The aim of this study is to explore how Greek youth understands their relationship to education, and how this understanding might change as a result of the interplay between participation in different educational/social arrangements and structural factors such as gender, socio?economic background and area of residence. In total, 800 young people (i.e. four groups?students in upper?secondary school, tertiary education, vocational education and training and working young people) were surveyed. The results yield an impressive homogeneity of the young people?s views corresponding (...) to a ?pragmatic? image of schooling, though they are partially differentiated with respect to attitudes and practices. Moreover, boundaries are discerned between the young people following academic and non?academic educational trajectories, and between the learning opportunities provided within and outside the formal educational system. Finally, females appear to be more mobilized, but less satisfied by educational services. These findings are contextualized and discussed against a background of relevant trends in other European countries, as well as of wider social, historical and political forces affecting Greek society. (shrink)

An argument that there are perceptual mechanisms that retrieve information in cognitively and conceptually unmediated ways and that this sheds light on various ...

Empirical research suggests that motive states modulate perception affecting perceptual processing either directly, or indirectly through the modulation of spatial attention. The affective modulation of perception occurs at various latencies, some of which fall within late vision, that is, after 150 ms. poststimulus. Earlier effects enhance the C1 and P1 ERP components in early vision, the former enhancement being the result of direct emotive effects on perceptual processing, and the latter being the result of indirect effects of emotional stimuli on (...) perceptual processing that automatically capture exogenous attention. Other research suggests that emotional stimuli do not capture attention automatically but attentional capture is conditioned on the context. Since context dependent effects are first registered with the elicitation of N1 ERP component about 170 ms. poststimulus, emotional stimuli affect late vision. However, the early affective modulation of early vision by emotive states threatens the cognitive impenetrability of early vision since emotive states are associated with learning and past experiences. I argue that the emotive modulation of early vision does not entail the cognitive penetrability of early vision. First, the early indirect affective modulation of P1 is akin to the effects of spatial pre-cueing by non-emotive cues and these preparatory effects do not signify the cognitive impenetrability of early vision. Second, because the direct modulation of C1 signifies an initial, involuntary appraisal of threat in the incoming stimulus that precedes any cognitive states. (shrink)

We discuss at some length evidence from the cognitive science suggesting that the representations of objects based on spatiotemporal information and featural information retrieved bottomup from a visual scene precede representations of objects that include conceptual information. We argue that a distinction can be drawn between representations with conceptual and nonconceptual content. The distinction is based on perceptual mechanisms that retrieve information in conceptually unmediated ways. The representational contents of the states induced by these mechanisms that are available to a (...) type of awareness called phenomenal awareness constitute the phenomenal content of experience. The phenomenal content of perception contains the existence of objects as separate things that persist in time and time, spatiotemporal information, and information regarding relative spatial relations, motion, surface properties, shape, size, orientation, color, and their functional properties. (shrink)

We adjust the notion of typicality originated with Russell, which was introduced and studied in a previous paper for general first-order structures, to make it expressible in the language of set theory. The adopted definition of the class ${\rm NT}$ of nontypical sets comes out as a natural strengthening of Russell's initial definition, which employs properties of small (minority) extensions, when the latter are restricted to the various levels $V_\zeta$ of $V$. This strengthening leads to defining ${\rm NT}$ as the (...) class of sets that belong to some countable ordinal definable set. It follows that ${\rm OD}\subseteq {\rm NT}$ and hence ${\rm HOD}\subseteq {\rm HNT}$. It is proved that the class ${\rm HNT}$ of hereditarily nontypical sets is an inner model of ${\rm ZF}$. Moreover the (relative) consistency of $V\neq {\rm NT}$ is established, by showing that in many forcing extensions $M[G]$ the generic set $G$ is a typical element of $M[G]$, a fact which is fully in accord with the intuitive meaning of typicality. In particular it is consistent that there exist continuum many typical reals. In addition it follows from a result of Kanovei and Lyubetsky that ${\rm HOD}\neq {\rm HNT}$ is also relatively consistent. In particular it is consistent that ${\cal P}(\omega)\cap {\rm OD}\subsetneq{\cal P}(\omega)\cap {\rm NT}$. However many questions remain open, among them the consistency of ${\rm HOD}\neq {\rm HNT}\neq V$, ${\rm HOD}={\rm HNT}\neq V$ and ${\rm HOD}\neq {\rm HNT}= V$. (shrink)

