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 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)

Many logical systems are such that the addition of Prior's binary connective tonk to them leads to triviality, see [1, 8]. Since tonk is given by some introduction and elimination rules in natural deduction or sequent rules in Gentzen's sequent calculus, the unwanted effects of adding tonk show that some kind of restriction has to be imposed on the acceptable operational inferences rules, in particular if these rules are regarded as definitions of the operations concerned. In this paper, a number (...) of simple observations is made showing that the unwanted phenomenon exemplified by tonk in some logics also occurs in contexts in which tonk is acceptable. In fact, in any non-trivial context, the acceptance of arbitrary introduction rules for logical operations permits operations leading to triviality. Connectives that in all non-trivial contexts lead to triviality will be called non-trivially trivializing connectives. (shrink)

The present article discusses shared epistemological characteristics of two distinct areas of research: the field of first-person inquiry and the field of quantum mechanics. We outline certain philosophical challenges that arise in each of the two lines of inquiry, and point towards the central similarity of their observational situation: the impossibility of disregarding the interrelatedness of the observed phenomena with the act of observation. We argue that this observational feature delineates a specific category of research that we call the non-trivial (...) domain. Unlike the trivial domain, non-trivial research cannot assume the view from nowhere on which the observed phenomena could be regarded as existing independently of the process of observation. Presenting first-person inquiry and quantum mechanics as two of its examples, we show that non-trivial research violates several fundamental observational presuppositions of the trivial domain, exemplified in the principles of classical physics. Drawing on Niels Bohr’s philosophy of quantum mechanics and the constructivist notion of enaction, we stress the constructive, participatory, and irreversible nature of observation in the non-trivial domain. We discuss the possibility of developing a non-representationalist epistemology of the non-trivial, and consider the implications of our discussion for research in the non-trivial domain, as well as for the general understanding of the scientific inquiry. (shrink)

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)

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 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)

The standard Lewis–Stalnaker semantics of counterfactuals, given the Strong Centering Thesis, implies that all true–true counterfactuals are trivially true. McGlynn developed a theory, based on Penczek, to rehabilitate the non-triviality of true–true counterfactuals. I show here that counterfactuals with true but irrelevant components are counterexamples to McGlynn’s account. I argue that an extended version of the connection hypothesis is sustainable, and grounds a full theory of counterfactuals explicable in a broadly standard way, if an indispensable asymmetry between semifacuals and other (...) counterfactuals is acknowledged. (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.

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 presents a range of new triviality proofs pertaining to naïve truth theory formulated in paraconsistent relevant logics. It is shown that excluded middle together with various permutation principles such as A → (B → C)⊩B → (A → C) trivialize naïve truth theory. The paper also provides some new triviality proofs which utilize the axioms ((A → B)∧ (B → C)) → (A → C) and (A → ¬A) → ¬A, the fusion connective and the Ackermann constant. An (...) overview over various ways to formulate Leibniz’s law in non-classical logics and two new triviality proofs for naïve set theory are also provided. (shrink)

We introduce and study the model-theoretic notions of absolute connectedness and type-absolute connectedness for groups. We prove that groups of rational points of split semisimple linear groups (that is, Chevalley groups) over arbitrary infinite fields are absolutely connected and characterize connected Lie groups which are type-absolutely connected. We prove that the class of type-absolutely connected group is exactly the class of discretely topologized groups with the trivial Bohr compactification, that is, the class of minimally almost periodic groups.

Your replica is created on Mars and you, on Earth, are destroyed. Parfit claims that your replica may still have what prudentially matters for you – provided that you are psychologically connected and continuous with your replica. If someone accidentally destroys the tapes containing your psychological profile used in the production of your replica and this same action fortuitously produces a functionally equivalent tape, Ehring claims that Parfit should maintain that the resulting new individual may still have what matters. Nihilism (...) about what matters follows, or so Ehring claims. I argue that Ehring is wrong and that the difference between the two ways of creating a replica is not trivial – there is no trivial survival. (shrink)

