According to physicalism, everything is physical, namely there are no entities (or no more restricted sorts of entities) that are not physical. In this paper, I shall examine the truth of this thesis by presenting a triviality objection against physicalism that is somehow similar to the one advanced against presentism. Firstly, I shall distinguish between two different definitions of the physical (roughly, every entity is physical-1 iff it has some feature F, such as impenetrability or exact spatio-temporal location, while (...) every entity is physical-2 iff it is accepted by some ideal, true and complete physical theory) and between unrestricted and restricted versions of physicalism (according to the former ones, physicalism is true for every entity while, according to the latter ones, it is true only with regard to some restricted domain of entities). Secondly, I shall argue that physicalists have to deal with six different problems: the triviality of some versions of physicalism, the content-indeterminacy of the physical and the justification of the “faith” according to which we will formulate some ideal, true and complete physical theory (given the definition of the physical-2), the restricted domain problem (so that restricted versions of physicalism seem not to exclude the existence of seemingly non-physical entities), the (possible and plausible) incompatibility between the two different definitions of the physical, the extension of the physical investigation problem. (shrink)

This paper challenges defenders/advocates of the semantic-completeness route towards gluts to explain, in simple and plausible terms, why the ‘trivializer paradox’, framed in terms of closure relatives on theories, fails to undermine their argument.

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)

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.

A triviality result for what Lewis called “the Desire by Necessity Thesis” and Broome : 265–267, 1991) called “the Desire as Expectation Thesis” is presented. The result shows that this thesis and three other reasonable conditions can be jointly satisfied only in trivial cases. Some meta-ethical implications of the result are discussed. The discussion also highlights several issues regarding Lewis ’ original triviality result for “the Desire as Belief Thesis” that have not been properly understood in the literature.

Presentism is typically characterised as the thesis that everything is present, and therefore there are no dinosaurs or Martian presidential inaugurations. Putting aside the vexed question of exactly what it is to be present in this context, this thesis seems quite straightforward. However, a number of authors—such as Merricks, Lombard, Meyer, Tallant and Sakon —have argued that Presentism so characterised is either trivially true or false even by Presentist lights. This is the so-called Triviality Argument against Presentism. In this (...) paper I show that three of the four premises of the Triviality Argument are plausibly false. I conclude that Presentists have nothing to fear from the Triviality Argument. (shrink)

We show that any relational generic structure whose theory has finite closure and amalgamation over closed sets is stable CM-trivial with weak elimination of imaginaries.

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.

The strongest possible Lewisian triviality result for the indicative conditional is proven.

Suppose that people in the affluent countries can easily save the lives of the starving needy in poor countries. Then, three points seem to follow. First, it is wrong for these people not to make the easy rescue . Second, it is wrong to stop making the easy rescue even if they have made many rescues already . Third, if we accept the first two points, the demands of morality are super-extreme. That is, people have to keep making trivial sacrifices (...) until there is no more trivial sacrifices to make . Here, predictably, our commonsense will resist the third point. However, I argue in this paper that, since the first two points are harder to refute, we have to accept the third point anyway. (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)

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)

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)

The thesis that probabilities of conditionals are conditional probabilities has putatively been refuted many times by so-called ‘triviality results’, although it has also enjoyed a number of resurrections. In this paper I assault it yet again with a new such result. I begin by motivating the thesis and discussing some of the philosophical ramifications of its fluctuating fortunes. I will canvas various reasons, old and new, why the thesis seems plausible, and why we should care about its fate. I (...) will look at some objections to Lewis’s famous triviality results, and thus some reasons for the pursuit of further triviality results. I will generalize Lewis’s results in ways that meet the objections. I will conclude with some reflections on the demise of the thesis—or otherwise. (shrink)

According to contextualism, a gender term such as ‘woman’ does not invariantly refer to a specific social or biological kind. Instead, gender terms have different extensions depending on the context of utterance. Contextualism accommodates that speakers are perfectly able to use gender terms in very different ways and still be coherent and successful in their communicative exchanges. However, while the flexibility of contextualism is its primary asset, it has also turned out to be its potential demise. The worry is that (...) the view not only makes trans-including claims true but also allows that trans-excluding claims can be true and therefore, does justice to the claims of trans people only in a trivial sense. This paper defends the view that contextualists can respond to this worry by showing why trans-excluding claims are often morally problematic even in contexts where they are true. Contextualists are well-equipped to say that when speakers insist on using gender terms in trans-excluding ways, they engage in a meta-linguistic negotiation about how gender terms ought to be used – where using them trans-excluding is treated as normatively superior. This constitutes a kind of epistemic injustice. (shrink)

After indicating why this is needed, the paper proves a non-triviality result for paraconsistent theory containing arithmetic, naive truth and denotation predicates, and descriptions. The result is obtained by dualising a construction of Kroon. Its most notable feature is that there is a trivial object- one that has every property.