Transforming growth factor‐β (TGF‐β) and its related proteins regulate broad aspects of body development, including cell proliferation, differentiation, apoptosis and gene expression, in various organisms. Deregulated TGF‐β function has been causally implicated in the generation of human fibrotic disorders and in tumor progression. Nevertheless, the molecular mechanisms of TGF‐β action remained essentially unknown until recently. Here, we discuss recent progress in our understanding of the mechanism of TGF‐β signal transduction with respect to the regulation of gene expression, the control of (...) cell phenotype and the potential usage TGF‐β for the treatment of human diseases. (shrink)

To comprehend the world around us, we first have to decipher how our brains work. This book outlines a new approach to knowledge and understanding based on the elucidation of several basic neuronal mechanisms. This book explores the crucial fact that unconscious processes and conscious experiences form a continuum, which introduces the concept of 'rerepresentations'. Examples of rerepresentations can be seen in language, mathematics, technology and the arts. This fundamental notion captures the essence of being human, namely what separates us (...) from our evolutionary predecessors. For this reason, an effort has been made to present all notions from first principles, without assuming any background specialized knowledge. Although this volume will be more easily accessible to individuals with a background in sciences and medicine, Ways of Comprehending presents, in an accessible manner, important information which should be common knowledge, but is lacking among the vast majority of scientists, technocrats, and humanities scholars. The interdisciplinary, integrative approach presented in this book implies that different disciplines and notions which appear disconnected, are actually closely related. This approach elucidates how we think about topics such as mathematics, physics, painting, music, and philosophy. More importantly, it helps us understand the origin of our thoughts, feelings and actions. This finally brings deep insight and fulfilment or, more precisely, eudemonia. (shrink)

I elaborate on Pylyshyn's definition of the cognitive impenetrability (CI) of early vision, and draw on the role of concepts in perceptual processing, which links the problem of the CI or cognitive penetrability (CP) of early vision with the problem of the nonconceptual content (NCC) of perception. I explain, first, the sense in which the content of early vision is CI and I argue that if some content is CI, it is conceptually encapsulated, that is, it is NCC. Then, I (...) examine the definitions of NCC and argue that they lead to the view that the NCC of perception is retrieved in a stage of visual processing that is CI. Thus, the CI of a state and content is a sufficient and necessary condition for the state and its content to be purely NCC, the CI?≡?NCC thesis. Since early vision is CI, the purely NCC of perception is formed in early vision. I defend the CI?≡?NCC thesis by arguing against objections raised against both the sufficient and the necessary part of the thesis. (shrink)

In this paper, I claim that since there is a cognitively impenetrable stage of visual perception, namely early vision, and cognitive penetrability and theory-ladenness are coextensive, the CI of early vision entails that early vision content is theory neutral. This theory-neutral part undermines relativism. In this paper, I consider two objections against the thesis. The one adduces evidence from cases of rapid perceptual learning to undermine my thesis that early vision is CI. The other emphasizes that the early perceptual system, (...) in order to solve various underdetermination problems, relies on certain principles, which may be taken to constitute a sort of a theory about the world that affect early vision, rendering it theory-laden. Both objections purport to show that early vision is CP and theory-laden. Against this thesis, I argue that the evidence on which the two objections are based does not show that early vision is CP and is fully compatible with the view that early vision is CI. (shrink)

We present a formal first-order theory of artificial objects, i.e., objects made out of a finite number of parts and subject to assembling and dismantling processes. These processes are absolutely reversible. The theory is an extension of the theory of finite sets with urelements. The notions of transformation and identity are defined and studied on the assumption that the objects are homogeneous, that is to say, all their atomic parts are of equal ontological importance. Particular emphasis is given to the (...) behavior of classes of artifacts in time. We call such classes satisfying certain preservation conditions worlds. Various results concerning the existence, extension, and completeness of worlds are proved. (shrink)

