Representation of the Universe as a Dendrogramic Hologram Endowed with Relational Interpretation

A proposal for a fundamental theory is described in which classical and quantum physics as a representation of the universe as a gigantic dendrogram are unified. The latter is the explicate order structure corresponding to the purely number-theoretical implicate order structure given by p-adic numbers. This number field was zero-dimensional, totally disconnected, and disordered. Physical systems (such as electrons, photons) are sub-dendrograms of the universal dendrogram. Measurement process is described as interactions among dendrograms; in particular, quantum measurement problems can be resolved using this process. The theory is realistic, but realism is expressed via the the Leibniz principle of the Identity of Indiscernibles. The classical-quantum interplay is based on the degree of indistinguishability between dendrograms (in which the ergodicity assumption is removed). Depending on this degree, some physical quantities behave more or less in a quantum manner (versus classic manner). Conceptually, our theory is very close to Smolin’s dynamics of difference and Rovelli’s relational quantum mechanics. The presence of classical behavior in nature implies a finiteness of the Universe-dendrogram. (Infinite Universe is considered to be purely quantum.) Reconstruction of events in a four-dimensional space type is based on the holographic principle. Our model reproduces Bell-type correlations in the dendrogramic framework. By adjusting dendrogram complexity, violation of the Bell inequality can be made larger or smaller.

On making a difference: towards a minimally non-trivial version of the identity of indiscernibles

The identity of indiscernibles (PII) states that indiscernible objects must be identical. Many philosophers have held that the PII turns out to be either true but trivial, or non-trivial but false, depending on how the notion of (in)discernibility is spelled out. In this paper, I propose and defend an account of this notion which aims to yield a minimally non-trivial and yet plausible version of the PII. I argue moreover that this version of the principle is immune to a number of well-known and recent objections to the PII.

Making Mistakes Saves the Single World of the Extended Wigner’s Friend Experiment

The Extended Wigner’s Friend thought experiment comprising a quantum system containing an agent who draws conclusions, upon observing the outcome of a measurement of a qubit prepared in two non-orthogonal versions by another agent led its authors to conclude that quantum theory cannot consistently describe the use of itself. It has also been proposed that this thought experiment is equivalent to coherent entangled state (Bell type) experiments. It is argued in this paper that the assumption of the freedom of choice of the first Wigner’s friend invalidates such equivalency. It is also argued that the assumption of locality (physical space) introduces superfluous identity of indiscernibles metric axiom, which is invalid in quantum domain and generally disproven by the Ugly duckling mathematical theorem.

Universales indiscernibles

Universals have traditionally thought to obey the identity of indiscernibles, that is, it has traditionally been thought that there can be no perfectly similar universals. But at least in the conception of universals as immanent, there is nothing that rules out there being indiscernible universals. In this paper, I shall argue that there is useful work indiscernible universals can do, and so there might be reason to postulate indiscernible universals. In particular, I shall argue that postulating indiscernible universals can allow a theory of universals to identify particulars with bundles of universals, and that postulating indiscernible universals can allow a theory of universals to develop an account of the resemblance of quantitative universals that avoids the objections that Armstrong’s account faces. Finally, I shall respond to some objections and I shall undermine the criterion of distinction between particulars and universals that says that the distinction between particulars and universals lies in that while there can be indiscernible particulars, there cannot be indiscernible universals.

Particulares nus: uma defesa da teoria do substrato

The present work aims to present the debate of the bare particulars proposal and its critics. We seek here to discuss how the thesis of Bare Particulars is presented today by taking the works of proponents of this thesis. In the following we will present the most current criticisms that are raised upon the thesis and how these criticisms arise based on realism, and specifically from defenders of the bundle theory, that aim to discredit the study of any particular substratum. Finally, we will seek answers to the criticisms and how the defense of the thesis is presented, grounding also from the current literature. Based on the debate between the position of Bare Particulars and the bundle theory, we will seek to defend the theory of the substrate as the simplest way to highlight the identity of objects without incurring in the error of Leibniz’s Principle of Identity of Indiscernibles.