We study the connection between Schnorr triviality and genericity. We show that while no 2-generic is Turing equivalent to a Schnorr trivial and no 1-generic is tt-equivalent to a Schnorr trivial, there is a 1-generic that is Turing equivalent to a Schnorr trivial. However, every such 1-generic must be high. As a corollary, we prove that not all K-trivials are Schnorr trivial. We also use these techniques to extend a previous result and show that the bases of cones of (...) Schnorr trivial Turing degrees are precisely those whose jumps are at least 0". (shrink)

"Making Sense of Nonsense: Trivial Remarks on the Nature of Language" is an inquiry into the nature and significance of nonsense for philosophers and other human beings. Philosophers have been accused of indulging in nonsense. Wittgenstein complains that philosophers take language on holiday. If an utterance is nonsense in virtue of being on holiday, we might expect meaningful utterances to be meaningful in virtue of their being at work, at home. When we look at language at home, we find that, (...) despite the tribute philosophers of language ordinarily pay to the a priori, meaning is a most contingent and subjective family of phenomena. On the rough ground of everyday discourse, we find language stamped with the desires and agendas of certain groups of mammals. Language shows us its rough edges when we clear away the unarticulated presuppositions smuggled in by dominant philosophical methodology. There are a number of strategies for attaining an unclouded vantage point on language. One is to imagine oneself into the position of someone to whom our language and way of life is unfamiliar. Another is to actually occupy a point of view from which the language and way of life we take for granted begins to seem strange. ;The theory of meaning that emerges from the kind of attention to language here described can be stated thus: meaning is grounded in concernful engagement with the world. Or, to put it another way: we talk about what we care about. As a result, language can serve as a deep reserve of human history. What it tells us about ourselves is not always pleasant. As the language reveals the concerns and agendas of speakers, it reveals the imbalances and abuses of power among those speakers. Insofar as language constructs the worlds we inhabit, the injustices and prejudices we find in language are mirror images of reality as we know it. The good news is the liberatory potential of our realization of the extent to which meaning, and hence reality, are "man-made." This potential is realized in the work of many radical lesbian feminist philosophers. (shrink)

S. Kierkegaard argued that our highest task as humans is to realize an “intensified” or “developed” form of subjectivity—his name for self-responsible agency. A self-responsible agent is not only responsible for her actions. She also bears responsibility for the individual that she is. In this paper, I review Kierkegaard’s account of the role that our capacity for reflective self-evaluation plays in making us responsible for ourselves. It is in the exercise of this capacity that we can go from being subjective (...) in a degraded sense—merely being an idiosyncratic jumble of accidental and arbitrary attitudes and affects—to being a subject in the ideal or eminent sense. The latter requires the exercise of my capacity for reflective self-evaluation, since it involves recognizing, identifying with, and reinforcing those aspects of my overall make-up that allow me to express successfully a coherent way of being in the world. Kierkegaard argues that taking immortality seriously is one way to achieve the right kind of reflective stance on one’s own character or personality. Thus, Kierkegaard argues that immortality as a theoretical posit can contribute to one’s effort to own or assume responsibility for being the person one is. (shrink)

In the present paper I analyse the modularity thesis and, more specifically, the thesis of domain-specificity of processing. I argue that this thesis is not trivial only under the assumption of a variety of processes which differ from each other at the implementation level; otherwise, the variety of cognitive processes can only be explained as emergent on the basic mechanism of associative activation in that it operates on domain-specific representations, which is something that no one would deny. But that assumption (...) is untenable: there are no other processes than associative activation (and inhibition) at the implementation level. Any claim to the contrary is the result of a conceptual confusion between two senses of “associative”: a behavioural one, relative to which there are cognitive processes that exceed the ability to code elementary spatio-temporal contingencies, and one that lies instead at the implementation level. Since the assumption of a plurality of processes at the implementation level is untenable, the only viable interpretation of modularism (as far as domain-specificity is concerned) is a trivial one. By this I do not mean that the thesis is devoid of any content. However, its content is scarcely debatable, and far less thrilling than the debate has suggested so far. (shrink)

“Triviality arguments” against functionalism in the philosophy of mind hold that the claim that some complex physical system exhibits a given functional organization is either trivial or has much less content than is usually supposed. I survey several earlier arguments of this kind, and present a new one that overcomes some limitations in the earlier arguments. Resisting triviality arguments is possible, but requires functionalists to revise popular views about the “autonomy” of functional description.