We reformulate slightly Russell's notion of typicality, so as to eliminate its circularity and make it applicable to elements of any first‐order structure. We argue that the notion parallels Martin‐Löf (ML) randomness, in the sense that it uses definable sets in place of computable ones and sets of “small” cardinality (i.e., strictly smaller than that of the structure domain) in place of measure zero sets. It is shown that if the domain M satisfies, then there exist typical elements and only (...) non‐typical ones. In particular this is true for the standard model of second‐order arithmetic. By allowing parameters in the defining formulas, we are led to relative typicality, which satisfies most of van Lambalgen's axioms for relative randomness. However van Lambalgen's theorem is false for relative typicality. The class of typical reals is incomparable (with respect to ⊆) with the classes of ML‐random, Schnorr random and computably random reals. Also the class of typical reals is closed under Turing degrees and under the jump operation (both ways). (shrink)

Fodor has argued that observation is theory neutral, since the perceptual systems are modular, that is, they are domain‐specific, encapsulated, mandatory, fast, hard‐wired in the organism, and have a fixed neural architecture. Churchland attacks the theoretical neutrality of observation on the grounds that (a) the abundant top‐down pathways in the brain suggest the cognitive penetration of perception and (b) perceptual learning can change in the wiring of the perceptual systems. In this paper I introduce a distinction between sensation, perception, and (...) observation and I argue that although Churchland is right that observation involves top‐down processes, there is also a substantial amount of information in perception which is theory‐neutral. I argue that perceptual learning does not threaten the cognitive impenetrability of perception, and that the neuropsychological research does not provide evidence in favor of the top‐down character of perception. Finally, I discuss the possibility of an off‐line cognitive penetrability of perception. (shrink)

In this paper I discuss Newton's first optical paper. My aim is to examine the type of argument which Newton uses in order to convince his readers of the truth of his theory of colors. My claim is that this argument is an induction by elimination, and that the Newtonian method of justification is a kind of “generative justification”, a term due to T. Nickles. To achieve my aim I analyze in some detail the arguments in Newton's first optical paper, (...) relating the paper with Newton's other writings in optics, and especially his early correspondence in defence of his theory of colors. (shrink)

We give a necessary and sufficient condition in order that a type-shifting automorphism be constructed on a model of the Theory of Simple Types (TST) by forcing. Namely it is proved that, if for every n ≥ 1 there is a model of TST in the ground model M of ZFC that contains an n-extendible coherent pair, then there is a generic extension M[G] of M that contains a model of TST with a type-shifting automorphism, and hence M[G] contains a (...) model of NF. The converse holds trivially. It is also proved that there exist models of TST containing l-extendible coherent pairs. (shrink)

European identity is a complex, multi-faced and inherently imprecise concept relating to a range of socio-political and psychological factors. Addressing this topic in educational practice, particularly with respect to Higher Education students, constitutes a complex and open problem for research. This paper reports on an experimental study designed to explore the effectiveness of the educational game “RUEU?” in supporting university students in understanding the key socio-political issues regarding European identity. Quantitative data regarding Greek university students’ attitudes to European identity, before (...) and after playing the game, were collected. Students’ performance of the game group was compared with that of a control group who explored the same issues about European identity through a tutor-guided discussion. The findings showed that both instructional interventions were effective but in different ways. The participants in the game-based group appeared more attached to the EU after the intervention and moved toward a more balanced description of their Greek and European identity. On the other hand, the students in the control group rated higher what “European identity” and being EU citizen means to them. The findings indicated the potential of game-based interventions to deliver not only academic content but also to promote students’ reflection and influence them at an attitudinal and emotional level. (shrink)

This book is about the interweaving between cognitive penetrability and the epistemic role of the two stages of perception, namely early and late vision, in justifying perceptual beliefs. It examines the impact of the epistemic role of perception in defining cognitive penetrability and the relation between the epistemic role of perceptual stages and the kinds of cognitive effects on perceptual processing. The book presents the argument that early vision is cognitively impenetrable because neither is it affected directly by cognition, nor (...) does cognition affect its epistemic role. It also argues that late vision, even though it is cognitively penetrated and, thus, affected by concepts, is still a perceptual state that does not involve any discursive inferences and does not belong to the space of reasons. Finally, an account is given as to how cognitive states with symbolic content could affect perceptual states with iconic, analog content, during late vision. (shrink)

In this paper I argue for the cognitive impenetrability of perception by undermining the argument from reentrant pathways. To do that I will adduce psychological and neuropsychological evidence showing that (a) early vision processing is not affected by our knowledge about specific objects and events, and (b) that the role of the descending pathways is to enable the early-vision processing modules to participate in higher-level visual or cognitive functions. My thesis is that a part of observation, which I will call (...) perception, is bottom-up and theory neutral. As such, perception could play the role of common ground on which a naturalized epistemology can be built and relativism avoided. (shrink)

We show that the notion of cardinality of a set is independent from that of wellordering, and that reasonable total notions of cardinality exist in every model of ZF where the axiom of choice fails. Such notions are either definable in a simple and natural way, or non-definable, produced by forcing. Analogous cardinality notions exist in nonstandard models of arithmetic admitting nontrivial automorphisms. Certain motivating phenomena from quantum mechanics are also discussed in the Appendix.

