In this paper, we propose a mathematical model of subjective experience in terms of classes of hierarchical geometries of representations (“n-awareness”). We first outline a general framework by recalling concepts from higher category theory, homotopy theory, and the theory of (infinity,1)-topoi. We then state three conjectures that enrich this framework. We first propose that the (infinity,1)-category of a geometric structure known as perfectoid diamond is an (infinity,1)-topos. In order to construct a topology on the (infinity,1)-category of diamonds we then propose (...) that topological localization, in the sense of Grothendieck-Rezk-Lurie (infinity,1)-topoi, extends to the (infinity,1)-category of diamonds. We provide a small-scale model using triangulated categories. Finally, our meta-model takes the form of Efimov K-theory of the (infinity,1)-category of perfectoid diamonds, which illustrates structural equivalences between the category of diamonds and subjective experience (i.e.its privacy, self-containedness, and self-reflexivity). Based on this, we investigate implications of the model. We posit a grammar (“n-declension”) for a novel language to express n-awareness, accompanied by a new temporal scheme (“n-time”). Our framework allows us to revisit old problems in the philosophy of time: how is change possible and what do we mean by simultaneity and coincidence? We also examine the notion of “self” within our framework. A new model of personal identity is introduced which resembles a categorical version of the “bundle theory”: selves are not substances in which properties inhere but (weakly) persistent moduli spaces in the K-theory of perfectoid diamonds. (shrink)

In this paper, we develop a mathematical model of awareness based on the idea of plurality. Instead of positing a singular principle, telos, or essence as noumenon, we model it as plurality accessible through multiple forms of awareness (“n-awareness”). In contrast to many other approaches, our model is committed to pluralist thinking. The noumenon is plural, and reality is neither reducible nor irreducible. Nothing dies out in meaning making. We begin by mathematizing the concept of awareness by appealing to the (...) mathematical formalism of higher category theory. The beauty of higher category theory lies in its universality. Pluralism is categorical. In particular, we model awareness using the theories of derived categories and (infinity, 1)-topoi which will give rise to our meta-language. We then posit a “grammar” (“n-declension”) which could express n-awareness, accompanied by a new temporal ontology (“n-time”). Our framework allows us to revisit old problems in the philosophy of time: how is change possible and what do we mean by simultaneity and coincidence? Another question which could be re-conceptualized in our model is one of soteriology related to this pluralism: what is a self in this context? A new model of “personal identity over time” is thus introduced. (shrink)

The paper investigates the kind of dependence relation that best portrays Machian frame-dragging in general relativity. The question is tricky because frame-dragging relates local inertial frames to distant distributions of matter in a time-independent way, thus establishing some sort of non-local link between the two. For this reason, a plain causal interpretation of frame-dragging faces huge challenges. The paper will shed light on the issue by using a generalized structural equation model analysis in terms of manipulationist counterfactuals recently applied in (...) the context of metaphysical enquiry by Schaffer (2016) and Wilson (2017). The verdict of the analysis will be that frame-dragging is best understood in terms of a novel type of dependence relation that is half-way between causation and grounding. (shrink)

Singularitățile la care se ajunge în relativitatea generală prin rezolvarea ecuațiilor lui Einstein au fost și încă mai sunt subiectul a numeroase dezbateri științifice: Există sau nu, singularități? Big Bang a fost o singularitate inițială? Dacă singularitățile există, care este ontologia acestora? Este teoria generală a relativității o teorie care și-a arătat limitele în acest caz? În acest eseu argumentez faptul că există singularități, iar teoria generală a relativității, ca de altfel oricare altă teorie științifică din prezent, nu este valabilă (...) în interiorul orizontului evenimentelor. Dar asta nu presupune, așa cum consideră unii oameni de știință, că ea trebuie considerată ca fiind perimată. După o scurtă prezentare a aspectelor specifice din teoria clasică newtoniană și teoria specială a relativității, și o scurtă prezentare a teoriei generale a relativității, în capitolul Ontologia relativității generale prezint aspectele ontologice specifice relativității generale. Următorul capitol, Singularități, este dedicat prezentării singularităților care rezultă în relativitatea generală, a aspectelor specifice ale găurilor negre și orizontul evenimentelor, inclusiv dezbaterea despre Big Bang ca singularitate inițială, și argumentele în favoarea existenței singularităților. În Ontologia singularităților vorbesc despre posibilitățile de încadrare ontologică a singularităților în general și a găurilor negre în special, despre argumentul găurii pus în evidență de Einstein, și argumentele prezentate de oamenii de știință că nu există singularități și deci că teoria generală a relativității este în impas. Închei cu Concluziile în care expun și reiau pe scurt argumentele care ămi susțin opiniile prezentate mai sus. Aceasta este o traducere din limba engleză a lucrării: Sfetcu, Nicolae, "The singularities as ontological limits of the general relativity". (shrink)

