. Distinguishing this kind of argumentative moves is (...) important for evaluating its appropriateness in critical discussions where knowing the honest opinion of arguers is relevant, as in political controversies or interpersonal communication. (shrink)

One of the most expected properties of a logical system is that it can be algebraizable, in the sense that an algebraic counterpart of the deductive machinery could be found. Since the inception of da Costa's paraconsistent calculi, an algebraic equivalent for such systems have been searched. It is known that these systems are non self-extensional (i.e., they do not satisfy the replacement property). More than this, they are not algebraizable in the sense of Blok-Pigozzi. The same negative results hold (...) for several systems of the hierarchy of paraconsistent logics known as Logics of Formal Inconsistency (LFIs). Because of this, these logics are uniquely characterized by semantics of non-deterministic kind. This paper offers a solution for two open problems in the domain of paraconsistency, in particular connected to algebraization of LFIs, by obtaining several LFIs weaker than C1, each of one is algebraizable in the standard Lindenbaum-Tarski's sense by a suitable variety of Boolean algebras extended with operators. This means that such LFIs satisfy the replacement property. The weakest LFI satisfying replacement presented here is called RmbC, which is obtained from the basic LFI called mbC. Some axiomatic extensions of RmbC are also studied, and in addition a neighborhood semantics is defined for such systems. It is shown that RmbC can be defined within the minimal bimodal non-normal logic E+E defined by the fusion of the non-normal modal logic E with itself. Finally, the framework is extended to first-order languages. RQmbC, the quantified extension of RmbC, is shown to be sound and complete w.r.t. BALFI semantics. (shrink)

Moral contextualism is the view that claims like ‘A ought to X’ are implicitly relative to some (contextually variable) standard. This leads to a problem: what are fundamental moral claims like ‘You ought to maximize happiness’ relative to? If this claim is relative to a utilitarian standard, then its truth conditions are trivial: ‘Relative to utilitarianism, you ought to maximize happiness’. But it certainly doesn’t seem trivial that you ought to maximize happiness (utilitarianism is a highly controversial position). Some people (...) believe this problem is a reason to prefer a realist or error theoretic semantics of morals. I argue two things: first, that plausible versions of all these theories are afflicted by the problem equally, and second, that any solution available to the realist and error theorist is also available to the contextualist. So the problem of triviality does not favour noncontextualist views of moral language. (shrink)

In this paper I will explore the question whether the Trivialization construction of transparent intensional logic (TIL) can be understood in terms of the Execution construction, specifically, in terms of its degenerate case known as the 0-Execution. My answer will be positive and the apparent contrast between the intuitive understanding of Trivialization and 0-Execution will be explained as a matter of distinct yet related informal perspectives, not as a matter of technical or conceptual differences.

The problem of how to accommodate inconsistencies has attracted quite a number of researchers, in particular, in the area of database theory. The problem is also of concern in the study of belief change. For inconsistent beliefs are ubiquitous. However, comparatively little work has been devoted to discussing the problem in the literature of belief change. In this paper, I examine how adequate the AGM theory is as a logical framework for belief change involving inconsistencies. The technique is to apply (...) to Grove’s sphere system, a semantical representation of the AGM theory, logics that do not infer everything from contradictory premises, viz., paraconsistent logics. I use three paraconsistent logics and discuss three sphere systems that are based on them. I then examine the completeness of the postulates of the AGM theory with respect to the systems. At the end, I discuss some philosophical implications of the examination. (shrink)

In this article we derived an important example of the inconsistent countable set in second order ZFC (ZFC_2) with the full second-order semantics. Main results: (i) :~Con(ZFC2_); (ii) let k be an inaccessible cardinal, V is an standard model of ZFC (ZFC_2) and H_k is a set of all sets having hereditary size less then k; then : ~Con(ZFC + E(V)(V = Hk)):.