We provide a new semantics and a slightly different formalisation for the propositional logic with superposition introduced and studied in Tzouvaras [. Propositional superposition logic...

We establish some similarities/analogies between uncountable cardinals or powersets and the class V of all sets. They concern mainly the Boolean algebras, for a regular cardinal κ, and (the class of subclasses of the universe V), endowed with some ideals, especially the ideal for, and the ideal of sets V for.

In this paper I propose to link [Hesiod] fr. 276 M.-W. with the mythological narrative preserved on PSI 14. 1398, which relates the death of Teiresias. This narrative belong to a work that drew on the lost Melampodia and provides information regarding this Hesiodic poem that had hitherto escaped our notice. Regarding the type of text preserved on PSI 14. 1398, the scanty remnants of the papyrus’ second column, where we read traces of what appears to be κeuqein and dendroκomov, (...) both poetic words, suggest that it must have been a prose text quoting poetry. Possibilities include a text on the history of divination, such as Philochorus peri mantiκnv, which offered a historical overview of famous exponents of the mantic art and included poetic quotations, or alternatively a text that belongs to the commentary genre broadly conceived, perhaps even a text akin to the so-called ‘Homeric anthologies’. (shrink)

One of the perennial themes in philosophy is the problem of our access to the world around us; do our perceptual systems bring us into contact with the world as it is or does perception depend upon our individual conceptual frameworks? This volume of new essays examines reference as it relates to perception, action and realism, and the questions which arise if there is no neutral perspective or independent way to know the world. The essays discuss the nature of referring, (...) concentrating on the way perceptual reference links us with the observable world, and go on to examine the implications of theories of perceptual reference for realism and the way in which scientific theories refer and thus connect us with the world. They will be of interest to a wide range of readers in philosophy of science, epistemology, philosophy of psychology, cognitive science and action theory. (shrink)

'Epistemological constructivism' holds that vision is mediated by background preconceptions and is theory-laden. Hence, two persons with differing theoretical commitments see the world differently and they could agree on what they see only if they both espoused the same conceptual framework. This, in its turn, undermines the possibility of theory testing and choice on a common theory-neutral empirical basis. In this paper, I claim that the cognitive sciences suggest that a part of vision may be only indirectly penetrated by cognition (...) in a way that does not threaten retrieval of information from a visual scene in a bottom-up way. That blocks the constructivist epistemological thesis. However, since spatial attention, which can be cognitively driven, seems to permeate all stages of visual processes, one is led to conclude that there is no part of vision immune to direct cognitive interference. Against this, I elaborate on the role of spatial attention and argue that it does influence vision in a top-down manner, but it does so only in an indirect way. I then argue that the existence of visual processes that are only indirectly penetrated by cognition undermines the epistemological conclusions of constructivism. (shrink)

In this paper we address the issue of grounding for experiential concepts. Given that perceptual demonstratives are a basic form of such concepts, we examine ways of fixing the referents of such demonstratives. To avoid ‘encodingism’, that is, relating representations to representations, we postulate that the process of reference fixing must be bottom-up and nonconceptual, so that it can break the circle of conceptual content and touch the world. For that purpose, an appropriate causal relation between representations and the world (...) is needed. We claim that this relation is provided by spatial and object-centered attention that leads to the formation of object files through the function of deictic acts. This entire causal process takes place at a pre-conceptual level, meeting the requirement for a solution to the grounding problem. Finally we claim that our account captures fundamental insights in Putnam’s and Kripke’s work on “new” reference. (shrink)

