It is often claimed that the debate between presentism and eternalism is merely verbal, because when we use tensed, detensed or tenseless notions of existence, there is no difference in the accepted metaphysical statements between the adherents of both views. On the contrary, it is shown in this paper that when we express their positions making use, in accordance with intentions of the presentists and the eternalists, of the tensed notion of existence (in the case of the presentists) and the (...) detensed or tenseless notion (in the case of the eternalists), the controversy remains deep and very important for us, because both ontological claims express a different attitude to the existence of the flow of time. It is shown that not only does the proposed approach to presentism and eternalism exactly express the intentions of the adherents of both views but it also offers a better understanding of them joining together seemingly different theses maintained by the presentists and the eternalists, and explaining at the same time the dynamism of the presentists' ontology. The paper takes for granted that we should assess metaphysical theories in a similar way as we assess scientific theories, that is on the basis of their explanatory value. (shrink)

We defend the view that defines the rigidity of general terms as sameness of designated universal across possible worlds from the objection that such a characterization is incapable of distinguishing rigid from non-rigid readings of general terms and, thus, that it trivializes the notion of rigidity. We also argue that previous attempts to offer a solution to the trivialization problem do no succeed.

According to the simple proposal about rigidity for predicates, a predicate is rigid (roughly) if it signifies the same property across the relevant worlds. Recent critics claim that this suffers from a trivialization problem: any predicate whatsoever would turn out to be trivially rigid, according to the proposal. In this paper a corresponding "problem" for ordinary singular terms is considered. A natural solution is provided by intuitions concerning the actual truth-value of identity statements involving them. The simple proposal (...) for predicates is then defended, by exploiting corresponding intuitions concerning statements involving their nominalizations, in an analogous manner. (shrink)

In this paper I am concerned with the problem of applying the notion of rigidity to general terms. In Naming and Necessity, Kripke has clearly suggested that we should include some general terms among the rigid ones, namely, those common nouns semantically correlated with natural substances, species and phenomena, in general, natural kinds -'water', 'tiger', 'heat'- and some adjectives -'red', 'hot', 'loud'. However, the notion of rigidity has been defined for singular terms; after all, the notion that Kripke has (...) provided us with is the notion of a rigid designator. But general terms do not designate single individuals: rather, they apply to many of them. In sum, the original concept of rigidity cannot be straightforwardly applied to general terms: it has to be somehow redefined in order to make it cover them. As is known, two main positions have been put forward to accomplish that task: the identity of designation conception, according to which a rigid general term is one that designates the same property or kind in all possible worlds, and the essentialist conception, which conceives of a rigid general term as an essentialist one, namely, a term that expresses an essential property of an object. My purpose in the present paper is to defend a particular version of the identity of designation conception: on the proposed approach, a rigid general term will be one that expresses the same property in all possible worlds and names the property it expresses. In my opinion, the position can be established on the basis of an inference to the best explanation of our intuitive interpretation and evaluation, relative to counterfactual circumstances, of statements containing different kinds of general terms, which is strictly analogous to our intuitive interpretation and evaluation, relative to such circumstances, of statements containing different kinds of singular ones. I will argue that it is possible to offer a new solution to the trivialization problem that is thought to threaten all versions of the identity of designation conception of rigidity. Finally, I will also sketch a solution to the so-called 'over-generalization and under-generalization problems', both closely related to the above-mentioned one. (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 article, I argue that desire-satisfaction theories of well-being face the problem of trivially satisfied desires. First, I motivate the claim that desire-satisfaction theories need an aggregation principle and reconstruct four possible principles desire-satisfactionists can adopt. Second, I contend that one of these principles seems implausible on numerous counts. Third, I argue that the other three principles, which hold that the creation and satisfaction of new desires is good for individuals and can be called proliferationist, are vulnerable to (...) an objection from trivially satisfied desires. They implausibly imply that forming desires that are trivially satisfied is good for individuals. Finally, I argue that trivially satisfied desires may also worsen desire-satisfactionism's classical problem of pointless desires. Together, these claims constitute a challenge to desire-satisfactionism. (shrink)

