We explore a general method based on trees of elementary submodels in order to present highly simplified proofs to numerous results in infinite combinatorics. While countable elementary submodels have been employed in such settings already, we significantly broaden this framework by developing the corresponding technique for countably closed models of size continuum. The applications range from various theorems on paradoxical decompositions of the plane, to coloring sparse set systems, results on graph chromatic number and constructions from point-set topology. Our main (...) purpose is to demonstrate the ease and wide applicability of this method in a form accessible to anyone with a basic background in set theory and logic. (shrink)

A permutation group G on a set A is ${\kappa }$ -homogeneous iff for all $X,Y\in \bigl [ {A} \bigr ]^ {\kappa } $ with $|A\setminus X|=|A\setminus Y|=|A|$ there is a $g\in G$ with $g[X]=Y$. G is ${\kappa }$ -transitive iff for any injective function f with $\operatorname {dom}(f)\cup \operatorname {ran}(f)\in \bigl [ {A} \bigr ]^ {\le {\kappa }} $ and $|A\setminus \operatorname {dom}(f)|=|A\setminus \operatorname {ran}(f)|=|A|$ there is a $g\in G$ with $f\subset g$.Giving a partial answer to a question of (...) P. M. Neumann [6] we show that there is an ${\omega }$ -homogeneous but not ${\omega }$ -transitive permutation group on a cardinal ${\lambda }$ provided (i) ${\lambda } {\omega }$ we give a method to construct large ${\kappa }$ -homogeneous, but not ${\kappa }$ -transitive permutation groups. Using this method we show that there exist ${\kappa }^+$ -homogeneous, but not ${\kappa }^+$ -transitive permutation groups on ${\kappa }^{+n}$ for each infinite cardinal ${\kappa }$ and natural number $n\ge 1$ provided $V=L$. (shrink)

We study combinatorial principles known as stick and club. Several variants of these principles and cardinal invariants connected to them are also considered. We introduce a new kind of side by-side product of partial orderings which we call pseudo-product. Using such products, we give several generic extensions where some of these principles hold together with ¬CH and Martin's axiom for countable p.o.-sets. An iterative version of the pseudo-product is used under an inaccessible cardinal to show the consistency of the club (...) principle for every stationary subset of limits of ω1 together with ¬CH and Martin's axiom for countable p.o.-sets. (shrink)

Let denote the class of all cardinal sequences of length α associated with compact scattered spaces. Also put If λ is a cardinal and α λ1>>λn−1 and ordinals α0,…,αn−1 such that α=α0++αn−1 and where each .The proofs are based on constructions of universal locally compact scattered spaces.

