Abstract Objects, Misc

Taking mathematics as a language based on empirical experience, I argue for an account of mathematics in which its objects are abstracta that describe and communicate the structure of reality based on some of our ancestral interactions with their environment. I argue that mathematics as a language is mostly invented, and it is mind-dependent in a specific sense. However, the bases of mathematics will characterize it as a real, non-fictional science of structures.

Intuitivamente, la realidad está formada por entidades y hechos existentes y concretos. Sin embargo, nuestro lenguaje y pensamiento versa también sobre hechos meramente posibles, sobre cosas inexistentes y entidades abstractas. ¿Cómo es esto posible? ¿Significa ello que cuando hablamos y pensamos de estas otras cosas no hablamos de nada real? ¿o mas bien la realidad está mas poblada de lo que pensábamos y hay diferentes maneras de formar parte de la realidad además de la de existir de manera positiva y (...) concreta? En este libro trataremos de arrojar luz a estas y otras preguntas similares, poniendo atención a las estrategias argumentativas generales que suelen esgrimirse en esta rama de la filosofía. (shrink)

World news can be discouraging these days. In order to counteract the effects of fake news and corruption, scientists have a duty to present the truth and propose ethical solutions acceptable to the world at large. -/- By starting from scratch, we can lay down the scientific principles underlying our very existence, and reach reasonable conclusions on all major topics including quantum physics, infinity, timelessness, free will, mathematical Platonism, happiness, ethics and religion, all the way to creation and a special (...) type of multiverse. -/- This article amounts to a summary of my personal Theory of Everything. -/- DOI: 10.13140/RG.2.2.36046.31049. (shrink)

In this paper, I argue that all expressions for abstract objects are meaningless. My argument closely follows David Lewis’ argument against the intelligibility of certain theories of possible worlds, but modifies it in order to yield a general conclusion about language pertaining to abstract objects. If my Lewisian argument is sound, not only can we not know that abstract objects exist, we cannot even refer to or think about them. However, while the Lewisian argument strongly motivates nominalism, it also undermines (...) certain nominalist theories. (shrink)

Kaplan (1990; 2011) argues that there are no unspoken words. Hawthorne and Lepore (2011) put forward examples that purport to show that there can be such words. Here, I argue that Kaplan is correct, if we grant him a minor variation. While Hawthorne and Lepore might be right that there can be unspoken words, I will argue that they fail to show that there can be uninstantiated words.

Abstract artifacts such as musical works and fictional entities are human creations; they are intentional products of our actions and activities. One line of argument against abstract artifacts is that abstract objects are not the kind of objects that can be created. This is so, it is argued, because abstract objects are causally inert. Since creation requires being caused to exist, abstract objects cannot be created. One common way to refute this argument is to reject the causal inefficacy of abstracta. (...) I argue that creationists should rather reject the principle that creation requires causation. Creation, in my view, is a non-causal relation that can be explained using an appropriate notion of ontological dependence. The existence and the creation of abstract artifacts depend on certain individuals with appropriate intentions, along with events of a certain kind that include but are not limited to creations of certain concrete objects. (shrink)

Este artículo pretende mostrar que, a través de la obra de Lovecraft, es posible ilustrar una forma de realismo estructural óntico (REO). Se postula que la literatura de Lovecraft permite ejemplificar una ontología orientada hacia las relaciones (entre entidades), y no a las entidades mismas. Además, puesto que en esta forma de REO las entidades se definirían por sus relaciones, se concluye que estas deberían ser abstractas, habilitadas para contar con todas las características que extrínsecamente les sean asignadas en una (...) actualización determinada de la estructura que las alberga. (shrink)