This study investigated the cognitive processes involved in inductive reasoning. Sixteen undergraduates solved quadratic function–finding problems and provided concurrent verbal protocols. Three fundamental areas of inductive activity were identified: Data Gathering, Pattern Finding, and Hypothesis Generation. These activities are evident in three different strategies that they used to successfully find functions. In all three strategies, Pattern Finding played a critical role not previously identified in the literature. In the most common strategy, called the Pursuit strategy, participants created new quantities from (...) x and y, detected patterns in these quantities, and expressed these patterns in terms of x. These expressions were then built into full hypotheses. The processes involved in this strategy are instantiated in an ACT‐based model that simulates both successful and unsuccessful performance. The protocols and the model suggest that numerical knowledge is essential to the detection of patterns and, therefore, to higher‐order problem solving. (shrink)

As it stands, Frege’s semantic theory does not provide sufficient general keys for interpreting assertible sentences at different levels of complexity, such as (a) counterfactual-modal-intensional sentences and (b) extensional sentences. It is possible to devise that general key by adding non-classical parameters such as possible worlds, which allow sentences with a high degree of non-extensional complexity to occupy a trivial place in Tarski’s hierarchy as T-scheme-eligible substitutes. The paper argues that finding these non-false (if true) conditions under which complex propositions (...) can be trivially treated as eligible T-scheme substitutes is not trivial. It is a challenge that requires several consistency improvements to deal with various competing extensions of the predicate “true”. We will conclude that Frege-Tarski’s semantic conception (enriched by non- classical presuppositions), misrepresents that challenge. It distorts the problem we face in daily practice to strengthen our assertion systems, plan successful assertion strategies, and protect our assertions from semantic value reversals. The true challenge for us is pragmatic and cannot confuse (1) complicated scientific and empirical conditions of assertiveness with (2) the rewardable scoring-conditions under which one learns to use sentences in his native language. (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.

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.

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)

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)

Presentism is usually understood as the thesis that only the present exists whereas the rival theory of eternalism is usually understood as the thesis that past, present, and future things are all equally real. The significance of this debate has been threatened by the so-called triviality objection, which allegedly shows that the presentist thesis is either trivially true or obviously false: Presentism is trivially true if it is read as saying that everything that exists now is present, and it (...) is obviously false if read as saying that everything that has existed, exits or will exist is present. If eternalism is taken as the negation of presentism, it is also either trivially false or obviously true. In this paper, I try to respond to the triviality objection on behalf of presentism. In second section, I will examine how the argument proceeds. In third section, I will reflect on three possible ways to respond but will argue that none of them succeeds in giving a satisfactory solution. I will then try to clarify the core idea of presentism and to suggest that if we characterise presentism accurately, the problem will disappear. In fourth section, I will offer a plausible definition of presentism and will show how it can avoid the triviality objection and demonstrate why it is advantageous to accept the version of presentism I offer. (shrink)

§1. Introduction. The classical propositional calculus has an undeserved reputation among logicians as being essentially trivial. I hope to convince the reader that it presents some of the most challenging and intriguing problems in modern logic. Although the problem of the complexity of propositional proofs is very natural, it has been investigated systematically only since the late 1960s. Interest in the problem arose from two fields connected with computers, automated theorem proving and computational complexity theory. The earliest paper (...) in the subject is a ground-breaking article by Tseitin [62], the published version of a talk given in 1966 at a Leningrad seminar. In the three decades since that talk, substantial progress has been made in determining the relative complexity of proof systems, and in proving strong lower bounds for some restricted proof systems. However, major problems remain to challenge researchers. The present paper provides a survey of the field, and of some of the techniques that have proved successful in deriving lower bounds on the complexity of proofs. A major area only touched upon here is the proof theory of bounded arithmetic and its relation to the complexity of propositional proofs. The reader is referred to the book by Buss [10] for background in bounded arithmetic. The forthcoming book by Krajíček [40] also gives a good introduction to bounded arithmetic, as well as covering most of the basic results in complexity of propositional proofs. (shrink)

The origin of Paraconsistent Logic is closely related with the argument that from the assertion of two mutually contradictory statements any other statement can be deduced, which can be referred to as ex contradict!one sequitur quodlibet (ECSQ). Despite its medieval origin, only in the 1930s did it become the main reason for the unfeasibility of having contradictions in a deductive system. The purpose of this paper is to study what happened before: from Principia Mathematica to that time, when it became (...) well established. The main historical claims that I am going to advance are the following: the first explicit use of ECSQ as the main argument for supporting the necessity of excluding any contradiction from deductive systems is to be found in the first edition (1928) of the book Grundzüge der theoretischen Logik by Hilbert and Ackermann. At the end, I will suggest that the aim of the 20th century usage of ECSQ was to change from the centuries long philosophical discussion about contradictions to a more "technical" one. But with Paraconsistent Logic viewed as a technical solution to this restriction, the philosophical problem revives, but now with an improved understanding of it at one's disposal. (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 (...) 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)