This paper investigates the link between informational consequence and credence. I first suggest a natural constraint, namely that informational consequence should preserve certainty: on any rational credence distribution, when the premises of an informational inferences have credence 1, the conclusion also has credence 1. Then I show that the certainty‐preserving constraint leads to triviality. In particular, the following three claims are incompatible: (i) informational consequence is extensionally distinct from classical consequence; (ii) informational inferences preserve certainty; (iii) credences obey (a (...) subset of) classical Bayesian constraints. The proof is straightforward, but the theoretical implications are substantial. Informational theorists need to either give up the idea that credence applies to epistemic discourse, or develop a nonclassical theory of credence and credal update. Moreover, the result also suggests that there is a connection between informational consequence and triviality results, including classical triviality results like Lewis's. (shrink)

We study the theory of the structure induced by parameter free formulas on a “dense” algebraically independent subset of a model of a geometric theory T. We show that while being a trivial geometric theory, inherits most of the model theoretic complexity of T related to stability, simplicity, rosiness, the NIP and the NTP2. In particular, we show that T is strongly minimal, supersimple of SU‐rank 1, has the NIP or the NTP2 exactly when has these properties. We show that (...) if T is superrosy of thorn rank 1, then so is, and that the converse holds if T satisfies acl = dcl. (shrink)

We show that every reduct of a stable. CM-trivial theory of finite U-rank is CM-trivial.

Opponents of the computational theory of mind have held that the theory is devoid of explanatory content, since whatever computational procedures are said to account for our cognitive attributes will also be realized by a host of other ‘deviant’ physical systems, such as buckets of water and possibly even stones. Such ‘triviality’ claims rely on a simple mapping account of physical implementation. Hence defenders of CTM traditionally attempt to block the trivialization critique by advocating additional constraints on the implementation (...) relation. However, instead of attempting to ‘save’ CTM by constraining the account of physical implementation, I argue that the general form of the triviality argument is invalid. I provide a counterexample scenario, and show that SMA is in fact consistent with empirically rich and theoretically plausible versions of CTM. This move requires rejection of the computational sufficiency thesis, which I argue is scientifically unjustified in any case. By shifting the ‘burden of explanatory force’ away from the concept of physical implementation, and instead placing it on salient aspects of the target phenomenon to be explained, it’s possible to retain a maximally liberal and unfettered view of physical implementation, and at the same time defuse the triviality arguments that have motivated defenders of CTM to impose various theory-laden constraints on SMA. (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)

We define a generalized version of CM-triviality, and show that in the presence of enough regular types, or solubility, a stable CM-trivial group is nilpotent-by-finite. A torsion-free small CM-trivial stable group is abelian and connected. The first result makes use of a generalized version of the analysis of bad groups.

Abstract In Reasons and Persons, Derek Parfit argues that personal identity is indeterminate and that identity is not what matters in personal survival. Parfit argues that traditional views of personal identity have counterintuitive consequences and that they violate a plausible requirement, suggested by Bernard Williams, that must be met by any acceptable criterion of identity. Parfit argues that, unlike traditional determinate views of personal identity, his view succeeds in accommodating intuitions and in meeting (an analogue to) Williams' requirement. I argue (...) that Parfit's view has more counterintuitive consequences than do the traditional views of identity. Though the traditional views do seem to violate Williams' requirement, Parfit's view fares no better. In fact, it seems that any theory of personal survival that appeals to connections that may hold to a greater or lesser extent will fail to meet the relevant requirement. This is an important general point, since the requirement is a plausible one. (shrink)

EveryK-trivial set is computable from an incomplete Martin-Löf random set, i.e., a Martin-Löf random set that does not compute the halting problem.

The paper generalizes Van McGee's well-known result that there are many maximal consistent sets of instances of Tarski's schema to a number of non-classical theories of truth. It is shown that if a non-classical theory rejects some classically valid principle in order to avoid the truth-theoretic paradoxes, then there will be many maximal non-trivial sets of instances of that principle that the non-classical theorist could in principle endorse. On the basis of this it is argued that the idea of classical (...) recapture, which plays such an important role for non-classical logicians, can only be pushed so far. (shrink)

In the present paper we analyse how intuitionist negation relates to the concept of triviality. A proposition is trivial if it implies every other proposition. We claim that for natural deduction intuitionist logic such concept affords us a negation introduction rule schema that corresponds by the inversion principle to the usual negation elimination shcema, ex contradictionerm quodlibet.1.