Musical works change. Bruckner revised his Eighth Symphony. Ella Fitzgerald and many other artists have made it acceptable to sing the jazz standard “All the Things You Are” without its original verse. If we accept that musical works genuinely change in these ways, a puzzle arises: why can’t I change Bruckner’s Eighth Symphony? More generally, why are some individuals in a privileged position when it comes to changing musical works and other artifacts, such as novels, films, and games? I give (...) a view of musical works that helps to answer these questions. Musical works, on this view, are created abstract objects with no parts. The paradigmatic changes that musical works undergo are socially determined normative changes in how they should be performed. Due to contingent social practices, Bruckner, but not I, can change how his symphony should be performed. Were social practices radically different, I would be able to change his symphony. This view extends to abstract artifacts beyond music, including novels, films, words, games, and corporations. (shrink)

This paper investigates the degree to which information theory, and the derived uses that make it work as a metaphor of our age, can be helpful in thinking about God’s immanence and transcendance. We ask when it is possible to say that a consciousness has to be behind the information we encounter. If God is to be thought about as a communicator of information, we need to ask whether a communication system has to pre-exist to the divine and impose itself (...) to God. If we want God to be Creator, and not someone who would work like a human being, ‘creating’ will mean sustaining in being as much the channel, the material system, as the message. Is information control? It seems that God’s actions are not going to be informational control of everything. To clarify the issue, we attempt to distinguish two kinds of ‘genialities’ in nature, as a way to evaluate the likelihood of God from nature. We investigate concepts and images of God, in terms of the history of ideas but also in terms of philosophical theology, metaphysics, and religious ontology. (shrink)

Here, I lay the foundations of a high-level ontology of particulars whose structuring principles differ radically from the 'continuant' vs. 'occurrent' distinction traditionally adopted in applied ontology. These principles are derived from a new analysis of the ontology of “occurring” or “happening” entities. Firstly, my analysis integrates recent work on the ontology of processes, which brings them closer to objects in their mode of existence and persistence by assimilating them to continuant particulars. Secondly, my analysis distinguishes clearly between processes and (...) events, in order to make the latter abstract objects of thought (alongside propositions). Lastly, I open my ontological inventory to properties and facts, the existence of which is commonly admitted. By giving specific roles to these primitives, the framework allows one to account for static and dynamic aspects of the physical world and for the way that subjects conceive its history: facts account for the life of substances (physical objects and processes), whereas events enable cognitive subjects to account for the life story of substances. (shrink)

In this thesis I argue against unrestricted mereological hybridism, the view that there are absolutely no constraints on wholes having parts from many different logical or ontological categories, an exemplar of which I take to be ‘mixed fusions’. These are composite entities which have parts from at least two different categories – the membered (as in classes) and the non-membered (as in individuals). As a result, mixed fusions can also be understood to represent a variety of cross-category summation such as (...) the abstract with the concrete, the physical with the non-physical, and the possible with the impossible, just to name a few. -/- Proposed by David Lewis (1991) alongside his defence of classical mereology (the major theory of parthood which permits such transcategorial composites through its principle of unrestricted composition) it is my contention that mixed fusions are an under-examined consequence of indiscriminate mereological fusion which harbour a multitude of complications. In my attempt to discern their substantive character, throughout this thesis I make a case study of mixed fusions and uncover several problematic consequences which I think follow from their most plausible assessment. -/- These include: (1) that mixed fusions’ probable membership relations may lead to dubious foundational loops in the mereological Universe, or (2) otherwise that mixed fusions oblige an implausible ontological priority of the mereological Universe as a whole; (3) that mixed fusions contradict the reductive account of set theory they are proposed within, by plausibly being seen to have the same members as their class parts, and (4) that mixed fusions therefore confound a mereological thesis of Composition as Identity, which some (including Lewis) use to support classical mereology – a consequence which is potentially self-defeating; (5) that mixed fusions as sums of abstract and concrete entities both subvert Lewis’s (1986) system of modal realism, while (6) also undermining less expansive theories of possible worlds; and finally, (7) that even where some of the foregoing is resisted, it remains implausible that mixed fusions are ontologically innocent, because their supposed distinction from their parts in this case ensures that they need to be counted as additional entities in one’s ontology. -/- To be clear, I do not advance a theory of mereological hybrid nihilism in the sense of denying all cases of transcategorial composition. (I only cover a few select instances of mereological hybridism via mixed fusions after all.) Rather, I deny that mereological hybridism is plausible in full generality, by demonstrating that any cases of it are at least limited by the constraints that I identify. This in turn vindicates a call for a restriction on parthood theories and composition principles which allow certain types of categorially mixed entities – including restricting classical mereology with its principle of unrestricted composition. -/- Although theories of parthood like the standard classical mereology are not ordinarily developed for the sake of mereological hybrids like mixed fusions, these and other transcategorial composites are still among the logical consequences of such parthood systems operating with sufficient generality. The significance of my thesis, then, comes from showcasing how some of these kinds of entities do not conform to the systems in which they are included as required, and hence I argue for the rejection of unrestricted mereological hybridism as well as any mereological principles which support it. (shrink)