Let be a countable first‐order language and be an ‐structure. “Definable set” means a subset of M which is ‐definable in with parameters. A set is said to be immune if it is infinite and does not contain any infinite definable subset. X is said to be partially immune if for some definable A, is immune. X is said to be totally non‐immune if for every definable A, and are not immune. Clearly every definable set is totally non‐immune. Here we (...) ask whether the converse is true and prove that it is false for every countable structure whose class of definable sets satisfies a mild condition. We investigate further the possibility of an alternative construction of totally non‐immune non‐definable sets with the help of a subclass of immune sets, the class of cohesive sets, as well as with the help of a generalization of definable sets, the semi‐definable ones (the latter being naturally defined in models of arithmetic). Finally connections are found between totally non‐immune sets and generic classes in nonstandard models of arithmetic. (shrink)

Dartnall claims that visual short-term memory stores nonconceptual content , in the form of compressed images. In this paper I argue against the claim that NCC can be stored in VSTM. I offer four reasons why NCC cannot be stored in visual memory and why only conceptual information can: NCC lasts for a very short time and does not reach either visual short-term memory or visual long-term memory; the content of visual states is stored in memory only if and when (...) object-centered attention modulates visual processing and this modulation signifies the onset of the conceptualization of that content; only categorical high-level information that characterizes conceptual content and not metric and precise iconic information that characterizes NCC can be stored in visual memory for long periods; and if NCC were stored in visual memory then this would allow recognitional judgments pertaining to NCC—one could recognize the precise shade of a color that one had seen before. However NCC does not allow such recognitional judgments. (shrink)

The chapters in this book address directly the issue of the cognitive penetrability of perception.

We extend the ordinary logic of knowledge based on the operator K and the system of axioms S₅ by adding a new operator Uφ, standing for "the agent utters φ", and certain axioms and a rule for U, forming thus a new system KU. The main advantage of KU is that we can express in it intentions of the speaker concerning the truth or falsehood of the claims he utters and analyze them logically. Specifically we can express in the new (...) language various notions of lying, as well as of telling the truth. Consequently, as long as lying or telling the truth about a fact is an intentional mode of the speaker, we can resolve the Liar paradox, or at least some of its variants, turning it into an ordinary (false or true) sentence. Also, using Kripke structures analogous to those employed by S. Kraus and D. Lehmann in [3] for modelling the logic of knowledge and belief, we offer a sound and complete semantics for KU. (shrink)

According to the cognitive penetrability hypothesis, our beliefs, desires, and possibly our emotions literally affect how we see the world. This book elucidates the nature of the cognitive penetrability and impenetrability hypotheses, assesses their plausibility, and explores their philosophical consequences. It connects the topic's multiple strands (the psychological findings, computationalist background, epistemological consequences of cognitive architecture, and recent philosophical developments) at a time when the outcome of many philosophical debates depends on knowing whether and how cognitive states can influence perception. (...) All sixteen chapters were written especially for the book. The first chapters provide methodological and conceptual clarification of the topic and give an account of the relations between penetrability, encapsulation, modularity, and cross-modal interactions in perception. Assessments of psychological and neuroscientific evidence for cognitive penetration are given by several chapters. Most of the contributions analyse the impact of cognitive penetrability and impenetrability on specific philosophical topics: high-level perceptual contents, the epistemological consequences of penetration, nonconceptual content, the phenomenology of late perception, metacognitive feelings, and action. The book includes a comprehensive introduction which explains the history of the debate, its key technical concepts (informational encapsulation, early and late vision, the perception-cognition distinction, hard-wired perceptual processing, perceptual learning, theory-ladenness), and the debate's relevance to current topics in the philosophy of mind and perception, epistemology, and philosophy of psychology. (shrink)

In the context of a distributive lattice we specify the sort of mappings that could be generally called ''negations'' and study their behavior under iteration. We show that there are periodic and nonperiodic ones. Natural periodic negations exist with periods 2, 3, and 4 and pace 2, as well as natural nonperiodic ones, arising from the interaction of interior and quasi interior mappings with the pseudocomplement. For any n and any even , negations of period n and pace s can (...) also be constructed, but in a rather ad hoc and trivial way. (shrink)

