I use generic embeddings induced by generic normal measures on that can be forced to exist if κ is an indestructibly weakly compact cardinal. These embeddings can be applied in order to obtain the forcing axioms in forcing extensions. This has consequences in : The Singular Cardinal Hypothesis holds above κ, and κ has a useful Jónsson-like property. This in turn implies that the countable tower works much like it does when κ is a Woodin limit of Woodin cardinals. One (...) consequence is that every set of reals in the Chang model is Lebesgue measurable and has the Baire Property, the Perfect Set Property and the Ramsey Property. So indestructible weak compactness has effects on cardinal arithmetic high up and also on the structure of sets of real numbers, down low, similar to supercompactness. (shrink)

This paper argues that we need to re-think the semantics/pragmatics distinction in the light of new evidence from embedding of irony. This raises a new version of the old problem of ‘embedded implicatures’. I argue that embedded irony isn’t fully explained by solutions proposed for other embedded implicatures. I first consider two strategies: weak pragmatics and strong pragmatics. These explain embedded irony as truth-conditional content. However, by trying to shoehorn irony into said-content, they raise problems of their own. (...) I conclude by considering how a modified Gricean model can explain that irony embeds qua implicature. This leads us to prefer a local implicature model. This has important consequences for how we draw the semantics/pragmatics distinction. (shrink)

We study what the existence of a classical embedding between computable structures implies about the existence of computable embeddings. In particular, we consider the effect of fixing and varying the computable presentations of the computable structures.

We consider the very weak paracomplete and paraconsistent logics that are obtained by a straightforward weakening of Classical Logic, as well as some of their maximal extensions that are a fragment of Classical Logic. We prove that these logics may be faithfully embedded in Classical Logic, and that the interpolation theorem obtains for them.

In lieu of an abstract, here is a brief excerpt of the content:Embedding Creativity in Teaching and LearningHoward Cannatella (bio)IntroductionCreative teaching ranges from the view that creativity is necessary for a changing knowledge economy to a more individualized view that encompasses a person-centered approach. None of these views are advanced in this essay, as I feel that there are important weaknesses in taking either position. Instead, my main purpose is to discuss how certain kinds of creative activity can substantially (...) transform educational practice without necessarily succumbing to any of the above conceptions of creativity. My educational approach to creative activity relates to one aspect of Alasdair Macintyre's, After Virtue; the notion that creativity only flourishes via a devotion to a particular practice.1 For such practice to flourish it has to immerse itself in a type of personal address that revolves and combines in various ways what Maurice Merleau-Ponty refers to as "self-others-things."2Any claim to suggest that education should engage creativity more than it currently does can stir some reasonable criticism, for there are clearly a plethora of other important factors to consider in student learning. Yet, to a degree, the practice of creativity is, I think, being dissipated and weakened, where ambivalence and ill-informed ideas are increasingly obscuring its place. My own thinking on this displacement which has some connections with John White's view and in a different sense with Howard Gardner's, is that if we offer via teaching situations geometrical puzzles, visual problem solving exercises and the like, such exercises although perhaps amusing in themselves are hardly taking up the same refined order of creative display exhibited by those most credited as being creatively talented.3 Indeed, to surmise that creativity is a construal of left hand side verses right hand side brain activity; that one can show different color cards on a monitor or play a short excerpt of Beethoven's Pastoral symphony in order to accelerate student learning are at the very least questionable creative assumptions. In [End Page 59] contrast, what I aim to show from one perspective as a crucial distinction is how creativity is involved in fundamental painstaking ways with the phenomenological. When the landscape of this kind of learning presupposes the opening of oneself to the world, the stretching of a mind, the thickening of one's perceptions, and the discovery of a deeper and richer self through living, one will tend to experience as life enhancing more of nature, previously unfelt and articulated modes of being in the world.Clearly, as a lecturer one has to inspire students. One of the best ways I know of doing this is through satisfying and intensifying students' creative appetite. Although I will not discuss it here there is some evidence to suggest that the need for creativity is biologically, physically, and psychologically an essential part of human nature, necessary for human-reproduction, growth, and cultural striving.4 The lecturer who fails to stimulate students' creativity, their being in the world, may be unwittingly inhibiting their cognitive, emotional, and physical well-being; preventing them from realizing their potential. Indeed, some learning problems can be attributed to the unconscious or deliberate stifling of creativity in student lives. We can see this happening when one feels emotionally or intellectually repressed, unable to express oneself openly, to take delight in what one has achieved, to note one's own unique sensitivity, and to experience personally the many wonders in the world. Although we may not articulate it, without a modicum of creative outlet, life can appear very cruel. Further, some of the benefits of creativity can be seen in studio teaching situations in which, as Charles Bingham and Alexander Sidorkin imply, the dynamics of aesthetic creativity encourage power-sharing and the fostering of non-dominated pedagogical relationships.5 As both Immanuel Kant and Friedrich Schiller realized two centuries ago, creativity has the capacity to foster educationally a particular kind of freedom essential to sustaining an alert, liberal, and questioning mind.6 There is also much empirical evidence, at least in the arts, to show how creative practice can assist the clarification of ideas, advancement in thought, and concentration in learning. The notebooks, papers, and recordings of Mozart... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Embedding Creativity in Teaching and LearningHoward Cannatella (bio)IntroductionCreative teaching ranges from the view that creativity is necessary for a changing knowledge economy to a more individualized view that encompasses a person-centered approach. None of these views are advanced in this essay, as I feel that there are important weaknesses in taking either position. Instead, my main purpose is to discuss how certain kinds of creative activity can substantially (...) transform educational practice without necessarily succumbing to any of the above conceptions of creativity. My educational approach to creative activity relates to one aspect of Alasdair Macintyre's, After Virtue; the notion that creativity only flourishes via a devotion to a particular practice.1 For such practice to flourish it has to immerse itself in a type of personal address that revolves and combines in various ways what Maurice Merleau-Ponty refers to as "self-others-things."2Any claim to suggest that education should engage creativity more than it currently does can stir some reasonable criticism, for there are clearly a plethora of other important factors to consider in student learning. Yet, to a degree, the practice of creativity is, I think, being dissipated and weakened, where ambivalence and ill-informed ideas are increasingly obscuring its place. My own thinking on this displacement which has some connections with John White's view and in a different sense with Howard Gardner's, is that if we offer via teaching situations geometrical puzzles, visual problem solving exercises and the like, such exercises although perhaps amusing in themselves are hardly taking up the same refined order of creative display exhibited by those most credited as being creatively talented.3 Indeed, to surmise that creativity is a construal of left hand side verses right hand side brain activity; that one can show different color cards on a monitor or play a short excerpt of Beethoven's Pastoral symphony in order to accelerate student learning are at the very least questionable creative assumptions. In [End Page 59] contrast, what I aim to show from one perspective as a crucial distinction is how creativity is involved in fundamental painstaking ways with the phenomenological. When the landscape of this kind of learning presupposes the opening of oneself to the world, the stretching of a mind, the thickening of one's perceptions, and the discovery of a deeper and richer self through living, one will tend to experience as life enhancing more of nature, previously unfelt and articulated modes of being in the world.Clearly, as a lecturer one has to inspire students. One of the best ways I know of doing this is through satisfying and intensifying students' creative appetite. Although I will not discuss it here there is some evidence to suggest that the need for creativity is biologically, physically, and psychologically an essential part of human nature, necessary for human-reproduction, growth, and cultural striving.4 The lecturer who fails to stimulate students' creativity, their being in the world, may be unwittingly inhibiting their cognitive, emotional, and physical well-being; preventing them from realizing their potential. Indeed, some learning problems can be attributed to the unconscious or deliberate stifling of creativity in student lives. We can see this happening when one feels emotionally or intellectually repressed, unable to express oneself openly, to take delight in what one has achieved, to note one's own unique sensitivity, and to experience personally the many wonders in the world. Although we may not articulate it, without a modicum of creative outlet, life can appear very cruel. Further, some of the benefits of creativity can be seen in studio teaching situations in which, as Charles Bingham and Alexander Sidorkin imply, the dynamics of aesthetic creativity encourage power-sharing and the fostering of non-dominated pedagogical relationships.5 As both Immanuel Kant and Friedrich Schiller realized two centuries ago, creativity has the capacity to foster educationally a particular kind of freedom essential to sustaining an alert, liberal, and questioning mind.6 There is also much empirical evidence, at least in the arts, to show how creative practice can assist the clarification of ideas, advancement in thought, and concentration in learning. The notebooks, papers, and recordings of Mozart... (shrink)