We investigate whether classical combinatorial theorems are provable in ZF. Some statements are not provable in ZF, but they are equivalent within ZF. For example, the following statements (i)–(iii) are equivalent: $$cf({\omega }_1)={\omega }_1$$ c f ( ω 1 ) = ω 1, $${\omega }_1\rightarrow ({\omega }_1,{\omega }+1)^2$$ ω 1 → ( ω 1, ω + 1 ) 2, any family $$\mathcal {A}\subset [{On}]^{<{\omega }}$$ A ⊂ [ On ] < ω of size $${\omega }_1$$ ω 1 contains a $$\Delta (...) $$ Δ -system of size $${\omega }_1$$ ω 1. Some classical results cannot be proven in ZF alone; however, we can establish weaker versions of these statements within the framework of ZF, such as $${{\omega }_2}\rightarrow ({\omega }_1,{\omega }+1)$$ ω 2 → ( ω 1, ω + 1 ), any family $$\mathcal {A}\subset [{On}]^{<{\omega }}$$ A ⊂ [ On ] < ω of size $${\omega }_2$$ ω 2 contains a $$\Delta $$ Δ -system of size $${\omega }_1$$ ω 1. Some statements can be proven in ZF using purely combinatorial arguments, such as: given a set mapping $$F:{\omega }_1\rightarrow {[{\omega }_1]}^{<{\omega }}$$ F : ω 1 → [ ω 1 ] < ω, the set $${\omega }_1$$ ω 1 has a partition into $${\omega }$$ ω -many F-free sets. Other statements can be proven in ZF by employing certain methods of absoluteness, for example: given a set mapping $$F:{\omega }_1\rightarrow {[{\omega }_1]}^{<{\omega }}$$ F : ω 1 → [ ω 1 ] < ω, there is an F-free set of size $${\omega }_1$$ ω 1, for each $$n\in {\omega }$$ n ∈ ω, every family $$\mathcal {A}\subset {[{\omega }_1]}^{{\omega }}$$ A ⊂ [ ω 1 ] ω with $$|A\cap B|\le n$$ | A ∩ B | ≤ n for $$\{A,B\}\in {[\mathcal {A}]}^{2}$$ { A, B } ∈ [ A ] 2 has property B. In contrast to statement (5), we show that the following ZFC theorem of Komjáth is not provable from ZF + $$cf({\omega }_1)={\omega }_1$$ c f ( ω 1 ) = ω 1 : (6$$ ^*$$ ∗ ) every family $$\mathcal {A}\subset {[{\omega }_1]}^{{\omega }}$$ A ⊂ [ ω 1 ] ω with $$|A\cap B|\le 1$$ | A ∩ B | ≤ 1 for $$\{A,B\}\in {[\mathcal {A}]}^{2}$$ { A, B } ∈ [ A ] 2 is essentially disjoint. A function f is a uniform denumeration on$${\omega }_1$$ ω 1 iff $${\text {dom}}(f)={\omega }_1$$ dom ( f ) = ω 1, and for every $$1\le {\alpha }<{\omega }_1$$ 1 ≤ α < ω 1, $$f({\alpha })$$ f ( α ) is a function from $${\omega }$$ ω onto $${\alpha }$$ α. It is easy to see that the existence of a uniform denumeration of $${\omega }_1$$ ω 1 implies $$cf({\omega }_1)={\omega }_1$$ c f ( ω 1 ) = ω 1. We prove that the failure of the reverse implication is equiconsistent with the existence of an inaccessible cardinal. (shrink)

Using Koszmider's strongly unbounded functions, we show the following consistency result: Suppose that κ, λ are infinite cardinals such that κ++ + ≤ λ, κ<κ = κ and 2κ = κ+, and η is an ordinal with κ+ ≤ η < κ++ and cf = κ+. Then, in some cardinal-preserving generic extension there is a superatomic Boolean algebra equation image such that equation image, equation image for every α < η and equation image. Especially, equation image and equation image can (...) be cardinal sequences of superatomic Boolean algebras. (shrink)

Continuing [6], [8] and [16], we study the consequences of the weak Freese-Nation property of (?(ω),⊆). Under this assumption, we prove that most of the known cardinal invariants including all of those appearing in Cichoń's diagram take the same value as in the corresponding Cohen model. Using this principle we could also strengthen two results of W. Just about cardinal sequences of superatomic Boolean algebras in a Cohen model. These results show that the weak Freese-Nation property of (?(ω),⊆) captures many (...) of the features of Cohen models and hence may be considered as a principle axiomatizing a good portion of the combinatorics available in Cohen models. (shrink)

Noetherian type and Noetherian π-type are two cardinal functions which were introduced by Peregudov in 1997, capturing some properties studied earlier by the Russian School. Their behavior has been shown to be akin to that of the cellularity, that is the supremum of the sizes of pairwise disjoint non-empty open sets in a topological space. Building on that analogy, we study the Noetherian π-type of κ-Suslin Lines, and we are able to determine it for every κ up to the first (...) singular cardinal. We then prove a consequence of Changʼs Conjecture for ℵω regarding the Noetherian type of countably supported box products which generalizes a result of Lajos Soukup. We finish with a connection between PCF theory and the Noetherian type of certain Pixley–Roy hyperspaces. (shrink)

This paper argues that Davidson's argument against conceptual schemes fail against so-called "Applied Relativisms", i.e. theories of conceptual relativism found outside philosophy such as Whorf's. These theories make no metaphysical claims, which Davidson seems to assume. Ultimately, the misunderstanding (and resulting strawman argument) illustrates (the effect of) differences in conceptual schemes more than that it undermines it.

