Ioannis G. Ntagkas

The paper begins with an examination of Gödel's views on absolute undecidability and related topics in set theory. These views are sharpened and assessed in light of recent developments. It is argued that a convincing case can be made for axioms that settle many of the questions undecided by the standard axioms and that in a precise sense the program for large cardinals is a complete success “below” CH. It is also argued that there are reasonable scenarios for settling CH and that there is not currently a convincing case to the effect that a given statement is absolutely undecidable

In this paper we investigate strong logics of first and second order that have certain absoluteness properties. We begin with an investigation of first order logic and the strong logics ω-logic and β-logic, isolating two facets of absoluteness, namely, generic invariance and faithfulness. It turns out that absoluteness is relative in the sense that stronger background assumptions secure greater degrees of absoluteness. Our aim is to investigate the hierarchies of strong logics of first and second order that are generically invariant and faithful against the backdrop of the strongest large cardinal hypotheses. We show that there is a close correspondence between the two hierarchies and we characterize the strongest logic in each hierarchy. On the first-order side, this leads to a new presentation of Woodin's Ω-logic. On the second-order side, we compare the strongest logic with full second-order logic and argue that the comparison lends support to Quine's claim that second-order logic is really set theory in sheep's clothing.

In this paper I examine Feferman’s reasons for maintaining that while the statements of first-order number theory are “completely clear'” and “completely definite,”' many of the statements of analysis and set theory are “inherently vague'” and “indefinite.”' I critique his four central arguments and argue that in the end the entire case rests on the brute intuition that the concept of subsets of natural numbers—along with the richer concepts of set theory—is not “clear enough to secure definiteness.” My response to this final, remaining point will be that the concept of “being clear enough to secure definiteness” is about as clear a case of an inherently vague and indefinite concept as one might find, and as such it can bear little weight in making a case against the definiteness of analysis and set theory.

Gödel argued that his incompleteness theorems imply that either “the mind cannot be mechanized” or “there are absolutely undecidable sentences.” In the precursor to this paper I examined the early arguments for the first disjunct. In the present paper I examine the most sophisticated argument for the first disjunct, namely, Penrose’s new argument. It turns out that Penrose’s argument requires a type-free notion of truth and a type-free notion of absolute provability. I show that there is a natural such system, DTK. I prove a series of results which show that Gödel’s disjunction is provable in the system, Penrose’s argument is invalid in the system, there can be no proof or refutation of either disjunct in the system, the independence results are robust in that they persist when one strengthens the principles governing absolute provability, and there are reasons to believe that the situation will not improve under any plausible alteration of the underlying theory of truth.

In this paper I address the question of whether the incompleteness theorems imply that “the mind cannot be mechanized,” where this is understood in the specific sense that “the mathematical outputs of the idealized human mind do not coincide with the mathematical outputs of any idealized finite machine.” Gödel argued that his incompleteness theorems implied a weaker, disjunctive conclusion to the effect that either “the mind cannot be mechanized” or “mathematical truth outstrips the idealized human mind.” Others, most notably, Lucas and Penrose, have claimed more—they have claimed that the incompleteness theorems actually imply the first disjunct. I will show that by sharpening the fundamental concepts involved and articulating the background assumptions governing them, one can prove Gödel’s disjunction, one can show that the arguments of Lucas and Penrose fail, and one can see what likely led proponents of the first disjunct astray.

What follows is a first step towards an ontology of conscious mental processes. We provide a theoretical foundation and characterization of conscious mental processes based on a realist theory of intentionality and using BFO as our top-level ontology. We distinguish three components of intentional mental process: character, directedness, and objective referent, and describe several features of the process character and directedness significant to defining and classifying mental processes. We arrive at the definition of representational mental process as a process that is the bringing into being, sustaining, modifying, or terminating of a mental representation. We conclude by outlining some benefits and applications of this approach.

In this paper we propose an Ontology of Commercial Exchange (OCE) based on Basic Formal Ontology. OCE is designed for re-use in the Industrial Ontologies Foundry (IOF) and in other ontologies addressing different aspects of human social behavior involving purchasing, selling, marketing, and so forth. We first evaluate some of the design patterns used in the Financial Industry Business Ontology (FIBO) and Product Types Ontology (PTO). We then propose terms and definitions that we believe will improve the representation of contractual obligations, sales processes, and their associated documents. A commercial exchange, for instance, involves mutual agreement to reciprocate actions, such as transferring money, performing a service, or transferring goods.

