Abstracts

Vincenzo Fano (University of Urbino)

A robust logical pluralism

The seminal book on logical pluralism written by Beall and Restall (2007) is discussed. The most relevant scholarly literature on the topic is critically presented. A more syntactical form of logical pluralism is defended. In particular, it is shown that the question of logical pluralism without a bit of Platonist commitment is not philosophically relevant.

Marianna Boero (University of Teramo)
Scientific Discourse and Social Media: Information Reliability and the Crisis of Expertise in the Post-Truth Society
Social networks offer a more immediate way for researchers to communicate with their audience, dismantling old epistemic hierarchies and reconciling science with society. However, the use of social networks in scientific debates poses critical issues, such as the increasing feeling of distrust for expert knowledge, stimulated by the perceived wisdom of influencers on the Internet and social media.
One of the principal hurdles posed by social media is the ease with which misinformation can be disseminated. This is especially true in the realm of science, where sensationalist headlines and clickbait articles can rapidly go viral, even if they lack a robust scientific basis. This has led to a proliferation of fake news, conspiracy theories, and pseudoscience that can undermine public trust in science and lead to harmful behaviors and beliefs. The possibility of debating science on social networks, dealing with technical subjects, such as climate change, vaccine safety, and food safety, highlights the difficulty of separating facts and opinions, reliable and false information, with the risk of spreading false news intentionally or unintentionally.
This process also causes a crisis of the figure of the expert, who is increasingly questioned due to the spread of misinformation and disinformation, often amplified by social networks. The campaign against COVID-19 vaccines is a clear example of this feeling of distrust. While in the past, experts were respected authorities who provided reliable and impartial assessments of scientific issues, in today’s social media landscape, they are often dismissed or derided, with their opinions viewed as biased or self-interested. This can foster a culture of distrust and skepticism that may be deleterious to both the scientific community and society as a whole.
The aim of this contribution is to delve deeper into these issues, as part of a broader reflection on the theme of fake news and post-truth. After an introductory section dedicated to the connection between social networks and scientific discourse, the paper will focus on the crisis of the figure of the expert in the age of social media. It will also analyze the role and reliability of scientific sources in public debates and the contribution of the semiotic gaze in describing these phenomena

Pierluigi Graziani (University of Urbino)
From Simplicity to Readability
(j.w.w. Pedro Quaresma, University of Coimbra)

At the dawn of the last century, David Hilbert (1862-1943) offered a list of problems to the mathematical community at the International Mathematical Congress in Paris. Hilbert presented only ten problems and later published a list containing twenty-three problems. However, Hilbert also had a 24th problem in mind. The omitted problem is recorded in his Mathematisches Notizbuch. Among the undated entries in the Notebook is a statement highlighting that he had in mind to present a twenty-fourth problem in Paris concerning the simplicity of proofs. At that time, Hilbert was not alone in his desire for maximal simplicity in mathematical proofs. This issue was also relevant to the French mathematician Emile Lemoine (1840-1912), who showed great interest in simplifying geometric construction. In February 1902, Èmile Lemoine published the final version of the work: Géometrographie---ou art des constructions géométriques. It was the result of many years of research on the measurement of simplicity in mathematics. 

In this talk, I will describe the method known as Geometrography, both in the original version designed by Émile Lemoine and in variants. After that, I will focus on a modernization of Lemoine's method to measure the readability of formal proofs produced by automated theorem provers for geometry. I will conclude by discussing future work on this topic in automated theorem proving and in mathematics education.

Danilo Pelusi  (University of Teramo)
Fuzzy logic and evolutionary algorithms for solving engineering problems

Several engineering problems can not be solved by using exact methods. In fact, such methods lead to huge computational complexity. Therefore, the definitive algorithm is not able to provide the output in a reasonable time. In order to avoid this kind of problem, suitable soft computing techniques may be applied.

This speech will focus on the combination of intelligent techniques to solve high complexity problems. In particular, fuzzy logic and nature-inspired algorithms will be taken into account. The fuzzy systems exploit the knowledge to assure an approximate reasoning. Nature-inspired algorithms are based on the behaviour  of living organisms and natural phenomena. 