The paper investigates possible readings of the later Heisenberg's remarks on the nature of quantum states. It discusses, in particular, whether Heisenberg should be seen as a proponent of the epistemic conception of states – the view that quantum states are not descriptions of quantum systems but rather reflect the state assigning observers' epistemic relations to these systems. On the one hand, it seems plausible that Heisenberg subscribes to that view, given how he defends the notorious "collapse of the wave (...) function" by relating it to a sudden change in the epistemic situation of the observer registering a measured result. On the other hand, his remarks on quantum probabilities as "potentia" or "objective tendencies" are difficult to reconcile with such a reading. The accounts that are attributed to Heisenberg by the different possible readings considered are subjected to closer scrutiny; at the same time, their respective virtues and problems are discussed. _German_ Diese Arbeit untersucht mögliche Lesarten von Heisenbergs späten Bemerkungen über die Natur von Quantenzuständen. Insbesondere wird die Frage diskutiert, ob Heisenberg als Vertreter der epistemischen Auffassung von Quantenzuständen gelten kann – der Idee, dass Quantenzustände nicht Beschreibungen der objektiven Eigenschaften von Quantensystemen sind sondern die epistemischen Beziehungen von Beobachtern zu diesen Systemen widerspiegeln. Einerseits erscheint es plausibel, dass Heisenberg dieser Sichtweise zustimmt, wenn man sich ansieht, wie er den berüchtigten,,Kollaps der Wellenfunktion" verteidigt, indem er ihn mit einer plötzlichen Änderung in der Kenntnis des ein Messergebnis registrierenden Beobachters in Zusammenhang bringt. Andererseits sind seine Bemerkungen über quantenmechanische Wahrscheinlichkeiten als,,Potentia" oder,,objektive Tendenzen" mit einer solchen Lesart nur schwer in Einklang zu bringen. Die Positionen, die Heisenberg den verschiedenen möglichen Lesarten zufolge vertritt, werden eingehenden Untersuchungen unterzogen; gleichzeitig werden ihre jeweiligen Vorzüge und Probleme diskutiert. (shrink)

The thesis I wish to argue for in this article is that spatial relations such as occupying and being 1 km distant from are external. In the “Section 1” section, I shall introduce the distinction between external and internal relations and some other basic concepts in the ontology of relations. Afterwards, in the subsequent sections, I shall deal with different theories of space: substantivalism and relationism ; the spatial property theory ; super-substantivalism and super-relationism ; and spatial essentialism. I shall (...) demonstrate that, in all such theories, spatial relations need to be considered external. Otherwise, unacceptable consequences or spatial properties that are non-relational by mere façon de parler are in order. Finally, in the “Section 6” section, I shall briefly tackle length contraction in special relativity theory. (shrink)

Relativitatea generală a generat diverse interpretări filosofice timpurii. Adepții lui au evidențiat "relativizarea inerției" și conceptul de simultaneitate, kantienii și neo-kantienii au subliniat abordarea anumitor "forme intelectuale" sintetice (în special principiul covarianței generale, iar empiriștii logici au accentuat semnificația filozofică metodologică a teoriei. Reichenbach a abordat relativitatea generală prin prisma tezei "relativității geometriei", încercând o "axiomatizare constructivă" a teoriei relativității pe baza "problemelor elementare de fapt" (Elementaratbestande) cu privire la comportamentul observabil al razelor de lumină, a tijelor și a ceasurilor. (...) DOI: 10.13140/RG.2.2.27826.76486. (shrink)