The conceptual structure of orthodox quantum mechanics has not provided a fully satisfactory and coherent description of natural phenomena. With particular attention to the measurement problem, we review and investigate two unorthodox formulations. First, there is the model advanced by GRWP, a stochastic modification of the standard Schrödinger dynamics admitting statevector reduction as a real physical process. Second, there is the ontological interpretation of Bohm, a causal reformulation of the usual theory admitting no collapse of the statevector. Within these two seemingly quite different approaches, we discuss in a comparative manner, several points: The meaning of the state vector, the status of quantum probability, the legitimacy of attributing macro objective properties to physical systems, and the possibility of retrieving the classical limit. Finally, we consider aspects of non-locality and relevant difficulties with formulating a relativistic generalization of the two approaches.

This paper examines the problem of founding irreversibility on reversible equations of motion from the point of view of the Brussels school's recent developments in the foundations of quantum statistical mechanics. A detailed critique of both their 'subdynamics' and 'transformation' theory is given. It is argued that the subdynamics approach involves a generalized form of 'coarse-graining' description, whereas, transformation theory cannot lead to truly irreversible processes pointing to a preferred direction of time. It is concluded that the Brussels school's conception of microscopic temporal irreversibility, as such, is tacitly assumed at the macroscopic level. Finally a logical argument is provided which shows, independently of the mathematical formalism of the theory concerned, that statistical reasoning alone is not sufficient to explain the arrow of time

The present study attempts to provide a consistent and coherent account of what the world could be like, given the conceptual framework and results of contemporary quantum theory. It is suggested that standard quantum mechanics can, and indeed should, be understood as a realist theory within its domain of application. It is pointed out, however, that a viable realist interpretation of quantum theory requires the abandonment or radical revision of the classical conception of physical reality and its traditional philosophical presuppositions. It is argued, in this direction, that the conceptualization of the nature of reality, as arising out of our most basic physical theory, calls for a kind of contextual realism. Within the domain of quantum mechanics, knowledge of 'reality in itself', 'the real such as it truly is' independent of the way it is contextualized, is impossible in principle. In this connection, the meaning of objectivity in quantum mechanics is analyzed, whilst the important question concerning the nature of quantum objects is explored

Standard quantum mechanics unquestionably violates the separability principle that classical physics (be it point-like analytic, statistical, or field-theoretic) accustomed us to consider as valid. In this paper, quantum nonseparability is viewed as a consequence of the Hilbert-space quantum mechanical formalism, avoiding thus any direct recourse to the ramifications of Kochen-Specker’s argument or Bell’s inequality. Depending on the mode of assignment of states to physical systems – unit state vectors versus non-idempotent density operators – we distinguish between strong/relational and weak/deconstructional forms of quantum nonseparability. The origin of the latter is traced down and discussed at length, whereas its relation to the all important concept of potentiality in forming a coherent picture of the puzzling entangled interconnections among spatially separated systems is also considered. Finally, certain philosophical consequences of quantum non-separability concerning the nature of quantum objects, the question of realism in quantum mechanics, and possible limitations in revealing the actual character of physical reality in its entirety are explored.

In the present study we attempt to incorporate the philosophical dialogue about physical reality into the instructional process of quantum mechanics. Taking into account that both scientific realism and constructivism represent, on the basis of a rather broad spectrum, prevalent philosophical currents in the domain of science education, the compatibility of their essential commitments is examined against the conceptual structure of quantum theory. It is argued in this respect that the objects of science do not simply constitute ‘personal constructions’ of the human mind for interpreting nature, as individualist constructivist consider,neither do they form products of a ‘social construction’, as sociological constructivist assume; on the contrary, they reflect objective structural aspects of the physical world. A realist interpretation of quantum mechanics, we suggest, is not only possible but also necessary for revealing the inner meaning of the theory’s scientific content. It is pointed out, however, that a viable realist interpretation of quantum theory requires the abandonment or radical revision of the classical conception of physical reality and its traditional metaphysical presuppositions. To this end, we put forward an alternative to the traditional realism interpretative scheme, which is in harmony with the findings of present-day quantum theory, and which, if adequately introduced into the instructional process of contemporary physics, is expected to promote the conceptual reconstruction of the learners towards an appropriate view of nature.