I present two puzzles about the metaphysics of stores, restaurants, and other such establishments. I defend a solution to the puzzles, according to which establishments are not material objects and are not constituted by the buildings that they occupy.

What are words? What makes two token words tokens of the same word-type? Are words abstract entities, or are they (merely) collections of tokens? The ontology of words tries to provide answers to these, and related questions. This article provides an overview of some of the most prominent views proposed in the literature, with a particular focus on the debate between type-realist, nominalist, and eliminativist ontologies of words.

‘Nominalism’ refers to a family of views about what there is. The objects we are familiar with (e.g. hands, laptops, cookies, and trees) can be characterized as concrete and particular. Nominalists agree that there are such things. But one group of nominalists denies that anything is non-particular and another group denies that anything is non-concrete. These two sorts of nominalism, referred to as ‘nominalism about universals’ and ‘nominalism about abstract objects’, have common motivations in contemporary philosophy.

Discussion of atomistic and monistic theses about abstract reality.

The main purpose of the paper is to outline the formal-logical, general theory of language treated as a particular ontological being. The theory itself is called the ontology of language, because it is motivated by the fact that the language plays a special role: it reflects ontology and ontology reflects the world. Language expressions are considered to have a dual ontological status. They are understood as either concretes, that is tokens – material, physical objects, or types – classes of tokens, (...) which are abstract objects. Such a duality is taken into account in the presented logical theory of syntax, semantics and pragmatics. We point to the possibility of building it on two different levels; one which stems from concretes, language tokens of expressions, whereas the other one – from their classes, types conceived as abstract, ideal beings. The aim of this work is not only to outline this theory as taking into account the functional approach to language, with respect to the dual ontological nature of its expressions, but also to show that the logic based on it is ontologically neutral in the sense that it abstracts from accepting some existential assumptions, related with the ontological nature of these linguistic expressions and their extra-linguistic ontological counterparts (objects). (shrink)

Peter van Inwagen has given an answer to the question ‘Why is there something rather than nothing?’. His answer is: Because there being nothing is as improbable as anything can be: it has probability 0. Here I shall examine his argument for this answer and I shall argue that it does not work because no good reasons have been given for two of the argument’s premises and that the conclusion of the argument does not constitute an answer to the question (...) van Inwagen wanted to answer. (shrink)

Instead of the half-century old foundational feud between set theory and category theory, this paper argues that they are theories about two different complementary types of universals. The set-theoretic antinomies forced naïve set theory to be reformulated using some iterative notion of a set so that a set would always have higher type or rank than its members. Then the universal u_{F}={x|F(x)} for a property F() could never be self-predicative in the sense of u_{F}∈u_{F}. But the mathematical theory of categories, (...) dating from the mid-twentieth century, includes a theory of always-self-predicative universals--which can be seen as forming the "other bookend" to the never-self-predicative universals of set theory. The self-predicative universals of category theory show that the problem in the antinomies was not self-predication per se, but negated self-predication. They also provide a model (in the Platonic Heaven of mathematics) for the self-predicative strand of Plato's Theory of Forms as well as for the idea of a "concrete universal" in Hegel and similar ideas of paradigmatic exemplars in ordinary thought. (shrink)

