We define a structure which is much simpler than a morass, but whose existence is equivalent to the existence of a morass.

We show that a $$ -simplified morass can be added by a forcing with working parts of size smaller than $\kappa $. This answers affirmatively the question, asked independently by Shelah and Velleman in the early 1990s, of whether it is possible to do so.Our argument use a modification of a technique of Mitchell’s for adding objects of size $\omega _2$ in which collections of models – all of equal, countable size – are used as side conditions. In (...) our modification, whilst the individual models are, as in Mitchell’s technique, taken ad hoc from quite general classes, the collections of models are very highly structured, in a way that is somewhat different from, perhaps more stringent than, Mitchell’s original, arguably making the method more wieldy and giving the prospect of further uses with more delicate working parts. (shrink)

We prove that in the Cohen extension adding ℵ3 generic reals to a model of containing a simplified (ω1, 2)‐morass, gap‐2 morass‐definable η1‐orderings with cardinality ℵ3 are order‐isomorphic. Hence it is consistent that and that morass‐definable η1‐orderings with cardinality of the continuum are order‐isomorphic. We prove that there are ultrapowers of over ω that are gap‐2 morass‐definable. The constructions use a simplified gap‐2 morass, and commutativity with morass‐maps and morass‐embeddings, to extend (...) a transfinite back‐and‐forth construction of order‐type ω1 to an order‐preserving bijection between objects of cardinality ℵ3. (shrink)

This paper concerns the theory of morasses. In the early 1970s Jensen defined (κ,α)-morasses for uncountable regular cardinals κ and ordinals $\alpha . In the early 1980s Velleman defined (κ, 1)-simplified morasses for all regular cardinals κ. He showed that there is a (κ, 1)-simplified morass if and only if there is (κ, 1)-morass. More recently he defined (κ, 2)-simplified morasses and Jensen was able to show that if there is a (κ, 2)-morass then (...) there is a (κ, 2)-simplified morass. In this paper we prove the converse of Jensen's result, i.e., that if there is a (κ, 2)-simplified morass then there is a (κ, 2)-morass. (shrink)

This paper concerns the theory of morasses. In the early 1970s Jensen defined -morasses for uncountable regular cardinals $\kappa$ and ordinals $\alpha < \kappa$. In the early 1980s Velleman defined -simplified morasses for all regular cardinals $\kappa$. He showed that there is a -simplified morass if and only if there is -morass. More recently he defined -simplified morasses and Jensen was able to show that if there is a -morass then there is a - (...) class='Hi'>simplified morass. In this paper we prove the converse of Jensen's result, i.e., that if there is a -simplified morass then there is a -morass. (shrink)

This paper concerns the theory of morasses. In the early 1970s Jensen defined -morasses for uncountable regular cardinals $\kappa$ and ordinals $\alpha < \kappa$. In the early 1980s Velleman defined -simplified morasses for all regular cardinals $\kappa$. He showed that there is a -simplified morass if and only if there is -morass. More recently he defined -simplified morasses and Jensen was able to show that if there is a -morass then there is a - (...) class='Hi'>simplified morass. In this paper we prove the converse of Jensen's result, i.e., that if there is a -simplified morass then there is a -morass. (shrink)

We further develop a previously introduced method of constructing forcing notions with the help of morasses. There are two new results: (1) If there is a simplified (ω 1 , 1)-morass, then there exists a ccc forcing of size ω 1 that adds an ω 2 -Suslin tree. (2) If there is a simplified (ω 1 , 2)-morass, then there exists a ccc forcing of size ω 1 that adds a 0-dimensional Hausdorff topology τ on ω (...) 3 which has spread s(τ) = ω 1 . While (2) is the main result of the paper, (1) is only an improvement of a previous result, which is based on a simple observation. Both forcings preserve GCH. To show that the method can be changed to produce models where CH fails, we give an alternative construction of Koszmider's model in which there is a chain 〈X α | α < ω 2 〉 such that X α ⊆ ω 1 , X β — X α is finite and X α — X β has size ω 1 for all β < α < ω 2. (shrink)

We show how to construct Gitik’s short extenders gap-3 forcing using a morass, and that the forcing notion is of Prikry type.

By using the notion of a simplified (κ,1)-morass, we construct κ-thin-tall, κ-thin-thick and, in a forcing extension, κ-very thin-thick superatomic Boolean algebras for every infinite regular cardinal κ.

