In this article we derived an important example of the inconsistent countable set in second order ZFC (ZFC_2) with the full second-order semantics. Main results: (i) :~Con(ZFC2_); (ii) let k be an inaccessible cardinal, V is an standard model of ZFC (ZFC_2) and H_k is a set of all sets having hereditary size less then k; then : ~Con(ZFC + E(V)(V = Hk)):.

This paper analyses the hidden use of new axioms in set-theoretic practice with a focus on large cardinal axioms and presents a general overview of set-theoretic practices using large cardinal axioms. The hidden use of a new axiom provides extrinsic reasons in support of this axiom via the idea of verifiable consequences, which is especially relevant for set-theoretic practitioners with an absolutist view. Besides that, the hidden use has pragmatic significance for further important sub-groups of the set-theoretic community---set-theoretic practitioners with (...) a pluralist view and set-theoretic practitioners who aim for ZFC-proofs. By describing this, the paper gives a more complete picture of new axioms in set-theoretic practice. These observations, for instance, show that set-theoretic practitioners interested in ZFC-proofs use tools that go beyond ZFC. The analysis is based on empirical data that was collected in an extensive interview study with set-theoretic practitioners. (shrink)

We investigate a recently devised polyhedral semantics for intermediate logics, in which formulas are interpreted in n-dimensional polyhedra. An intermediate logic is polyhedrally complete if it is complete with respect to some class of polyhedra. The first main result of this paper is a necessary and sufficient condition for the polyhedral completeness of a logic. This condition, which we call the Nerve Criterion, is expressed in terms of Alexandrov’s notion of the nerve of a poset. It affords a purely combinatorial (...) characterisation of polyhedrally complete logics. Using the Nerve Criterion we show, easily, that there are continuum many intermediate logics that are not polyhedrally complete but which have the finite model property. We also provide, at considerable combinatorial labour, a countably infinite class of logics axiomatised by the Jankov–Fine formulas of ‘starlike trees’ all of which are polyhedrally complete. The polyhedral completeness theorem for these ‘starlike logics’ is the second main result of this paper. (shrink)

In previous articles, it has been shown that the deductive system developed by Aristotle in his "second logic" is a natural deduction system and not an axiomatic system as previously had been thought. It was also stated that Aristotle's logic is self-sufficient in two senses: First, that it presupposed no other logical concepts, not even those of propositional logic; second, that it is (strongly) complete in the sense that every valid argument expressible in the language of the system is deducible (...) by means of a formal deduction in the system. Review of the system makes the first point obvious. The purpose of the present article is to prove the second. Strong completeness is demonstrated for the Aristotelian system. (shrink)

We show that early vision can use monocular cues to rapidly complete partially-occluded objects. Visual search for easily detected fragments becomes difficult when the completed shape is similar to others in the display; conversely, search for fragments that are difficult to detect becomes easy when the completed shape is distinctive. Results indicate that completion occurs via the occlusion-triggered removal of occlusion edges and linking of associated regions. We fail to find evidence for a visible filling-in of contours or surfaces, (...) but do find evidence for a "functional" filling-in that prevents the constituent fragments from being rapidly accessed. As such, it is only the completed structures—and not the fragments themselves—that serve as the basis for rapid recognition. (shrink)

: In the first edition of his book on the completeness of Kant’s table of judgments, Klaus Reich shortly indicates that the B-version of the metaphysical exposition of space in the Critique of pure reason is structured following the inverse order of the table of categories. In this paper, I develop Reich’s claim and provide further evidence for it. My argumentation is as follows: Through analysis of our actually given representation of space as some kind of object, the metaphysical exposition (...) will show that this representation is secondary to space considered as an original, undetermined and as such unrepresentable intuitive manifold. Now, following Kant, the representation of any kind of object involves diversity, synthesis and unity. In the case of our representation of space as formal intuition, this involves, firstly, a manifold a priori, i.e. space as pure form, delivered by the transcendental Aesthetic, secondly, a figurative, productive synthesis of that manifold, and, thirdly, the unity provided by the categories. Analysing our given representation of space – the task of the metaphysical exposition – amounts to dismantling its unity and determine its characteristics with respect to the categories. (shrink)