TheK-trivial sets form an ideal in the Turing degrees, which is generated by its computably enumerable members and has an exact pair below the degree of the halting problem. The question of whether it has an exact pair in the c.e. degrees was first raised in [22, Question 4.2] and later in [25, Problem 5.5.8].We give a negative answer to this question. In fact, we show the following stronger statement in the c.e. degrees. There exists aK-trivial degreedsuch that (...) for all degreesa, bwhich are notK-trivial anda > d, b > dthere exists a degreevwhich is notK-trivial anda > v, b > v. This work sheds light to the question of the definability of theK-trivial degrees in the c.e. degrees. (shrink)

Even though the strong relationship between proof-theoretic and model-theoretic notions in one’s logical theory can be shown by soundness and completeness proofs, whether we can define the model-theoretic notions by means of the inferences in a proof system is not at all trivial. For instance, provable inferences in a proof system of classical logic in the logical framework do not determine its intended models as shown by Carnap (Formalization of logic, Harvard University Press, Cambridge, 1943), i.e., there are non-Boolean models (...) that satisfy its provable inferences. In the literature, this is known as the Categoricity problem or Carnap’s problem. In this paper, we will discuss the Categoricity problem (or Carnap’s problem) for three-valued logics K3 and LP. We will provide three different restrictions on admissible models that will deliver us categoricity results, some of which draw from the solutions provided for the Categoricity problem for classical logic in Belnap and Massey (Stud Log 49(1):67–82, 1990) and Bonnay and Westerståhl (Erkenntis 81(4):721–739, 2016). We will then argue that two of those solutions are philosophically well-motivated: (1) restricting the admissible models where negation is interpreted as a Strong Kleene truth-function, and (2) restricting the admissible models where a complex formula is assigned the third value when its immediate subformulas are assigned the third value. (shrink)

"THE central problem in moral philosophy is commonly known as the is-ought problem." So runs the opening sentence of the introduction to a recent volume of readings on this issue. [1] Taken as a statement about the preoccupations of moral philosophers of the present century, we can accept this assertion. The problem of how statements of fact are related to moral judgments has dominated recent moral philosophy. Associated with this problem is another, which has also been (...) given considerable attention - the question of how morality is to be defined. The two issues are linked, since some definitions of morality allow us to move from statements of fact to moral judgments, while others do not. In this article I shall take the two issues together, and try to show that they do not merit the amount of attention they have been given. I shall argue that the differences between the contending parties are terminological, and that there are various possible terminologies, none of which has, on balance, any great advantage over any other terminology. So instead of continuing to regard these issues as central, moral philosophers could, I believe, "agree to disagree" about the "is-ought" problem, and about the definition of morality, provided only that everyone was careful to stipulate how he was using the term "moral" and was aware of the implications and limitations of the definition he was using. Moral philosophers could then move on to consider more important issues. (shrink)

I argue that the trivial neuron doctrine as characterized by Gold & Stoljar is not trivial; it appears to be inconsistent with property dualism as well as some forms of functionalism and externalism. I suggest that the problem is not so much with the particular way in which Gold & Stoljar draw the distinction as with the unruliness of the distinction itself. Their failure to see this may be why they misunderstand the views of the Churchlands.

Proponents of Veritism believe that truth is the sole non-instrumental epistemic good. This view is often taken to entail that all truths should be of equal epistemic value. Hence, it is put under stress by the presence of trivial truths: truths to which we attach relatively little or no epistemic value. Pritchard, in the defense of Veritism, has tried to argue that the best way to understand the implications of Veritism is to think in terms of how an intellectually virtuous (...) inquirer would pursue truth. Furthermore, he thinks that such an inquirer would prefer weighty truths and set aside trivial ones. As such, he thinks that our epistemic disregard for trivial truths is just to be expected given Veritism. We argue that Pritchard’s defense of Veritism fails, and the problem of trivial truths remains a significant challenge for Veritism. (shrink)