THE MYTH OF NEUROSIS: OVERCOMING THE ILLNESS EXCUSE by Garth Wood New York: Harper and Row, 1986. 294 pp., $15.45, $7.95 paper.

In their recent contribution to this journal, Brian D. Earp, Anders Sandberg, and Julian Savulescu argue that "the 'medicalization of love' need not necessarily be problematic, on balance, but could plausibly be expected to have either good or bad consequences depending upon how it unfolds." Although I find myself in agreement with the majority of the points the authors make to this end, as well as with the general thrust of their position, I am nevertheless left feeling rather unsatisfied by (...) their overall exposition. This is largely because they fail to provide any substantial love-specific argument, as I demonstrate in this paper. (shrink)

Many philosophers believe there to be a fundamental difference between the present and past and future times, but they tend to disagree amongst themselves about what this difference is. Some think that the present is singled out by consciousness, while others believe that it marks the position to which the flow of time has advanced. According to presentism, the current moment is ontologically privileged: nothing exists that is not present. My aim in this chapter is to argue that this particular (...) attempt at distinguishing the present from other times is unsuccessful. (shrink)

Bypassing Lewis’ Triviality Results. A Kripke-Style Partial Semantics for Compounds of Adams’ Conditionals Alberto Mura University of Sassari Abstract According to Lewis’ Triviality Results (LTR), conditionals cannot satisfy the equa­tion (E) P(C if A) = P(C | A), except in trivial cases. Ernst Adams (1975), however, provided a probabilistic semantics for the so-called simple conditionals that also sat­isfies equation (E) and provides a probabilistic counterpart of logical consequence (called p-entailment). Adams’ probabilistic semantics is coextensive to Stalnaker­Thomason’s (1970) and (...) Lewis’ (1973) semantics as far as simple conditionals are concerned. A theorem, proved in McGee 1981, shows that no truth-functional many-valued logic allows a relation of logical consequence coextensive with Adams’ p-entailment. This paper presents a modified modal (Kripke-style) version of de Finetti’s se­mantics that escapes McGee’s result and provides a general truth-conditional se­mantics for indicative conditionals. It agrees with Adams’ logic and is not affected by LTR. The new framework encompasses and extends Adams’ probabilistic se­mantics (APS) to compounds of conditionals. A generalised set of axioms for prob­ability over the set of tri-events is provided, which coincide with the standard axioms over the set of the two-valued ordinary sentences. -/- Keywords: Conditionals, Probability logic, de Finetti, Tri-events, Adams’ logic, Stal­naker’s thesis, Partial logic, Lewis’ triviality results, Ramsey test. (shrink)

In this paper I criticize Wright’s claim that Cognitive Command is a significant test for discerning realist from antirealist discourses. The antirealist semantics explicitly advocated by Wright, entails that every discourse whose truth predicate is superassertibility exerts Cognitive Command, and so that every assertoric discourse deserves a realistic treatment. Whenever two disputants disagree as to the truth value of a sentence expressible within the discourse, provided that they master the relevant vocabulary, they must have committed a cognitive mistake. For they (...) disagree as to the warranted assertibility of the sentence in the light of the available evidence: hence either one of them misrepresents it, or one of them fails to to take into account its evidential status. (shrink)

According to Tarski, a theory of truth for a language L is a theory which logically implies for each sentence S of L a sentence of the form:S is true-in-L if and only if p,where rS1 is replaced by a canonical description of a sentence of L and rp1 is replaced by that sentence if L is contained in the metalanguage or by a translation of S if it is not so contained. Tarski constructed consistent and finitely axiomatized theories of (...) truth for various formal languages and showed how to explicitly define ‘is true in L’ within these theories. We all agree that Tarski's theories of truth have enormous philosophical significance, but there is much less agreement on precisely what that significance consists in. (shrink)

This article is an extension of that published in the Fall, 1987, issue of Theory and Research in Social Education in which analytic categories were determined and four series of primary-grade social studies textbooks were examined using those categories. The present study expands the earlier categories and examines two additional text series. The findings of this study reflect the findings of the previous study in that we read no texts to which we could give whole-hearted support.

In this paper we explain that the paraconsistent logic LP promoted by Graham Priest can only be supported by trivial dialetheists, i.e., those who believe that all sentences are dialetheias.

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)

We give several characterizations of Schnorr trivial sets, including a new lowness notion for Schnorr triviality based on truth-table reducibility. These characterizations allow us to see not only that some natural classes of sets, including maximal sets, are composed entirely of Schnorr trivials, but also that the Schnorr trivial sets form an ideal in the truth-table degrees but not the weak truth-table degrees. This answers a question of Downey, Griffiths and LaForte.

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)