[Originariamente pubblicato in data 10 marzo 2019]

Vuoi leggere un libro su questo tema? L’eterna battaglia della mente – Scacchi e filosofia della guerra!
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Vuoi leggere un libro su questo tema? L’eterna battaglia della mente – Scacchi e filosofia della guerra!
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How does language connect to the world? A simple, ancient question that should hunt every serious scholar in any field. For example, what do we mean when we say, ‘The army fought bravely against Nazi Germany’ or ‘All crows are black’? How can we connect an ‘army’ to ‘braveness’ and its ‘fighting’ ‘against Nazi Germany’? What do we actually mean by ‘all crows’? No matter how one wants to tackle the problem, this is quite an astonishing open-ended hurdle that every new generation of thinkers must recalibrate or reframe.[1]
Plato started the quest because of his idealist conceptualization of knowledge, which was understood only as perfect in terms of access to the ideas which, in turn, must refer to the world somehow. However, how to connect his ideas to a specific ‘table’ is not an easy endeavor and Aristotle tried to reverse the process: we describe ‘tables’ given the knowledge we get from every specific table. But then, how can we have a general notion of tables? From where this ‘generality’ comes from and how can it be justified? Ultimately, these answers can be partially given reformulating the problem in terms of meaning. The meaning of the sentence ‘the table is black’ depends on the meanings of its constituent components. What does meaning mean? We need to clarify what the meanings of words (in theory, all of them, including prepositions, indexicals, and prepositions).
Interestingly, so-called idealist philosophers such as Renè Descartes and Baruch Spinoza reinterpreted the idealist vision in subjective terms. Plato assumed that ideas are external non-causal entities existing outside the phenomenon and the mind. They stay there eternally unmoving mysteriously able to give us a real glimpse of a stable world. Firstly, Descartes reinterpreted this concept within the subject itself: ideas are stable construction of the cognitive subject whose access is granted by direct introspection whose strength is supplemented by reason. However, the grasp of concepts can be independent from reason, which has the primary goal to make arguments based on those ideas and concepts. Of course, Descartes had the same problem Plato had; that is, how to connect ideas to the world. In his case, he had to make a brilliant and convoluted argument based on the alignment between ideas and the world granted by God and by the general architecture of cognition.[2] Spinoza, partially endorsing and criticizing Descartes, extended those lines of arguments: not only ideas can be explicitly grasped directly through a special direct introspection (intuition) but reason is the sole means to grant justification in elaborating new ideas.[3]

La storia del pensiero antico sulla felicità si è incentrato su alcuni concetti e termini comuni. La felicità è il risultato dell’applicazione della virtù ed essa è alla portata dell’uomo, purché quest’ultimo si concentri nel pieno dispiegamento della sua stessa natura che, come abbiamo visto, è concepita essenzialmente nella sua razionalità. “Sii la tua ragione” poteva essere il comandamento comune alle teorie considerate sino ad ora e la visione dell’uomo come essere razionale è il fil rouge che unisce le teorie dell’antichità classica. Ma con l’avvento del cristianesimo si introduce un nuovo termine nella complessa equazione il cui risultato è la suprema felicità: il Dio creatore cristiano.
In queste pagine abbiamo già incontrato la figura del dio, ora declinata come puro pensiero di pensiero (il caso di Aristotele), ora declinata come provvidenza immanente nel mondo (come nella filosofia stoica), ora concepita come semplice entità indifferente rispetto alle sorti degli esseri umani (come sosteneva Epicuro). Ma nella filosofia cristiana e, come vedremo, nel pensiero di Agostino, il ruolo di Dio, un Dio creatore la cui essenza è l’amore, è di gran lunga di maggior spessore anche perché in Lui Agostino rintraccia la fonte stessa della felicità umana. Per tale ragione, il nostro percorso inizierà proprio da una succinta analisi di cosa sia il Dio di Agostino e quale sia la sua connessione con l’uomo e la felicità.