General Relativity generated various early philosophical interpretations. His adherents have highlighted the "relativization of inertia" and the concept of simultaneity, Kantians and Neo-Kantians have underlined the approach of certain synthetic "intellectual forms" (especially the principle of general covariance, and logical empirics have emphasized the philosophical methodological significance of the theory. Reichenbach approached the GR through the "relativity of geometry" thesis, trying to build a "constructive axiomatization" of relativity based on "elementary matters of fact" (Elementartatbestande) for the observable behavior of light (...) rays, rods and clocks. The mathematician Hermann Weyl attempted a reconstruction of Einstein's theory based on the epistemology of a "pure infinitesimal geometry", an extended geometry with additional terms that formally identified with the potential of the electromagnetic field. DOI: 10.13140/RG.2.2.11641.93281. (shrink)

The singularities from the general relativity resulting by solving Einstein's equations were and still are the subject of many scientific debates: Are there singularities in spacetime, or not? Big Bang was an initial singularity? If singularities exist, what is their ontology? Is the general theory of relativity a theory that has shown its limits in this case? In this essay I argue that there are singularities, and the general theory of relativity, as any other scientific theory at present, is not (...) valid for singularities. But that does not mean, as some scientists think, that it must be regarded as being obsolete. After a brief presentation of the specific aspects of Newtonian classical theory and the special theory of relativity, and a brief presentation of the general theory of relativity, the chapter Ontology of General Relativity presents the ontological aspects of general relativity. The next chapter, Singularities, is dedicated to the presentation of the singularities resulting in general relativity, the specific aspects of the black holes and the event horizon, including the Big Bang debate as original singularity, and arguments for the existence of the singularities. In Singularity Ontology, I am talking about the possibilities of ontological framing of singularities in general and black holes in particular, about the hole argument highlighted by Einstein, and the arguments presented by scientists that there are no singularities and therefore that the general theory of relativity is in deadlock. In Conclusions I outline and summarize briefly the arguments that support my above views. -/- DOI: 10.58679/TW62329. (shrink)

We analyze the geometric foundations of classical Yang-Mills theory by studying the relationships between internal relativity, locality, global/local invariance, and background independence. We argue that internal relativity and background independence are the two independent defining principles of Yang-Mills theory. We show that local gauge invariance -heuristically implemented by means of the gauge argument- is a direct consequence of internal relativity. Finally, we analyze the conceptual meaning of BRST symmetry in terms of the invariance of the gauge fixed theory under general (...) local gauge transformations. (shrink)

En el ámbito de la teoría general de la relatividad (TGR), se considera que el espaciotiempo es una entidad real. En este sentido, atendiendo al realis mo sobre entidades, surgen problemas como ¿qué tipo de entidad es el espaciotiempo?, ¿cuál es su naturaleza? Tradicionalmente, en atención a dicha teoría conviven dos concepciones realistas: la substancialista, donde el espaciotiempo sería una substancia; y la relacionista, tal que el espaciotiempo correspondería a una “relación entre substancias”.

We outline an argument that a single-particle universe (a universe containing precisely one pointlike particle) can be described mathematically, in which observation can be considered meaningful despite the a priori impossibility of distinguishing between an observer and the observed. Moreover, we argue, such a universe can be observationally similar to the world we see around us. It is arguably impossible, therefore, to determine by experimental observation of the physical world whether the universe we inhabit contains one particle or many—modern scientific (...) theories cannot, therefore, be regarded as descriptions of ‘reality’, but are at best human artefacts. Our argument uses a formal model of spacetime that can be considered either relational or substantivalist depending on one’s preferred level of abstraction, and therefore suggests that this long-held distinction is also to some extent illusory. (shrink)