In 1980 F. Wattenberg constructed the Dedekind completion

d of the Robinson non-archimedean field

and established basic algebraic properties of

d [6]. In 1985 H. Gonshor established further fundamental properties of

d [7].In [4] important construction of summation of countable sequence of Wattenberg numbers was proposed and corresponding basic properties of such summation were considered. In this paper the important applications of the Dedekind completion

d in transcendental number theory were considered. We dealing using set theory ZFC
(
-model (...) of ZFC).Given an class of analytic functions of one complex variable f  

z, we investigate the arithmetic nature of the values of fz at transcendental points en, n  .Main results are: (i) the both numbers e
 and e   are irrational, (ii) number ee is transcendental. Nontrivial generalization of the Lindemann- Weierstrass theorem is obtained. (shrink)

The present work is focussed on the completeness of physics, or what is here called the Completeness Thesis: the claim that the domain of the physical is causally closed. Two major questions are tackled: How best is the Completeness Thesis to be formulated? What can be said in defence of the Completeness Thesis? My principal conclusions are that the Completeness Thesis can be coherently formulated, and that the evidence in favour if it significantly outweighs that against it. In opposition to (...) those who argue that formulation is impossible because no account of what is to count as physical can be provided, I argue that as long as the purpose of the argument in which the account is to be used are borne in mind there are no significant difficulties. The account of the physical which I develop holds as physical whatever is needed to fix the likelihood of pre-theoretically given physical effects, and hypothesises in addition that no chemical, biological or psychological factors will be needed in this way. The thus formulated Completeness Thesis is coherent, and has significant empirical content. In opposition to those who defend the doctrine of emergentism by means of philosophical arguments I contend that those arguments are flawed, setting up misleading dichotomies between needlessly attenuated alternatives and assuming the truth of what is to be proved. Against those who defend emergentism by appeal to the evidence, I argue that the history of science since the nineteenth century shows clearly that the empirical credentials of the view that the world is causally closed at the level of a small number of purely physical forces and types of energy is stronger than ever, and the credentials of emergentism correspondingly weaker. In opposition to those who argue that difficulties with reductionism point to the implausibility of the Completeness Thesis I argue that completeness in no way entails the kinds of reductionism which give rise to the difficulties in question. I argue further that the truth of the Completeness Thesis is in fact compatible with a great deal of taxonomic disorder and the impossibility of any general reduction of non-fundamental descriptions to fundamental ones. In opposition to those who argue that the epistemological credentials of fundamental physical laws are poor, and that those laws should in fact be seen as false, I contend that truth preserving accounts of fundamental laws can be developed. Developing such an account, I test it by considering cases of the composition of forces and causes, where what takes place is different to what is predicted by reference to any single law, and argue that viewing laws as tendencies allows their truth to be preserved, and sense to be made of both the experimental discovery of laws, and the fact that composition enables accurate prediction in at least some cases. (shrink)

The first-order temporal logics with □ and ○ of time structures isomorphic to ω (discrete linear time) and trees of ω-segments (linear time with branching gaps) and some of its fragments are compared: the first is not recursively axiomatizable. For the second, a cut-free complete sequent calculus is given, and from this, a resolution system is derived by the method of Maslov.

A strongly independent preorder on a possibly in finite dimensional convex set that satisfi es two of the following conditions must satisfy the third: (i) the Archimedean continuity condition; (ii) mixture continuity; and (iii) comparability under the preorder is an equivalence relation. In addition, if the preorder is nontrivial (has nonempty asymmetric part) and satisfi es two of the following conditions, it must satisfy the third: (i') a modest strengthening of the Archimedean condition; (ii') mixture continuity; and (iii') completeness. Applications (...) to decision making under conditions of risk and uncertainty are provided. (shrink)

Any explanation of one fact in terms of another will appeal to some sort of connection between the two. In a causal explanation, the connection might be a causal mechanism or law. But not all explanations are causal, and neither are all explanatory connections. For example, in explaining the fact that a given barn is red in terms of the fact that it is crimson, we might appeal to a non-causal connection between things’ being crimson and their being red. Many (...) such connections, like this one, are general rather than particular. I call these general non-causal explanatory connections 'laws of metaphysics'. In this paper I argue that some of these laws are to be found in the world at its most fundamental level, forming a bridge between fundamental reality and everything else. It is only by admitting fundamental laws, I suggest, that we can do justice to the explanatory relationship between what is fundamental and what is not. And once these laws are admitted, we are able to provide a nice resolution of the puzzle of why there are any non-fundamental facts in the first place. (shrink)

All first-order Gödel logics G_V with globalization operator based on truth value sets V C [0,1] where 0 and 1 lie in the perfect kernel of V are axiomatized by Ciabattoni’s hypersequent calculus HGIF.