It is a commonplace in the philosophy of physics that any local physical theory can be represented using arbitrary coordinates, simply by using tensor calculus. On the other hand, the physics literature often claims that spinors \emph{as such} cannot be represented in coordinates in a curved space-time. These commonplaces are inconsistent. What general covariance means for theories with fermions, such as electrons, is thus unclear. In fact both commonplaces are wrong. Though it is not widely known, Ogievetsky and Polubarinov constructed (...) spinors in coordinates in 1965, enhancing the unity of physics and helping to spawn particle physicists' concept of nonlinear group representations. Roughly and locally, these spinors resemble the orthonormal basis or "tetrad" formalism in the symmetric gauge, but they are conceptually self-sufficient and more economical. The typical tetrad formalism is de-Ockhamized, with six extra field components and six compensating gauge symmetries to cancel them out. The Ogievetsky-Polubarinov formalism, by contrast, is Ockhamized, with most of the fluff removed. As developed nonperturbatively by Bilyalov, it admits any coordinates at a point, but "time" must be listed first. Here "time" is defined in terms of an eigenvalue problem involving the metric components and the matrix $diag$, the product of which must have no negative eigenvalues in order to yield a real symmetric square root that is a function of the metric. Thus even formal general covariance requires reconsideration; the atlas of admissible coordinate charts should be sensitive to the types and \emph{values} of the fields involved. Apart from coordinate order and the usual spinorial two-valuedness, Ogievetsky-Polubarinov spinors form, with the metric, a nonlinear geometric object, for which important results on Lie and covariant differentiation are recalled. Such spinors avoid a spurious absolute object in the Anderson-Friedman analysis of substantive general covariance. They also permit the gauge-invariant localization of the infinite-component gravitational energy in General Relativity. Density-weighted spinors exploit the conformal invariance of the massless Dirac equation to show that the volume element is absent. Thus instead of an arbitrary nonsingular matrix with 16 components, 6 of which are gauged away by a new local $O$ gauge group and one of which is irrelevant due to conformal covariance, one can, and presumably should, use density-weighted Ogievetsky-Polubarinov spinors coupled to the 9-component symmetric square root of the part of the metric that fixes null cones. Thus $\frac{7}{16}$ of the orthonormal basis is eliminated as surplus structure. Greater unity between spinors and tensors and the like is achieved, such as regarding conservation laws. Regarding the conventionality of simultaneity, an unusually wide range of $\epsilon$ values is admissible, but some extreme values are inadmissible. Standard simultaneity uniquely makes the spinor transformation law linear and independent of the metric, because transformations among the standard Cartesian coordinate systems fall within the conformal group, for which the spinor transformation law is linear. The surprising mildness of the restrictions on coordinate order as applied to the Schwarzschild solution is exhibited. (shrink)

This paper is about the underlying logical principles of scientific theories. In particular, it concerns ex contradictione quodlibet (ECQ) the principle that anything follows from a contradiction. ECQ is valid according to classical logic, but invalid according to paraconsistent logics. Some advocates of paraconsistency claim that there are ‘real’ inconsistent theories that do not erupt with completely indiscriminate, absurd commitments. They take this as evidence in favor of paraconsistency. Michael (2016) calls this the non-triviality strategy (NTS). He argues that (...) this strategy fails in its purpose. I will show that Michael's criticism significantly over-reaches. The fundamental problem is that he places more of a burden on the advocate of paraconsistency than on the advocate of classical logic. The weaknesses in Michael's argument are symptomatic of this preferential treatment of one viewpoint in the debate over another. He does, however, make important observations that allow us to clarify some of the complexities involved in giving a logical reconstruction of a theory. I will argue that there are abductive arguments deserving of further consideration for the claim that paraconsistent logic offers the best explanation of the practice of inconsistent science. In this sense, the debate is still very much open. (shrink)

The article examines the problems of the political, developed in the modern discourse of analytical philosophy. The theoretical and methodological foundations of the work are based on views, which reflect new approaches to political phenomena in their relationship with the realities of public life, supplemented by non-trivial analytical rigorous methodologies. The clarification of the lack of unity in the analytical direction is given. The author's position is focused on the consistent study of political analysts who relied on three methodological strategies (...) – libertarian, utilitarian and Marxist. The research carried out in this article represents what contribution the analytical philosophers have made to the understanding of the political, how the meanings laid down by the representatives of the three classical concepts are transformed. In addition, it is obvious that the rationalization of the political pragmatic effect correlates with the proposed analytical methodology, which becomes in many respects decisive when making demands on the functioning power structures. In conclusion, the author summarizes the main results of the work and draws conclusions. (shrink)

This paper provides moderate criticism of so-called normative theories of thinking and reasoning. The discussion focuses on the problems of idealization, adequacy, inconsistent yet non-trivial logics, logical omniscience etc. I called them “internal” to the normative approach, because they stem from the very properties of formal systems used to model these two human activities. Some arguments, however, refer to the current theories in cognitive science, including those which are developed within “descriptive” framework.

