In this article, we address fallacious analogical reasoning and the Metaphoric Fallacy to a Deductive Inference (MFDI), recently discussed by B. Lightbody and M. Berman (2010). We claim that the authors’ proposal to introduce a new fallacy is only partly justified. We also argue that, in some relevant cases, fallacious analogical reasoning involving metaphors is only affected by the use of quaternio terminorum.

The proof of God’s existence, known as Ratio Anselmi, is being analyzed. Four first-order theories are constructed to mirror versions of Anselm’s reasoning. God’s existence is shown to be provable in all of them. A traditional objection to the employment of a concept of God is overruled. And yet, Anselm’s proof is eventually found to be incorrect. The error attributed to Anselm consists in an illegitimate use of the words “greater‘ and “conceivable‘, and is identified as quaternio terminorum (...) or petitio principii, depending on circumstances. It is claimed that there is no direct way to improve the argument. (shrink)

Il volume intende presentare in una prospettiva organica la letteratura medievale sugli Insolubilia. Gli insolubili sono stati definiti come proposizioni autoreferenziali che hanno origine direttamente dalla tradizione del paradosso del mentitore. L’impostazione del presente lavoro vuole essere sia filologica che teorica in modo che da un lato si possano inserire le analisi speculative sugli Insolubilia in un contesto critico–storico più ampio che restituisca la peculiarità della trattazione medievale, e dall’altro, possa essere effettuata una analisi precisa dei tentativi di soluzione proposti (...) anche attraverso gli strumenti della logica moderna (quando possibile e non fuorviante). (shrink)

In epoca medievale si è molto discusso su alcuni concetti chiave come prova o giustificazione. La teoria della prova contenuta nei trattati di logica medievale prende il nome tecnico di consequentia, che è un tipo di ragionamento fondato sul passaggio dalla concessione (o negazione) di uno o più enunciati denominati antecedenti alla concessione (o negazione) di uno o più enunciati denominati conseguenti. Questo tipo di teoria ha avuto un correlato a livello dei singoli termini che compongono l’enunciato all'interno della teoria (...) nota come suppositio terminorum. Prende, infatti, il nome di descensus, la regola che permette la verifica del passaggio da un termine maggiore (un termine comune) ad un termine minore (che denota individui). La stessa definizione di alcune ramificazioni della teoria della suppositio è col-legata alla possibilità di ammettere o meno il descensus cioè questa "discesa" da un termine comune ad una congiunzione o disgiunzione di termini singolari. Il presente lavoro intende descrivere la teoria del descensus come un tipo particolare di consequentia mostrandone le connessioni con le moderne tecniche logiche. I trattati che si affronteranno appartengono al XIV e al XV secolo, cioè ad un periodo caratterizzato da una sistemazione della materia che li rende confrontabili con un quadro teorico unitario. (shrink)

La Logique ou L'Art de Penser (LAP), also known as the Port-Royal Logic, is generally presented as a "logic of ideas" in which the idea, the central epistemological entity, is the starting point of this logic based on Cartesian ontology. Structured around the four main operations of the mind - conceiving, judging, reasoning and ordering - the first part of the LAP contains "reflections on ideas". The idea, "the form by which we represent things [objects]", thus takes the place of (...) the concept in Aristotelian-inspired logic. Some of the chapters in this first part deal with the problems raised in scholasticism by the theory of _proprietates terminorum_, which means that it is also a semantics of terms. The word 'term' itself must be understood in its logical and grammatical dimensions. The analyses of the 'Messieurs' of Port-Royal often have a logico-grammatical character, because, according to the anthropology of the authors, men need to make their thoughts heard by one another through language (institutional signs) and, therefore, "it is necessary in logic to consider ideas joined to words, and words joined to ideas". In this text, we shall endeavour to show the importance and innovative character of the semantics of terms in this logic of ideas which makes LAP a pivotal moment in the evolution of the language sciences, reviving the tradition and allowing dialogue with future developments (extension vs. comprehension, explanation, determination of terms, etc.). We will pay particular attention to the chapters on definition, "a remedy for the confusion that arises in our thoughts and speech from the confusion of words". (shrink)

Analytical philosophy is ruled by the alliance of logic, linguistics and mathematics since its beginnings in the syllogistic calculus of terms and premises in Aristotle's Analytica protera, in the theories of medieval logic that dealt with what are Proprietatis Terminorum (significatio, suppositio, appellatio), in the theological apologetics of argumentation with the combinatorics of symbols by Raymundus Llullus in the work Ars Magna, Generalis et Ultima (1305-08), in what is presented as Theologia Combinata (cf. Tomus II.p.251) in Ars Magna Sciendi (...) sive Combinatoria by Athanasius Kircher (1669), in analytical combinatorics based in Leibniz's dissertation Ars Combinatoria (1666), where language is understood as a lingua characteristica and as a calculus ratiocinator, in the combinatorics of classes that have the meanings 1 or 0 given in the idea of Boolean functions (1854), in Frege's work Begriffschrift, eine der arithmeticeschen nachgebildete Fomelsprache des reinen Denkens (Concept letter, the language of formulas of pure thought made according to the model in arithmetical language), in Cantor's study of set theory / Grundlagen einer allgemeinen Mannigfaltigkeitstheorie (1883) and up to algorithms of fuzzy logic as a "means of approximate thinking that is in the human prior" (Zadeh, 1990) and fuzzy linguistics in computer semantics (Burghard B. Rieger, 1993). These are all the philosophical ideas of mathematicians and logicians that founded what we call logical pragmatism here as a demand that logic be absolutely used in every way in which it will dominate the grammar of language until logic itself becomes the philosophical grammar of the mind!!! (shrink)