Classical interpretations of Goedels formal reasoning, and of his conclusions, implicitly imply that mathematical languages are essentially incomplete, in the sense that the truth of some arithmetical propositions of any formal mathematical language, under any interpretation, is, both, non-algorithmic, and essentially unverifiable. However, a language of general, scientific, discourse, which intends to mathematically express, and unambiguously communicate, intuitive concepts that correspond to scientific investigations, cannot allow its mathematical propositions to be interpreted ambiguously. Such a language must, therefore, define mathematical truth (...) verifiably. We consider a constructive interpretation of classical, Tarskian, truth, and of Goedel's reasoning, under which any formal system of Peano Arithmetic---classically accepted as the foundation of all our mathematical Languages---is verifiably complete in the above sense. We show how some paradoxical concepts of Quantum mechanics can, then, be expressed, and interpreted, naturally under a constructive definition of mathematical truth. (shrink)

According to an increasing number of authors, the best, if not the only, argument in favour of physicalism is the so-called 'overdetermination argument'. This argument, if sound, establishes that all the entities that enter into causal interactions with the physical world are physical. One key premise in the overdetermination argument is the principle of the causal closure of the physical world, said to be supported by contemporary physics. In this paper, I examine various ways in which physics may support the (...) principle, either as a methodological guide or as depending on some other laws and principles of physics. (shrink)

Recent progress in geroscience holds the promise of significantly slowing down or even reversing ageing and age-related diseases, and thus increasing our healthspans. In this paper, I offer a novel argument in favour of developing such technology and making it unconditionally available to everyone. In particular, I argue that justice requires that each person be provided with sufficient opportunities to have a ‘complete life’, that many people currently lack such opportunities, and that we would substantially improve the status quo by (...) giving them access to anti-ageing technology. (shrink)

The present first part about the eventual completeness of mathematics (called “Hilbert mathematics”) is concentrated on the Gödel incompleteness (1931) statement: if it is an axiom rather than a theorem inferable from the axioms of (Peano) arithmetic, (ZFC) set theory, and propositional logic, this would pioneer the pathway to Hilbert mathematics. One of the main arguments that it is an axiom consists in the direct contradiction of the axiom of induction in arithmetic and the axiom of infinity in set theory. (...) Thus, the pair of arithmetic and set are to be similar to Euclidean and non-Euclidean geometries distinguishably only by the Fifth postulate now, i.e. after replacing it and its negation correspondingly by the axiom of finiteness (induction) versus that of finiteness being idempotent negations to each other. Indeed, the axiom of choice, as far as it is equivalent to the well-ordering “theorem”, transforms any set in a well-ordering either necessarily finite according to the axiom of induction or also optionally infinite according to the axiom of infinity. So, the Gödel incompleteness statement relies on the logical contradiction of the axiom of induction and the axiom of infinity in the final analysis. Nonetheless, both can be considered as two idempotent versions of the same axiom (analogically to the Fifth postulate) and then unified after logicism and its inherent intensionality since the opposition of finiteness and infinity can be only extensional (i.e., relevant to the elements of any set rather than to the set by itself or its characteristic property being a proposition). So, the pathway for interpreting the Gödel incompleteness statement as an axiom and the originating from that assumption for “Hilbert mathematics” accepting its negation is pioneered. A much wider context relevant to realizing the Gödel incompleteness statement as a metamathematical axiom is consistently built step by step. The horizon of Hilbert mathematics is the proper subject in the third part of the paper, and a reinterpretation of Gödel’s papers (1930; 1931) as an apology of logicism as the only consistent foundations of mathematics is the topic of the next second part. (shrink)

The 'completeness of physics' is the key premise in the causal argument for physicalism. Standard formulations of it fail to rule out emergent downwards causation. I argue that it must do this if it is tare in a valid causal argument for physicalism. Drawing on the notion of conferring causal power, I formulate a suitable principle, 'strong completeness'. I investigate the metaphysical implications of distinguishing this principle from emergent downwards causation, and I argue that categoricalist accounts of properties are better (...) equipped to sustain the distinction than dispositional essentialist accounts. Finally, I argue that the additional evidence needed for strong completeness renders the causal argument otiose for any properties amenable to scientific reduction. (shrink)