Uma abordagem reducionista ao problema da identidade dos indiscerníveis

I aim to defend the thesis that the truth of any proposition about the number of particulars that exist in the world is supervenient upon the truth of all propositions exclusively about universals (i.e., properties and relations). If this thesis is correct, all facts about the individuation of particulars are reducible to facts exclusively about universals, and there is no primitive individuation of particulars. I present two arguments against the possibility of this kind of primitive individuation. The first is that the possibility of primitively individuated particulars raises radical skeptical doubts about the number of particulars with which we are acquainted. The second is that primitively individuated particulars are theoretically redundant since the qualitative character of any possible world can be exhaustively described if we talk only about universals. The classical bundle theory is the most common variety of reductionism about the number of particulars, but I also want to defend that it is not the only possible variety. More specifically, I present an alternative according to which particulars are individuated by spatial relations. This alternative, in contrast to bundle theory, does not commit us to the controversial principle of the identity of indiscernibles, but it implies a transcendent conception of universals.

A Logical Reconstruction of Leibniz’s Argument for His Complete Concept Conception of the Nature of Substance in Discours §8

This paper develops a valid reconstruction in first-order predicate logic of Leibniz’s argument for his complete concept definition of substance in §8 of the Discours de Métaphysique. Following G. Rodriguez-Pereyra, it construes the argument as resting on two substantial premises, the “merely verbal” Aristotelian definition and Leibniz’s concept containment theory of truth, and it understands the resulting “real” definition as saying not that an entity is a substance iff its complete concept contains every predicate of that entity, but iff its complete concept contains every predicate of any subject to which that concept is truly attributable. An account is suggested of why Leibniz criticises the Aristotelian definition as merely nominal and how he takes his own definition to overcome this shortcoming: while on the Aristotelian basis the predication relation could generate endless chains, so that substances as endpoints of predication would be impossible, Leibniz’s definition reveals lowest species as such endpoints, which he therefore identifies with individual substances. Since duplicate lowest species make no sense, the Identity of Indiscernibles for substances follows. The reading suggests a Platonist interpretation according to which substances do not so much have but are individual essences, natures or forms.

Quantum prescriptions are more ontologically distinct than they are operationally distinguishable

Based on an intuitive generalization of the Leibniz principle of `the identity of indiscernibles', we introduce a novel ontological notion of classicality, called bounded ontological distinctness. Formulated as a principle, bounded ontological distinctness equates the distinguishability of a set of operational physical entities to the distinctness of their ontological counterparts. Employing three instances of two-dimensional quantum preparations, we demonstrate the violation of bounded ontological distinctness or excess ontological distinctness of quantum preparations, without invoking any additional assumptions. Moreover, our methodology enables the inference of tight lower bounds on the extent of excess ontological distinctness of quantum preparations. Similarly, we demonstrate excess ontological distinctness of quantum transformations, using three two-dimensional unitary transformations. However, to demonstrate excess ontological distinctness of quantum measurements, an additional assumption such as outcome determinism or bounded ontological distinctness of preparations is required. Moreover, we show that quantum violations of other well-known ontological principles implicate quantum excess ontological distinctness. Finally, to showcase the operational vitality of excess ontological distinctness, we introduce two distinct classes of communication tasks powered by excess ontological distinctness.

The Correspondence with Clarke

The correspondence between Leibniz and Samuel Clarke—mediated by Leibniz’s erstwhile friend and disciple at the electoral court in Hanover, Caroline of Brandenburg-Ansbach, princess of Wales—is arguably the most famous and influential of philosophical correspondences. In this chapter, I begin by tracing the background of the correspondence and the role that Caroline played in its inception and development. I then turn to a discussion of the main themes of the correspondence, paying particular attention to the importance of Caroline’s presence in shaping the themes of the debate: the principle of sufficient reason, the identity of indiscernibles, God’s choice in creating this world, space and time, God’s presence and activity in the world, miracles, and gravity.

AMR Similarity Metrics from Principles

Different metrics have been proposed to compare Abstract Meaning Representation (AMR) graphs. The canonical Smatch metric (Cai and Knight, 2013 ) aligns the variables of two graphs and assesses triple matches. The recent SemBleu metric (Song and Gildea, 2019 ) is based on the machine-translation metric Bleu (Papineni et al., 2002 ) and increases computational efficiency by ablating the variable-alignment. In this paper, i) we establish criteria that enable researchers to perform a principled assessment of metrics comparing meaning representations like AMR; ii) we undertake a thorough analysis of Smatch and SemBleu where we show that the latter exhibits some undesirable properties. For example, it does not conform to the identity of indiscernibles rule and introduces biases that are hard to control; and iii) we propose a novel metric S2 match that is more benevolent to only very slight meaning deviations and targets the fulfilment of all established criteria. We assess its suitability and show its advantages over Smatch and SemBleu.