Conceptual analysis, like any exclusively theoretical activity, is far from overrated in current psychology. Such a situation can be related both to the contingent influences of contextual and historical character and to the more essential metatheoretical reasons. After a short discussion of the latter it is argued that even within a strictly empirical psychology there are non-trivial tasks that can be attached to well-defined and methodologically reliable, conceptual work. This kind of method, inspired by the ideas of Ludwig Wittgenstein, Peter (...) Strawson (conceptual grammar), and Gilbert Ryle (conceptual geography), is proposed and formally depicted as being holistic, descriptive, and connective. Finally, the newly presented framework of connective conceptual analysis is defended against the “Charge from Psychology,” in a version developed by William Ramsey, claiming that conceptual analysis is based on psychological assumptions that have already been refuted by empirical psychology. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:How Philosophers Trivialize Art: Bleak House, Oedipus Rex, "Leda and the Swan"Michael D. HurleyIIt is a Perverse but unsurprising irony that answers to the question of whether art can give us knowledge characteristically trivialize that which draws us to individual artworks in the first place. The experience of art is sidelined in favor of the apparent after-effect of that experience. Even those writing against each other tend to converge (...) on this. In an essay contesting Nelson Goodman's epistemic claims for art, Gordon Graham nonetheless agrees that, "The question to be asked of such a work is not, 'Does this effectively capture the scene portrayed?', but 'Does this make us see this sort of occasion differently?'"1 Even attempts to distinguish art as "gift" as opposed to commodity predictably figure its value in terms of what might be taken away: "I went to see a landscape painter's works, and that evening, walking among pine trees near my home, I could see the shapes and the colors I had not seen the day before."2This state of affairs is perversely ironic for two reasons. Firstly, because the possibility of art's cognitive content is only prompted at all by the immediate experience it offers: without this, art would not excite us the way it does and there would be no debate to be had. Secondly, and more significantly, because a defining part of what constitutes an interest in art is, I should like to suggest, an experience of knowledge; or, more accurately, an experience of knowing. This irony is unsurprising because it is merely another expression of a recalcitrant prejudice in western epistemology that idealizes knowledge as an objectively true, justified belief—perforce excluding the possibility of knowing as a subjective [End Page 107] experience of believing. No wonder the author of Theætetus elsewhere finds poets incapable of offering anything but lies.Plato's lingering legacy assures that the cognitive content of art be assized according to what might be extracted from the artwork—cashed in like so many casino chips—when we are done with our experience of it. This applies whether the knowledge-bearing being argued for, or against, is conceptual or propositional (e.g., Putnam, Novitz, John),3 or imaginative (e.g., Goodman, Robinson, Currie),4 as well as for the claim that art can offer us moral instruction (e.g., Beardsmore, Eldridge, Nussbaum, Sharpe, Kieran, John).5 There is less consensus as to whether the capacity of art to give us knowledge enriches the aesthetic value of that artwork, but those who would advance this position have been on the back-foot in recent years following a wave of criticisms from, among others, Beardsley, Lamarque and Olsen, Diffey, and Gaut.6This article addresses art's capacity to give us knowledge as well as the conjunct of whether such knowledge might inform its value qua art. In so doing, it presses a case that has already been disallowed by the terms in which the question of the relationship between art and knowledge is typically put. Whatever efferent knowledge art might offer, it also provides the conditions for a kind of knowing that cannot be translated beyond itself. Only such an experience of knowledge-as-knowing, which is realized through the untranslatable singularity of an artwork, may be considered constitutive of art's aesthetic value. Couched another way: epistemology meets aesthetics not where it has most often been located, in the perfective, at the congruence of the thought and the felt, but in the present continuous, in the engagement of thinking and feeling. Connecting the epistemic and the aesthetic in this way is, then, exactly the opposite proposition to that presented by Douglas Morgan, for whom, "although many words in many arts can and do give us knowledge of many kinds, nonetheless if this knowledge were the key and limit to the love of art, the world of art would be even sorrier than it now is."7IILiterature has generated by far the greatest volume of commentary in the debate on art and knowledge. This is to be expected given the bias towards categorizing knowledge as something like data... (shrink)

Dreadful and dreaded outcomes are sometimes brought about via the accumulation of individually trivial effects. Think about inching toward terrible health or toward an environmental disaster. In some such cases, the outcome is seen as unacceptable but is still gradually realized via an extended sequence of moves each of which is trivial in terms of its impact on the health or environment of those involved. Cases of this sort are not only practically challenging, they are theoretically challenging as well. For, (...) they raise puzzling complications concerning the assessment of conduct. In particular, given cases of this sort, we seem forced to conclude that, sometimes, each current doing in an extended sequence of moves can be correctly assessed as permissible (relative to a certain set of concerns) even though the sequence foreseeably leads to an outcome that is unacceptable (relative to that same set of concerns) and even though acceptable outcomes are available. And this seems paradoxical. I argue that this (apparent) puzzle glosses over complications associated with action individuation and units of agency. Reflection on these complications makes it clear that in cases of the sort that have given rise to the puzzle, there is an accurate way of seeing what is being done at various particular moments that clearly brings out the tight connection between a current doing and non-trivial damage that is to be expected (and is indeed bound to occur if the doing is completed without a hitch). (shrink)