I address two related questions. First: what value is there in visiting a museum and becoming acquainted with the objects on display? For art museums the answer seems obvious: we go to experience valuable works of art, and experiencing valuable works of art is itself valuable. In this paper I focus on non-art museums, and while these may house aesthetically valuable objects, that is not their primary purpose, and at least some of the objects they house might not be particularly (...) aesthetically valuable at all. Second: to what ontological type or category do museum objects belong? What type of item should be featured on an inventory of a museum collection? I distinguish between typical objects and special objects. While these are different types of object, both, I argue, are abstracta, not concreta. The answer to the second question, concerning the ontological category of special objects, throws new light on various philosophical questions about museums and their collections, including the question about the value of museum experiences. But it also throws light on important questions concerning the preservation and restoration of museum objects. (shrink)

I here defend a theory consisting of four claims about ‘property’ and properties, and argue that they form a coherent whole that can solve various serious problems. The claims are (1): ‘property’ is defined by the principles (PR): ‘F-ness/Being F/etc. is a property of x iff F’ and (PA): ‘F-ness/Being F/etc. is a property’; (2) the function of ‘property’ is to increase the expressive power of English, roughly by mimicking quantification into predicate position; (3) property talk should be understood at (...) face value: apparent commitments are real and our apparently literal use of ‘property’ is really literal; (4) there are no properties. In virtue of (1)–(2), this is a deflationist theory and in virtue of (3)–(4), it is an error theory. (1) is fleshed out as a claim about understanding conditions, and it is argued at length, and by going through a number of examples, that it satisfies a crucial constraint on meaning claims: all facts about ‘property’ can be explained, together with auxiliary facts, on its basis. Once claim (1) has been expanded upon, I argue that the combination of (1)–(3) provides the means for handling several problems: they help giving a happy-face solution to what I call the paradox of abstraction , they form part of a plausible account of the correctness of committive sentences, and, most importantly, they help respond to various indispensability arguments against nominalism. (shrink)

I here investigate whether there is any version of the principle of charity both strong enough to conflict with an error-theoretic version of nominalism (EN) about abstract objects, and supported by the considerations adduced in favour of interpretive charity in the literature. I argue that in order to be strong enough, the principle, which I call (Charity), would have to read, “For all expressions e, an acceptable interpretation must make true a sufficiently high ratio of accepted sentences containing e”. I (...) next consider arguments based on Davidson's intuitive cases for interpretive charity, the reliability of perceptual beliefs, and the reliability of “non-abstractive inference modes”, and conclude that none support (Charity). I then propose a diagnosis of the view that there must be some universal principle of charity ruling out (EN). Finally, I present a reason to think (Charity) is false, namely, that it seems to exclude the possibility of such disagreements as that between nominalists and realists. (shrink)

In this paper I confront what I take to be the crucial challenge for fictional realism, i.e. the view that fictional characters exist. This is the problem of accounting for the intuition that corresponding negative existentials such as ‘Sherlock Holmes does not exist’ are true (when, given fictional realism, taken literally they seem false). I advance a novel and detailed form of the response according to which we take them to mean variants of such claims as: there is no concrete (...) x such that x is Sherlock Holmes. (shrink)

Awareness is a two-place determinable relation some determinates of which are seeing, hearing, etc. Abstract objects are items such as universals and functions, which contrast with concrete objects such as solids and liquids. It is uncontroversial that we are sometimes aware of concrete objects. In this paper I explore the more controversial topic of awareness of abstract objects. I distinguish two questions. First, the Existence Question: are there any experiences that make their subjects aware of abstract objects? Second, the Grounding (...) Question: if an experience makes its subject aware of an abstract object, in virtue of what does it do so? I defend the view that intuitions, specifically mathematical intuitions, sometimes make their subjects aware of abstract objects. In defending this view, I develop an account of the ground of intuitive awareness. (shrink)