Kirkham’s book is not a plain attempt of asking the questions like ‘What is truth?’ since it would, according to him, be one more mistake followed by confusion. The components of this four-dimensional confusion (vagueness, ambiguity, several ways of describing the same project, and one answer for two distinctly different questions about truth) find its original explanation in Kirkham’s book. Having stated that all of the previous theories of truth were just irrelevant to the question of “What is truth” because (...) when asking different questions about truth, he draws his non-trivial approach of assigning each theorist to the particular question (or ‘project’) he or she was trying to answer with his or her theory of truth. So, the main merit of Kirkham’s work is the clarification of this most urgent philosophical problem of truth on the way of metaphysics. (shrink)

Ten years after the publication of “Heng Xian and the Problem of Studying Looted Artifacts” in Dao, this rejoinder to critics begins by recapitulating my original argument, then considers the leading objections that have appeared in the interim. After dispensing with two trivial and ad hominem responses (that I am a hypocrite and an imperialist), the discussion focuses on the one serious objection, namely, that the benefits of studying looted artifacts outweigh the costs. I conclude with my reasons for (...) disagreeing with this judgment. (shrink)

The paper describes the problem for robust moral realism of explaining the supervenience of the moral on the non-moral, and examines five objections to the argument: The moral does not supervene on the descriptive, because we may owe different obligations to duplicates. If the supervenience thesis is repaired to block, it becomes trivial and easy to explain. Supervenience is a moral doctrine and should get an explanation from within normative ethics rather than metaethics. Supervenience is a conceptual truth and (...) should be explained by the nature of our concepts rather than by a metaphysical theory. The moral does not supervene on the descriptive, because moral principles are not metaphysically necessary. It concludes that none of these objections is successful, so Robust Realists do have an explanatory debt to worry about. (shrink)

According to Zagzebski, understanding something is justified by the exercise of cognitive skills and intellectual virtues the knower possesses. Zagzebski develops her view by suggesting that “understanding has internalist conditions for success”. Against this view, Grimm raises an objection: what justifies understanding is the reliability of the processes by which we come to understand, and we need not be aware of the outcome of all reliable processes. Understanding is no exception, so, given that understanding something results from reliable processes, we (...) need not always be aware of what we understand. I reply to Grimm’s objection; I argue that Zagzebski’s internalist requirement is best conceived as accessibility to conscious reflection. The accessibility condition is satisfied because understanding solves problems on the knower’s research agenda. And whenever problem-solving is non-trivial, the knower needs to reflect on what the best solving strategy is. (shrink)

As anyone who has flown out of a cloud knows, the boundaries of a cloud are a lot less sharp up close than they can appear on the ground. Even when it seems clearly true that there is one, sharply bounded, cloud up there, really there are thousands of water droplets that are neither determinately part of the cloud, nor determinately outside it. Consider any object that consists of the core of the cloud, plus an arbitrary selection of these droplets. (...) It will look like a cloud, and circumstances permitting rain like a cloud, and generally has as good a claim to be a cloud as any other object in that part of the sky. But we cannot say every such object is a cloud, else there would be millions of clouds where it seemed like there was one. And what holds for clouds holds for anything whose boundaries look less clear the closer you look at it. And that includes just about every kind of object we normally think about, including humans. Although this seems to be a merely technical puzzle, even a triviality, a surprising range of proposed solutions has emerged, many of them mutually inconsistent. It is not even settled whether a solution should come from metaphysics, or from philosophy of language, or from logic. Here we survey the options, and provide several links to the many topics related to the Problem. (shrink)

