Philosophy of Logic

The thesis is an investigation into the logical pluralism debate, aiming to understand how the philosophical commitments sustaining each side to the debate connects to more general issues connected to the foundations of logic. My investigation centers on the following three notions: (1) Epistemic justification, (2) The metaphysical "ground" for logical truth, and (3) Normativity. Chapter 1 traces the monistic and pluralistic conception of logic back to its philosophical/mathematical roots, which we find in the writings of Rudolf Carnap and Gottlob Frege. I argue that logical pluralism - in its more plausible, epistemic (rather than ontic) form - was enabled by the semantic shift which Carnap seems to have anticipated and that, from a conventionalist perspective, his 'Principle of Tolerance' follows as a consequence of that shift. Chapter 2 concerns the issues ensuing from Willard V. O Quine’s critique of Carnap's conventionalism, which had a devastating effect for his foundationalist project. The aim is in particular to address the issue of meaning-variance, a crucial assumption for the conventionalist approach to pluralism. In chapter 3, I present another framework for pluralism, due to Stewart Shapiro’s [2014] ‘modelling’ conception of logic, according which logic is conceived as a mathematical model of natural language. Shapiro argues that our concept of logical consequence is vague and in need of a sharpening to attain a fixed meaning. Pluralism follows from there being two or more equally "correct" such sharpenings; i.e., relative to our theoretical aims. I argue that the modelling-conception is the best way to approach a justification of basic logical laws. However, since that conception also grounds Timothy Williamson’s [2017] argument for monism, I argue that the conception ultimately fails to establish logical pluralism. Since both Williamson and Shapiro take a pragmatic approach to justification, I conclude that the question of pluralism does not turn on epistemological commitments (i.e., on (1)), and suggest instead that it is a matter of (2), i.e., of one's conception of the "ground" for logical truth.

Alfred Tarski’s semantic conception of truth is arguably the most influential – certainly, most discussed - modern conception of truth. It has provoked many different interpretations and reactions, some thinkers celebrating it for successfully explicating the notion of truth, whereas others have argued that it is no good as a philosophical account of truth. The aim of this work is to offer a systematic and critical investigation of its nature and significance, based on the thorough explanation of its conceptual, technical as well as historical underpinnings.

The methodological strategy adopted in the thesis reflects the author’s belief that in order to evaluate the import of Tarski’s conception we need to understand what logical, mathematical and philosophical aspects it has, what role they play in his project of theoretical semantics, which of them hang in together, and which should be kept separate. Chapter 2 therefore starts with a detailed exposition of the conceptual and historical background of Tarski’s semantic conception of truth and his method of truth definition for formalized languages, situating it within his project of theoretical semantics, and Chapter 3 explains the formal machinery of Tarski’s truth definitions for increasingly more complex languages. Chapters 4 - 7 form the core of the thesis, all being concerned with the problem of significance of Tarski’s conception. Chapter 4 explains its logico-mathematical import, connecting it to the related works of Gödel and Carnap. Having explained the seminal ideas of the model-theoretic approach to semantics, Chapter 5 tackles the question to what extent Tarski’s ‘The Concept of Truth in Formalized Languages’ (and related articles from the 1930s) anticipates this approach, and what elements might be missing from it. Chapter 6 then deals with the vexed question of its philosophical import and value as a theory of truth, reviewing a number of objections and arguments that purport to show that the method fails as an explanation (explication) of the ordinary notion of truth, and, in particular, that it is a confusion to think that Tarski’s truth definitions have semantic import. Finally, Chapter 7 is devoted to the question whether Tarski’s theory of truth is a robust or rather a deflationary theory of truth.

On the basis of a careful analysis, the thesis aims to substantiate the following view. [A] Tarski’s theory with its associated method of truth definition was primarily designed to serve logico-mathematical purposes. [B] It can be regarded a deflationary theory of a sort, since it completely abstracts from meta- semantical issues concerning the metaphysical or epistemological basis or status of semantic properties. Indeed, [C] this can be interpreted as its laudable feature, since by separating formal (or logico-mathematical) from meta-semantical (or foundational) aspects it usefully divides the theoretical labour to be done in the area of meaning and semantic properties in general. [D] In spite of the fact that Tarski’s conception of truth has this deflationary flavour, the formal structure of its method of truth-definition is quite neutral in that it can be interpreted and employed in several different ways, some of them deflationary, others more robust.