An analysis of the physical implications of abstractness reveals the reality of three interconnected modes of existence: abstract, virtual and concrete, corresponding in physics to information, energy and matter. This triple-aspect monism clarifies the ontological status of subatomic quantum particles. It also provides a non-spooky solution to the weirdness of quantum physics and a new outlook for the mind-body problem. The ontological implications are profound for both physics and philosophy.

There is a widely shared account of the distinction between types and tokens, which might be termed the standard account. However, it has some surprising consequences that are not always realized. According to the standard account, a type is a contingent abstract object that can be created by us, but it does not allow any change and can never be destroyed once it is created, because it is an abstract object. I would like to present an alternative account of types (...) and tokens, according to which types are concrete objects that are located in space and time. This new account is based on a concept that I call a "token generator", which is something that specifies in detail how to produce the tokens. (shrink)

I consider the field of aesthetics to be at its most productive and engaging when adopting a broadly philosophically informative approach to its core issues (e.g., shaping and testing putative art theoretic commitments against the relevant standard models employed in philosophy of language, metaphysics, and philosophy of mind) and to be at its most impotent and bewildering when cultivating a philosophically insular character (e.g., selecting interpretative, ontological, or conceptual models solely for fit with pre-fixed art theoretic commitments). For example, when (...) philosophical aesthetics tends toward insularity, we shouldn’t be surprised to find standard art-ontological categories incongruous with those standardly employed in contemporary metaphysics. Of course, when contemporary metaphysics tends to ignore aesthetic and art theoretic concerns, perhaps we likewise shouldn’t be surprised to find the climate of contemporary metaphysics inhospitable for a theory of art. While this may seem to suggest at least a prima facie tension between our basic art theoretic commitments considered from within philosophical aesthetics and our standard ontological commitments considered from without, I think any perceived tension or antagonism largely due to metaphysicians and aestheticians (at least implicitly) assuming there to be but two available methodological positions with respect to the relationship between contemporary metaphysics and philosophical aesthetics (in the relevant overlap areas). I call these two opposing views the Deference View and the Independence View. I argue that either view looks to lead to what I call the Paradox of Standards. (shrink)

En la filosofía de Aristóteles y en la filosofía escolástica de cuño aristotélico, la abstracción constituía un acto fundamental del proceso cognitivo: marcaba el salto o ascenso de la sensibilidad a la inteligibilidad, del conocimiento del individuo al conocimiento de su esencia. En la teoría del conocimiento de Hegel, por el contrario, el concepto abstracto o, como Hegel prefiere llamarlo, la “representación abstracta” o “representación universal” es tan sólo un momento intermedio en el proceso fluido que va del conocimiento del (...) objeto como algo sensible -en la forma de la intuición y la subforma de la imagen- al conocimiento de su naturaleza intrínseca -en la forma del pensar. Sobre la base, por un lado, de los escasos textos en los que Hegel se ocupa expresamente del tema, y, por el otro, de la contextualización de estos textos en un análisis general de la filosofía del espíritu subjetivo teórico, el presente trabajo busca reconstruir las tesis fundamentales de Hegel sobre la abstracción y esclarecer con ello el sentido y función que la misma tiene en su teoría del conocimiento. The concept of abstraction in Hegel's theory of knowledgeIn both Aristotelian philosophy and the scholastic philosophy that bears its stamp, the concept of abstraction constitutes a fundamental act in the cognitive process; it signaled the leap or ascent from the realm of the senses to the realm of intellection, from knowledge of the individual to knowledge of his essence. By way of contrast, in Hegel's theory of knowledge, the abstract concept -or, as Hegel himself preferred to call it, “abstract representation” or “universal representation”­- is nothing but an intermediate moment in the fluid process of going from knowing the object as something given to the senses -in the form of intuition and the subform of image- to knowing its intrinsic nature -in the form of thought. Based on the scant writings by Hegel wherein he expressly addresses the matter, and by subsequently placing these texts into the broader context of an analysis of Hegel's philosophy of theoretical subjective spirit, this paper attempts to reconstruct Hegel's most significant ideas on abstraction. Hopefully, this will serve to clarify both the meaning and the role of that notion in Hegelian theory of knowledge. (shrink)