Run out and find me a four-year-old child. I can’t make head or tail out of it. – Groucho Marx
For many years I studied formal logics and set theory alongside everything else. They were the intrinsic foundation of my background work, the one that never appeared on the surface because it was too personal and too specific at the same time.[1] Moreover, in spite of many applications of formal logic thinking from war to society, I never fully embraced the sheer love for machinery or formal symbolism because I am much more semantically driven.[2] In fact, I am obsessed by semantics and natural language and the more I think about them the deeper the obsession. Although I have been always skeptical on analytic philosophy implicitly share belief that it is all about bad use of unclarified language and truth-values, I am in fact as obsessed as the later Wittgenstein or Kant in the three major critiques, which are essentially a quest for understanding how our judgements (statements) is even possible. In fact, I even argued that the deconstruction of judgement through language was ultimately what Kant achieved in the Critique of Pure Reason.[3]
However, this does not change my sheer admiration for those pillars of thought who elaborated formal logics how we know it and Kurt Godel has been my logical hero since I started my logical quest twenty-four years ago.[4] As a result of my effort to teach formal and informal logics, I arrived to conceive an idea to how teach basic principles of formal logics to kids. I am not very versatile with very young kids, that is, less than 14 and I don’t have any evidence of specific applications of the system I am proposing here, but the idea is very simple. Formal logic is about creating a system of codified symbols to be manipulated syntactically, that is, through the ‘simple’ application of rules, we can be creative in selecting what symbols we want to use. What if we are creative and use emoticons for formalizing propositional logic?
With this intuition in mind, I propose the following formal logic game that could be used for teaching logic to kids. I welcome any reader to try and report what happened and how it worked in the comments section.

Ludwig van Beethoven (1770-1827) is an unreplaceable milestone in the history of Western civilization, whose dimension is so crystal clear that, no matter the weaving moment of political and moral fashion of the day, his music is executed everywhere in the world. The reason is simple. Those who had the fortune to encounter and understand his music will never stop to be baffled by it, by its unique capacity to embed human sentiments inside a strict iron rational logic.
Differently from Chopin, who is so emotional to be undigestible to some, differently from Bach, whose love for abstract structure makes him the embodiment of the XVII century mechanicism, Beethoven is the unique pinnacle of intellect, reason and sensibility, a rare Kantian union of different aspects of human cognition and experience. But what about the life behind the music? Is Beethoven a man unlike many others? The answer is ambivalent when reading a selection of biographical notes and other annotations left in his Conversation Books and here, I will only draw some remarks without entering in the specificities of Beethoven’s life, which is assumed sufficiently known to the reader.
What I want to report here are the common threads that Beethoven shared with many other great thinkers. Yes, thinkers, because Beethoven only by accident was a musician, as his music is a philosophical act as Kubrick’s movies. As argued elsewhere, philosophy is not the land of written language necessarily but of argumentation for the sake of truth reached through a merciless critique of language. As such, it is pointless to draw a rigid line between Beethoven and Kant or Spinoza, to mention two major thinkers whose life wasn’t as different from Beethoven’s – Gens una sumus.

Economics was time ago dubbed as the ‘sad science,’ because of its intrinsic predictive limitations, in spite of its colossal mathematical foundation. In this regard, economic libraries seem to disprove Galileo’s abused saying that ‘the book of nature is written in mathematical language.’ It might be so only because we, humans, so decided.[1] Alas, portions of this book do not seem to respond very well to mathematics.[2] Marxists and neo-Keynesians differently embraced the need to change economics in a ‘happy’ science, finally able, as all the rest of the successful sciences, to predict future facts and events through mathematical calculations over axioms and logical derivations. They tried the endeavor differently.

Natural language and set theoretical and formal logic reductions – A philosophical account
A sheer love for propositions – An obsession with analytic philosophy, logics and mathematics
Analytic philosophy was born out of the general problem of solving metaphysics through a careful diagnostic of natural language. After the early days of formal logics and set theory with Boole and Cator, Frege and Russell arrived at the conclusion that natural language spontaneously produces irreducible paradoxes such as the liar and the sorites paradoxes. Through the length of these paradoxes, they concluded that traditional metaphysics was a gigantic mistake, formulable as it was under mistaken conception of language. The idea was ingenuous and simple to grasp. If I use very bad components and tools, I can only produce flawed engines, whose appearance is similar to a working engine until we check it. This ‘diagnostic’ approach to philosophy is as old as the Greeks, who were the first to outline different ways to ‘unveil life-threating mistakes through reasoning’. This was firstly tried in the realm of ethics, especially during the Alexandrine philosophies.[1] Wildly differently, this was tried again by the founding fathers of analytic philosophy.
Frege elaborated an entire philosophical system out of a new conception of logics applied to semantics through the instruments of the ‘new’ developments in formal logic, a Leibnizian ideal language through which all problems could be formulated and, then, solved by ‘brute force’ calculations.[2] In this broad category I am including set theory – in fact, it is arguable that formal logics and set theory cannot even be thought independently in the human mind.[3] In the following writing, I will consider set theory as the broad category including naïve set theory and Zermelo-Frankel theory plus the axiom of choice (ZFC).[4] It could be a matter of contentious, but set theory is, itself, a parallel endeavor that overlaps with the development of formal logic as we know. Moreover, set theory and formal logics are intended to mirror one another, where the sets are intended to be the object-domain of the propositions formulable in a formal language.[5] Set theory and formal logics tied together for solving all the natural language’s problems posed to human understanding, or so the founding fathers of analytic philosophy believed.

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