In the early twentieth century, Uchiyama Gudō, Seno’o Girō, Lin Qiuwu, and others advocated a Buddhism that was radical in two respects. Firstly, they adopted a more or less naturalist stance with respect to Buddhist doctrine and related matters, rejecting karma or other supernatural beliefs. And secondly, they held political and economic views that were radically anti-hegemonic, anti-capitalist, and revolutionary. Taking the idea of such a “radical Buddhism” seriously, A Buddha Land in This World: Philosophy, Utopia, and Radical Buddhism asks (...) whether it is possible to develop a philosophy that is simultaneously naturalist, anti-capitalist, Buddhist, and consistent. Rather than a study of radical Buddhism, then, this book is an attempt to radicalize it. The foundations of this “radicalized radical Buddhism” are provided by a realist interpretation of Yogācāra, elucidated and elaborated with some help from thinkers in the broader Tiantai/Tendai tradition and American philosophers Donald Davidson and W.V.O. Quine. A key implication of this foundation is that only this world and only this life are real, from which it follows that if Buddhism aims to alleviate suffering, it has to do so in this world and in this life. Twentieth-century radical Buddhists (as well as some engaged Buddhists) came to a similar conclusion, often expressed in their aim to realize “a Buddha land in this world.” Building on this foundation, but also on Mahāyāna moral philosophy, this book argues for an ethics and social philosophy based on a definition of evil as that what is or should be expected to cause death or suffering. On that ground, capitalism should be rejected indeed, but utopianism must be treated with caution as well, which raises questions about what it means – from a radicalized radical Buddhist perspective – to aim for a Buddha land in this world. (shrink)

Rājadhamma is a list of ten royal virtues or duties that occurs in the jātaka tales and that has been influential in Southeast Asian Buddhist political thought. Like pre-modern political thought in Europe—that is, thought before the Sattelzeit—Buddhist political thought lacks a concept of the “state” and is concerned with kings and similar rulers. Here I propose a modernized interpretation of rājadhamma as virtues/duties of the state.

This paper deals with the origin, history and various appearances of the problem of coincidences (matches, rencontres) in the theory of probability.

Othering is the construction and identification of the self or in-group and the other or out-group in mutual, unequal opposition by attributing relative inferiority and/or radical alienness to the other/out-group. The notion of othering spread from feminist theory and post-colonial studies to other areas of the humanities and social sciences, but is originally rooted in Hegel’s dialectic of identification and distantiation in the encounter of the self with some other in his “Master-Slave dialectic”. In this paper, after reviewing the philosophical (...) and psychological background of othering, I distinguish two kinds of othering, “crude” and “sophisticated”, that differ in the logical form of their underlying arguments. The essential difference is that the former is merely self-other distantiating, while the latter – as in Hegel’s dialectic – partially depends on self-other identification. While crude othering is closer to the paradigmatic notion of othering, sophisticated othering is closer to Hegel’s, but so is quasi-othering, which is nearly identical in form to sophisticated othering, but which misses the defining feature of othering – attributing relative inferiority and/or radical alienness. Because Hegel’s dialectic applies to any encounter of an interpreting self with some other, sophisticated or quasi-othering is at least potentially a very common occurrence in the interpretation of others, especially of those who do not belong to the in-group. However, although othering is usually undesirable, the Hegelian varieties can provide a “mirror”, which can be used as a tool to improve understanding of both the other and the interpreting self, and the malignant aspects of othering can be avoided through charity. (shrink)

The gravity-related model of spontaneous wave function collapse, a longtime hypothesis, damps the massive Schrödinger Cat states in quantum theory. We extend the hypothesis and assume that spontaneous wave function collapses are responsible for the emergence of Newton interaction. Superfluid helium would then show significant and testable gravitational anomalies.