The logic of a physical theory reflects the structure of the propositions referring to the behaviour of a physical system in the domain of the relevant theory. It is argued in relation to classical mechanics that the propositional structure of the theory allows truth-value assignment in conformity with the traditional conception of a correspondence theory of truth. Every proposition in classical mechanics is assigned a definite truth value, either ‘true’ or ‘false’, describing what is actually the case at a certain moment of time. Truth-value assignment in quantum mechanics, however, differs; it is known, by means of a variety of ‘no go’ theorems, that it is not possible to assign definite truth values to all propositions pertaining to a quantum system without generating a Kochen–Specker contradiction. In this respect, the Bub–Clifton ‘uniqueness theorem’ is utilized for arguing that truth-value definiteness is consistently restored with respect to a determinate sublattice of propositions defined by the state of the quantum system concerned and a particular observable to be measured. An account of truth of contextual correspondence is thereby provided that is appropriate to the quantum domain of discourse. The conceptual implications of the resulting account are traced down and analyzed at length. In this light, the traditional conception of correspondence truth may be viewed as a species or as a limit case of the more generic proposed scheme of contextual correspondence when the non-explicit specification of a context of discourse poses no further consequences

Standard quantum mechanics undeniably violates the notion of separability that classical physics accustomed us to consider as valid. By relating the phenomenon of quantum nonseparability to the all-important concept of potentiality, we effectively provide a coherent picture of the puzzling entangled correlations among spatially separated systems. We further argue that the generalized phenomenon of quantum nonseparability implies contextuality for the production of well-defined events in the quantum domain, whereas contextuality entails in turn a structural-relational conception of quantal objects, viewed as carriers of dispositional properties. It is finally suggested that contextuality, if considered as a conditionalization preparation procedure of the object to be measured, naturally leads to a separable concept of reality whose elements are experienced as distinct, well-localized objects having determinate properties. In this connection, we find it necessary to distinguish the meaning of the term reality from the criterion of reality for us. The implications of the latter considerations for the notion of objectivity in quantum mechanics are also discussed.

La sémantique sous-jacente à la structure propositionnelle de la mécanique quantique des espaces de Hilbert implique une ambiguïté intrinsèque concernant l'impossibilité d'assigner des valeurs de vérité définies à toutes les propositions ayant trait à un système quantique sans générer de contradiction de type Kochen-Specker. Bien que ledit résultat de Kochen-Specker interdise une assignation globale et absolue des valeurs de vérité aux propositions de la mécanique quantique, il n'exclut pas les assignations contextuelles. À cet égard, le théorème d'unicité de Bub-Clifton est utilisé pour montrer que le caractère défini des valeurs de vérité est restauré de façon cohérente pour un sous-ensemble déterminé de propositions, défini par l'état du système quantique considéré et une observable préférée appropriée. Il est suggéré que le choix le plus naturel pour cette dernière, en particulier vis-à-vis du problème de l'assignation de valeurs de vérité en mécanique quantique, est que ce soit l'observable sur le point d'être mesurée qui ait une valeur déterminée. On fournit ainsi une conception de la vérité de la correspondance contextuelle qui est appropriée au domaine quantique du discours. La conception de la vérité qui en résulte est compatible avec une conception réaliste de la vérité, qui nie qu'il puisse exister un contexte de référence universel ou un point d'appui archimédien à partir duquel la totalité des faits de la nature puisse être évaluée logiquement.

In this paper, I propose to analyse two objections raised by Turner Jr in his paper “On Two Reasons Christian Theologians Should Reject The Intermediate State” in order to show that the intermediate state is an incoherent theory. As we shall see, the two untoward consequences that he mentions do not imply a metaphysical or logical contradiction. Consequently, I shall defend an Intermediate State and I shall propose briefly one metaphysical conception of the human being able to reply to Turner Jr’s objections.

In “What’s So Bad about Scientism?” (Mizrahi 2017), I argue that Weak Scientism, the view that “Of all the knowledge we have, scientific knowledge is the best knowledge” (Mizrahi 2017, 354; emphasis in original) is a defensible position. That is to say, Weak Scientism “can be successfully defended against objections” (Mizrahi 2017, 354). In his response to Mizrahi (2017), Christopher Brown (2017) provides more objections against Weak Scientism, and thus another opportunity for me to show that Weak Scientism is a defensible position, which is what I will do in this reply. In fact, I think that I have already addressed Brown’s (2017) objections in Mizrahi (2017), so I will simply highlight these arguments here.