In this paper we view the first order set theory ZFC under the canonical frst order semantics and the second order set theory ZFC_2 under the Henkin semantics. Main results are: (i) Let M_st^ZFC be a standard model of ZFC, then ¬Con(ZFC + ∃M_st^ZFC ). (ii) Let M_stZFC_2 be a standard model of ZFC2 with Henkin semantics, then ¬Con(ZFC_2 +∃M_stZFC_2). (iii) Let k be inaccessible cardinal then ¬Con(ZFC + ∃κ). In order to obtain the statements (i) and (ii) examples of (...) the inconsistent countable set in a set theory ZFC + ∃M_stZFC and in a set theory ZFC2 + ∃M_st^ZFC_2 were derived. It is widely believed that ZFC + ∃M_stZFC and ZFC_2 + ∃M_st^ZFC_2 are consistent, i.e. ZFC and ZFC_2 have a standard models. Unfortunately this belief is wrong. Book. Advances in Mathematics and Computer Science Vol. 1 Chapter 3 There is No Standard Model of ZFC and ZFC2 ISBN-13 (15) 978-81-934224-1-0 See Part II of this paper DOI: 10.4236/apm.2019.99034 . (shrink)

Main results are:(i) Let M_st be standard model of ZFC. Then ~Con(ZFC+∃M_st), (ii) let k be an inaccessible cardinal then ~Con(ZFC+∃k),[10],11].

In this article we proved so-called strong reflection principles corresponding to formal theories Th which has omega-models or nonstandard model with standard part. An posible generalization of Lob’s theorem is considered.Main results are: (i)
Con
ZFC 
Mst ZFC, (ii)
Con
ZF 
V  L, (iii)
Con
NF 
Mst NF, (iv)
Con
ZFC2, (v) let k be inaccessible cardinal then
Con
ZFC 

.

Etude de l'extension par la negation semi-intuitionniste de la logique positive des propositions appelee logique C, developpee par A. Urquhart afin de definir une semantique relationnelle valable pour la logique des valeurs infinies de Lukasiewicz (Lw). Evitant les axiomes de contraction et de reduction propres a la logique classique de Dummett, l'A. propose une semantique de type Routley-Meyer pour le systeme d'Urquhart (CI) en tant que celle-la ne fournit que des theories consistantes pour la completude de celui-ci.

This paper is part of a project that is based on the notion of a dialectical system, introduced by Magari as a way of capturing trial and error mathematics. In Amidei et al. (2016, Rev. Symb. Logic, 9, 1–26) and Amidei et al. (2016, Rev. Symb. Logic, 9, 299–324), we investigated the expressive and computational power of dialectical systems, and we compared them to a new class of systems, that of quasi-dialectical systems, that enrich Magari’s systems with a natural mechanism (...) of revision. In the present paper we consider a third class of systems, that of p-dialectical systems, that naturally combine features coming from the two other cases. We prove several results about p-dialectical systems and the sets that they represent. Then we focus on the completions of first-order theories. In doing so, we consider systems with connectives, i.e. systems that encode the rules of classical logic. We show that any consistent system with connectives represents the completion of a given theory. We prove that dialectical and q-dialectical systems coincide with respect to the completions that they can represent. Yet, p-dialectical systems are more powerful; we exhibit a p-dialectical system representing a completion of Peano Arithmetic that is neither dialectical nor q-dialectical. (shrink)

Two strategies to infinity are equally relevant for it is as universal and thus complete as open and thus incomplete. Quantum mechanics is forced to introduce infinity implicitly by Hilbert space, on which is founded its formalism. One can demonstrate that essential properties of quantum information, entanglement, and quantum computer originate directly from infinity once it is involved in quantum mechanics. Thus, thеse phenomena can be elucidated as both complete and incomplete, after which choice is the border between them. A (...) special kind of invariance to the axiom of choice shared by quantum mechanics is discussed to be involved that border between the completeness and incompleteness of infinity in a consistent way. The so-called paradox of Albert Einstein, Boris Podolsky, and Nathan Rosen is interpreted entirely in the same terms only of set theory. Quantum computer can demonstrate especially clearly the privilege of the internal position, or “observer”, or “user” to infinity implied by Henkin’s proposition as the only consistent ones as to infinity. (shrink)

This paper discusses three inter-related themes in Barbara Herman's Moral Literacy norm-constituted power completes’ practical reason or rational agency.