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)

I will present a novel account of justification in terms of knowledge on which one is justified in believing p just in case one could know that p. My main aim is to unravel some of the formal properties that justification has in virtue of its connection to knowledge. Assuming that safety is at least a necessary condition for knowledge, I show that justification doesn’t iterate trivially; isn’t a luminous condition; is closed under a certain kind of multi-premise closure principle, (...) but; surprisingly one can nevertheless believe with justification a set of claims that’s jointly inconsistent. This last feature allows for a rather satisfying solution to the preface paradox. Finally, I contrast my account with other knowledge-first accounts of justification. (shrink)

We prove that there is no Borel connection for non-trivial pairs of unsplitting relations. This was conjectured in [3].

David Lewis introduced a new kind of reductio ad absurdum style of argument: while the claims, suitably formalized, do not lead to outright contradiction, he showed they are tenable only in trivial ways. Lewis proved what are known as triviality results against the claims. The claims are "Probabilities of conditionals are conditional probabilities." "Desires are beliefs about what is good." The author argues that the tenuous connections between the claims go considerably further still: the claims give rise to debates that (...) display a remarkably parallel structure. He brings out their many similarities to illuminate both of them, and to point the way to some promising avenues for future research. He displays structural similarities between the fluctuating fortunes of Stalnaker's Thesis, and those of Desire‐as‐Belief. Lewis concludes telegraphically by saying that Desire by Necessity is "a form of anti‐Humeanism, sure enough, but not the right form of anti‐Humeanism"; and that's it. (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)

Examination of a comprehensive database of political knowledge, constructed from pooled 1988 and 1992 National Election Studies, refutes criticisms that haue sometimes been lodged against standard tests that seem to reveal profound levels of public ignorance. Although most people know something about politics, the typical citizen is poorly informed, and only a small group is very knowledgeable about politics. Differentiating people according to their perceptions of the most important national problem does not reveal pockets of well‐informed “issue publics” among the (...) electorate. The NES data also show that knowledge makes a difference in how people feel about government spending for social‐welfare programs, and in how well citizens were able to connect their partisanship and ideological proclivities to their votes in the 2000 presidential election. (shrink)

It is shown that the so called slow growing hierarchy depends non trivially on the choice of its underlying structure of ordinals. To this end we investigate the growth rate behaviour of the slow growing hierarchy along natural subsets of notations for $\Gamma_0$. Let T be the set-theoretic ordinal notation system for $\Gamma_0$ and $T^{tree}$ the tree ordinal representation for $\Gamma$. It is shown in this paper that $_{\alpha \in T}$ matches up with the class of functions which are elementary (...) recursive in the Ackermann function as does $_{\alpha \in T^{tree}}$. By thinning out terms in which the addition function symbol occurs we single out subsystems $T* \subseteq T$ and $T^{tree*} \subseteq T^{tree}$ and prove that $_{\alpha \in T^{tree*}}$ still matches up with $_{\alpha \in T^{tree}}$ but $_{\alpha \in T*}$ now consists of elementary recursive functions only. We discuss the relationship between these results and the $\Gamma_0$-based termination proof for the standard rewrite system for the Ackermann function. (shrink)

In this article the author adduces a non‐positivist argument for a necessary connection between law and morality; the argument is based on the claim to correctness, and it is directed to an attack stemming from Eugenio Bulygin. The heart of the controversy is the claim to correctness. The author first attempts to show that there are good reasons for maintaining that law necessarily raises a claim to correctness. He argues, second, for the thesis that this claim has moral implications. Finally, (...) he attempts to refute Bulygin's objection that the claim‐based argument for non‐positivism boils down to contradiction and triviality. (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)

§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)

Many in education suggest that to have studentsadopt healthy and active lifestyles, then theymust be offered meaning rich physical activityexperiences. This paper adds to thisconversation in two ways. First, this paperadds depth and richness to traditionalconceptualizations of the meaning in movement.In doing so, we interrogate the physical,cognitive and affective meaning that studentsmay derive from participation in movement.Second, this paper examines the role ofphysical activity in theme-based, integratedcurriculum. We highlight how physical activitycan be incorporated into theme-based units insubstantial and non-trivial ways.