The limited aim here is to explain what John Dewey might say about the formulation of the grue example. Nelson Goodman’s problem of distinguishing good and bad inductive inferences is an important one, but the grue example misconstrues this complex problem for certain technical reasons, due to ambiguities that contemporary logical theory has not yet come to terms with. Goodman’s problem is a problem for the theory of induction and thus for logical theory in general. Behind the whole discussion of these issues over the last several decades is a certain view of logic hammered out by Russell, Carnap, Tarski, Quine, and many others. Goodman’s nominalism hinges in essential ways on a certain view of formal logic with an extensional quantification theory at its core. This raises many issues, but the one issue most germane here is the conception of predicates ensconced in this view of logic. The problem here is the implicit assumption that there is just one type of first-order predicate. P...

Classic and fuzzy logic and their usefulness in clinical diagnosis. The theory of probability is often considered a device to protect the classical two-valued logic from the evidence of its inadequacy to understand and show the complexity of world [1]. This can be true, but it is not possible to discard the theory of probability. I will argue that the problems and the application fields of the theory of probability are very different from those of fuzzy logic. After the introduction on the theoretical bases of fuzzy approach to logic, I have reported some diagnostic argumentations employing fuzzy logic. The state of normality and the state of disease often fight their battle on scalar quantities of biological values and it is not hard to establish a correspondence between the biological values and the percent values of fuzzy logic. Accordingly, I have suggested some applications of fuzzy logic in clinical diagnosis and in particular I have utilised a fuzzy curve to recognise subjects with diabetes mellitus, renal failure and liver disease. The comparison between classic and fuzzy logic findings seems to indicate that fuzzy logic is more adequate to study the development of biological events. In fact, fuzzy logic is useful when we have a lot of pieces of information and when we dispose to scalar quantities. In conclusion, increasingly the development of technology offers new instruments to measure pathological parameters through scalar quantities, thus it is reasonable to think that in the future fuzzy logic will be employed more in clinical diagnosis.

We investigate the treatment of fractions in Russell’s 1919 classic Introduction to Mathematical Philosophy. In contrast to rational numbers, every fraction has an integral numerator and a non-zero integral denominator, but usage varies on exactly which integers are involved (. Our interest was first drawn to the topic by the following surprising result—paraphrasing Russell’s page 66].

Russell 1919’s Fraction-Separator Theorem: the fraction whose numerator is the sum of the numerators of two unequal given fractions and whose denominator is the sum of the denominators is between the two given fractions—excluding cases when the sum of the denominators equals zero.

Although Russell gives none, proof is obtainable from page 270 of De Morgan 1831.
REFERENCE LINKS

Russell 1919’s fraction-separator theorem. Bulletin of Symbolic Logic. 24 (2018) 381.
https://www.academia.edu/s/4f60c070ca/russell-1919s-fraction-separator-theorem?source=link
https://www.academia.edu/34438558/2_Russell_1919_s_fraction-separator_theorem_090117.pdf
Semiotic confusions in Russell 1919. Bulletin of Symbolic Logic. 24 (2018) 382–3.
(Co-author: Kevin Tracy) https://www.academia.edu/34195085/Semiotic_confusions_in_Russell_1919.AC
https://www.academia.edu/34195085/Semiotic_confusions_in_Russell_1919.AC
HOW CAN THIS BE IMPROVED?

Traducción del texto de Donald Gillies "“The Fregean Revolution in Logic”, en Revolutions in Mathematics , ed. Gillies, D.
Oxford: Oxford University Press, 1995).

Traducción de Marcela del Pilar Gómez y Ángel Rivera Novoa. En: "Saga", No. 20, 71-107, 2009.