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

In a recent pair of publications, Richard Bradley has offered two novel no-go theorems involving the principle of Preservation for conditionals, which guarantees that one’s prior conditional beliefs will exhibit a certain degree of inertia in the face of a change in one’s non-conditional beliefs. We first note that Bradley’s original discussions of these results—in which he finds motivation for rejecting Preservation, first in a principle of Commutativity, then in a doxastic analogue of the rule of modus ponens —are problematic (...) in a significant number of respects. We then turn to a recent U-turn on his part, in which he winds up rescinding his commitment to modus ponens, on the grounds of a tension with the rule of Import-Export for conditionals. Here we offer an important positive contribution to the literature, settling the following crucial question that Bradley leaves unanswered: assuming that one gives up on full-blown modus ponens on the grounds of its incompatibility with Import-Export, what weakened version of the principle should one be settling for instead? Our discussion of the issue turns out to unearth an interesting connection between epistemic undermining and the apparent failures of modus ponens in McGee’s famous counterexamples. (shrink)

This paper accomplishes three goals. First, the essay demonstrates that Edmund Husserl’s theory of meaning consciousness from his 1901 Logical Investigations is internally inconsistent and falls apart upon closer inspection. I show that Husserl, in 1901, describes non-intuitive meaning consciousness as a direct parallel or as a ‘mirror’ of intuitive consciousness. He claims that non-intuitive meaning acts, like intuitions, have substance and represent their objects. I reveal that, by defining meaning acts in this way, Husserl cannot account for our experiences (...) of countersensical, absurd, or impossible meanings. Second, I examine how Husserl came to recognize this 1901 mistake in his 1913/14 Revisions to the Sixth Logical Investigation. I discuss how he accordingly reformulates his understanding of non-intuitive meaning acts from the ground up in those Revisions, where this also allows for him to properly account for the experience of impossible meanings. Instead of describing them as mirrors of intuitions, Husserl takes non-intuitive meaning acts to be modifications of intuitions, where they have no substance and do not represent their objects. Finally, in the conclusion to this essay, I demonstrate how this fundamental change to his understanding of meaning consciousness forced Husserl to revise other central tenets of his philosophy, such that the trajectory of his thought can only be properly understood in light of these revisions to his theory of non-intuitive meaning consciousness. (shrink)

Presentists argue that only present entities exist absolutely and unrestrictedly. Presentism, which itself is a temporal analog of the modal doctrine of actualism, is an ontological idea about time and existence against theories such as eternalism, possibilism, and growing block theory. Thus, presentists deny the existence of atemporal or timeless entities and describe presentism as a version of the (A-theory), which makes a difference between present, past, and future. Also, presentists are not able to ontologically, justify the existence of some (...) entities such as Socrates and the year 3000 in the past and the future and the relations involving non-present objects like ‘Abraham Lincoln was taller than Napoleon Bonaparte’. However, presentism is altered via the addition of an abstract four-dimensional manifold of ersatz time, which is a type of (B-theory) series, to identify all ontological entities and justify the dynamic world. This inquiry is an attempt to put a completely different perspective on presentism and, the result obtained that despite the new conceptualization of time, there is an inconsistency between time and being in presentism. Therefore, presentists have failed to determine the ontological identification of cross-temporal relations, reference and propositions, and truth-makers. Also, whatever the final outcome of the debate between presentism and other views is significantly eternalism, according to ersatz presentism, it is hard to make sense of the idea that things change from one moment to the next. (shrink)

Though the social world is real and objective, the way that social facts arise out of other facts is in an important way shaped by human thought, talk and behaviour. Building on recent work in social ontology, I describe a mechanism whereby this distinctive malleability of social facts, combined with the possibility of basic human error, makes it possible for a consistent physical reality to ground an inconsistent social reality. I explore various ways of resisting the prima facie case for (...) social inconsistency. I conclude, however, that the prima facie case survives scrutiny, and draw out some of the ramifications. (shrink)