This paper concerns a prima facie tension between the claims that (a) agents have normative reasons obtaining in virtue of the nature of the options that confront them, and (b) there is a non-trivial connection between the grounds of normative reasons and the upshots of sound practical reasoning. Joint commitment to these claims is shown to give rise to a dilemma. I argue that the dilemma is avoidable on a response dependent account of normative reasons accommodating both (a) and (b) (...) by yielding (a) as a substantial constraint on sound practical reasoning. This fact is shown to have significance for the contemporary dialectic between moral realists and their opponents. (shrink)

Karl Popper developed a theory of deductive logic in the late 1940s. In his approach, logic is a metalinguistic theory of deducibility relations that are based on certain purely structural rules. Logical constants are then characterized in terms of deducibility relations. Characterizations of this kind are also called inferential definitions by Popper. In this paper, we expound his theory and elaborate some of his ideas and results that in some cases were only sketched by him. Our focus is on Popper's (...) notion of duality, his theory of modalities, and his treatment of different kinds of negation. This allows us to show how his works on logic anticipate some later developments and discussions in philosophical logic, pertaining to trivializing connectives, the duality of logical constants, dual-intuitionistic logic, the conservativeness of language extensions, the existence of a bi-intuitionistic logic, the non-logicality of minimal negation, and to the problem of logicality in general. (shrink)

Judgment-aggregation theory has always focused on the attainment of rational collective judgments. But so far, rationality has been understood in static terms: as coherence of judgments at a given time, defined as consistency, completeness, and/or deductive closure. This paper asks whether collective judgments can be dynamically rational, so that they change rationally in response to new information. Formally, a judgment aggregation rule is dynamically rational with respect to a given revision operator if, whenever all individuals revise their judgments in light (...) of some information (a learnt proposition), then the new aggregate judgments are the old ones revised in light of this information, i.e., aggregation and revision commute. We prove an impossibility theorem: if the propositions on the agenda are non-trivially connected, no judgment aggregation rule with standard properties is dynamically rational with respect to any revision operator satisfying some basic conditions on revision. Our theorem is the dynamic-rationality counterpart of some well-known impossibility theorems for static rationality. We also explore how dynamic rationality might be achieved by relaxing some of the conditions on the aggregation rule and/or the revision operator. Notably, premise-based aggregation rules are dynamically rational with respect to so-called premise-based revision operators. (shrink)

The problem of probabilities of conditionals is one of the long-standing puzzles in philosophy of language. We defend and update Adams' solution to the puzzle: the probability of an epistemic conditional is not the probability of a proposition, but a probability under a supposition. -/- Close inspection of how a triviality result unfolds in a concrete scenario does not provide counterexamples to the view that probabilities of conditionals are conditional probabilities: instead, it supports the conclusion that probabilities of conditionals violate (...) standard probability theory. -/- This does not call into question probability theory per se; rather, it calls for a more careful understanding of its role: probability theory is a theory of probabilities of propositions; but as conditionals do not express propositions, their probabilities are not subject to the standard laws. -/- We argue that both conditional probabilities and probabilities of conditionals are best understood in terms of the dynamics of supposing, modeled as a restriction operation on a probability space. This version of the suppositionalist view allows us to connect Adams' Thesis to the widely held restrictor view of the semantics of conditionals. -/- We address two common objections to Adams' view: that the relevant probabilities are ‘probabilities only in name’, and that giving up conditional propositions puts us at a disadvantage when it comes to interpreting compounds. -/- Finally, we argue that some putative counterexamples to Adams' Thesis can be diagnosed as fallacies of probabilistic reasoning: they arise from applying to conditionals laws of standard probability theory which are invalid for them. (shrink)

The connection between the probabilities of conditionals and the corresponding conditional probabilities has long been explored in the philosophical literature, but its implementation faces both technical obstacles and objections on empirical grounds. In this paper I ?rst outline the motivation for the probabilistic turn and Lewis’ triviality results, which stand in the way of what would seem to be its most straightforward implementation. I then focus on Richard Jeffrey’s ’random-variable’ approach, which circumvents these problems by giving up the notion that (...) conditionals denote propositions in the usual sense. Even so, however, the random-variable approach makes counterintuitive predictions in simple cases of embedded conditionals. I propose to address this problem by enriching the model with an explicit representation of causal dependencies. The addition of such causal information not only remedies the shortcomings of Jeffrey’s conditional, but also opens up the possibility of a uni?ed probabilistic account of indicative and counterfactual conditionals. (shrink)

We shed light on an old problem by showing that the logic LP cannot define a binary connective $\odot$ obeying detachment in the sense that every valuation satisfying $\varphi$ and $(\varphi\odot\psi)$ also satisfies $\psi$ , except trivially. We derive this as a corollary of a more general result concerning variable sharing.