The main of the paper is to discuss the meaning of negation involved in the logic of First Degree Entailment in the context of a dialogical analysis of tonk-like operators The dialogical framework is an approach to meaning that provides an alternative to both the model-theoretical and the proof-theoretical semantics. However, dialogic had and still has a bias towards antirealism. The dialogical approach to logic is not a logic but a semantic rule-based framework where different logics could be developed, combined or compared. But are there any constraints? Can we introduce rules ad libitum to define whatever logical constant? This study should provide the first conceptual moves towards the notion of Dialogical Harmony.

CITE AS: Corcoran, John. 1999.  “Laws of thought”.  Cambridge Dictionary of Philosophy.  R. Audi, Ed.  Cambridge: Cambridge UP. p. 489.

Laws of thought are laws by which or in accordance with which valid thought proceeds, or that justify valid inference, or to which all valid deduction is reducible. Laws of thought are rules that apply without exception to any subject matter of thought, etc.; sometimes they are said to be the object of logic. The expression, rarely used in exactly the same sense by different authors, has long been associated with three equally ambiguous expressions: the law of identity (ID), the law of contradiction (or non-contradiction; NC), and the law of excluded middle (EM).
The so-called “logical truths” of standard first-order logic as discussed in mainstream logic works such as Corcoran-Masoud 2014 and 2015 are uninterpreted sentences and thus not even true.
Nevertheless, they too have been called laws of thought even though they are not laws in any normal sense. Other people unacquainted with traditional usage are inclined to think that a law of thought is a law that might be arrived at by thought, which could make ‘law of thought’ coextensive with ‘law’.
Sometimes, these three expressions—ID, NC, and EM— are taken as propositions of formal ontology having the widest possible subject matter, propositions that apply to entities per se: (ID), every thing is (i.e., is identical to) itself; (NC) no thing having a given quality also has the negative of that quality (e.g., no even number is non-even); (EM) every thing either has a given quality or has the negative of that quality (e.g., every number is either even or non-even).

Аннотация: В докладе предложена формализованная процедура тре-компонентной оценки аргументов на основе многозначных логик аргументации Д.Бочвара – В. Финна. Процедура обоснована при помощи понятия пост-правды и трех концепций истины, корреспондентной, когерентной и прагматической, и проиллюстрирована на примере судебных вердиктов в делах Дмитрия Карамазова и Родиона Раскольникова из романов Ф. Достоевского «Братья Карамазовы» и «Преступление и наказание». Abstract: In the paper, I propose a three-component algorithm of arguments' evaluation, which is constructed on the basis of D. Bochvar's and V. Finn's many-valued logic. The algorithm contrasts the notion of post-truth and employs three different truth conceptions, the correspondent, the coherent and the pragmatic. The algorithm is applied to legal argumentation in Dmitry Karamazov and Rodion Raskolnikov cases in F. Dostoyevsky's The Karamazov's brothers and Crime and Punishment. Ключевые слова: пост-правда, концепции истины, судебная аргументация, многозначная логика, Д. Бочвар, В. Финн.

Este artículo muestra como nustra noción de infinito elimina el carácter paradójico de la Paradoja de Yablo.
Comenzando con conjuntos finitos (que no generan situaciones paradójicas) y extrapolando a infinito, nuestra noción de infinito nos permite eliminar la paradoja.

In this interview Haack not only discusses with Dra. Carmen Vazquez not only her work in logic, epistemology, metaphysics, philosophy of science, etc., and in legal philosophy, but also tells some good stories abut her life, and the very varied influences on her thinking.

Estudiante de Licenciatura en Filosofía de la Universidad del Valle. Acaba de presentar trabajo de grado en área de lógica, recibiendo la mención Laureada. También ha sido monitor de los cursos Introducción a la lógica e Introducción a la filosofía de la ciencia. Desde hace dos años es ayudante de investigación del grupo de investigación Episteme: Filosofía y Ciencia, adscrito al Departamento de Filosofía de la Universidad del Valle clasificado por Colciencias categoría A. Ha publicado el artículo El modelo nomológico deductivo de explicación científica frente al problema de la irrelevancia en la edición número 8 de la Revista Légein de estudiantes de filosofía.

