by Gianfranco Basti, Joseph Brown, Giancarlo Succi

Classes of Prof. Gianfranco Basti

## Part I (Classes November 1-2, 2019)

## Bibliography of the Classes of Prof. Basti

- Abramsky Samson and Tzevelekos Nikos, "Introduction to categories and categorical logic," in
New structures for physics. CLASS Notes in Physics, 813, B. Coecke, Ed., Berlin-New York, Springer, 2011, pp. 3-94 (pdf)- Barbieri Marcello, “Biosemiotics: a new understanding of life”,
Naturewissehschaften,2008, DOI 10.1007/s00114-008-0368-x(pdf).- Basti Gianfranco,
Philosophy of nature and of science, vol. I: the foundations,Lateran University Press, Rome, 2011 (pdf)- Basti Gianfranco, “Intelligence and reference. Formal ontology of the natural computation. In:
Computing Nature, Gordana Dodig-Crnkovic and Raffaela Giovagnoli (Eds.), Springer-Verlag, Berlin Heidelberg, 2013, pp. 139-159 (Sapere, 7).- Basti Gianfranco, “The Post‐Modern Transcendental of Language in Science and Philosophy”. In:
Epistemology and Transformation of Knowledge in Global Age, Zlatan Delic (Ed.), InTech, London, 2017, pp. 35-62 (pdf)- Basti Gianfranco, The quantum field theory (QFT) dual paradigm in fundamental physics and the semantic information content and measure in cognitive sciences", In
: Representation and Reality in Humans, Other Living Organisms and Intelligent Machines,Dodig-Crnkovic, Gordana and Giovagnoli, Raffaela (Eds.), Springer International Publishing, Berlin-New York, 2017, pp. 177-210 (pdf).- Basti Gianfranco, «From formal logic to formal ontology. The new dual paradigm in natural sciences», in

(Un-)Certainty and (In-)Exactness. Proceedings of the Ist Colloquium on Philosophy and Formal Sciences, a cura di Fabio M. Bertato e Gianfranco Basti , Campinas UP & Aracne Edizioni , Campinas-Rome, 2018, pp. 63-108 (pdf)- Basti, Gianfranco, Capolupo, Antonio, and Vitiello, Giuseppe, "Quantum field theory and coalgebraic logic in theoretical computer science."
Progress in Biophysics and Molecular Biology130(2017), pp. 39-52 (pdf)- P. Blackburn, F. J. van Benthem, & F. Wolter (Eds.),
Handbook of Modal Logic. Amsterdam: Elsevier, 2007- Davis martin,
The universal computer. The road from Leibniz to Turing,CRC Press, Taylor and Francis Group, Boca Raton, FL, 2012.- Del Giudice Emilio, “Old and new views on the structure of matter and the special case of living matter”,
J. of Physics Conf. Series,vol. 67, (2007) 012006 (pdf).- Freeman Walter and Vitiello Giuseppe, "Nonlinear brain dynamics as macroscopic manifestation of underlying many-body field dynamics",
Physics of Life Reviews,vol. 3, no. 2, pp. 93-118, 2006 (pdf)- Goranko, V., & Otto, M. "Model theory of modal logic". In P. Blackburn, F. J. van Benthem, & F. Wolter (Eds.),
Handbook of Modal Logic. Amsterdam: Elsevier, 2007, pp. 225-331.- Hameroff Stuart, “How quantum brain biology can rescue conscious free will”,
Frontiers in Integrative Neuroscience6, 2012, 93 (pdf).- Hansson, Sven Ove, Hendricks, Vincent F. (Eds.),
Introduction to formal philosophy,Springer, Berlin-New York, 2018.- Huges, G. E., Cresswell, M. J.;
A new introduction to modal logic,Routledge, London, 1986- Nagel Ernst, Newmann James R.,
Goedel’s Proof. Revised edition,New York UP, New York, 2011.- Levy Neil,
Neuroethics: challenges for the 21th century,Cambridge UP, Cambridge, 2009- Deutsch David, “Quantum theory, the Church-Turing principle and the universal quantum computer”,
Proc. Royal Soc. A,400(1985), 97-117.## Syllabus of the Classes: Part I (November 1-2, 2019)