This paper defends the idea that Cassirer's methodology is idealistic in regard to validity claims and the structuralist views he holds and at the same time empiric in regard to the facts and genealogy of culture. This perspective is best to be unfolded along Cassirer's model of representation. The author does so by showing that Cassirer's triad of symbolic articulation (expressive, presentational, significative) and the triad of symbolic development (mimetic, analogical, symbolic) form a coherent and exhaustive theory of symbolic formation. (...) In order to defend this view, two main objections from the secondary literature against the consistency of this essential theory piece of The Philosophy of Symbolic Forms have to be rejected. (shrink)

There is a standard way of interpreting physicalism. This is as a completeness thesis of some kind. Completeness physicalists believe there is or in principle could be some future physics that provides a complete explanatory or ontological basis for our universe. And this provides a sense in which physics is special among the sciences, the sense in which it is fundamental. This paper contrasts this standard completeness physicalism with what is a more plausible maximality physicalism. Maximality physicalists believe physics is (...) special only in its providing an epistemic framework that is ontologically or explanatorily superior in some respect. This paper shows how completeness physicalists cannot, while maximality physicalists can, provide an adequate explanation of the empirical support for and the pragmatic usefulness of physicalism. It also shows how maximality physicalism is better supported in light of several developments from late twentieth century philosophy of science. (shrink)

The objective of this document is to present three introductory notes on set theory: The first note presents an overview of this discipline from its origins to the present, in the second note some considerations are made about the evaluation of reasoning applying the first-order Logic and Löwenheim's theorems, Church Indecidibility, Completeness and Incompleteness of Gödel, it is known that the axiomatic theories of most commonly used sets are written in a specific first-order language, that is, they are developed within (...) the framework of first-order logic, so this note is relevant; and the third note refers to the presence of mathematical platonism in the axioms of ZFC and in the axioms of "complete ordered field", it is known that the last axioms mentioned characterize (except isomorphism) the real number system and are currently used to develop the real Analysis in the context of set theory. It is hoped that this article will be of pedagogical utility for students interested in set theory and in the philosophy of mathematics (that are beginning in the subject). (shrink)

“Substance-in-relation” is W. Norris CLARKE’s own contribution to the thought of Aquinas on the metaphysics of the human person. Clarke argues that a dynamic notion of the human person with an intrinsic dynamic substance and a primordial relation is implicit in the thought of Aquinas and he wants to make them explicit. His approach was to “creatively retrieve” this intrinsic dynamic notion in Aquinas and to “complete” it with the rich relational notion that was well-developed by some contemporary existential phenomenologists, (...) personalists and psychotherapists. He argues that the human person possesses dyadic structures of substance and relation that are equally primordial. So, for him, “to be” a human person is to be a “substance-in-relation.” This implies that substance alone, even though dynamic, is insufficient to constitute a human person. In this way, Clarke seems to differ from Aquinas who argued that the human person is a substance composed of body and soul. In fact, the conclusions reached by Clarke on the basic seminal ideas of the human person leaned more towards the thoughts of the above contemporary thinkers than that of Aquinas, suggesting that he must have departed significantly from St. Thomas. This raises doubt about to what extent he retrieved the thought of Aquinas. This research, therefore, is an attempt to furnish some elements that would help the reader to evaluate whether Clarke’s work could be considered more as a “creative retrieval” or more as a “creative completion” of the thought of Aquinas. The method employed here is to trace the background to the formation of Clarke’s thought. There is also an analysis of his thought. This is followed by a critical analysis of his notion of human substance and of relation. Finally, certain elements are furnished to help the reader in this evaluation. (shrink)

Some of the most important developments of symbolic logic took place in the 1920s. Foremost among them are the distinction between syntax and semantics and the formulation of questions of completeness and decidability of logical systems. David Hilbert and his students played a very important part in these developments. Their contributions can be traced to unpublished lecture notes and other manuscripts by Hilbert and Bernays dating to the period 1917-1923. The aim of this paper is to describe these results, focussing (...) primarily on propositional logic, and to put them in their historical context. It is argued that truth-value semantics, syntactic ("Post-") and semantic completeness, decidability, and other results were first obtained by Hilbert and Bernays in 1918, and that Bernays's role in their discovery and the subsequent development of mathematical logic is much greater than has so far been acknowledged. (shrink)

The first aim of this paper is to prove a topological completeness theorem for a weak version of Stalnaker’s logic KB of knowledge and belief. The weak version of KB is characterized by the assumption that the axioms and rules of KB have to be satisfied with the exception of the axiom (NI) of negative introspection. The proof of a topological completeness theorem for weak KB is based on the fact that nuclei (as defined in the framework of point-free topology) (...) give rise to a profusion of topological belief operators that are compatible with the familiar topological knowledge operator. Thereby a canonical topological model for weak KB can be constructed. For this canonical model a truth lemma for the K and B holds such that a completeness theorem for KB can be proved in the familiar way. The second aim of this paper is to show that the topological interpretation of knowledge K comes along with a complete Heyting algebra of belief operators B that all fit the knowledge operator K in the sense that the pairs (K, B) satisfy all axioms of weak KB. This amounts to a pluralistic relation between knowledge and belief: Knowledge does not fully determine belief, rather it designs a conceptual space for belief operators where different (competing) belief operators coexist. (shrink)