This work studies some problems connected to the role of negation in logic, treating the positive fragments of propositional calculus in order to deal with two main questions: the proof of the completeness theorems in systems lacking negation, and the puzzle raised by positive paradoxes like the well-known argument of Haskel Curry. We study the constructive com- pleteness method proposed by Leon Henkin for classical fragments endowed with implication, and advance some reasons explaining what makes difficult to extend this constructive (...) method to non-classical fragments equipped with weaker implications (that avoid Curry's objection). This is the case, for example, of Jan Lukasiewicz's n-valued logics and Wilhelm Ackermann's logic of restricted implication. Besides such problems, both Henkin's method and the triviality phenomenon enable us to propose a new positive tableau proof system which uses only positive meta-linguistic resources, and to mo- tivate a new discussion concerning the role of negation in logic proposing the concept of paratriviality. In this way, some relations between positive reasoning and infinity, the possibilities to obtain a ¯first-order positive logic as well as the philosophical connection between truth and meaning are dis- cussed from a conceptual point of view. (shrink)

We present the unification of Riemann–Cartan–Weyl (RCW) space-time geometries and random generalized Brownian motions. These are metric compatible connections (albeit the metric can be trivially euclidean) which have a propagating trace-torsion 1-form, whose metric conjugate describes the average motion interaction term. Thus, the universality of torsion fields is proved through the universality of Brownian motions. We extend this approach to give a random symplectic theory on phase-space. We present as a case study of this approach, the invariant Navier–Stokes equations for (...) viscous fluids, and the kinematic dynamo equation of magnetohydrodynamics. We give analytical random representations for these equations. We discuss briefly the relation between them and the Reynolds approach to turbulence. We discuss the role of the Cartan classical development method and the random extension of it as the method to generate these generalized Brownian motions, as well as the key to construct finite-dimensional almost everywhere smooth approximations of the random representations of these equations, the random symplectic theory, and the random Poincaré–Cartan invariants associated to it. We discuss the role of autoparallels of the RCW connections as providing polygonal smooth almost everywhere realizations of the random representations. (shrink)

What is the connection between valid inference and true conditionals? Many conditional logics require that when A is a logical consequence of B, "if B then A" is true. Taking counterlogical conditionals seriously leads to systems that permit counterexamples to that general rule. However, this leaves those of us who endorse non-trivial accounts of counterpossible conditionals to explain what the connection between conditionals and consequence is. The explanation of the connection also answers a common line of objection to non-trivial counterpossibles, (...) which is based on a transition from valid arguments to the corresponding conditionals. It also contributes to the wider project of illuminating the connections between contexts of utterance, on the one hand, and the truth-conditions of conditionals uttered in those contexts, on the other. (shrink)

We explore a relation we call 'anticipation' between formulas, where A anticipates B (according to some logic) just in case B is a consequence (according to that logic, presumed to support some distinguished implicational connective →) of the formula A → B. We are especially interested in the case in which the logic is intuitionistic (propositional) logic and are much concerned with an extension of that logic with a new connective, written as "a", governed by rules which guarantee that for (...) any formula B, aB is the (logically) strongest formula anticipating B. The investigation of this new logic, which we call ILa, will confront us on several occasions with some of the finer points in the theory of rules and with issues in the philosophy of logic arising from the proposed explication of the existence of a connective (with prescribed logical behaviour) in terms of the conservative extension of a favoured logic by the addition of such a connective. Other points of interest include the provision of a Kripke semantics with respect to which ILa is demonstrably sound, deployed to establish certain unprovability results as well as to forge connections with C. Rauszer's logic of dual intuitionistic negation and dual intuitionistic implication, and the isolation of two relations (between formulas), head-implication and head-linkage, which, though trivial in the setting of classical logic, are of considerable significance in the intuitionistic context. (shrink)