Downey and Lempp 1215–1240) have shown that the contiguous computably enumerable degrees, i.e. the c.e. Turing degrees containing only one c.e. weak truth-table degree, can be characterized by a local distributivity property. Here we extend their result by showing that a c.e. degree a is noncontiguous if and only if there is an embedding of the nonmodular 5-element lattice N5 into the c.e. degrees which maps the top to the degree a. In particular, this shows that local nondistributivity (...) coincides with local nonmodularity in the computably enumerable degrees. (shrink)

A positive topology is a set equipped with two particular relations between elements and subsets of that set: a convergent cover relation and a positivity relation. A set equipped with a convergent cover relation is a predicative counterpart of a locale, where the given set plays the role of a set of generators, typically a base, and the cover encodes the relations between generators. A positivity relation enriches the structure of a locale; among other things, it is a tool to (...) study some particular subobjects, namely the overt weakly closed sublocales. We relate the category of locales to that of positive topologies and we show that the former is a reflective subcategory of the latter. We then generalize such a result to the category of suplattices, which we present by means of cover relations. Finally, we show that the category of positive topologies also generalizes that of formal topologies, that is, overt locales. (shrink)

This paper considers two of the most prominent kinds of evidence that have been used to argue that certain embedded questions receive weakly exhaustive interpretations. The first kind is exemplified by judgments of consistency for declarative sentences that attribute knowledge of a wh-question and ignorance of the negation of that question to the same person, and the second concerns asymmetries between the role of positive and negative information in validating question-embedding surprise ascriptions, and similar judgments for other attitudes. I (...) argue that neither type suffices to show weak exhaustivity. The first can be analyzed in terms of strong exhaustivity in combination with domain restriction effects, while the second can be analyzed in terms of a mention-some interpretation. These kinds of evidence have served as the empirical basis for many claims about weakly exhaustive readings, so the observation that they are unreliable calls into questions a large body of established work on the semantics of question embedding. (shrink)

Questions embedded under responsive predicates and definite descriptions both give rise to a variety of phenomena which can be grouped under the term plurality effects: quantificational variability, cumulativity, and homogeneity effects. This similarity has not gone unnoticed, and many proposals have taken inspiration in theories of definite plurals to account for these effects with embedded questions. Recently these phenomena have received less attention, as the field has focused on the so-called intermediate exhaustive reading of embedded questions instead, after Spector called (...) into question the traditional dichotomy between weak and strong exhaustive readings. As a result, the intermediate exhaustive reading has been accounted for at the expense of empirical coverage in other areas. In this paper, I propose a modular theory which derives the currently much discussed exhaustive readings without giving up the rich semantics necessary to account for plurality effects. My account of quantificational variability, cumulativity, and homogeneity effects builds on recent work on these phenomena in the nominal domain by adopting a categorial approach to embedded questions, while the strong and intermediate exhaustive readings are implemented using an independent strengthening mechanism suggested in Klinedinst and Rothschild :1–23, 2011). The resulting theory not only recovers important results on plurality effects; it offers new, simple solutions for some puzzles presented in George :166–177, 2013) and Paillé and Schwarz Proceedings of WCCFL 36, vol 36, Cascadilla Proceedings Project, Somerville, 2018), naturally derives readings that had been postulated in previous literature, makes correct predictions in many unexplored cases, and is compatible with recent results in psycholinguistics. In the last sections I justify my assumptions and show how possible limitations I inherit from the theories I build on can be accommodated under standard assumptions. (shrink)