This study deals with Peirce's writings on topology by explaining key aspects of their historical contexts and philosophical significances. The first part provides an historical background. The second part offers considerations about Peirce's topological vocabulary and provides a comparison between Peirce's topology and contemporary topology. The third part deals with various relations between Peirce's philosophy and topology, such as the importance of topology for Peirce's philosophy of space, time, cosmology, continuity, and logic. Finally, a lexicon of Peirce's main topological concepts is provided.

The Laws of Form was created to represent propositional logic and Boolean algebra. But Spencer Brown (and later commentators) also claimed that it could represent Aristotelian syllogistic logic although, as he showed in his book, at least one invalid syllogism appeared to be valid. This paper explores the extent to which the Laws of Form can correctly deal with all syllogisms. There are in fact 256 possible syllogisms and only fifteen of them are uncontroversially valid (a further nine are valid if certain existence assumptions are made). Using truth tables implemented in a spread sheet, all 256 syllogisms were evaluated and it was discovered that, in fact, 83 invalid syllogisms appear to be valid when simply represented in Laws of Form notation (in the primary algebra) and ignoring Spencer Brown’s Interpretative Theorem 2, an issue that will be explored in detail in the paper. This is clearly a significant number. Further investigation show that the problem might be caused by the way that “some/some not” propositions are conventionally represented and a variety of alternative are explored, some related to free logic. One particular interpretation reduces the number of wrongly categorised syllogisms to only seventeen and, surprisingly, fifteen of the 17 are mirror images of the fifteen valid ones.

Resumen
Muchos creadores, a lo largo de la historia, se han sumergido en un ámbito oscuro y trasgresor; las pinturas negras y la trágica serie "Los desastres de la guerra", de Goya; los seres metamorfoseados y devorados en un violento acto sexual de Picasso; el mundo oscuro y árido dibujado por A. Kubin; Francis Bacon, a través de desnudos deformes e incoherentes, sangrientos y deshuesados; el mundo caótico y viscoso de David Lynch con criaturas que fluctúan cambiando su anatomía, amorfas y monstruosas (Eraserhead). Tod Browning, que presenta un circo repleto de seres con deformaciones espeluznantes que la misma naturaleza ha creado (Freaks). Lo extremo, lo abyecto, lo grotesco y lo monstruoso, son características que muchos artistas han izado como bandera de su trabajo. Desde los violentos desajustes picassianos a las hinchazones de Dobuffer, las mutilaciones y las laceraciones de De Kooning, el grupo Cobra y seguidores como Saura, los alargamientos de Giacometti o los sutiles desajustes entre forma y color de Léger y de Warhol, por no mencionar los hirientes trazados de Beuys, se podría establecer una catalogación de todas las violencias a las cuales el artista ha sometido a lo real en el momento de representarlo.
Dr. Adolfo Vasquez Rocca

Parallel to David Bohm´s development of a realistic interpretation of quantum physics, German philosopher and logician Gotthard Günther worked on a generalization of the classical two-valued logic to satisfy the ontological requirements of quantum physics as well as of cybernetics. Both of these new disciplines introduced information and consciousness into the terminology of science. These terms and concepts need to be reflected in logic, ontology and the theory of science. David Bohm suggested an expansion of his own model by generalization and iteration of the quantum potential to include consciousness and mental states into a new psycho-physical theory. This article proposes Günther´s four-valued logical system of meaning/reflection as a theoretical scientific frame for this expansion of Bohm´s theory and discusses its ontological implications.