An argument that what is usually dismissed as the “mystical shell” of Hegel's thought—the concept of absolute knowledge—is actually its most “rational kernel.” This book sets out from a counterintuitive premise: the “mystical shell” of Hegel's system proves to be its most “rational kernel.” Hegel's radicalism is located precisely at the point where his thought seems to regress most. Most current readings try to update Hegel's thought by pruning back his grandiose claims to “absolute knowing.” Comay and Ruda invert this (...) deflationary gesture by inflating what seems to be most trivial: the absolute is grasped only in the minutiae of its most mundane appearances. Reading Hegel without presupposition, without eliminating anything in advance or making any decision about what is essential and what is inessential, what is living and what is dead, they explore his presentation of the absolute to the letter. The Dash is organized around a pair of seemingly innocuous details. Hegel punctuates strangely. He ends the Phenomenology of Spirit with a dash, and he begins the Science of Logic with a dash. This distinctive punctuation reveals an ambiguity at the heart of absolute knowing. The dash combines hesitation and acceleration. Its orientation is simultaneously retrospective and prospective. It both holds back and propels. It severs and connects. It demurs and insists. It interrupts and prolongs. It generates nonsequiturs and produces explanations. It leads in all directions: continuation, deviation, meaningless termination. This challenges every cliché about the Hegelian dialectic as a machine of uninterrupted teleological progress. The dialectical movement is, rather, structured by intermittency, interruption, hesitation, blockage, abruption, and random, unpredictable change—a rhythm that displays all the vicissitudes of the Freudian drive. (shrink)

What is the connection between reasons and motives? According to Reasons Internalism there is a non-trivial conceptual connection between normative reasons and the possibility of rationally accessing relevant motivation. Reasons Internalism is attractive insofar as it captures the thought that reasons are for reasoning with and repulsive insofar as it fails to generate sufficient critical distance between reasons and motives. Rather than directly adjudicate this dispute, I extract from it two generally accepted desiderata on theories of normative reasons and argue (...) that a new theory can satisfy both. The new theory locates part of the meaning of normative reason statements in their role in normative discussion. It generates a view of the connection between reasons and motives that is distinct from Reasons Internalism, yet distinctively in its spirit. (shrink)

Far from being unwelcome or impossible in a mathematical setting, indeterminacy in various forms can be seen as playing an important role in driving mathematical research forward by providing “sources of newness” in the sense of Hutter and Farías :434–449, 2017). I argue here that mathematical coincidences, phenomena recently under discussion in the philosophy of mathematics, are usefully seen as inducers of indeterminacy and as put to work in guiding mathematical research. I suggest that to call a pair of mathematical (...) facts a coincidence is roughly to suggest that the investigation of connections between these facts isn’t worthwhile. To say of this pair, “That’s no coincidence!” is to suggest just the opposite. I further argue that this perspective on mathematical coincidence, which pays special attention to what mathematical coincidences do, may provide us with a better view of what mathematical coincidences are than extant accounts. I close by reflecting on how understanding mathematical coincidences as generating indeterminacy accords with a conception of mathematical research as ultimately aiming to reduce indeterminacy and complexity to triviality as proposed in Rota Indiscrete thoughts, Birkhäuser, 1997). (shrink)

We consider the connections between belief revision, conditional logic and nonmonotonic reasoning, using as a foundation the approach to theory change developed by Alchourrón, Gärdenfors and Makinson (the AGM approach). This is first generalized to allow the iteration of theory change operations to capture the dynamics of epistemic states according to a principle of minimal change of entrenchment. The iterative operations of expansion, contraction and revision are characterized both by a set of postulates and by Grove's construction based on total (...) pre-orders on the set of complete theories of the belief logic. We present a sound and complete conditional logic whose semantics is based on our iterative revision operation, but which avoids Gärdenfors's triviality result because of a severely restricted language of beliefs and hence the weakened scope of our extended postulates. In the second part of the paper, we develop a computational approach to theory dynamics using Rott's E-bases as a representation for epistemic states. Under this approach, a ranked E-base is interpreted as standing for the most conservative entrenchment compatible with the base, reflecting a kind of foundationalism in the acceptance of evidence for a belief. Algorithms for the computation of our iterative versions of expansion, contraction and revision are presented. Finally, we consider the relationship between nonmonotonic reasoning and both conditional logic and belief revision. Adapting the approach of Delgrande, we show that the unique extension of a default theory expressed in our conditional logic of belief revision corresponds to the most conservative belief state which respects the theory: however, this correspondence is limited to propositional default theories. Considering first order default theories, we present a belief revision algorithm which incorporates the assumption of independence of default instances and propose the use of a base logic for default reasoning which incorporates uniqueness of names. We conclude with an examination of the behavior of an implemented system on some of Lifschitz's benchmark problems in nonmonotonic reasoning. (shrink)