Extrapolating from the work of Mahlo , one can prove that given any pair of countable closed totally bounded subsets of complete separable metric spaces, one subset can be homeomorphically embedded in the other. This sort of topological comparability is reminiscent of the statements concerning comparability of well orderings which Friedman has shown to be equivalent to ATR0 over the weak base system RCA0. The main result of this paper states that topological comparability is also equivalent to ATR0. In (...) Section 1, the pertinent subsystems of second-order arithmetic and results on well orderings are reviewed. Sections 2 and 3 overview the encoding of metric spaces and homeomorphisms in second-order arithmetic. Section 4 contains a proof of the topological comparability result in ATR0. Section 5 contains the reversal, a derivation of ATR0 from the topological comparability result. In Section 6, additional information about the structure of the embeddings is obtained, culminating in an application to closed subsets of the real numbers. (shrink)

The notion of countable well order admits an alternative definition in terms of embeddings between initial segments. We use the framework of reverse mathematics to investigate the logical strength of this definition and its connection with Fraïssé’s conjecture, which has been proved by Laver. We also fill a small gap in Shore’s proof that Fraïssé’s conjecture implies arithmetic transfinite recursion over $\mathbf {RCA}_0$, by giving a new proof of $\Sigma ^0_2$ -induction.

This paper develops some of Austin’s ideas on excuses, stressing their “dimensional” character and relating it to Searle’s distinction between intention-in-action and previous intention, in order to show that the original speech-act shaped distinction between weakness of the will and moral weakness can be embedded in a quite different theoretical framework such as Davidson’s, while Austin’s dimensional classification of actions cannot. Finally, the article analyzes how Grice’s critique of Davidson’s views on akrasia is more faithful to Austin and more radical (...) in its conclusions concerning the justificatory aspect of reasons and the rational features of action. (shrink)

We have two polynomial time results for the uniform word problem for a quasivariety Q: The uniform word problem for Q can be solved in polynomial time iff one can find a certain congruence on finite partial algebras in polynomial time. Let Q* be the relational class determined by Q. If any universal Horn class between the universal closure S and the weak embedding closure S̄ of Q* is finitely axiomatizable then the uniform word problem for Q is (...) solvable in polynomial time. This covers Skolem's 1920 solution to the uniform word problem for lattices and Evans' 1953 applications of the weak embeddability property for finite partial V algebras. (shrink)

Emotive-factive predicates, such as surprise or be happy, are a source of empirical and theoretical puzzles in the literature on embedded questions. Although they embed wh-questions, they seem not to embed whether-questions. They have complex interactions with negative polarity items such as any or even, and they have been argued to preferentially give rise to weakly exhaustive readings with embedded questions. We offer an empirical overview of the situation in three experiments collecting acceptability judgments, monotonicity judgments, and truth-value judgments. The (...) results straightforwardly confirm the special selectional properties of emotive-factive predicates. More interestingly, they reveal the existence of strongly exhaustive readings for surprise. The results also suggest that the special properties of emotive-factives cannot be solely explained by their monotonicity profiles, because they were not found to differ from the profiles of other responsive predicates. (shrink)

We study the notion of weak amalgamation in the context of diagonal conjugacy classes. Generalizing results of Kechris and Rosendal, we prove that for every countable structure M, Polish group G of permutations of M, and \, G has a comeager n-diagonal conjugacy class iff the family of all n-tuples of G-extendable bijections between finitely generated substructures of M, has the joint embedding property and the weak amalgamation property. We characterize limits of weak Fraïssé classes that (...) are not homogenizable. Finally, we investigate 1- and 2-diagonal conjugacy classes in groups of ball-preserving bijections of certain ordered ultrametric spaces. (shrink)

This is a defence of the authenticity of Plato’s Epistula vii against the recent onslaught by Frede and Burnyeat (2015). It focusses on what Ep. vii has to say about writing and the embedded philosophical Digression and evaluates this in the context of other mainly late dialogues. In the Cratylus, Socrates ends with resignation regarding the potential of language study as a source of truth. This is also the case in Ep. vii, where the four means of knowledge (names, definitions, (...) images (diagrams) and knowledge/insight/true opinion) do not offer the essence of reality due to the weakness of language, in this case owing to a diagram with contrary properties. Consequently, name and definition are impermanent and conventional. Contra Burnyeat, definition is not impossible but useful in the acquisition of knowledge. Only after dialectical examination comes a flash of insight into reality. So, reality (truth) must, as in the Cratylus, be studied directly. Significantly for Plato (as opposed to Socrates), the epistemology is illustrated by a mathematical case. Hence it is relevant to look at mathematical procedure in middle and late dialogues. Moreover, the possible role of division is considered. Finally, the critique of writing justified by the Digression is placed in the context of the general aversion to the written word. The epistemology of the Digression is shown to be a fair and competent synopsis of the later Plato’s epistemology. Hence, there seems to be no reason thus far to doubt that Ep. vii is a genuine work of Plato. (shrink)

We present several examples of hereditary classes of finite structures satisfying the joint embedding property and the weak amalgamation property, but failing the cofinal amalgamation property. These include a continuum‐sized family of classes of finite undirected graphs, as well as an example due to Pouzet with countably categorical generic limit.