Buddhist Ethics. The Path to Nirvana. Hammalawa Saddhatissa. Wisdom Books, London 1987. £6.95/$12.95.

L'étude de la communication peut offrir une perspective sur le contexte de la théologie, un examen de sa structure, et une reflexion sur son contenu. La communication est primordiale pour la société contemporaine, affectant la façon dont les gens utilisent leur temps, façonnant les informations qu'ils reçoivent, influençant la manière dont ils pensent , et les rendant plus soupçonneux vis à vis de l'autorité. L'histoire de la théologie montre les effets des formes de communication, reflétant la narration, la rhétorique, et (...) les structures polémiques des cultures orales, aussi bien que les instruments analytiques de l'écriture et l'imprimerie. Finalement, l'étude de la communication suggère une façon différente de considérer des sujets théologiques traditionnels. Le salut divin, par exemple, peut se concentrer sur la communication en interprètant l'histoire du salut comme une histoire de l'auto-communication de Dieu et la restauration de la communication humaine. (shrink)

This paper analyzes some grammatical aspects of the English verb "to mean" and its nominalizations, and based on that, argues that meaning is something that people do rather than something that words have.

This paper presents a simple model to estimate the number of languages that existed throughout history, and considers philosophical and linguistic implications of the findings. The estimated number is 150,000 plus or minus 50,000. Because only few of those remain, and there is no reason to believe that that remainder is a statistically representative sample, we should be very cautious about universalistic claims based on existing linguistic variation.

Two of the most fundamental distinctions in metaphysics are (1) that between reality (or things in themselves) and appearance, the R/A distinction, and (2) that between entities that are fundamental (or real, etcetera) and entities that are ontologically or existentially dependent, the F/D distinction. While these appear to be two very different distinctions, in Buddhist metaphysics they are combined, raising questions about how they are related. In this paper I argue that plausible versions of the R/A distinction are essentially a (...) special kind of F/D distinction, and conversely, that many F/D distinctions imply an R/A distinction. Nevertheless, while this does suggest that the F/D distinction is more basic than the R/A distinction, it does not favor a particular understanding of the F/D distinction. There are many kinds of existential or ontological dependence that cannot be meaningfully combined into a single notion, and reality does not force us to accept any specific kind of dependence as more fundamental. Consequently, what we consider to be ‘real’, ‘fundamental’, or ‘really existing’ is not entirely given by reality, but partially up to us. (shrink)

(First paragraphs.) — The notion of “mental time” refers to the experience and awareness of time, including that of past, present, and future, and that of the passing of time. This experience and awareness of time raises a number of puzzling questions. How do we experience time? What exactly do we experience when we experience time? Do we actually experience time? Or do we infer time from something in, or some aspect of our experience? And so forth. These and many (...) related questions in the “philosophy of mental time”, the topic of this special issue of the Annals of the Japan Association for Philosophy of Science, are not purely philosophical questions. Or at least, they are not likely to be satisfactorily answered by philosophers alone. Rather, they also need the input of neuroscientists, psychologists, physicists, linguists, and others. And conversely, answers to these questions may have implications outside the scope of philosophy. The papers in this special issue illustrate this inherent multi- or interdisciplinarity of the philosophy and science of mental time. In this theme introduction, we want to give a few more examples to illustrate this interdisciplinarity, but also to point out that much of the field is still wide open—that is, these illustrations raise more questions than answers. (shrink)

Episodic memory (EM) involves re-experiencing past experiences by means of mental imagery. Aphantasics (who lack mental imagery) and people with severely deficient autobiographical memory (SDAM) lack the ability to re-experience, which would imply that they don't have EM. However, aphantasics and people with SDAM have personal and affective memories, which are other defining aspects of EM (in addition to re-experiencing). This suggests that these supposed aspects of EM really are independent faculties or modules of memory, and that EM is a (...) composite faculty rather than a natural kind. Apparent varieties of (normal and "defective") EM (as well as some closely related kinds of memory) are different combinations of these modules, and the EM construct itself adds little if any explanatory value to these modules. (shrink)