The speech will illustrate some suitable combinations between fuzzy systems and swarm algorithms for optimizing specific engineering problems.

Massimiliano Palmiero  (University of Teramo)
Creativity as a process: the key role of convergent thinking
Creativity supports human civilization, progress, and innovation in a variety of domains (arts, scientific, economic, personal, etc.), reflecting the individual’s ability to make something original and functional in a given context. According to the so-called 4P model, creativity can be conceived in terms of: Process (e.g., conscious or unconscious), Product (e.g., tangible or intangible), Person (e.g., pre-dispositions and attitudes of the creator), and Place (e.g., socio-cultural environments). Focusing on the process aspect, generally creativity relies on both divergent thinking, that supports the ability to find many different new and appropriate ideas to a given open-ended problem, and convergent thinking,  that in turn supports the ability to find one single solution to a given closed problem. This latter provides not only criteria of effectiveness and novelty of  ideas generated via divergent thinking, but also emphasizes logic, combines what belongs together from adjacent fields, recognize and preserves the already known within specific limits, and supports feelings of security and safety. With this in mind, it appears that creativity, one of the most complex process that  of human mind, can be completely understood and deeply explored if different perspectives, including even the most rational and logic ones, are taken.

Davide Pietrini (University of Urbino)

Signs of the principle of virtual work and of the “principle of conservation” in the Mechanicorum Liber by Guidobaldo del Monte.

Abstract: From a historical point of view, the principle of virtual work and the so-called “principle of conservation” follow different paths and have different origins. Some authors attributed the principle of virtual work to pseudo-Aristotle’s Mechanical Problems. The principle of virtual work was defined by Bernoulli: “for a system of forces that maintains a point, a surface, on a body in equilibrium, the sum of positive energies equals that of negative energies, considered with their absolute value”. Some signs of the “principle of conservation” can be found in Galileo Galilei’s The Dialogue Concerning the Two Chief World Systems: “Now fix it well in mind as a true and well-known principle that the resistance coming from the speed of motion compensates that which depends upon the weight of another moving body”. In Guidobaldo del Monte’s Mechanicorum Liber the concept of virtual work and the compensation of force, time, weight and space seem to be connected. In this talk, I will investigate this connection. Firstly, I present the well-known statements about the roots of the principle of virtual works and the “principle of conservation”. Secondly, I will examine the procedures used by Guidobaldo to study the behaviour of simple machines in equilibrium. Finally, I will analyse the relation between the equilibrium systems subjected to constraint reactions and the proportion of time, force, velocity and space in the Mechanicorum Liber.

Ludovico Fusco (University of Urbino)
From Mal'cev products to semilattice sums
A Mal'cev product is a special multiplicative operation between abstract classes of similar algebras. First introduced (clearly under another name) by Anatolij Mal'cev in 1967, Mal'cev products quickly turned out to be extremely versatile constructions, being primarily applied to the study of lattices of (quasi)varieties (e.g., for establishing alternative structure theorems when the usual characterizations are impractical). In this talk I will discuss the key role played by Mal'cev products in the theory of semilattice sums, a class of well known techniques for constructing new algebras over semilattice-ordered systems of structures of a fixed type. Płonka sums are the oldest and best known example of semilattice sums, with many remarkable applications in algebra, logic and computer science. I will show how the theory of Mal'cev products can shed new light on these constructions, laying down the foundations for new research directions.

Davide Fazio  (University of Teramo)
Some remarks on the logic of probabilistic relevance
(j.w.w. Raffaele Mascella)
In this talk we deepen some aspects of the statistical approach to relevance by providing logics for the syntactical treatment of probabilistic relevance relations. Specifically, we define conservative expansions of Classical Logic endowed with a ternary connective ↝ - indeed, a constrained material implication - whose intuitive reading is “x materially implies y and it is relevant to y under the evidence z”. In turn, this ensures the definability of a formula in three-variables R(x,z,y) which is the representative of relevance in the object language. We outline the algebraic semantics of such logics, and we apply the acquired machinery to investigate some term-defined weakly connexive implications with some intuitive appeal. As a conse- quence, a further motivation of (weakly) connexive principles in terms of relevance and background assumptions obtains.