(NOTE: This is a transcript of the class. FOR THE FULL PAPER, please click on "Maxson J. McDowell".) A complete transcript of an experiment performed within a class on dream interpretation. Knowing only the dreamers age and gender, we interpreted his dream from its text. Our interpretation included predictions about the dreamer's psychological issues, and about his defenses. It also identified a series of jokes within the dream which would tend to penetrate the dreamer's defenses. When we had finished our (...) 'blind' interpretation, the bringer of the dream gave us more information about the dreamer against which we tested the accuracy of our predictions. A paper on this experiment has been submitted for publication. A link to an AUDIO-RECORDING of this class is given on the first page of this transcript. (shrink)

Summary Giancarlo Trombini presents the continuation of his research on the question of which criteria can be used to assess the progress of therapy in an objectively verifiable way and to make the decision on the completion of therapy. In the first phase of his research, the phenomenological criterion of a qualitative change in the patient’s relations toward the positive and higher complexity was proposed for this purpose. In terms of the working method in analytic therapy, this meant concretely: (...) attention should be paid to what development is shown in the comparison of the relationships that occur in the dream narrative and in the subsequent associations. This criterion was therefore given the name manifest dream/association comparison (MDAC)—comparison between the manifest dream and the subsequent associations. The idea can easily be transferred to those therapy methods, which do not primarily work with reports of dream memories and subsequent associations—also, in other ways of working, it is possible to pay attention, in the way suggested by Trombini, to the qualitative development of the relationships which are thematized by the clients in the course of an hour. To this first criterion, another phenomenological criterion is now added in the present article: that of the “concluding therapeutic turn” (CTT). If the patient’s development reaches this turn in the course of the therapy in one session, this indicates, according to Trombini, that the therapy can soon be concluded. The fulfillment of this criterion can be recognized by the fact that in the sequence of dream narration and subsequent associations in a session, a relational dynamic toward the positive and higher complexity becomes recognizable and that is, at the same time, connected with a reconciliation of the three temporal reference systems (past, present, and future). The achievement of this CTT indicates that the patient is aware of the changes made in therapy and makes it evident to the therapist that the therapy is nearing completion. (shrink)

Higher-order theories of properties, relations, and propositions are known to be essentially incomplete relative to their standard notions of validity. It turns out that the first-order theory of PRPs that results when first-order logic is supplemented with a generalized intensional abstraction operation is complete. The construction involves the development of an intensional algebraic semantic method that does not appeal to possible worlds, but rather takes PRPs as primitive entities. This allows for a satisfactory treatment of both the modalities and the (...) propositional attitudes, and it suggests a general strategy for developing a comprehensive treatment of intensional logic. (shrink)

In his 1802 article for the Critical Journal, “Relationship of Skepticism to Philosophy,” Hegel attempts to articulate a form of skepticism that is “at one with every true philosophy.” Focusing on the priority that Hegel gives to ancient skepticism over its modern counterpart, Michael Forster and other commentators suggest that it is Pyrrhonism that Hegel views as one with philosophy. Since Hegel calls attention to the persistence of dogmatism even in the work of Sextus Empiricus, however, I argue that it (...) is only a sublated form of Pyrrhonism, what in the Phenomenology of Spirit he calls “self-completing skepticism,” that Hegel takes to be part of genuine philosophical cognition. In this way, I hope to show that the insight that motivates Hegel’s engagement with skepticism in the 1802 essay comes to inform the philosophical itinerary of the Phenomenology of Spirit. (shrink)

Examining Seneca’s account of friendship produces an interpretative puzzle: if the good of the Stoic sage is already both complete and self-sufficient, how can friendship be a good? I reject the solution that friendship is simply a preferred indifferent instead of a good and argue that though Seneca’s account can consistently explain both why friendship’s nature as a good does not threaten the completeness or the self-sufficiency of the sage, Stoic friends must choose between intimate friendships that leave them vulnerable (...) or impersonal friendships that lack intimacy but do not undermine their happiness. The consistent Stoic must choose the latter, but I argue that this conflict shows why we ought to reject the Stoic model of friendship. (shrink)