“What the Tortoise said to Achilles” (WTSA), sometimes known as Carroll’s paradox of inference, appeared in the leading British journal "Mind" in 1895. Unlike Carroll’s earlier publication, “A logical paradox” (1894), commonly known as the barbershop paradox, which immediately attracted responses from serious logicians, none for WTSA was received in Carroll’s lifetime. However, WTSA has since been widely discussed among philosophers and is currently considered as a classic text in the philosophy of logic. What is more remarkable is that in the articles that have appeared in journals and books for over 120 years, there has been no accepted resolution to the problem Carroll posed in WTSA. Many scholars even believe that Carroll did not write his paper with a specific purpose in mind. It is true that little is known on the genesis and the writing of this fascinating article. Hence, confusion and mystery have long surrounded the reception of Carroll’s WTSA. Mystery might never vanish, but it is the aim of this volume to lessen confusion. Here we offer a set of papers providing key elements to the history and purpose of this enigmatic piece that will contribute to Carrollian studies and more generally, to philosophy.

1981. A note on categoricity and completeness, History and Philosophy of Logic 2, 113–19.

Current study of axiomatic method presupposes concepts and results of string theory and set theory. But axiomatic method was vigorously pursued in the last half of the nineteenth century without explicit reference to the theory of strings, which was not axiomatized until the 1930s (independently by Tarski 1934 and by Hermes
1938). For historical remarks on string theory see Corcoran, Frank and Maloney1974. Moreover, although it is natural to read modern set-theoretic ideas in early methodological work, it is clear that early postulate theorists such as Dedekind, Peano, Hilbert, Huntington and Veblen were not working in any formal set-theoretic framework. Indeed, close correspondence between modern precise explications of methodological concepts and imprecise formulations found in the writings of early postulate theorists suggests that the creators of modern mathematical logic, particularly Carnap, Tarski, and Church, may have been guided by the goal of putting the early ideas on a more mathematically precise basis.