## CLASS 9-13: Formal philosophy: The ancient age, language & realism

- The notion of formal philosophy as formalization of philosophical doctrines using the axiomatic method, as a formal tool of interdisciplinary dialogue between human and mathematical sciences – computer science and AI before all.
- It is based on the distinction between standard mathematical logic (extensional interpretation of predication as membership) and philosophical logic (intensional interpretation(s) of predication in different contexts). The philosophical logic is based on the axiomatization of modal logical calculus, of which different intensional logics are as many semantics (ontic, epistemic, deontic) of the same modal calculus.
- Exemplifying applications to the classical ontologies of the Platonic logical realism and of the Aristotelian natural realism
Refs.:7. 9. 13. 15. 16.## CLASS 14-15: Formal philosophy: The modern age, language & cognitivism

- The Galilei affair: apodictic
vs.hypothetical method in modern Galilean science- Descartes’ first development of analytic (algebraic) geometry and the supposed apodictic value of mathematical sciences
- This is based on self-consciousness as cognitivist foundation of self-identity of a logical tautology, extended by Newton to the self-evident character of the three laws of Newtonian mechanics (
hypotheses non fingo).- This is made explicit by Leibniz’s distinction between analytic and synthetic judgements, as well as – following Newton – by its empiricist counterpart by Hume, Locke and Berkeley, and finally, by the Kantian theory of the synthetic a-apriori judgements about pure mathematics and physics.
Refs.: 3. (ch. 1), and 10.## CLASS 16: Formal philosophy: The post-modern age, language & naturalism

- The birth of the hypothetical-deductive method because of the discovery of the non-Euclidean geometries and their axiomatization by Riemann’s completion of Descartes’ initial algebrization of geometry.
- The abandon of the belief in the apodictic character of mathematics determined, on the one side, the abandon of trusting the cognitivist principle of evidence in epistemology, and on the other side, the necessity of demonstrating the consistency of mathematics, and specifically of calculus, by a proper metalanguage individuated by Weierstrass and Cantor in the set theory.
- Birth of the mathematical logic by Frege’s notion of propositional function, and the discovery of the logical antinomies leading to the development of several axiomatic set theories such as ZF, all characterized by the Skolem paradox (their axioms are expressed in first-order logic, but their semantics must be necessarily of a higher order).
- All this determined in the philosophy of science the so-called “linguistic turn” by Wittengstein’s and Carnap’s logical atomism
,with the birth of the neo-positivistic school and its criticism by Popper’s “evolutionary approach” on biological and then informational basis to epistemology. Even though such a linguistic turn from modern cognitivism, with its Popperian untenable irrational outcomes, is incomplete until its completion by the semiotic (algebraic) approach.Refs.: 3. (chs. 3-4) 10. 17.## CLASS 17: Beyond cognitivism I: the Peirce lesson of semiotics

- The algebraic origins of modern mathematical logic in Boole’s and Schröder’s work and the convergent criticism to the purely syntactic formalism of Schröder’s approach by Husserl – from the cognitivist standpoint – and by Peirce from an algebraic standpoint, vindicating the triadic character of every signifying algebraic structure underlying any predication in logic, constituting the core of his interpretation of logic as “formal semiotics”.
- This led Peirce to the development of his famous ante-predicative theory of algebraic categories (firstness-secondness-thirdness) as underlying any predicative theory of categories in logic, as well as to the development of his pioneering algebraic theory of mathematical logic that was contemporary to Frege’s mathematic logic based on his logic of classes.
- This invention by Peirce of the algebra of relations remained however not valorized till Tarski’s axiomatization of the logic of relations into a calculus of relations during the second half of XX cent., including the axiomatization also of the algebraic notion of category, underlying the actual development of the Category Theory as metalanguage of logic and mathematics in many senses wider than standard set theory.
Refs.:5.

Table of Classes SlidesClassesTopics PART I (November 1-2, 2019)9-13Formal philosophy: The ancient age, language & realism14-15Formal philosophy: The modern age, language & cognitivism16Formal philosophy: The post-modern age, language & naturalism17Beyond cognitivism I: the Peirce lesson of semiotics