Methodological pragmatists argue that, given the dire state of the environment, the primary goal of environmentalists, including philosophers who work in environmental ethics, must be to work together to ensure that environmentally friendly policies are put into place. They must set aside their differences and not argue over their competing theoretical justifications of environmental policies, as that contributes to divisiveness among environmentalists and prevents this cooperation from occurring. The proposal to ignore disagreements over theory gets cashed out in three distinct (...) ways, however, and consequently one can identify three distinct versions of methodological pragmatism. Radical methodological pragmatists propose that environmentalists give up on the task of providing well-founded theoretical justifications for environmentally friendly policies and stop engaging in debates over these justifications; rather, they should focus on providing reasons for these policies that connect with whatever values people already have. Moderate methodological pragmatists propose that although there is nothing problematic in offering theoretical justifications in contexts where environmental philosophers disagree on what policy should be adopted, they should work together and put aside their theoretical differences where policy recommendations coincide. Finally, weak methodological pragmatists hold only that environmental philosophers should work together where their policies coincide and there are no additional practical or moral considerations that might be relevant to their ability to work together. The first two positions involve interesting claims, but they are fundamentally flawed. On the other hand, the third is unobjectionable but largely trivial. Thus, there is no reason to think that method­ological pragmatism can contribute to the resolution of problems in environmental ethics. (shrink)

Is there a nontrivial automorphism of the Turing degrees? It is a major open problem of computability theory. Past results have limited how nontrivial automorphisms could possibly be. Here we consider instead how an automorphism might be induced by a function on reals, or even by a function on integers. We show that a permutation of ω cannot induce any nontrivial automorphism of the Turing degrees of members of 2ω, and in fact any permutation that induces the trivial automorphism (...) must be computable.A main idea of the proof is to consider the members of 2ω to be probabilities, and use statistics: from random outcomes from a distribution we can compute that distribution, but not much more. (shrink)

There seem to be some very good reasons for a philosopher of science to be a deductivist about scientific reasoning. Deductivism is apparently connected with a demand for clarity and definiteness in the reconstruction of scientists' reasonings. And some philosophers even think that deductivism is the way around the problem of induction. But the deductivist image is challenged by cases of actual scientific reasoning, in which hard-to-state and thus discursively ill-defined elements of thought nonetheless significantly condition what practitioners accept (...) as cogent argument. And arguably, these problem cases abound. For example, even geometry--for most of its history--was such a problem case, despite its exactness and rigor. It took a tremendous effort on the part of Hilbert and others, to make geometry fit the deductivist image. Looking to the empirical sciences, the problems seem worse. Even the most exact and rigorous of empirical sciences--mechanics--is still the kind of problem case which geometry once was. In order for the deductivist image to fit mechanics, Hilbert's sixth problem (for mechanics) would need to be solved. This is a difficult, and perhaps ultimately impossible task, in which the success so far achieved is very limited. I shall explore some consequences of this for realism as well as for deductivism. Through discussing links between non-monotonicity, skills, meaning, globality in cognition, models, scientific understanding, and the ideal of rational unification, I argue that deductivists can defend their image of scientific reasoning only by trivializing it, and that for the adequate illumination of science, insights from anti-deductivism are needed as much as those which come from deductivism. (shrink)

Real-world agents do not know all consequences of what they know. But we are reluctant to say that a rational agent can fail to know some trivial consequence of what she knows. Since every consequence of what she knows can be reached via chains of trivial cot be dismissed easily, as some have attempted to do. Rather, a solution must give adequate weight to the normative requirements on rational agents’ epistemic states, without treating those agents as mathematically ideal reasoners. I’ll (...) argue that agents can fail to know trivial consequences of what they know, but never determinately. Such cases are epistemic oversights on behalf of the agent in question, and the facts about epistemic oversights are always indeterminate facts. As a result, we are never in a position to assert that such-and-such constitutes an epistemic oversight for agent i (for we may rationally assert only determinate truths). I then develop formal epistemic models according to which epistemic accessibility relations are vague. Given these models, we can show that epistemic oversights always concern indeterminate cases of knowledge. (shrink)

Hempel’s Dilemma is a challenge that has to be met by any formulation of physicalism that specifies the physical by reference to a particular physical theory. It poses the problem that if one’s specification of the physical is ‘current’ physical theory, then the physicalism which depends on it is false because current physics is false; and if the specification of the physical is a future or an ideal physics, the physicalism based on it would be trivial as it would (...) be tautologously true, or because very little (if anything at all) can be inferred from or about a physics that does not yet exist. I review the reasons for thinking that the dilemma is a perpetual problem for currentist specifications of the physical, then introduce the argument that the standard positions on the specification question are wanting because they lack a generality which physicalism is generally accepted to have. I end with a suggestion for a way forward for physicalism. (shrink)