Obsah FORMÁLNÍ A TRANSCENDENTÁLNÍ LOGIKA Úvod PŘÍPRAVNÉ ÚVAHY § 1. Východisko od významů slova logos: mluvení, myšlení, myšlené § 2. Idealita jazykového. Vyloučení určitých příslušných problémů § 3. Jazyk jako výraz "myšlení". Myšlení v nejširším smyslu jako prožitek konstituující smysl § 4. Problém vymezení podstaty "myšlení" způsobilého k významové funkci § 5. Předběžné vymezení logiky jako apriorní teorie vědy § 6. Formální povaha logiky. Formální a kontingentní apriori § 7. Normativní a praktická funkce logiky § 8. Dvojstrannost logiky; subjektivní a objektivní směr její tematiky § 9. Bezprostřední tematika "objektivních či "pozitivních věd. Idea dvojstranných věd § 10. Historická psychologie a subjektivně zaměřená tematika věd 3. kapitola. Teorie deduktivních systémů a teorie multiplicity § 28. Nejvyšší stupeň formální logiky: teorie deduktivních systémů či teorie multiplicity § 29. Formalizující redukce nomologických věd a nauka o multiplicitě § 30. Nauka o multiplicitě počínaje Riemannem § 31. Pregnantní pojem multiplicity nebo "deduktivního", "nomologického" systému vyjasněný pojmem "definitnosti § 32. Nejvyšší idea nauky o multiplicitě jakožto univerzální nomologické vědy o formách multiplicity § 33. Skutečná formální matematika a matematika herních pravidel § 34. Úplná formální matematika je identická s úplnou logickou analytikou § 35. Proč se v oblasti mathesis universalis jakožto univerzální analytiky mohou stát tematickými pouze deduktivní formy teorií a) Pouze deduktivní teorie má systémovou formu čistě analytickou b) Položení otázky: kdy má nějaký systém vět systémovou formu, která může být analyticky charakterizována § 36. Ohlédnutí zpět a předznačení dalších úkolů B. FENOMENOLOGICKÉ OBJASNĚNÍ DVOUSTRANNOSTI FORMÁLNÍ LOGIKY JAKO FORMÁLNÍ APOFANTIKY A FORMÁLNÍ ONTOLOGIE 4. kapitola. Zaměření na předměty a zaměření na soudy § 37. Otázka vztahu formální apofantiky a formální ontologie; nedostatečnost dosavadních ujasnění § 38. Předměty soudů jako takové a syntaktické útvary § 39. Rozšíření pojmu soudu na všechny výtvory syntaktických akcí § 40. Formální analytika jako myšlenková hra a logická analytika. Vztah k možné aplikaci patří k logickému smyslu formální mathesis § 41. Rozdíl mezi apofantickým a ontologickým postojem a úkol jeho objasnění § 42. Řešení tohoto úkolu a) Souzení není zaměřeno na soud, nýbrž na tematickou předmětnost b) Identita tematického předmětu v proměně syntaktických operací "Matematika matematiků" § 53. Osvětlení na příkladu eukleidovské multiplicity § 54. Závěrečné stanovení poměru mezi formální logikou a formální ontologií a) položení otázky b) Korelativní dvojí smysl formální logiky c) Idea formální ontologie má být oddělena od ideje teorie vědy DRUHÝ ODDÍL OD FORMÁLNÍ LOGIKY K LOGICE TRANSCENDENTÁLNÍ 1. Kapitola. Psychologismus a transcendentální založení logiky § 55. Otázka, jestli s rozvojem logiky jakožto logiky objektivně-formální je už učiněno zadost ideji i jenom formální teorie vědy § 56. Výtka psychologismu namířená proti každému subjektivně zaměřenému zkoumání logických útvarů § 57. Logický psychologismus a logický idealismus a) Motivy pro tento psychologismus b) Idealita logických útvarů jakožto ireálné vystupování v logicko-psychické sféře § 58. Evidence ideálních předmětů je analogická k evidenci předmětů individuálních § 59. Obecná charakteristika evidence jakožto samodání § 60. Základní zákonitost intencionality a univerzální funkce evidence § 61. Funkční vztahy evidence se všemi, ať již reálnými nebo ireálnými předměty jakožto syntetickými jednotami § 62. Idealita všech druhů předmětností oproti konstituujícímu vědomí. Mylný pozitivistický výklad přírody jako jistý druh psychologismu § 63. Původně vytvářející aktivita jakožto samodání logických útvarů a smysl řeči o jejich vytváření § 64. Přednost bytí reálných předmětů před ireálnými předměty § 65. Obecnější pojem psychologismu § 66. Psychologistický idealismus a idealismus fenomenologický. Analytická a transcendentální kritika poznání § 67. Výtka psychologismu jakožto nepochopení nutné logické funkce transcendentální kritiky poznání § 68. Výhled na další úkoly 2. Kapitola. Výchozí otázky transcendentálně logické problematiky: problémy týkající se základních pojmů § 69. Logické útvary jsou dány v přímé evidenci. Úloha reflektivního tematizování této evidence § 70. Smysl požadovaných vyjasnění jako konstitutivního zkoumání původu a) Posuny intencionálních zacílení a ekvivokace. b) Ujasnění rozlišovaných základních pojmů logických disciplín jako odhalení skryté subjektivní metody utváření těchto pojmů a jako její kritika. § 71. Problémy základů věd a konstitutivní zkoumání původu. Logika povolána k vůdčí roli 3. Kapitola. Idealizující předpoklady logiky a jejich konstitutivní kritika § 73. Idealizující předpoklady matematické analytiky jako témata konstitutivní kritiky. Ideální identita soudových útvarů jako konstitutivní problém § 74. Ideality mající formu "a tak dále", ideality konstruktivních nekonečností a jejich subjektivní korelát § 75. Analytický zákon sporu a jeho subjektivní obrat § 76. Přechod k subjektivní problematice pravdivostní logiky § 77. Idealizující předpoklady obsažené ve větě o sporu a o vyloučeném třetím § 78. Obrat zákonů modus ponens a tollens v subjektivní zákony evidence § 79. Předpoklady pravdivosti a nepravdivosti o sobě předpoklad a rozhodnutelnost všech soudů § 80. Evidence předpokladu pravdivosti a úkol její kritiky § 81. Formulace dalších problémů 4. Kapitola. Zpětné převedení kritiky evidence logických principů na kritiku evidence zkušenosti § 82. Redukce soudů na poslední soudy. Původní kategoriální obměny něčeho a původní substrát individuum § 83. Paralelní redukce pravd. Zpětné vztažení všech pravd na svět individuí § 84. Stupňový sled evidencí; evidence zkušenosti je evidencí o sobě první. Pregnantní pojem zkušenosti § 85. Pravé úkoly takzvané teorie soudů. Geneze smyslů soudů jako vodítko k vyhledání stupňového uspořádání evidencí § 86. Evidence předpredikativní zkušenosti jakožto o sobě první téma § 99. Psychologická a transcendentální subjektivita. Problém transcendentálního psychologismu § 100. Historicko-kritické poznámky k vývoji transcendentální filosofie a obzvláště k transcendentální problematice formální logiky 7. kapitola. Objektivní logika a fenomenologie rozumu § 101. Subjektivní založení logiky jako transcendentální fenomenologie rozumu § 102. Vztaženost tradiční logiky ke světu a otázka po povaze "poslední" logiky normující její transcendentální ujasnění samo § 103. Absolutní založení poznání je možné pouze v univerzální vědě o transcendentální subjektivitě jakožto jediném absolutně jsoucím § 104. Transcendentální fenomenologie jako sebevýklad transcendentální subjektivity § 105. Přípravy pro závěr transcendentální kritiky logiky. Obvyklé teorie evidence zaváděny na chybnou cestu předpokladem absolutní pravdy § 106. Další poznámky ke kritice předpokladu absolutní pravdy a dogmatických teorií evidence § 107. Náčrt transcendentální teorie evidence jakožto intencionálního výkonu a) Evidence vnější (smyslové) zkušenosti b) Evidence "vnitřní zkušenosti" c) Hyletická data a intencionální funkce. Evidence imanentních časových dat. d) Evidence jako apriorní strukturní forma vědomí ZÁVĚR PŘÍLOHA I SYNTAKTICKÉ FORMY A SYNTAKTICKÉ LÁTKY, JÁDROVÉ FORMY A JÁDROVÉ LÁTKY § 1. Členění predikativních soudů