In principle, a proof can be any sequence of logical deductions from axioms and previously-proved statements that concludes with the proposition in question. This freedom in constructing a proof can seem overwhelming at first. How do you even start a proof? Here’s the good news: many proofs follow one of a handful of standard templates. Proofs all differ in the details, of course, but these templates at least provide you with an outline to fill in. We’ll go through several of (...) these standard patterns, pointing out the basic idea and common pitfalls and giving some examples. Many of these templates fit together; one may give you a top-level outline while others help you at the next level of detail. And we’ll show you other, more sophisticated proof techniques later on. The recipes below are very specific at times, telling you exactly which words to write down on your piece of paper. You’re certainly free to say things your own way instead; we’re just giving you something you could say so that you’re never at a complete loss. (shrink)

BackgroundSocial cognition and competence are a key part of daily interactions and essential for satisfying relationships and well-being. Pediatric neurological and psychological conditions can affect social cognition and require assessment and remediation of social skills. To adequately approximate the complex and dynamic nature of real-world social interactions, innovative tools are needed. The aim of this study was to document the performance of adolescents on two versions of a serious video game presenting realistic, everyday, socio-moral conflicts, and to explore whether their (...) performance is associated with empathy or sense of presence, factors known to influence social cognition.MethodsParticipants first completed a pre-test measure of socio-moral reasoning based on three dilemmas from a previously validated computer task. Then, they either played an evaluative version or an adaptive version of a video game presenting nine social situations in which they made socio-moral decisions and provided justifications. In the evaluative version, participants’ audio justifications were recorded verbatim and coded manually to obtain a socio-moral reasoning maturity score. In the adaptive version, tailored feedback and social reinforcements were provided based on participant responses. An automatic coding algorithm developed using artificial intelligence was used to determine socio-moral maturity level in real-time and to provide a basis for the feedback and reinforcements in the game. All participants then completed a three-dilemma post-test assessment.ResultsThose who played the adaptive version showed improved SMR across the pre-test, in-game and post-test moral maturity scores, F = 9.81, pHF < 0.001, ϵ2 = 0.21, but those who played the Evaluative version did not. Socio-moral reasoning scores from both versions combined did not correlate with empathy or sense of presence during the game, though results neared significance. The study findings support preliminary validation of the game as a promising method for assessing and remediating social skills during adolescence. (shrink)

is a (κ, 1)-simplified morass if θα | α < κ is an increasing sequence of ordinals less than κ, θκ = κ+, and each Fαβ is a collection of maps from θα to θβ such that the following properties hold.

Some subfamilies of κ, for κ regular, κ λ, called -semimorasses are investigated. For λ = κ+, they constitute weak versions of Velleman's simplified -morasses, and for λ > κ+, they provide a combinatorial framework which in some cases has similar applications to the application of -morasses with this difference that the obtained objects are of size λ κ+, and not only of size κ+ as in the case of morasses. New consistency results involve existence of nonreflecting objects of (...) singular sizes of uncountable cofinality such as a nonreflecting stationary set in κ, a nonreflecting nonmetrizable space of size λ, a nonreflecting nonspecial tree of size λ. We also characterize possible minimal sizes of nonspecial trees without uncountable branches. (shrink)

In this paper we prove that, in the Cohen extension of a model M of ZFC+CH containing a simplified -morass, η1-orderings without endpoints having cardinality of the continuum, and satisfying specified technical conditions, are order-isomorphic. Furthermore, any order-isomorphism in M between countable subsets of the η1-orderings can be extended to an order-isomorphism between the η1-orderings in the Cohen extension of M. We use the simplified -morass, and commutativity conditions with morass maps on terms in the (...) forcing language, to extend countable partial functions on terms in the forcing language that are forced in all generic extensions to be order-preserving injections. This technique provides for the construction of functions in Cohen extensions adding 2 generic reals for which the only known arguments require transfinite constructions of order type no greater than ω1 in models of ZFC+CH. The specific example presented in this paper is an extension of Tarski’s classic result that in models of ZFC+CH, η1-orderings are order-isomorphic. (shrink)

We propose developing the theory of consequences of morasses relevant in mathematical applications in the language alternative to the usual one, replacing commonly used structures by families of sets originating with Velleman’s neat simplified morasses called 2-cardinals. The theory of related trees, gaps, colorings of pairs and forcing notions is reformulated and sketched from a unifying point of view with the focus on the applicability to constructions of mathematical structures like Boolean algebras, Banach spaces or compact spaces. The paper (...) is dedicated to the memory of Jim Baumgartner whose seminal joint paper :109–129, 1987) with Saharon Shelah provided a critical mass in the theory in question. A new result which we obtain as a side product is the consistency of the existence of a function \ with the appropriate \-version of property \ for regular \ satisfying \. (shrink)