This paper is concerned with neo-Fregean accounts of reference to abstract objects. It develops an objection to the most familiar such accounts, due to Bob Hale and Crispin Wright, based upon what I call the 'proliferation problem': Hale and Wright's account makes reference to abstract objects seem too easy, as is shown by the fact that any equivalence relation seems as good as any other. The paper then develops a response to this objection, and offers an account of what it (...) is for abstracta to exist that is Fregean in spirit but more robust than familiar views. (shrink)

Much attention has been given to the question of ontic vagueness, and the issues usually center around whether certain paradigmatically concrete entities – cats, clouds, mountains, etc. – are vague in the sense of having indeterminate spatial boundaries. In this paper, however, I wish to focus on a way in which some abstracta seem to be locationally vague. To begin, I will briefly cover some territory already covered regarding certain types of “traditional” abstracta and the ways they are currently alleged (...) to be vague. I then wish to discuss two types of “nontraditional” abstracta and the sense in which I think some of these objects are locationally vague. I will next reexamine some of the traditional abstracta and discuss whether any of these objects are locationally vague in the novel way suggested for the nontraditional sorts. I’ll finish by discussing objections, and conclude with some remarks about characterizing the abstract/concrete distinction. (shrink)

The paper is about the relationship between Scotus’s notion of ‘natura communis,’ for an examination of the main features that Scotus ascribes to ‘common natures’ can shed substantial light on the nature of metaphysics in itself. Some preliminary observations on historiography are also deemed to be in order.

By logical foundations of language syntax ontology we understand here the construction of formalized linguistic theories based on widely conceived mathematical logic and dependent on two trends in language ontology. The formalization includes exclusively the syntactic aspect of logical analysis of language characterized categorially according to Ajdukiewicz's approach [1935, 1960]. Any categorial language L is characterized formally on two levels: on one of them it concerns the language of expression-tokens, on the other one - that of expression-types. Accepting the view (...) that expression-concretes, that is expression-tokens - thus, physical objects are fundamental language layer, whereas the secondary layer for L are expression-abstracts, that is expression-types - thus, ideal objects, it is the nominalistic, concretistic philosophical view on the ontological nature of language entities that is adhered to. Supporting the view that expression-types are the basic language layer, while expression-concretes are the secondary one, we take the opposite standpoint - platonizing one. We prove that the two dual approaches towards the two-level syntax theory of language are logically eqivalent. In the scope of language syntax, both conceptions deriving from two different existential assumption are equivalent. This statement is philosophical significance, since it proves that in syntactical studies on language the assumption of the existence of abstract language beings (interpreted as classes equiform tokens) can be neglected. The idea was signalized by author in ealier paper "On the type-token relationships'' [1986) and than, in a slighly diffrent form in English "On the eliminatibility of ideal linguistic entities, Studia Logica 48,no 4 (1989), pp. 587-615. (shrink)