What is aesthetic appreciation? What values is it concerned with? This dissertation consists of three distinct papers tackling problems related to these questions. Chapter One According to what I call the Merit Principle, roughly, works of art that attempt to elicit unmerited responses fail on their own terms and are thereby aesthetically flawed. In the first chapter, I show how the principle leads to paradox when applied to an undertheorized class of artworks I call “seductive artworks”, which invite an unmerited (...) first-order response in order to invite a repudiation of that response. I consider a number of unsuccessful solutions to the paradox, before rejecting the Merit Principle as it stands. I conclude by briefly discussing what is challenging about seductive artworks and by proposing a revision to the Merit Principle. Chapter Two Generally, we cooperate imaginatively with literary fictions, however bizarre, and the things authors write into their stories become true in the fiction. But for some claims, such as moral falsehoods, this seems not to be straightforwardly the case, which raises the question: Why not? The puzzles such cases raise are sometimes grouped under the heading “imaginative resistance”. In this paper, I argue against what I take to be the best attempts to dismiss the puzzles and solve them. I also tease out subtleties not sufficiently addressed in the existing literature and end by defending a unified solution of my own. The solution’s novelty lies in its giving a normative rather than psychological or alethic explanation for the puzzling phenomena. Chapter Three The third chapter looks at the tenability of understanding our engagement with sport along the lines of our engagement with works of fiction. Specifically, it addresses an incongruity in our attitudes towards the outcomes of competitive games and asks why these outcomes frequently prompt intense reactions, while often also seeming utterly trivial. I show why the temptation to understand our engagement with sport as akin to our engagement with works of fiction—as involving games of make-believe—faces serious theoretical obstacles. I end by exploring two alternative possibilities to the proposal. (shrink)

I argue that the problem of evil, As a problem with theological significance, Cannot be specified in terms simply of truth and logic. For a problem specified in this way can be seen to be either trivial or necessarily insoluble before any of the substantive issues are decided. I then argue that it should be construed as a special sort of rhetorical problem, One posed by beliefs about the compatibility of other beliefs. On the basis of (...) the logic and truth values involved I distinguish two sub-Classes of such problems, And discuss appropriate methods of resolving them. (shrink)

I defend a formulation of the Ramsey Test with a condition for accepting negations of conditionals. It is implicit in the assumptions of the triviality theorems of Gärdenfors, Harper, and Lewis; and it allows for a unified proof of those theorems, from weaker assumptions about belief revision. This leads to a proof of McGee’s thesis that iterated conditionals do not obey modus ponens. †To contact the author, please write to: Institute of Philosophy, University of Leuven, Kardinaal Mercierplein 2, B‐3000 (...) Leuven, Belgium; e‐mail: [email protected]. (shrink)

The classical theory of semantic information (ESI), as formulated by Bar-Hillel and Carnap in 1952, does not give a satisfactory account of the problem of what information, if any, analytically and/or logically true sentences have to offer. According to ESI, analytically true sentences lack informational content, and any two analytically equivalent sentences convey the same piece of information. This problem is connected with Cohen and Nagel's paradox of inference: Since the conclusion of a valid argument is contained in (...) the premises, it fails to provide any novel information. Again, ESI does not give a satisfactory account of the paradox. In this paper I propose a solution based on the distinction between empirical information and analytic information. Declarative sentences are informative due to their meanings. I construe meanings as structured hyperintensions, modelled in Transparent Intensional Logic as so-called constructions. These are abstract, algorithmically structured procedures whose constituents are sub-procedures. My main thesis is that constructions are the vehicles of information. Hence, although analytically true sentences provide no empirical information about the state of the world, they convey analytic information, in the shape of constructions prescribing how to arrive at the truths in question. Moreover, even though analytically equivalent sentences have equal empirical content, their analytic content may be different. Finally, though the empirical content of the conclusion of a valid argument is contained in the premises, its analytic content may be different from the analytic content of the premises and thus convey a new piece of information. (shrink)

I argue that there are cases in which ecumenical expressivism cannot distinguish between endorsement of certain trivial and substantive normative judgments. I consider the extent to which this problem generalizes across different formulations of the ecumenical view. I suggest that we may not be able to escape the problem if we hope to retain the ability to solve the Frege-Geach problem in the way promised by ecumenical expressivism.