Free-will incompatibilism has become a motte-and-bailey doctrine (Shackel 2014), and is currently being maintained by standard motte-and-bailey strategies. In this paper, I explain why incompatibilism has a motte-and-bailey structure and why philosophers who do not aim to dismantle it are complicit in both the maintenance of this problematic doctrine and the normalization of a host of bad practices engaged in by those who actively exploit it. To solidify the diagnosis, I provide a paradigmatic motte-and-baileying case that has been ongoing for (...) over a decade. Specifically, I discuss how motte-and-baileying has generated widespread confusion surrounding the logical structure and conclusion of manipulation arguments. Even more specifically, I look at Mele's so-called "Zygote Argument for incompatibilism". I point out that Mele currently conflates under two distinct arguments with different logical forms and substantively different conclusions under that heading, and explain how this has needlessly impeded progress in the free-will debate. The original variant of the Zygote Argument was invalid because it aimed to establish that determinism precludes (destroys, undermines, is antagonistic to) free will, but its supported a far weaker non-explanatory conclusion. In direct response to this invalidity objection, Mele took his critic's suggestion to change the conclusion of his argument to the thesis that free will and determinism are perhaps spuriously associated -- but he also covertly changed his preferred definition of 'incompatibilism' to pick out the non-explanatory conclusion of the new variant of the Zygote Argument which allowed him to continue speaking AS IF his argument was still an argument for incompatibilism according to his original definition of 'incompatibilism'. It is not simply that Mele made these changes or that he failed to mention in print that he made them (despite having over a decade to do so), but that he has actively attempted to discredit his critics by insisting--contrary to fact--that those who do not use his negative definition of 'incompatibilism' are using the term in a nonstandard and nontraditional way that he has "never had any use for" and there is some kind of connection (which he does describe) between the invalidity objection to his original argument that the definition of 'incompatibilism' one prefers. Oddly, Mele has mentioned only one "invalidity objection" in print, but this objection is direct at the revised Zygote Argument--even though no one had ever pressed an invalidity objection to his new argument (the form of which is patently valid). As a direct result of Mele's evasive behaviors (covertly redefining jargon to cover changes to the form/conclusion of his argument), many people--including Mele's own former graduate students--have published articles in which they fail to recognize that Mele changed his argument and redefined terms, thereby perpetuating the false narrative that the new Zygote Argument has the same "incompatibilist" conclusion as the original (which, notably, had the same conclusion as its predecessor, Pereboom's Four-Case Argument). Moreover, Mele has not even ONCE corrected those who "misdescribe" his revised argument as concluding that determinism is antagonstic to (precludes, undermines, rules out, etc.) free will. For example, Mele never corrects those who mistakenly claim that the revised Zygote Argument has the same "incompatibilist" conclusion as Pereboom's, nor has Mele ever mentioned that he now defines the term 'incompatibilism' differently than Pereboom--since Pereboom since uses this term to refer to the explanatory conclusion of the original Zygote Argument, which had the same explanatory conclusion of his Four-Case Argument. To further throttle his critics, Mele has obliquely suggested that the invalidity objection to his original Zygote Argument works only if one accepts his critic's idiosyncratic definition of 'incompatibilism' -- a patently false charge (since the term 'incompatibilism' doesn't even appear in his arguments) and one that has needlessly confused his audience. Indeed, other philosophers have now made this false and quite indefensible accusation explicitly in print, thereby helping Mele and others to continue motte-and-baileying with impunity. I close by preemptively responding to strategies commonly used by motte-and-bailey apologists to suppress legitimate criticisms of their equivocation and well-poisoning strategies (e.g. "Philosophers are allowed to define their technical terms however they like" and "the motte/bailey divide is a distinction without a difference") which have hitherto kept their philosophical audience from participating in a legitimate discussion about why tracking the distinction between the the "motte" thesis (a negative, arguably spurious association claim) and the "bailey" thesis (a positive explanatory claim) is not trivial, but is instead one that is absolutely essential to making progress in the free-will debate. Of course, a single critic cannot (almost by definition) undermine a motte-and-bailey doctrine once it has been established. As such, even if every diagnosis in this essay is accurate, it will not change the discourse. The motte-and-baileying will continue, and the debate will remain in needless deadlock, until a critical threshold of OBSERVERS learn about the motte/bailey distinction and ask apologists for motte-and-bailey incompatibilism to stop their motte-and-baileying. -/- Manuscript available upon request, plz gmail me: kristin.mickelson.42@. (shrink)