If we distinguish phenomenal effects from their noumenal causes, the former being our conceptual(ized) experiences, the latter their grounds or causes in reality ‘as it is’ independent of our experience, then two contradictory positions with regards to the relationship between these two can be distinguished: either phenomena are identical with their noumenal causes, or they are not. Davidson is among the most influential modern defenders of the former position, metaphysical non-dualism. Dharmakīrti’s strict distinction between ultimate and conventional reality, on the (...) other hand, may be one of the most rigorously elaborated theories of the opposite position, metaphysical dualism. Despite this fundamental difference, their theories about the connection between phenomena and their noumenal causes are surprisingly similar in important respects. Both Dharmakīrti in his theory of ‘apoha’ and Davidson in his theory of ‘triangulation’ argued that the content of words or concepts depends on a process involving at least two communicating beings and shared noumenal stimuli. The main point of divergence is the nature of classification, but ultimately Dharmakīrti’s and Davidson’s conclusions on the noumenal-phenomenal relationship turn out to be complementary more than contradictory, and an integrative reconstruction suggests a ‘middle path’ between dualism and non-dualism. (shrink)

Davidson was right when he said that the idea of truth as a goal or norm makes no sense — truth is not something we can aim for, and whenever we say that we aim for truth, what we are really aiming for is some kind of epistemic justification. Nevertheless, the notion of a concern for or with truth can be understood in (at least) three ways that do make sense: (1) it can refer to a philosophical concern with the (...) nature of truth, theories of truth, and related philosophical problems; (2) it can refer to a concern (or aim) for ‘strong’ justification; and (3) it can refer to an attitude or ideal of truth(fulness). Concern for epistemic justification can be found in the Chinese and Indian philosophical traditions as well, and is probably universal among philosophical and scientific traditions. Assessing the third sense of concern for truth is more complicated, but considering that a lack of desire for the truth of one’s theories and ideas seems anathema to science and philosophy, it seems likely that something like this concern is universal among philosophical and scientific traditions as well. Concern with truth in the most literal sense — that is, a philosophical concern with truth in its basic sense as captured in Tarski’s schema — appears to be rare, however, and may even be unique to the Western tradition. (shrink)

This is my reply to McLeod’s reply (2015a) to my (2015) paper commenting on his (2011) interpretation of Wang Chong 王充 as an alethic pluralist.

Saṃvega is a morally motivating state of shock that -- according to Buddhaghosa -- should be evoked by meditating on death. What kind of mental state it is exactly, and how it is morally motivating is unclear, however. This article presents a theory of saṃvega -- what it is and how it works -- based on recent insights in psychology. According to dual process theories there are two kinds of mental processes organized in two" systems" : the experiential, automatic system (...) 1, and the rational, controlled system 2. In normal circumstances, system 1 does not believe in its own mortality. Saṃvega occurs when system 1 suddenly realizes that the "subjective self" will inevitably die (while system 2 is already disposed to affirm the subject's mortality). This results in a state of shock that is morally motivating under certain conditions. Saṃvega increases mortality salience and produces insight in suffering, and in combination with a strengthened sense of loving-kindness or empathic concern both mortality salience and insight in suffering produce moral motivation. (shrink)