The standard semantics for modality, together with the influential restrictor analysis of conditionals (Kratzer, 1986, 2012) renders conditional ought claims like “If John’s stealing, he ought to be stealing” trivially true. While this might seem like a problem specifically for the restrictor analysis, the issue is far more general. Any account must predict that modals in the consequent of a conditional sometimes receive obligatorily unrestricted interpretation, as in the example above, but sometimes appear restricted, as in, e.g., “If John’s (...) speeding, he ought to pay the fine.” And the problem runs deeper, for there are non-conditional variants of the data. Thus, the solution cannot lie in adopting a particular analysis of conditionals, nor a specific account of the interaction between conditionals and modals. Indeed, with minimal assumptions, the standard account of modality will render a myriad of claims about what one ought to, must, or may, do trivially true. Worse, the problem extends to a wide range of non-deontic modalities, including metaphysical modality. But the disaster has a remedy. I argue that the source of the problem for the standard account lies in its failure to capture an inferential evidence constraint encoded in the meaning of a wide range of modal constructions. I offer an account that captures this constraint, and show it provides a general and independently motivated solution to the problem. (shrink)

Any enthymeme can be made logically valid by adding as a suppressed premise a conditional that reiterates the argument's stated content and inferential structure in if-then form, We cannot blanketly prohibit reiteration to avoid this sort of trivialization, because some enthymemes legitimately require completion by reiterative conditionals, The solution proposed here is to allow reiterative expansions, but to rank them, other things being equal, as less charitable than nonreiterative expansions. Reiterative expansions can then be chosen as the most charitable only (...) when all nonreiterative expansions have been eliminated for independent reasons. This pluralistic model encourages experimentation with a number of different permissible expansions in evaluating enthymemes, from the least controversial or problematic to the most trivializing and the least charitable. (shrink)

In a brief and deeply interesting 2017 Acta Analytica paper, Peter Baumann argues that there are cases of necessarily incompatible but mutually consistent desires, that this is a common problem, and that there is no solution in sight. I’ll argue that Baumann fails to note certain non-trivial assumptions that must be made for the possibility of consistent incompatible desires; if consistent incompatible desires do exist then they’re sometimes beneficial; and if they are sometimes involved with problematic outcomes then the (...) mere presence of incompatibility and consistency does not cause the subject to frustrate the (more) beneficial desire. In short, if there is a problem of consistent incompatible desires then it is not the problem that Baumann identifies. (shrink)

Finite model theory is currently not one of the hot topics in the philosophy and history of mathematics, not even in the philosophy and history of mathematical logic. The philosophy of mathematics and mathematical logic has concentrated on infinite structures, closely related to foundational issues. In that context, finite models deserved only marginal attention because it was taken for granted that the study of finite structures is trivial compared to the study of infinite structures. In retrospect, research on finite structures (...) turned out to be neither trivial nor irrelevant but had an important impact on theoretical computer science. A closer look at the early history of the spectrum problem shows that the birth of finite model theory has roots in formal logic, at a time when computer science did not yet exist. (shrink)

This paper takes up a recent challenge to mechanistic approaches to computational implementation, the view that computational implementation is best explicated within a mechanistic framework. The challenge, what has been labelled “the abstraction problem”, claims that one of MAC’s central pillars – medium independence – is deeply confused when applied to the question of computational implementation. The concern is that while it makes sense to say that computational processes are abstract (i.e. medium-independent), it makes considerably less sense to say (...) that they are also concrete processes of a mechanism. After outlining the problem and its effect on MAC, I examine a recent response from Kuokkanen and Rusanen [2018. “Making Too Many Enemies: Hutto and Myin’s Attack on Computationalism.” Philosophical Explorations 21 (2): 282–294. doi:10.1080/13869795.2018.1477980]. I argue that Kuokkanen and Rusanen’s response comes up short insofar as it makes problematic trade-offs among various desiderata we have for a theory of implementation. This leads to a general dilemma for MAC: either give up being an objective theory of implementation or concede the abstraction problem and so reintroduce triviality concerns. In response, I argue that conceiving of computations as abstracta rather than illata provides a way to avoid the proposed dilemma and articulate a notion of medium independence that addresses the abstraction problem. (shrink)