Local connectedness functions for (κ, 1)-simplified morasses, localisations of the coupling function c studied in [M96, §1], are defined and their elementary properties discussed. Several different, useful, canonical ways of arriving at the functions are examined. This analysis is then used to give explicit formulae for generalisations of the local distance functions which were defined recursively in [K00], leading to simple proofs of the principal properties of those functions. It is then extended to the properties of local connectedness functions (...) in the context of κ-M-proper forcing for sucessor κ. The functions are shown to enjoy substantial strengthenings of the properties (particularly the ∆-properties) hitherto proved for both c and for Todorcevic’s ρ-functions in the special case κ = ω1. A couple of examples of the use of local connectedness functions in consort with κ-M-proper forcing are then given. (shrink)

Dan Talayco has recently defined the gap cohomology group of a tower in p/fin of height ω1. This group is isomorphic to the collection of gaps in the tower modulo the equivalence relation given by two gaps being equivalent if their levelwise symmetric difference is not a gap in the tower, the group operation being levelwise symmetric difference. Talayco showed that the size of this group is always at least 2N0 and that it attains its greatest possible size, 2N1, if (...) ⋄ holds and also in some generic extensions in which CH fails, for example on adding many Cohen or random reals. In this paper it is shown that there is always some tower whose gap cohomology group has size 2N1. It is still open as to whether there are models in which there are towers whose gap cohomology group has size less than 2ω1. (shrink)

Assume that M is a transitive model of $ZFC+CH$ containing a simplified $(\omega _1,2)$ -morass, $P\in M$ is the poset adding $\aleph _3$ generic reals and G is P-generic over M. In M we construct a function between sets of terms in the forcing language, that interpreted in $M[G]$ is an $\mathbb R$ -linear order-preserving monomorphism from the finite elements of an ultrapower of the reals, over a non-principal ultrafilter on $\omega $, into the Esterle algebra of formal (...) power series. Therefore it is consistent that $2^{\aleph _0}>\aleph _2$ and, for any infinite compact Hausdorff space X, there exists a discontinuous homomorphism of $C(X)$, the algebra of continuous real-valued functions on X. (shrink)

Frank and Nagel are very interested in the causes and consequences of moralizing about addiction. If addiction is a disease, moralistic concerns are sidelined. If it's a choice, we'd better identify clear reasons to absolve addicts from blame. While these are interesting considerations, they don't have much to do with the model of addiction I put forward in the target article.

In this book a noted physiologist and neuroscientist introduces the concept of simplexity, the set of solutions living organisms find that enable them to deal with information and situations, while taking into account past experiences and anticipating future ones. Such solutions are new ways of addressing problems so that actions may be taken more quickly, more elegantly, and more efficiently. In a sense, the history of living organisms may be summed up by their remarkable ability to find solutions that avoid (...) the world's complexity by imposing on it their own rules and functions. Evolution has resolved the problem of complexity not by simplifying but by finding solutions whose processes--though they can sometimes be complex--allow us to act in the midst of complexity and of uncertainty. Nature can inspire us by making us realize that simplification is never simple and requires instead that we choose, refuse, connect, and imagine, in order to act in the best possible manner. Such solutions are already being applied in design and engineering and are significant in biology, medicine, economics, and the behavioral sciences. (shrink)

The paper discusses various relationships between the concepts mentioned in the title. In Section 1 Todorcevic functions are shown to arise from both morasses and square. In Section 2 the theme is of supplements to morasses which have some of the flavour of square. Distinctions are drawn between differing concepts. In Section 3 forcing axioms related to the ideas in Section 2 are discussed.

This paper continues the work of Priest and Sylvan in Simplified Semantics for Basic Relevant Logics, a paper on the simplified semantics of relevant logics, such as B⁺ and B. We show that the simplified semantics can also be used for a large number of extensions of the positive base logic B⁺, and then add the dualising '*' operator to model negation. This semantics is then used to give conservative extension results for Boolean negation.