A structural (as opposed to Zadeh's quantitative) approach to fuzziness is given, based on the operator "very", which is added to the language of set theory together with some elementary axioms about it. Due to the axiom of foundation and to a lifting axiom, the operator is proved trivial on the cumulative hierarchy of ZF. So we have to drop either foundation or lifting. Since fuzziness concerns complemented predicates rather than sets, a class theory is needed for the very operator. (...) And of them the Kelley-Morse (KM) theory is more appropriate for reasons of class existence. Several definable realizations of the very-operator are presented in KM⁻. In the last section we consider the operator "very" without the lifting axiom on classes of urelements. To each structurally fuzzy set X a traditional quantitative fuzzy set X̄ is assigned -- its quantitative representation. This way we are able partly to recover ordinary fuzzy sets from the structurally fuzzy ones. (shrink)

We give a sufficient condition for a countable model M of PA to be expandable to an ω-model of AST with absolute Ω-orderings. The condition is in terms of saturation schemes or, equivalently, in terms of the ability of the model to code sequences which have some kind of definition in (M, ω). We also show that a weaker scheme of saturation leads to the existence of wellorderings of the model with nice properties. Finally, we answer affirmatively the question of (...) whether the intersection of all β-expansions of a β-expandable model M is the set RA(M, ω)--the ramified analytical hierarchy over (M, ω). The results are based on forcing constructions. (shrink)

A continuum is here a primitive notion intended to correspond precisely to a path-connected subset of the usual euclidean space. In contrast, however, to the traditional treatment, we treat here continua not as pointsets, but as irreducible entities equipped only with a partial ordering ≤ interpreted as parthood. Our aim is to examine what basic topological and geometric properties of continua can be expressed in the language of ≤, and what principles we need in order to prove elementary facts about (...) them. Surprisingly enough ≤ suffices to formulate the very heart of continuity (=jumpless and gapless transitions) in a general setting. Further, using a few principles about ≤ (together with the axioms of ZFC), we can define points, joins, meets and infinite closeness. Most important, we can develop a dimension theory based on notions like path, circle, line (=one-dimensional continuum), simple line and surface (=two-dimensional continuum), recovering thereby in a rigorous way Poincaré's well-known intuitive idea that dimension expresses the ways in which a continuum can be torn apart. We outline a classification of lines according to the number of circles and branching points they contain. The ordering (C,≤) is a topped and bottomed, atomic, almost dense and complete partial ordering, weaker than a lattice. Continuous transformations from C to C are also defined in a natural way and results about them are proved. (shrink)

We discuss in some length evidence from the cognitive science suggesting that the representations of objects based on spatiotemporal information and featural information retrieved bottom‐up from a visual scene precede representations of objects that include conceptual information. We argue that a distinction can be drawn between representations with conceptual and nonconceptual content. The distinction is based on perceptual mechanisms that retrieve information in conceptually unmediated ways. The representational contents of the states induced by these mechanisms that are available to a (...) type of awareness called phenomenal awareness constitute the phenomenal content of experience. The phenomenal content of perception contains the existence of objects as separate things that persist in time and time, spatiotemporal information, and information regarding relative spatial relations, motion, surface properties, shape, size, orientation, color, and their functional properties. (shrink)

We present a formalization of collections that Cornelius Castoriadis calls “magmas”, especially the property which mainly characterizes them and distinguishes them from the usual cantorian sets. It is the property of their elements to depend on other elements, either in a one-way or a two-way manner, so that one cannot occur in a collection without the occurrence of those dependent on it. Such a dependence relation on a set A of atoms (or urelements) can be naturally represented by a pre-order (...) relation $$\preccurlyeq $$ of A with the extra condition that it contains no minimal elements. Then, working in a mild strengthening of the theory $$\textrm{ZFA}$$, where A is an infinite set of atoms equipped with a primitive pre-ordering $$\preccurlyeq $$, the class of magmas over A is represented by the class $$LO(A,\preccurlyeq )$$ of nonempty open subsets of A with respect to the lower topology of $$\langle A,\preccurlyeq \rangle $$. The non-minimality condition for $$\preccurlyeq $$ implies that all sets of $$LO(A,\preccurlyeq )$$ are infinite and none of them is $$\subseteq $$ -minimal. Next the pre-ordering $$\preccurlyeq $$ is shifted (by a kind of simulation) to a pre-ordering $$\preccurlyeq ^+$$ on $${{\mathcal {P}}}(A)$$, which turns out to satisfy the same non-minimality condition as well, and which, happily, when restricted to $$LO(A,\preccurlyeq )$$ coincides with $$\subseteq $$. This allows us to define a hierarchy $$M_\alpha (A)$$, along all ordinals $$\alpha \ge 1$$, the“magmatic hierarchy”, such that $$M_1(A)=LO(A,\preccurlyeq )$$, $$M_{\alpha +1}(A)=LO(M_\alpha (A),\subseteq )$$, and $$M_\alpha (A)=\bigcup _{\beta <\alpha }M_\beta (A)$$, for a limit ordinal $$\alpha $$. For every $$\alpha \ge 1$$, $$M_\alpha (A)\subseteq V_\alpha (A)$$, where $$V_\alpha (A)$$ are the levels of the universe V(A) of $$\textrm{ZFA}$$. The class $$M(A)=\bigcup _{\alpha \ge 1}M_\alpha (A)$$ is the “magmatic universe above A.” The axioms of Powerset and Union (the latter in a restricted version) turn out to be true in $$\langle M(A),\in \rangle $$. Besides it is shown that three of the five principles about magmas that Castoriadis proposed in his writings (mildly modified and adapted to the needs of formalization), $$M2^*$$, $$M3^*$$ and $$M5^*$$, are true of M(A). A selection of excerpts from these writings, in which the concept of magma was first introduced and elaborated, is presented in the Introduction. (shrink)