In this paper, I challenge the standard reading of complete virtue (ἀρετή τελεία) in those disputed passages of Nicomachean Ethics and Eudemian Ethics. I argue that, for Aristotle, complete virtue is neither (i) wisdom nor (ii) a whole set of all virtues. Rather, it is a term used by Aristotle to denote any virtue that is in its complete or perfect form. In light of this reading, I offer a pluralist interpretation of Aristotelian happiness. I argue that for Aristotle, the (...) life-long exercise of a predominant virtue—as long as it is exercised in its complete or perfect form—will suffice for human happiness. The so-called inclusivist and intellectualist notions of Aristotelian happiness, thus understood, are merely two forms (viz. the composite and the non-composite form) of the pluralist notion of Aristotelian happiness. And if I am right, my pluralist interpretation provides an alternative, if not better, solution to the long-standing problem of “dual happiness” in Aristotle. (shrink)

5-MeO-DMT is a psychedelic substance with a short duration of action and intensive effects. Its therapeutic efficacy and practicality may significantly surpass those of classical psychedelics such as ayahuasca and LSD. -/- This retrospective ethnographic inquiry features a woman in her mid-thirties who witnessed her mother's violent suicide and its bloody aftermath at the age of three. Before and after that, her childhood was characterized by domestic violence and sexual abuse perpetrated by several members of her family and extended family. (...) In her twenties and thirties, she dated a member of the local mafia with the intention of asking him to kill her father, who had been the main perpetrator of the sexual abuse and violence. This plan was eventually not carried out, but it reflected her deep bitterness and wrath. -/- A process initiated in her early thirties involving four 5-MeO-DMT sessions and a few additional sessions with psilocybin and ayahuasca in the course of two years completely resolved her symptoms related to the abuses, to the extent that she could rebuild a functional relationship with her father and feel love and compassion towards him. This outcome, i.e., the complete reversal of her attitude and emotions towards her father, appeared highly unusual. For the last three years, the outcome had remained stable. -/- The article also presents the perspective of a female facilitator of this treatment process. The article contributes to a better understanding of the use of 5-MeO-DMT in severe traumatization as well as exemplifies the possible positive contributions of actors who are not medical professionals in resolving deep collective traumatization in societies. (shrink)

Following Post program, we will propose a linguistic and empirical interpretation of Gödel’s incompleteness theorem and related ones on unsolvability by Church and Turing. All these theorems use the diagonal argument by Cantor in order to find limitations in finitary systems, as human language, which can make “infinite use of finite means”. The linguistic version of the incompleteness theorem says that every Turing complete language is Gödel incomplete. We conclude that the incompleteness and unsolvability theorems find limitations in our finitary (...) tool, which is our complete language. (shrink)

Gentzen’s approach by transfinite induction and that of intuitionist Heyting arithmetic to completeness and the self-foundation of mathematics are compared and opposed to the Gödel incompleteness results as to Peano arithmetic. Quantum mechanics involves infinity by Hilbert space, but it is finitist as any experimental science. The absence of hidden variables in it interpretable as its completeness should resurrect Hilbert’s finitism at the cost of relevant modification of the latter already hinted by intuitionism and Gentzen’s approaches for completeness. This paper (...) investigates both conditions and philosophical background necessary for that modification. The main conclusion is that the concept of infinity as underlying contemporary mathematics cannot be reduced to a single Peano arithmetic, but to at least two ones independent of each other. Intuitionism, quantum mechanics, and Gentzen’s approaches to completeness an even Hilbert’s finitism can be unified from that viewpoint. Mathematics may found itself by a way of finitism complemented by choice. The concept of information as the quantity of choices underlies that viewpoint. Quantum mechanics interpretable in terms of information and quantum information is inseparable from mathematics and its foundation. (shrink)

In Nicomachean Ethics 1.8, Aristotle seems to argue that certain external goods are needed for happiness because, in the first place, they are needed for virtuous activity. This has puzzled scholars. After all, it seems possible for a virtuous agent to exercise her virtuous character even under conditions of extreme hardship or deprivation. Indeed, it is natural to think these are precisely the conditions under which one's virtue shines through most clearly. Why then does Aristotle think that a wide range (...) of external goods is required for virtuous activity, and therefore, for happiness? -/- I argue that there is good sense to be made of Aristotle's stance on external goods. Specifically, I explain how, on this view, a range of external goods is required for the full exercise of virtue, and I show that it is only this full exercise that is constitutive of eudaimonia. Drawing on passages in Politics 7.13 and Nicomachean Ethics 3.1, I develop and defend a distinction between the "mere" exercise of virtue, and the full or complete exercise of virtue. I argue that, for Aristotle, the distinguishing feature of this distinction is the value of the virtuous action's ends. An action that fully expresses virtue aims at an end that is unqualifiedly good, while an action that merely exercises virtue does not. I argue that the external goods Aristotle mentions in NE 1.8 are necessary for performing actions with unqualifiedly good ends, and so necessary for the complete exercise of virtue. In addition to providing a more satisfactory account than existing proposals of the role of external goods in Aristotelian happiness, my interpretation has two additional upshots. First, it brings to light an under-appreciated and independently compelling feature of Aristotle's ethical thought: the value of virtuous actions depends in part on the value of the ends they aim to realize. Second, it finds in Aristotle a distinct and powerful way of thinking about the badness of certain kinds of misfortune and deprivation: they are bad in part because they prevent us from fully realizing our capacity for moral agency, from fully engaging with value in the world. (shrink)