We introduce a novel point of view on the “models as mediators” framework in order to emphasize certain important epistemological questions about models in science which have so far been little investigated. To illustrate how this perspective can help answer these kinds of questions, we explore the use of simplified models in high energy physics research beyond the Standard Model. We show in detail how the construction of simplified models is grounded in the need to mitigate pressing epistemic (...) problems concerning the uncertainty inherent in the present theoretical and experimental contexts. (shrink)

A simplified variant of Gödel’s ontological argument is presented. The simplified argument is valid already in basic modal logics K or KT, it does not suffer from modal collapse, and it avoids the rather complex predicates of essence (Ess.) and necessary existence (NE) as used by Gödel. The variant presented has been obtained as a side result of a series of theory simplification experiments conducted in interaction with a modern proof assistant system. The starting point for these experiments (...) was the computer encoding of Gödel’s argument, and then automated reasoning techniques were systematically applied to arrive at the simplified variant presented. The presented work thus exemplifies a fruitful human-computer interaction in computational metaphysics. Whether the presented result increases or decreases the attractiveness and persuasiveness of the ontological argument is a question I would like to pass on to philosophy and theology. (shrink)

In this note we give a simplified ordinal analysis of first-order reflection. An ordinal notation system$OT$is introduced based on$\psi $-functions. Provable$\Sigma _{1}$-sentences on$L_{\omega _{1}^{CK}}$are bounded through cut-elimination on operator controlled derivations.

This article presents a simplified proof of the result that bounded depth propositional proofs of the pigeonhole principle are exponentially large. The proof uses the new techniques for proving switching lemmas developed by Razborov and Beame. A similar result is also proved for some examples based on graphs.

This paper offers a unified semantic explanation of two observations that prove to be problematic for classical analyses of modals, conditionals, and disjunctions: the fact that disjunctions scoping under possibility modals give rise to the free choice effect and the fact that counterfactuals license simplification of disjunctive antecedents. It shows that the data are well explained by a dynamic semantic analysis of modals and conditionals that uses ideas from the inquisitive semantic tradition in its treatment of disjunction. The analysis explains (...) why embedding a disjunctive possibility under negation reverts disjunction to its classical behavior, is general enough to predict less studied simplification patterns, and also makes progress toward a unified perspective on the distinction between informative, inquisitive, and attentive content. (shrink)

Doxastic dualists acknowledge both outright beliefs and credences, and they maintain that neither state is reducible to the other. This gives rise to the ‘Bayesian Challenge’, which is to explain why we need beliefs if we have credences already. On a popular dualist response to the Bayesian Challenge, we need beliefs to simplify our reasoning. I argue that this response fails because credences perform this simplifying function at least as well as beliefs do.

We give a simplified treatment of revised countable support (RCS) forcing iterations, previously considered by Shelah (see [Sh, Chap. X]). In particular we prove the fundamental theorem of semi-proper forcing, which is due to Shelah: any RCS iteration of semi-proper posets is semi-proper.

In this chapter, I discuss the possibility of using genome editing technologies in the context of assisted reproduction. I present the most prominent arguments in favour of and against this use of genome editing technologies, and explore two strategies used in bioethics in the event of moral disagreement to analyse the questions at hand and to develop morally sound policies. These strategies are: the clarification of the facts regarding a new technology and the formulation of the best philosophical argument. I (...) contend that both approaches are theoretically flawed and might result in states of affairs that fail to promote peoples’ well-being. I then argue that we should focus instead on finding at least some common ground in order to move forward in the debate on genome editing, building a regulatory framework that lightens “the burden of human existence”, whilst still accommodating opposing views as much as possible. Furthermore, I argue that insights from moral psychology and democratic governance can assist us in these challenges. (shrink)

What is truth? What precisely is it that truths have that falsehoods lack? Pluralists about truth (or “alethic pluralists”) tend to answer these questions by saying that there is more than one way for a proposition, sentence, belief—or any chosen truth-bearer—to be true. In this paper, I argue that two of the most influential formations of alethic pluralism, those of Wright (1992, 2003a) and Lynch (2009), are subject to serious problems. I outline a new formulation, which I call “simple determination (...) pluralism,” that I claim offers better prospects for alethic pluralism, with the potential to have applications for pluralist theories beyond truth. (shrink)

Several philosophers maintain that outright belief exists because it plays a reasoning simplifying role (Holton 2008; Ross and Schroeder 2014; Staffel 2019; Weisberg 2020). This claim has been recently contested, on the grounds that credences also can simplify reasoning (Dinges 2021). This paper takes a step back and asks: what features of an attitude explain its alleged ability to simplify reasoning? The paper contrasts two explanations, one in terms of dispositions and the other in terms of representation, arguing in favour (...) of the latter and against the former. The proposed explanation yields two interesting results: first, both belief and other attitudes, such as acceptance and imagination, can play a reasoning simplifying role; second, credences do not simplify our reasoning. (shrink)