The paper contains an overview of the most important results presented in the monograph of the author "Teorie Językow Syntaktycznie-Kategorialnych" ("Theories of Syntactically-Categorial Languages" (in Polish), PWN, Warszawa-Wrocław 1985. In the monograph four axiomatic systems of syntactically-categorial languages are presented. The first two refer to languages of expression-tokens. The others also takes into consideration languages of expression-types. Generally, syntactically-categorial languages are languages built in accordance with principles of the theory of syntactic categories introduced by S. Leśniewski [1929,1930]; they are connected (...) with- the Ajdukiewicz’s work [1935] which was a continuation of Leśniewski’s idea and further developed and popularized in the research on categorial grammars, by Y. Bar-Hillel [1950,1953,1964]. To assign a suitable syntactic category to each word of the vocabulary is the main idea of syntactically-categorial approach to language. Compound expressions are built from the words of the vocabulary and then a suitable syntactic-category is assigned to each of them. A language built in this way should be decidable, which means that there should exist an algorithm for deciding about each expression of it, whether it is well-formed or is syntactically connected . The traditional, originating from Husserl, understanding of the syntactic category confronts some difficulties. This notion is defined by abstraction using the concept of affiliation of two expressions to the same syntactic category. (shrink)

Alexius Meinong developed a notion of defective objects in order to account for various logical and psychological paradoxes. The notion is of historical interest, since it presages recent work on the logical paradoxes by Herzberger and Kripke. But it fails to do the job it was designed for. However, a technique implicit in Meinong's investigation is more successful and can be adapted to resolve a similar paradox discovered by Romane Clark in a revised version of Meinong's Theory of Objects due (...) to Rapaport. One family of paradoxes remains, but it is argued that they are unavoidable and relatively harmless. (shrink)

Translation in Greek of "A Geneticist's Roadmap to Sanity" (2019) by G.B. Côté. Μεταφράστηκε και στα Γαλλικά από τους Gilbert B. Côté και Roger Lapalme και προστέθηκε η βιβλιογραφία στις 28 του Απρίλη 2020: Pour comprendre le monde et revenir à la raison. La théorie du tout d'un généticien. Η ώθηση για τη συγγραφή ήταν η ανήθικη προεδρία του Donald J. Trump. Σε αυτό το κείμενο, θέλω να εξερευνήσω τα θεμέλια της ύπαρξής μας. Θα θίξω σύντομα την ενσυνείδηση, την ελεύθερη (...) βούληση, τη θρησκεία, την ηθική, τα βάσανα της ζωής , το πρόβλημα της δυαδικότητας του νου και του σώματος, την αχρονικότητα, τα πολλαπλά σύμπαντα και το ανθρώπινο πεπρωμένο. Για να διευκολύνω αυτήν την παρουσίαση, θα πρέπει πρώτα να δείξω ότι ο μαθηματικός πλατωνισμός είναι μια λογική αναγκαιότητα για την ύπαρξη οποιουδήποτε σύμπαντος, και θα εισαγάγω τους αφηρημένους, κβαντικούς και υλικούς τρόπους ύπαρξης (στη φιλοσοφία) που αντιστοιχούν στην πληροφόρηση, την ενέργεια και τη μάζα (στη φυσική). Το κείμενο αυτό αποτελεί μια σύνοψη της προσωπικής μου θεωρίας των πάντων. (shrink)

The handout of my talk at the Nordic Network in Metaphysics webinar on Friday 2/10/2020.

The idea that a being can be identical to its own essence has a long and venerable history in theological speculation. As with many ideas in theology, however, such an idea has never been given an adequate mathematical formulation. The key to such a formulation, I argue, is introducing an essence axiom into non-well-founded set theory. According to such an axiom, for every set, x, there is a set that contains all and only those sets that contain x. With such (...) an axiom, it becomes possible to introduce an essence function that takes each set to its essence. An object that is identical to its essence, then, is simply a fixed point of the essence function. In this paper, I first discuss a theorem according to which any fixed point of the essence function is universally symmetrical with respect to the set membership relation. After proving the theorem, I discuss its theological implications. I go on to argue that the process of counting the members of a set that is identical to its essence is a Sisyphusian process. Such a fact I suggest shows that the absurdity of human existence is not alleviated by the existence of God but rather is entailed by it. (shrink)