(First paragraphs.) The idea that our language somehow influences our thought can be found in philosophical and scientific traditions of different continents and with different roots and objectives. Yet, beyond the mere theoretical, explorations of the idea are relatively scarce, and are mostly limited to relations between very concrete conceptual categories and subjective experiencing and remembering – to some kind of ‘psychologies of folk-ontology’. Thought as process, reasoning or ‘thinking’, and the role of more complex or abstract concepts in (such) (...) thought tend to be mostly ignored in psychology and philosophy. Conceptual and intellectual history, on the other hand, cannot be accused of such neglect, but the common lack of a comparative perspective in those fields precludes any generalized inference. Furthermore, while a comparative study on the role of complex or abstract concepts in thought as process and its products (the aggregate ‘thought’ of schools, ages, and regions) could result in a considerable enrichment of our understanding of the relationships between language and thought, it would not necessarily be recognized as such because of a fundamental difference in the nature of the concepts involved, affecting the boundary of ‘language’ in the pair ‘language and thought’. More concretely, while the concepts of the ‘psychologies of folk-ontology’ are rather concrete categories of ‘things’ or aspects of experienced reality (hence, ‘folk-ontology’), the abstract concepts of (comparative) conceptual history, such as ‘society’ or ‘reason’, are categories of ideas. Consequently, conceptual history is inseparably tied to the history of ideas, and there is no strict boundary line between concepts, theories, ideas, and aggregate thought in general. It could, therefore, be argued that a comparative conceptual history would be a study of the influence of ideas on thought, rather than of language on thought. That argument, however, would either void language of content, or make the dubious claim that folk-ontology is a fundamentally different type of content than theoretical content. The ‘psychologies of folk-ontology’ study the influence of folk-ontological categories on folk-ontological thought (experiencing and remembering), and a comparative conceptual history would study the influence of theoretical categories (or conceptualized ideas) on theoretical thought (thinking, reasoning, etc.), and there does not seem to be a good reason to exclude either type of categories from ‘language’. Perhaps it should be argued instead that the ambiguous term ‘language’ in the pair ‘language and thought’ would better be replaced with ‘concepts’ or ‘categories’. (shrink)

In “Real Patterns” Daniel Dennett developed an argument about the reality of beliefs on the basis of an analogy with patterns and noise. Here I develop Dennett’s analogy into an argument for descriptivism, the view that belief reports do no specify belief contents but merely describe what someone believes, and show that this view is also supported by empirical evidence. No description can do justice to the richness and specificity or “noisiness” of what someone believes, and the same belief can (...) be described by different sentences or propositions (which is illustrated by Dennett’s analogy, some Gettier cases, and Frege’s puzzle), but in some contexts some of these competing descriptions are misleading or even false. Faithful (or truthful) description must be guided by a principle (or principles) related to the principle of charity: belief descriptions should not attribute irrationality to the believer or have other kinds of “deviant” implications. (shrink)

This essay describes the author's studies with bacteria in post‐war Hungary; the difficulties encountered, with funding, collaboration and publication; and how the Szeged Institute consolidated itseif as the one outstanding scientific Institute in Eastern Europe, with the author at the helm.

Name der Zeitschrift: Der Islam Jahrgang: 93 Heft: 2 Seiten: 532-580.

Putnam and Davidson both defended coherence theories of justification from the early 1980s onward. There are interesting similarities between these theories, and Putnam’s philosophical development lead to further convergence in the 1990s. The most conspicuous difference between Putnam’s and Davidson’s theories is that they appear to fundamentally disagree on the role and nature of conceptual schemes, but a closer look reveals that they are not as far apart on this issue as usually assumed. The veridicality of perceptual beliefs is a (...) cornerstone of both Davidson’s and Putnam’s later (but not earlier) coherentism. However, this thesis introduces a form of weak foundationalism into their theories, and consequently, those are strictly speaking not pure coherence theories, but hybrids between coherentism and foundationalism. (shrink)

In this paper we discuss the definitional problems of altered states of consciousness and their potential relevance in phenomenological investigation. We suggest that visionary states or visionary phantasy working induced by psychedelics, as extraordinary types of altered states, are appropriate subjects for phenomenological analysis. Naturally, visionary states are not quite ordinary workings of the human mind, however certain cognitive psychological and evolutionary epistemological investigations show that they can give new insights into the nature of consciousness. Furthermore, we suggest that contemporary (...) inquiries concerning altered states in consciousness studies give an opportunity to complete the contemporary phenomenological investigations of phantasy with the notion of visionary phantasy. Here we propose that the similarities and differences between Dieter Lohmar’s weak phantasy and Benny Shanon’s concept of vision are precisely discernible, and, consequently, it may be possible that weak phantasy and visionary phantasy are situated on the two outermost poles of the colorful spectrum of phantasy activity. (shrink)