What position on dualism does medicine require? Our understanding of that ques- tion has been dictated by holism, as defined by the biopsychosocial model, since the late twentieth century. Unfortunately, holism was characterized at the start with con- fused definitions of ‘dualism’ and ‘reductionism’, and that problem has led to a deep, unrecognized conceptual split in the medical professions. Some insist that holism is a nonreductionist approach that aligns with some form of dualism, while others insist it’s a reductionist view (...) that sets out to eradicate dualism. It’s important to consider each version. Nonreductive holism is philosophically consistent and clinically unprob- lematic. Reductive holism, however, is conceptually incoherent—yet it is the basis for the common idea that the boundary between medical and mental health disorders must be vague. When we trace that idea through to its implementation in medical practice, we find evidence that it compromises the safety of patient care in the large portion of cases where clinicians grapple with diagnosis at the boundary between psychiatry and medicine. Having established that medicine must embrace some form of nonreduc- tionism, I argue that Chalmers’ naturalistic dualism is a stronger prima facie candidate than the nonreductive alternatives. Regardless of which form of nonreductionism we prefer, some philosophical corrections are needed to give medicine a safe and coherent foundation. (shrink)

According to an increasingly popular epistemological view, people need outright beliefs in addition to credences to simplify their reasoning. Outright beliefs simplify reasoning by allowing thinkers to ignore small error probabilities. What is outright believed can change between contexts. It has been claimed that thinkers manage shifts in their outright beliefs and credences across contexts by an updating procedure resembling conditionalization, which I call pseudo-conditionalization (PC). But conditionalization is notoriously complicated. The claim that thinkers manage their beliefs via PC is (...) thus in tension with the view that the function of beliefs is to simplify our reasoning. I propose to resolve this puzzle by rejecting the view that thinkers employ PC. Based on this solution, I furthermore argue for a descriptive and a normative claim. The descriptive claim is that the available strategies for managing beliefs and credences across contexts that are compatible with the simplifying function of outright beliefs can generate synchronic and diachronic incoherence in a thinker’s attitudes. Moreover, I argue that the view of outright belief as a simplifying heuristic is incompatible with the view that there are ideal norms of coherence or consistency governing outright beliefs that are too complicated for human thinkers to comply with. (shrink)

We give a simplified version of the system introduced in ‘Non-Redundancy’, presented here as a Modal Logic whose primitive elements are finite sequences. It includes a treatment of Condition C, Condition B, Condition A, and the Locality of Variable Binding, but disregards quantification and Weak and Strong Crossover effects, which are treated in the longer paper.

Excerpt from Psychology Simplified The dormant condition of the avenues in the brain is the only thing intervening between man and the solution of psychic manifestations. Mind can remove the existing conditions in the brain and put man in touch with the solu tion of these things. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology (...) to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

This paper shows that a recent, simplified version of St. Anselm's proof of the existence of God has its flank open to Gaunilo's objection. Reformulating Anselm's line of reasoning in terms of the distinction between mediated and unmediated causal powers, as the simplified proof does, makes it harder for Anselm's supporters to refute the objection that the ontological argument absurdly entails the existence of all kinds of fictional entities.

In the present paper we examine very weak modal logics C1, D1, E1, S0.5◦, S0.5◦+(D), S0.5 and some of their versions which are closed under replacement of tautological equivalents (rte-versions). We give semantics for these logics, formulated by means of Kripke style models of the form , where w is a «distinguished» world, A is a set of worlds which are alternatives to w, and V is a valuation which for formulae and worlds assigns the truth-vales such that: (i) for (...) all formulae and all worlds, V preserves classical conditions for truth-value operators; (ii) for the world w and any formula ϕ, V(⬜ϕ,w) = 1 iff ∀x∈A V(ϕ,x) = 1; (iii) for other worlds formula ⬜ϕ has an arbitrary value. Moreover, for rte-versions of considered logics we must add the following condition: (iv) V(⬜χ,w) = V(⬜χ[ϕ/ψ],w), if ϕ and ψ are tautological equivalent. Finally, for C1, D1and E1 we must add queer models of the form in which: (i) holds and (ii') V(⬜ϕ,w) = 0, for any formula ϕ. We prove that considered logics are determined by some classes of above models. (shrink)