We give a decision procedure for the ∀∃-theory of the weak truth-table (wtt) degrees of the recursively enumerable sets. The key to this decision procedure is a characterization of the finite lattices which can be embedded into the r.e. wtt-degrees by a map which preserves the least and greatest elements: a finite lattice has such an embedding if and only if it is distributive and the ideal generated by its cappable elements and the filter generated by its cuppable (...) elements are disjoint. We formulate general criteria that allow one to conclude that a distributive upper semi-lattice has a decidable two-quantifier theory. These criteria are applied not only to the weak truth-table degrees of the recursively enumerable sets but also to various substructures of the polynomial many-one (pm) degrees of the recursive sets. These applications to the pm degrees require no new complexity-theoretic results. The fact that the pm-degrees of the recursive sets have a decidable two-quantifier theory answers a question raised by Shore and Slaman in [21]. (shrink)

We show that Weak Vopěnka’s Principle, which is the statement that the opposite category of ordinals cannot be fully embedded into the category of graphs, is equivalent to the large cardinal principle Ord is Woodin, which says that for every class [Formula: see text] there is a [Formula: see text]-strong cardinal. Weak Vopěnka’s Principle was already known to imply the existence of a proper class of measurable cardinals. We improve this lower bound to the optimal one by defining (...) structures whose nontrivial homomorphisms can be used as extenders, thereby producing elementary embeddings witnessing [Formula: see text]-strongness of some cardinal. (shrink)

We show that Weak Vopěnka’s Principle, which is the statement that the opposite category of ordinals cannot be fully embedded into the category of graphs, is equivalent to the large cardinal princi...

The following pcf results are proved:1. Assume thatκ>ℵ0κ>ℵ0is a weakly compact cardinal. Letμ>2κμ>2κbe a singular cardinal of cofinality κ. Then for every regularView the MathML sourceλ sup{suppcfσ⁎-complete|a⊆Reg∩and|a|<μ}.Turn MathJax onAs an application we show that:if κ is a measurable cardinal andj:V→Mj:V→Mis the elementary embedding by a κ-complete ultrafilter over κ, then for every τ the following holds:1. ifjjis a cardinal thenj=τj=τ;2. |j|=|j)||j|=|j)|;3. for any κ-complete ultrafilter W on κ, |j|=|jW||j|=|jW|.The first two items provide affirmative answers to questions from Gitik and (...) Shelah [2] and the third to a question of D. Fremlin. (shrink)

In this paper we study a reducibility that has been introduced by Klaus Weihrauch or, more precisely, a natural extension for multi-valued functions on represented spaces. We call the corresponding equivalence classes Weihrauch degrees and we show that the corresponding partial order induces a lower semi-lattice. It turns out that parallelization is a closure operator for this semi-lattice and that the parallelized Weihrauch degrees even form a lattice into which the Medvedev lattice and the Turing degrees can be embedded. The (...) importance of Weihrauch degrees is based on the fact that multi-valued functions on represented spaces can be considered as realizers of mathematical theorems in a very natural way and studying the Weihrauch reductions between theorems in this sense means to ask which theorems can be transformed continuously or computably into each other. As crucial corner points of this classification scheme the limited principle of omniscience LPO, the lesser limited principle of omniscience LLPO and their parallelizations are studied. It is proved that parallelized LLPO is equivalent to Weak Kőnig's Lemma and hence to the Hahn—Banach Theorem in this new and very strong sense. We call a multi-valued function weakly computable if it is reducible to the Weihrauch degree of parallelized LLPO and we present a new proof, based on a computational version of Kleene's ternary logic, that the class of weakly computable operations is closed under composition. Moreover, weakly computable operations on computable metric spaces are characterized as operations that admit upper semi-computable compact-valued selectors and it is proved that any single-valued weakly computable operation is already computable in the ordinary sense. (shrink)

Via the formulas-as-types embedding certain extensions of Heyting Arithmetic can be represented in intuitionistic type theories. In this paper we discuss the embedding of ω-sorted Heyting Arithmetic HA ω into a type theory WL, that can be described as Troelstra's system ML 1 0 with so-called weak Σ-elimination rules. By syntactical means it is proved that a formula is derivable in HA ω if and only if its corresponding type in WL is inhabited. Analogous results are proved (...) for Diller's so-called restricted system and for a type theory based on predicate logic instead of arithmetic. (shrink)

The author offers his own vision of the unification of four fundamental interactions through a philosophical analysis of the categories of time and space. Time and space are coexisting self-sufficient phenomena. Time connects three global spaces (inert, living and intelligent substances) into a single hierarchy of the universe. The unification of space and time took place at the first stage of the modern world structure, during the formation of the first global space-time. The cosmological singularity was determined by two main (...) parameters: substance (state of matter) and the energy embedded in it. The author comes to the conclusion that strong, weak and electromagnetic interactions are forces that determine different spaces (geometric constructions). All geometric constructions of fundamental particles are determined by 3 forces (energies). Gravitational force is time, "time-energy", relative to which and "in which" geometric constructions take place. (shrink)