Historically models of eternity have been grounded in divine attributes rather than the intrinsic structure of space-time. I examine the topology of Minkowski spacetime in comparison to the Euclidean space of Newtonian Mechanics, before highlighting five common approaches to eternity. Both atemporal and temporal models of eternity are examined to establish what they tell us about the nature of eternity outside the divine attributes, before being evaluated for their coherence with the Special Theory of Relativity. I argue that the most (...) coherent models of eternity in light of the Special Theory of Relativity are those that appeal to metaphysical rather than physical time as it remains unaffected by the conventionality and relativity of simultaneity. I conclude that the special Theory of Relativity has a valid role to play in establishing the coherence of eternity. However, due to the discontinuity of concepts of time between the Special Theory of Relativity, the General theory of Relativity and Quantum Mechanics, it cannot single-handedly be used to establish which models of eternity cohere with scientific models of time, but must be use alongside the General theory of Relativity and Quantum Mechanics. (shrink)

Left and right hands are incongruent counterparts. Yet each replicates the intrinsic properties of the other. This suggests that differing relations to space make the difference. Kant's and Weyl's discussions of the problem are critically discussed. It emerges that spatial relationism fails to explain how its relations may be interpreted. An excursion into visual geometry explains the basis of handedness in the orientable structure of space.

Populism is currently one of the most studied socio-political topics. However, no shared definition is present at the moment. Fortunately, common features are emerging in recent studies, so that the possibility to devise a comprehensive concept of populism does not seem illusory anymore. In this article I evaluate whether an ontological determination of the concept is conceivable, according to a critical and dynamical perspective. This means that epistemological questions are considered as fundamental, and ontology looks at dynamical systems theories in (...) order to conceptually organize the outcomes of scientific researches. Taking advantage of ontological and system theoretic categories, I try to delineate some not obvious issues in the current approaches to populism. (shrink)

The paper investigates the status of gravitational energy in Newtonian Gravity, developing upon recent work by Dewar and Weatherall. The latter suggest that gravitational energy is a gauge quantity. This is potentially misleading: its gauge status crucially depends on the spacetime setting one adopts. In line with Møller-Nielsen’s plea for a motivational approach to symmetries, we supplement Dewar and Weatherall’s work by discussing gravitational energy–stress in Newtonian spacetime, Galilean spacetime, Maxwell-Huygens spacetime, and Newton–Cartan Theory. Although we ultimately concur with Dewar (...) and Weatherall that the notion of gravitational energy is problematic in NCT, our analysis goes beyond their work. The absence of an explicit definition of gravitational energy–stress in NCT somewhat detracts from the force of Dewar and Weatherall’s argument. We fill this gap by examining the supposed gauge status of prima facie plausible candidates—NCT analogues of gravitational energy–stress pseudotensors, the Komar mass, and the Bel-Robinson tensor. Our paper further strengthens Dewar and Weatherall’s results. In addition, it sheds more light upon the subtle link between sufficiently rich inertial structure and the definability of gravitational energy in NG. (shrink)

Einstein’s “point-coincidence argument'” as a response to the “hole argument” is usually considered as an expression of “Leibniz equivalence,” a restatement of indiscernibility in the sense of Leibniz. Through a historical-critical analysis of Logical Empiricists' interpretation of General Relativity, the paper attempts to show that this labeling is misleading. Logical Empiricists tried explicitly to understand the point-coincidence argument as an indiscernibility argument of the Leibnizian kind, such as those formulated in the 19th century debate about geometry, by authors such as (...) Poincaré, Helmholtz or Hausdorff. However, they clearly failed to give a plausible account of General Relativity. Thus the point-coincidence/hole argument cannot be interpreted as Leibnizian indiscernibility argument, but must be considered as an indiscernibility argument of a new kind. Weyl's analysis of Leibniz's and Einstein's indiscernibility arguments is used to support this claim. (shrink)

We analyse the various conceptual notions that go under the umbrella “relationalism/substantivalism”. Our focus will be on evaluating the ontological status of spacetime in General Relativity. To this end we systematically develop the ontological framework that implicitly underlies the traditional debate and common understanding of physics. We submit that spacetime with its chronogeometric and inertial structure, represented by the triple of the bare manifold, the metric and the affine structure, is best construed as the totality of possible and actual spatiotemporal (...) relations of events. This can explain the non-fundamentality of general relativistic gravitational energy and suggests a non-causal, non-interactional understanding of the interdependence of matter in spacetime in GR. (shrink)