A structural approach to fuzziness is given, based on the operator "very", which is added to the language of set theory together with some elementary axioms about it. Due to the axiom of foundation and to a lifting axiom, the operator is proved trivial on the cumulative hierarchy of ZF. So we have to drop either foundation or lifting. Since fuzziness concerns complemented predicates rather than sets, a class theory is needed for the very operator. And of them the Kelley-Morse (...) theory is more appropriate for reasons of class existence. Several definable realizations of the very-operator are presented in KM⁻. In the last section we consider the operator "very" without the lifting axiom on classes of urelements. To each structurally fuzzy set X a traditional quantitative fuzzy set X̄ is assigned -- its quantitative representation. This way we are able partly to recover ordinary fuzzy sets from the structurally fuzzy ones. (shrink)

We investigate how the sentence choice semantics for propositional superposition logic developed in Tzouvaras could be extended so as to successfully apply to first-order superposition logic. There are two options for such an extension. The apparently more natural one is the formula choice semantics based on choice functions for pairs of arbitrary formulas of the basis language. It is proved however that the universal instantiation scheme of first-order logic, $\varphi \rightarrow \varphi $, is false, as a scheme of tautologies, with (...) respect to FCS. This causes the total failure of FCS as a candidate semantics. Then we turn to the other option, which is a variant of SCS, since it uses again choice functions for pairs of sentences only. This semantics however presupposes that the applicability of the connective | is restricted to quantifier-free sentences, and thus the class of well-formed formulas and sentences of the language is restricted too. Granted these syntactic restrictions, the usual axiomatizations of FOLS turn out to be sound and conditionally complete with respect to this second semantics, just like the corresponding systems of PLS. (shrink)

The Macpherson :24–62, 2012) argued that the perceptual experience of colors is cognitively penetrable. Macpherson also thinks that perception has nonconceptual content because this would provide a good explanation for several phenomena concerning perceptual experience. To have both, Macpherson must defend the thesis that the CP of perception is compatible with perception having NCC. Since the classical notion of CP of perception does not allow perception to have NCC, Macpherson proposes CP-lite. CP-lite makes room for an experience to have content (...) determined by concepts because the perceptual processes that produce the experience are affected by concepts rendering the experience, CP, while the same type of experience could have been had without any conceptual influences, in which case it would be CI. Macpherson then proceeds to show that CP-lite is compatible with some of the definitions of NCC. To do so, she argues that even when an experience is CP owing to the fact that it is produced by means of the mechanism posited by CP-lite, that is, through the interaction between bottom–up pure perception and top–down perceptual imagery, its content is NCC because it has the basic properties that characterize NCC. Based on this, Macpherson proceeds to criticize and undermine the definitions of NCC that are incompatible with CP-lite. In this paper, I argue that the possibility of CP-lite rests on the erroneous assumption that a state with conceptual content and a state with NCC can have the same phenomenology or content, and that the compatibility of CP-lite with NCC presupposes a view of NCC that does not conform to the usual construal of NCC. (shrink)