Journal of Mathematical Logic, Volume 22, Issue 02, August 2022. Motivated by results of Bagaria, Magidor and Väänänen, we study characterizations of large cardinal properties through reflection principles for classes of structures. More specifically, we aim to characterize notions from the lower end of the large cardinal hierarchy through the principle [math] introduced by Bagaria and Väänänen. Our results isolate a narrow interval in the large cardinal hierarchy that is bounded from below by total indescribability and from above by subtleness, (...) and contains all large cardinals that can be characterized through the validity of the principle [math] for all classes of structures defined by formulas in a fixed level of the Lévy hierarchy. Moreover, it turns out that no property that can be characterized through this principle can provably imply strong inaccessibility. The proofs of these results rely heavily on the notion of shrewd cardinals, introduced by Rathjen in a proof-theoretic context, and embedding characterizations of these cardinals that resembles Magidor’s classical characterization of supercompactness. In addition, we show that several important weak large cardinal properties, like weak inaccessibility, weak Mahloness or weak [math]-indescribability, can be canonically characterized through localized versions of the principle [math]. Finally, the techniques developed in the proofs of these characterizations also allow us to show that Hamkin’s weakly compact embedding property is equivalent to Lévy’s notion of weak [math]-indescribability. (shrink)

The Alperin-Goldschmidt Fusion Theorem [1, 5], when combined with pushing up [7], was a useful tool in the classification of the finite simple groups. Similar theorems are needed in the study of simple groups of finite Morley rank, in the even type case (that is, when the Sylow 2-subgroups are of bounded exponent, as in algebraic groups over fields of characteristic 2). In that context a body of results relating to fusion of 2-elements and the structure of 2-local subgroups is (...) needed: pushing up, and the classification of groups with strongly or weakly embedded subgroups, or have strongly closed abelian subgroups (c.f, [2]). Two theorems of Alperin-Goldschmidt type are proved here. Both are needed in applications.The following is an exact analog of the Alperin-Goldschmidt Fusion Theorem for groups of finite Morley rank, in the case of 2-elements:Theorem 1.1.Let G be a group of finite Morley rank, and P a Sylow2-subgroup of G.If A, B⊆P are conjugate in G, then there are subgroups Hi≤Pand elementsxi∈N(Hi)for1 ≤i≤n,and an elementy∈N(P),such that for all i:1.Hiis a tame intersection of two Sylow2-subgroups;2.CP(Hi) ≤Hi;3.N(Hi)/Hiis2-isolatedand(a)(b). (shrink)

A wide Aronszajn tree is a tree of size and height $\omega _{1}$ with no uncountable branches. We prove that under $MA$ there is no wide Aronszajn tree which is universal under weak embeddings. This solves an open question of Mekler and Väänänen from 1994. We also prove that under $MA$, every wide Aronszajn tree weakly embeds in an Aronszajn tree, which combined with a result of Todorčević from 2007, gives that under $MA$ every wide Aronszajn tree embeds into (...) a Lipschitz tree or a coherent tree. We also prove that under $MA$ there is no wide Aronszajn tree which weakly embeds all Aronszajn trees, improving the result in the first paragraph as well as a result of Todorčević from 2007 who proved that under $MA$ there are no universal Aronszajn trees. (shrink)

According to Thomas Metzinger, many human cognitive processes in the waking state are spontaneous and are deprived of the experience of epistemic agency. He considers mind wandering as a paradigm example of our recurring loss of epistemic agency. I will enrich this view by extending the scope of the concept of epistemic agency to include cases of depressive rumination and creative cognition, which are additional types of spontaneous cognition. Like mind wandering, they are characterized by unique phenomenal and functional properties (...) that give rise to varying degrees of epistemic agency. The main claim of this paper will be that the experience of being an epistemic agent within a certain time frame is a relational phenomenon that emerges from the organism’s capacity to interact with its cognitive niche. To explore this relation, I develop a new framework that integrates phenomenological considerations on epistemic agency with a functional account of the reciprocal coupling of the embodied organism with its cognitive niche. This account rests upon dynamical accounts of strong embodied and embedded cognition and recent work on cognitive niche construction. Importantly, epistemic agency and organism-niche coupling are gradual phenomena ranging from weak to strong realizations. The emerging framework will be employed to analyze mind wandering, depressive rumination, and creative cognition as well as their commonalities and differences. Mind wandering and depressive rumination are cases of weak epistemic agency and organism-niche coupling. However, there are also important phenomenological, functional, and neuronal differences. In contrast, creative cognition is a case of strong epistemic agency and organism-niche coupling. By providing a phenomenological and functional analysis of these distinct types of spontaneous cognition, we can gain a better understanding of the importance of organism-niche interaction for the realization of epistemic agency. (shrink)

I argue that the chapters in this section only modestly challenge the “traditional min- dreading account,” which sees the capacity for mental state attribution as central to human social cognition. This internalist, cognitivist account has already been refined in recent years to give greater attention to unreflective, dynamic social interaction and non-mindreading processes. The chapters here support a kind of embodied social cognition that does not involve mindreading. They also support the idea that an embedded/situated cognition perspective can inform the (...) nature of the mindread- ing and non-mindreading forms of social cognition, particularly their use during dynamic social interaction. Further, important empirical questions arise about the importance of social interaction in the development of mindreading. But the more radical extended cognition thesis only appears sporadically and is weakly defended. Thus, the 4E perspective represented here does not challenge the importance of the “representation-hungry,” internal capacity for mindreading. (shrink)

Journal of Mathematical Logic, Ahead of Print. Given a structure [math] and a stably embedded [math]-definable set [math], we prove tameness preservation results when enriching the induced structure on [math] by some further structure [math]. In particular, we show that if [math] and [math] are stable (respectively, superstable, [math]-stable), then so is the theory [math] of the enrichment of [math] by [math]. Assuming simplicity of [math], elimination of hyperimaginaries and a further condition on [math] related to the behavior of algebraic (...) closure, we also show that simplicity and NSOP1 pass from [math] to [math]. We then prove several applications for tame expansions of weakly minimal structures and, in particular, the group of integers. For example, we construct the first known examples of strictly stable expansions of [math]. More generally, we show that any stable (respectively, superstable, simple, NIP, NTP2, NSOP1) countable graph can be defined in a stable (respectively, superstable, simple, NIP, NTP2, NSOP1) expansion of [math] by some unary predicate [math]. (shrink)