A very influential idea in the epistemology of modality is that we acquire knowledge of metaphysical modality through knowledge of essence. As a consequence, the epistemology of essence becomes crucial in the attempt to answer the question of how we come to know modal propositions. In this paper I investigate Lowe’s and Hale’s approach to the epistemology of essence and argue that both of them remain in a crucial, structural sense incomplete. Systematizing this criticism against Lowe and Hale, I then (...) break down desiderata of what I call a structurally complete picture of the epistemology of essence. Finally, I discuss Husserl’s epistemology of essence and defend it against a notorious objection. However, Husserl’s approach also seems to remain incomplete, due to its appeal to imagination, which operates on the basis of background assumptions that are themselves in need of justification. I indicate, however, that a Husserlian theory of intuitive awareness of universals might supply us with (direct) justification of these background assumptions and, hence, that we might be able to paint a structurally complete picture of the epistemology of essence with Husserlian means. (shrink)

Investigation of a puzzle concerning complete yet authorless artworks.

This paper presents a formalization of the classical proof of completeness in Henkin-style developed by Troelstra and van Dalen for intuitionistic logic with respect to Kripke models. The completeness proof incorporates their insights in a fresh and elegant manner that is better suited for mechanization. We discuss details of our implementation in the Lean theorem prover with emphasis on the prime extension lemma and construction of the canonical model. Our implementation is restricted to a system of intuitionistic propositional logic with (...) implication, conjunction, disjunction, and falsity given in terms of a Hilbert-style axiomatization. As far as we know, our implementation is the first verified Henkin-style proof of completeness for intuitionistic logic following Troelstra and van Dalen's method in the literature. (shrink)

The Bare Theory was offered by David Albert as a way of standing by the completeness of quantum mechanics in the face of the measurement problem. This paper surveys objections to the Bare Theory that recur in the literature: what will here be called the oddity objection, the coherence objection, and the context-of-the-universe objection. Critics usually take the Bare Theory to have unacceptably bizarre consequences, but to be free from internal contradiction. Bizarre consequences need not be decisive against the Bare (...) Theory, but a further objection—dubbed here the calibration objection—has been underestimated. This paper argues that the Bare Theory is not only odd but also inconsistent. We can imagine a successor to the Bare Theory—the Stripped Theory—which avoids the objections and fulfills the original promise of the Bare Theory, but at the cost of amplifying the bizarre consequences. The Stripped Theory is either a stunning development in our understanding of the world or a reductio disproving the completeness of quantum mechanics. The Bare Theory The usual objections The calibration objection Beyond the Bare Theory. (shrink)

Amodal completion is the representation of occluded parts of perceived objects. We argue for the following three claims: First, at least some amodal completion-involved experiences can ground knowledge about the occluded portions of perceived objects. Second, at least some instances of amodal completion-grounded knowledge are not sensitive, that is, it is not the case that in the nearest worlds in which the relevant claim is false, that claim is not believed true. Third, at least some instances of (...) amodal completion-grounded knowledge are not safe, that is, it is not the case that in all or nearly all near worlds where the relevant claim is believed true, that claim is in fact true. Thus, certain instances of amodal completion-grounded knowledge refute both the view that knowledge is necessarily sensitive and the view that knowledge is necessarily safe. (shrink)

Amodal completion is usually characterized as the representation of those parts of the perceived object that we get no sensory stimulation from. In the case of the visual sense modality, for example, amodal completion is the representation of occluded parts of objects we see. I argue that relationalism about perception, the view that perceptual experience is constituted by the relation to the perceived object, cannot give a coherent account of amodal completion. The relationalist has two options: construe (...) the perceptual relation as the relation to the entire perceived object or as the relation to the unoccluded parts of the perceived object. I argue that neither of these options are viable. (shrink)

In this article we derived an important example of the inconsistent countable set in second order ZFC (ZFC_2) with the full second-order semantics. Main result: ~(Con(ZFC_2).