Many contemporary epistemologists take rational inference to be a conscious action performed by the thinker (Boghossian 2014; 2018; Valaris 2014; Malmgren 2018). It is tempting to think that rational evaluability requires responsibility, which in turn requires conscious action. In that case, unconscious cognition involves merely associative or otherwise arational processing. This paper argues instead for deep rationalism: unconscious inference often exhibits the same rational status and richly structured logical character as conscious inference. The central case study is rationalization, in which people shift their attitudes in logically structured, reason-responsive ways in response to evidence of their own incompetence or immorality. These attitude shifts are irrational in a way that reflects on the thinker. Thus rationally evaluable inference extends downward into the unconscious. Many take the sole aim of belief to be truth (Velleman 2000) or knowledge (Williamson 2000), but the prevalence of rationalization suggests that belief updating often aims instead at preserving our positive conceptions of ourselves—that is, belief updating is part of a psychological immune system (Gilbert 2006; Mandelbaum 2019). This paper argues that the psychological immune system comprises a suite of distinct cognitive mechanisms, some (ir)rational and some arational, which are united by a common function of avoiding the maladaptive predomination of negative affect and maintaining stable motivation. Other aspects of the psychological immune system include (i) a domain-general positive bias in evaluative attitudes and (ii) “terror management,” i.e., the systematic strengthening of meaning-conferring beliefs to avoid death anxiety. The multiplicity of processes underlying the psychological immune system point toward an irrational but adaptive function of cognition to keep us motivated in a world rife with negativity and death.

According to a classic but nowadays discarded philosophical theory, perceptual experience is a complex of nonconceptual sensory states and full-blown propositional beliefs. This classical dual-component theory of experience is often taken to be obsolete. In particular, there seem to be cases in which perceptual experience and belief conflict: cases of known illusions, wherein subjects have beliefs contrary to the contents of their experiences. Modern dual-component theories reject the belief requirement and instead hold that perceptual experience is a complex of nonconceptual sensory states and some other sort of conceptual state. The most popular modern dual-component theory appeals to sui generis propositional attitudes called ‘perceptual seemings’. This article argues that the classical dual-component theory has the resources to explain known illusions without giving up the claim that the conceptual components of experience are beliefs. The classical dual-component view, though often viewed as outdated and implausible, should be regarded as a serious contender in contemporary debates about the nature of perceptual experience.

According to one important proposal, the difference between perception and cognition consists in the representational formats used in the two systems (Carey, 2009; Burge, 2010; Block, 2014). In particular, it is claimed that perceptual representations are iconic, or image-like, while cognitive representations are discursive, or language-like. Taking object perception as a test case, this paper argues on empirical grounds that it requires discursive label-like representations. These representations segment the perceptual field, continuously pick out objects despite changes in their features, and abstractly represent high-level features, none of which appears possible for purely iconic representations.

The notion of an object file figures prominently in recent work in philosophy and cognitive science. Object files play a role in theories of singular reference, object individuation, perceptual memory, and the development of cognitive capacities. However, the philosophical literature lacks a detailed, empirically informed theory of object files. In this paper, we articulate and defend the multiple-slots view, which specifies both the format and architecture of object files. We argue that object files represent in a non-iconic, propositional format that incorporates discrete symbols for separate features. Moreover, we argue that features of separate categories are stored in separate memory slots within an object file. We supplement this view with a computational framework that characterizes how information about objects is stored and retrieved.

Perceptual experiences justify beliefs. A perceptual experience of a dog justifies the belief that there is a dog present. But there is much evidence that perceptual states can occur without being conscious, as in experiments involving masked priming. Do unconscious perceptual states provide justification as well? The answer depends on one’s theory of justification. While most varieties of externalism seem compatible with unconscious perceptual justification, several theories have recently afforded to consciousness a special role in perceptual justification. We argue that such views face a dilemma: either consciousness should be understood in functionalist terms, in which case our best current theories of consciousness do not seem to imbue consciousness with any special epistemic features, or it should not, in which case it is mysterious why only conscious states are justificatory. We conclude that unconscious perceptual justification is quite plausible.

Reid endorsed a doxastic theory of perception, on which beliefs are constituents of perceptual experiences. This theory faces the problem of known illusions: we can perceive that p while believing that not-p. Some scholars argue that the problem of known illusions and other problems entail that Reid’s view cannot be charitably interpreted as a doxastic theory. This paper explores Reid’s theoretical commitments with respect to belief acquisition and uses textual evidence to show that his theory is genuinely doxastic. It then argues that a Reidian response to the problem of known illusions can be formulated by appeal to the thesis that perceptual beliefs are formed noninferentially. Reid can also resist the intuition that we lack illusory beliefs in known-illusion cases given his independent reasons for doubting our capacity to identify perceptual beliefs by introspection. The paper then surveys other problems raised in the secondary literature and argues that none decisively undermine the doxastic interpretation of Reid.