It is shown that a fundamental question of revealed preference theory, namely whether the weak axiom of revealed preference (WARP) implies the strong axiom of revealed preference (SARP), can be reduced to a Hamiltonian cycle problem: A set of bundles allows a preference cycle of irreducible length if and only if the convex monotonic hull of these bundles admits a Hamiltonian cycle. This leads to a new proof to show that preference cycles can be of arbitrary length for more (...) than two but not for two commodities. For this, it is shown that a set of bundles satisfying the given condition exists if and only if the dimension of the commodity space is at least three. Preference cycles can be constructed by embedding a cyclic $(L-1)$ -polytope into a facet of a convex monotonic hull in $L$ -space, because cyclic polytopes always admit Hamiltonian cycles. An immediate corollary is that WARP only implies SARP for two commodities. The proof is intuitively appealing as this gives a geometric interpretation of preference cycles. (shrink)

Expressivism promises an illuminating account of the nature of normative judgment. But worries about the details of expressivist semantics have led many to doubt whether expressivism's putative advantages can be secured. Drawing on insights from linguistic semantics and decision theory, I develop a novel framework for implementing an expressivist semantics that I call ordering expressivism. I argue that by systematically interpreting the orderings that figure in analyses of normative terms in terms of the basic practical attitude of conditional weak (...) preference, the expressivist can explain the semantic properties of normative sentences in terms of the logical properties of that attitude. Expressivism's problems with capturing the logical relations among normative sentences can be reduced to the familiar, more tractable problem of explaining certain coherence constraints on preferences. Particular attention is given to the interpretation of wide-scope negation. The proposed solution is also extended to other types of embedded contexts—most notably, disjunctions. (shrink)

Living with people who differ—racially, ethnically, religiously, or economically—is the most urgent challenge facing civil society today. We tend socially to avoid engaging with people unlike ourselves, and modern politics encourages the politics of the tribe rather than of the city. In this thought-provoking book, Richard Sennett discusses why this has happened and what might be done about it. Sennett contends that cooperation is a craft, and the foundations for skillful cooperation lie in learning to listen well and discuss rather (...) than debate. In _Together_ he explores how people can cooperate online, on street corners, in schools, at work, and in local politics. He traces the evolution of cooperative rituals from medieval times to today, and in situations as diverse as slave communities, socialist groups in Paris, and workers on Wall Street. Divided into three parts, the book addresses the nature of cooperation, why it has become weak, and how it could be strengthened. The author warns that we must learn the craft of cooperation if we are to make our complex society prosper, yet he reassures us that we can do this, for the capacity for cooperation is embedded in human nature. (shrink)

Existing predominant approaches within virtue ethics (VE) assume humans as the typical agent and virtues as dispositions that pertain primarily to human–human interpersonal relationships. Similarly, the main accounts in the more specific area of environmental virtue ethics (EVE) tend to support weak anthropocentric positions, in which virtues are understood as excellent dispositions of human agents. In addition, however, several EVE authors have also considered virtues that benefit non-human beings and entities (e.g., environmental or ecological virtues). The latter correspond to (...) excellent character dispositions that would extend moral consideration and care for the benefit of non-human beings, entities, or entire ecosystems. In this direction, a few authors have argued that EVE could be considered non-anthropocentric insofar as it could: (a) promote non-human ends, well-being, and the flourishing of non-human beings and entities; (b) involve significant relations to non-humans. Drawing from different traditions, including ecofeminism and care ethics, we argue for a broader notion of self and a decentered notion of virtues. The broader notion of selfhood corresponds to the “ecological self”, one that can be enacted by both human and non-human beings, is embedded in a network of relations, and recognizes the more-than-human world as fundamental and yet indispensable otherness. We suggest that this broader notion of agency allows for an expansive understanding of virtues that includes a-moral functional ecological virtues, which can be exercised not only by humans but also by certain non-human beings. This alternative understanding of selfhood and ecological virtues within EVE could have several theoretical and practical implications, some of which may enable different types of agencies and transform collective action. (shrink)

Why does ethics only weakly contribute to the most crucial problems of the current world? Relational Agency and Environmental Ethics: A Journey Beyond Humanism as We Know It explores how the concept of moral agency embedded in modern humanist ethics, in its reliance on environmentally harmful and scientifically implausible presuppositions, prevents ethics from efficiently supporting a sustainability transition. The modernist individualist notion of agency includes conceptual dichotomies between moral agency and human nature, mind and body, reason and emotion, and knowledge (...) and will, yet it should be revised without dismissing responsibility, normativity, and a shared ground for critical assessment. Suvielise Nurmi proposes an agential shift resting on a relational concept of agency, combining ecofeminist and evolutionary criticisms of modernism together with various interdisciplinary discussions involving philosophy of mind, cognitive science, anthropology, social ontology, and developmental biology and psychology. This book argues that the relational shift can resolve the dilemma and bring environmental relationships to the core of ethical discourse: there is no ethics distinct from environmental ethics. Environmental responsibilities can be justified as responsibilities for one’s relationally considered agency. (shrink)

Moral encroachment holds that the epistemic justification of a belief can be affected by moral factors. If the belief might wrong a person or group more evidence is required to justify the belief. Moral encroachment thereby opposes evidentialism, and kindred views, which holds that epistemic justification is determined solely by factors pertaining to evidence and truth. In this essay I explain how beliefs such as ‘that woman is probably an administrative assistant’—based on the evidence that most women employees at the (...) firm are administrative assistants—motivate moral encroachment. I then describe weaknesses of moral encroachment. Finally I explain how we can countenance the moral properties of such beliefs without endorsing moral encroachment, and I argue that the moral status of such beliefs cannot be evaluated independently from the understanding in which they are embedded. (shrink)

The Lévy-Solovay Theorem [8] limits the kind of large cardinal embeddings that can exist in a small forcing extension. Here I announce a generalization of this theorem to a broad new class of forcing notions. One consequence is that many of the forcing iterations most commonly found in the large cardinal literature create no new weakly compact cardinals, measurable cardinals, strong cardinals, Woodin cardinals, strongly compact cardinals, supercompact cardinals, almost huge cardinals, huge cardinals, and so on.