This paper explores some connections between flavour perception, emotion, and temporal experience. Focussing on the question, If you like that taste of X and I do not, are we tasting the same thing X?, I will approach it by looking at some differences between how experts and nonexperts ‘taste’. I will eventually answer that if by ‘the same thing’ we mean the overall flavour profile of a complex sensory object, then the answer must be negative. I will argue that there (...) is indeed a relatively trivial sense in which one tastes the same thing, but that this is not an experience of flavour. In the process I will reject the view that there are real emergent flavour properties. (shrink)

Much recent work on Kant's argument that the Categorical Imperative is the fundamental principle of morality has focused on the gap in that argument between the conclusion that rational agents conform to laws that apply to every rational agent, and the requirement contained in the Universal Law of Nature formula.1 While it seems plausible – even trivial– that a rational agent, insofar as she is a rational agent, conforms to whatever laws there are that are valid for all rational agents, (...) there does not appear to be any obvious route from this seemingly trivial claim to the controversial and substantive principle of acting only on maxims that one can at the same time rationally will every rational agent to act on.2 In what follows, I argue that the connection between rational agency and mere conformity to universally valid laws is not as trivial as it may seem. Many readers, I suspect, assume that Kant makes the trivial claim about rational agency because rational agency is rational, and being rational requires conforming to those laws that apply to all rational beings. For instance, this assumption is implicit in Onora O'Neill claim that "the interest of a Kantian universality test is that it aims to ground an ethical theory on notions of consistency and rationality rather than upon considerations of desire and preference."3 But, as I contend in what follows, the requirement to conform to laws valid for all rational agents is based on the fact that rational agency is, not rational, but agency. Indeed, the arguments leading to the first formulation of the Categorical Imperative rely on the idea of rational willing as a kind of causation in order to show this. And, as it turns out, the claim that the concept of causation contains the idea of conformity to universally valid laws is not a trivial claim. (shrink)

This chapter reviews Davidson's main work on truth. It focuses on the connections between truth, meaning, and interpretation that form the core of Davidson's views, and on the relations of his views to traditional theories of truth. It highlights several key ideas that comprise Davidson's approach to truth: Tarski's work on truth is fundamental to understanding the concept, as is the relation of truth to meaning, and we fail to understand that connection adequately unless we take into account the constraints (...) of radical interpretation. Furthermore, in understanding those connections, we see that truth is not a redundant or trivial concept, but equally, it is not a locus for metaphysical commitments. (shrink)

Laws of nature take center stage in philosophy of science. Laws are usually believed to stand in a tight conceptual relation to many important key concepts such as causation, explanation, confirmation, determinism, counterfactuals etc. Traditionally, philosophers of science have focused on physical laws, which were taken to be at least true, universal statements that support counterfactual claims. But, although this claim about laws might be true with respect to physics, laws in the special sciences (such as biology, psychology, economics etc.) (...) appear to have—maybe not surprisingly—different features than the laws of physics. Special science laws—for instance, the economic law “Under the condition of perfect competition, an increase of demand of a commodity leads to an increase of price, given that the quantity of the supplied commodity remains constant” and, in biology, Mendel's Laws—are usually taken to “have exceptions”, to be “non-universal” or “to be ceteris paribus laws”. How and whether the laws of physics and the laws of the special sciences differ is one of the crucial questions motivating the debate on ceteris paribus laws. Another major, controversial question concerns the determination of the precise meaning of “ceteris paribus”. Philosophers have attempted to explicate the meaning of ceteris paribus clauses in different ways. The question of meaning is connected to the problem of empirical content, i.e., the question whether ceteris paribus laws have non-trivial and empirically testable content. Since many philosophers have argued that ceteris paribus laws lack empirically testable content, this problem constitutes a major challenge to a theory of ceteris paribus laws. (shrink)