Conditional logics were originally developed for the purpose of modeling intuitively correct modes of reasoning involving conditional—especially counterfactual—expressions in natural language. While the debate over the logic of conditionals is as old as propositional logic, it was the development of worlds semantics for modal logic in the past century that catalyzed the rapid maturation of the field. Moreover, like modal logic, conditional logic has subsequently found a wide array of uses, from the traditional (e.g. counterfactuals) to the exotic (e.g. conditional (...) obligation). Despite the close connections between conditional and modal logic, both the technical development and philosophical exploitation of the latter has outstripped that of the former, with the result that noticeable lacunae exist in the literature on conditional logic. My dissertation addresses a number of these underdeveloped frontiers, producing new technical insights and philosophical applications. -/- I contribute to the solution of a problem posed by Priest of finding sound and complete labeled tableaux for systems of conditional logic from Lewis' V-family. To develop these tableaux, I draw on previous work on labeled tableaux for modal and conditional logic; errors and shortcomings in recent work on this problem are identified and corrected. While modal logic has by now been thoroughly studied in non-classical contexts, e.g. intuitionistic and relevant logic, the literature on conditional logic is still overwhelmingly classical. Another contribution of my dissertation is a thorough analysis of intuitionistic conditional logic, in which I utilize both algebraic and worlds semantics, and investigate how several novel embedding results might shed light on the philosophical interpretation of both intuitionistic logic and conditional logic extensions thereof. -/- My dissertation examines deontic and connexive conditional logic as well as the underappreciated history of connexive notions in the analysis of conditional obligation. The possibility of interpreting deontic modal logics in such systems (via embedding results) serves as an important theoretical guide. A philosophically motivated proscription on impossible obligations is shown to correspond to, and justify, certain (weak) connexive theses. Finally, I contribute to the intensifying debate over counterpossibles, counterfactuals with impossible antecedents, and take—in contrast to Lewis and Williamson—a non-vacuous line. Thus, in my view, a counterpossible like "If there had been a counterexample to the law of the excluded middle, Brouwer would not have been vindicated" is false, not (vacuously) true, although it has an impossible antecedent. I exploit impossible (non-normal) worlds—originally developed to model non-normal modal logics—to provide non-vacuous semantics for counterpossibles. I buttress the case for non-vacuous semantics by making recourse to both novel technical results and theoretical considerations. (shrink)

Gricean pragmatics. Saying vs. implicating ; Discourse and cooperation ; Conversational implicatures ; Generalised vs. particularised ; Cancellability ; Gricean reasoning and the pragmatics of what is said -- The standard recipe for Q-implicatures. The standard recipe ; Inference to the best explanation ; Weak implicatures and competence ; Relevance ; Conclusion -- Scalar implicatures. Horn scales and the generative view ; Implicatures and downward entailing environments ; Disjunction : exclusivity and ignorance ; Conclusion -- Psychological plausibility. Charges of (...) psychological inadequacy ; Logical complexity ; Abduction ; Incremental processing ; The intentional stance ; Alternatives ; Conclusion -- Nonce inference or defaults?. True defaults ; Strong defaultism ; Weak defaultism ; Contextualism ; Conclusion -- Intentions, alternatives, and free choice. Free choice ; Problems with the standard recipe ; Intentions first ; Free choice explained ; Comparing alternatives ; Two flavours of Q-implicature ; Conclusion -- Embedded implicatures : the problems. The problems ; Varieties of conventionalism ; Against conventionalism ; Conclusion -- Embedded implicatures : a Gricean approach. Disjunction ; Belief reports ; Factives and other presupposition inducers ; Indefinites ; Contrastive construals and lexical pragmatics ; Conclusion. (shrink)

A general method for constructing a new class of topological Ramsey spaces is presented. Members of such spaces are infinite sequences of products of Fraïssé classes of finite relational structures satisfying the Ramsey property. The Product Ramsey Theorem of Sokič is extended to equivalence relations for finite products of structures from Fraïssé classes of finite relational structures satisfying the Ramsey property and the Order-Prescribed Free Amalgamation Property. This is essential to proving Ramsey-classification theorems for equivalence relations on fronts, generalizing the (...) Pudlák–Rödl Theorem to this class of topological Ramsey spaces. To each topological Ramsey space in this framework corresponds an associated ultrafilter satisfying some weak partition property. By using the correct Fraïssé classes, we construct topological Ramsey spaces which are dense in the partial orders of Baumgartner and Taylor generating p-points which are k-arrow but not \-arrow, and in a partial order of Blass producing a diamond shape in the Rudin-Keisler structure of p-points. Any space in our framework in which blocks are products of n many structures produces ultrafilters with initial Tukey structure exactly the Boolean algebra \\). If the number of Fraïssé classes on each block grows without bound, then the Tukey types of the p-points below the space’s associated ultrafilter have the structure exactly \. In contrast, the set of isomorphism types of any product of finitely many Fraïssé classes of finite relational structures satisfying the Ramsey property and the OPFAP, partially ordered by embedding, is realized as the initial Rudin-Keisler structure of some p-point generated by a space constructed from our template. (shrink)

Some algebraic structures of the set of all effects are investigated and summarized in the notion of a(weak) orthoalgebra. It is shown that these structures can be embedded in a natural way in lattices, via the so-calledMacNeille completion. These structures serve as a model ofparaconsistent quantum logic, orthologic, andorthomodular quantum logic.

This book consists of a collection of essays written between 1965 and 1981. Some have been published elsewhere; others appear here for the first time. Although dealing with different figures and different periods, they have a common theme: all are concerned with examining how the method of hy pothesis came to be the ruling orthodoxy in the philosophy of science and the quasi-official methodology of the scientific community. It might have been otherwise. Barely three centuries ago, hypothetico deduction was in (...) both disfavor and disarray. Numerous rival methods for scientific inquiry - including eliminative and enumerative induction, analogy and derivation from first principles - were widely touted. The method of hypothesis, known since antiquity, found few proponents between 1700 and 1850. During the last century, of course, that ordering has been inverted and - despite an almost universal acknowledgement of its weaknesses - the method of hypothesis (usually under such descriptions as 'hypothetico deduction' or 'conjectures and refutations') has become the orthodoxy of the 20th century. Behind the waxing and waning of the method of hypothesis, embedded within the vicissitudes of its fortunes, there is a fascinating story to be told. It is a story that forms an integral part of modern science and its philosophy. (shrink)

One of the numerous characterizations of a Ramsey cardinal κ involves the existence of certain types of elementary embeddings for transitive sets of size κ satisfying a large fragment of ZFC. We introduce new large cardinal axioms generalizing the Ramsey elementary embeddings characterization and show that they form a natural hierarchy between weakly compact cardinals and measurable cardinals. These new axioms serve to further our knowledge about the elementary embedding properties of smaller large cardinals, in particular those still consistent (...) with V = L. (shrink)

In this paper we introduce the Wholeness Axiom , which asserts that there is a nontrivial elementary embedding from V to itself. We formalize the axiom in the language {∈, j } , adding to the usual axioms of ZFC all instances of Separation, but no instance of Replacement, for j -formulas, as well as axioms that ensure that j is a nontrivial elementary embedding from the universe to itself. We show that WA has consistency strength strictly between (...) I 3 and the existence of a cardinal that is super- n -huge for every n . ZFC + WA is used as a background theory for studying generalizations of Laver sequences. We define the notion of Laver sequence for general classes E consisting of elementary embeddings of the form i :V β → M , where M is transitive, and use five globally defined large cardinal notions – strong, supercompact, extendible, super-almost-huge, superhuge – for examples and special cases of the main results. Assuming WA at the beginning, and eventually refining the hypothesis as far as possible, we prove the existence of a strong form of Laver sequence for a broad range of classes E that include the five large cardinal types mentioned. We show that if κ is globally superstrong, if E is Laver-closed at beth fixed points, and if there are superstrong embeddings i with critical point κ and arbitrarily large targets such that E is weakly compatible with i , then our standard constructions are E -Laver at κ . , there is an extendible Laver sequence at κ .) In addition, in most cases our Laver sequences can be made special if E is upward λ -closed for sufficiently many λ. (shrink)

Kantian moral theories must explain how their most basic moral values of dignity and autonomy should be interpreted and applied to human conditions. One place Kantians should look for inspiration is, surprisingly, the utilitarian tradition and its emphasis on generally accepted, informally enforced, publicly known moral rules of the sort that help us give assurances, coordinate our behavior, and overcome weak wills. Kantians have tended to ignore utilitarian discussions of such rules mostly because they regard basic moral principles as (...) a priori requirements that cannot be tailored to human foibles and limitations. I argue that Kantian moral theories should incorporate public moral rules as mid-level moral requirements for embodied and socially embedded human agents. I explain how certain specific moral judgments about how we ought to act are justified by public moral rules, which are themselves justified by more fundamental moral requirements. (shrink)

Over the last three decades, the rise of embodied cognition (EC) articulated in various schools (or versions) of embodied, embedded, extended and enacted cognition (Gallagher’s 4E) has offered AI a way out of traditional computationalism—an approach (or an understanding) loosely referred to as embodied AI. This view has split into various branches ranging from a weak form on the brink of functionalism (loosely represented by Clarks’ parity principle) to a strong form (often corresponding to autopoietic-friendly enactivism) suggesting that body−world (...) interactions constitute cognition. From an ontological perspective, however, constitution is a problematic notion with no obvious empirical or technical advantages. This paper discusses the ontological issues of these two approaches in regard to embodied AI and its ontological commitments: circularity, epiphenomenalism, mentalism, and disguised dualism. The paper also outlines an even more radical approach that may offer some ontological advantages. The new approach, called the mind-object identity, is then briefly compared with sensorimotor direct realism and with the embodied identity theory. (shrink)

This paper develops a formal framework to model a process in which the formation of individual opinions is embedded in a deliberative exchange with others. The paper opts for a low-resolution modeling approach and abstracts away from most of the details of the social-epistemic process. Taking a bird's eye view allows us to analyze the chances for the truth to be found and broadly accepted under conditions of cognitive division of labour combined with a social exchange process. Cognitive division of (...) labour means that only some individuals are active truth seekers, possibly with different capacities. Both mathematical tools and computer simulations are used to investigate the model. As an analytical result, the Funnel Theorem states that under rather weak conditions on the social process, a consensus on the truth will be reached if all individuals possess an arbitrarily small capacity to go for the truth. The Leading the pack Theorem states that under certain conditions even a single truth seeker may lead all individuals to the truth. Systematic simulations analyze how close agents can get to the truth depending upon the frequency of truth seekers, their capacities as truth seekers, the position of the truth (more to the extreme or more in the centre of an opinion space), and the willingness to take into account the opinions of others when exchanging and updating opinions. (shrink)