Truth-preservation, implication-preservation, and cognition-preservation.

This is one in a series of presentations designed to alert the philosophical community that claims made for the importance of truth-preservation are often overblown, frequently false, and—even when strictly speaking true--misleading and counter-productive. Truth-preservation per se is not nearly as important as implication-preservation; implication-preservation per se is not nearly as important as, cognition-preservation

One of the reasons colours, or better the conceptual organisation of the colour system, could be relevant to the philosophy of logic is that they necessitate some mutilation of truth tables by restricting truth functionality. This paper argues that the so-called 'Colour Exclusion Problem', the first great challenge for Wittgenstein's Tractatus, is a legitimate philosophical motivation for a systematic mutilation of truth tables. It shows how one can express, through these mutilations, some intensional logical relations usually expressed by the Aristotelian Square of Oppositions, as contrariety and subcontrariety.

First days of a logic course
This short paper sketches one logician’s opinion of some basic ideas that should be presented on the first days of any logic course. It treats the nature and goals of logic. It discusses what a student can hope to achieve through study of logic. And it warns of problems and obstacles a student will have to overcome or learn to live with. It introduces several key terms that a student will encounter in logic.

What would happen if we tried to read the thinking and some writings of Machiavelli using the propositional logic? This short paper moves from this aim: clarify the arguments of the Florentine thinker, making explicit the inferences just through the propositional logic, its rules and its theorems. In particular, the logical patterns, that we try to find inside the Machiavelli's text, are the reductio ad absurdum (negation Introduction), the case analysis and a particular version of the constructive dilemma in some its proofs: the conditional proof. The paradigmatic parts of the of the Machiavelli's writings, that we will use for extract some important topics of his arguments, are the twenty-fifth chapter of the Il Principe and the ninth chapter of the Discorsi sopra la prima deca di Tito Livio's third book.

Che cosa succederebbe se provassimo ad interpretare il pensiero e alcuni scritti di Machiavelli tramite la logica proposizionale? Questo short paper muove da questo intento: chiarire le argomentazioni del pensatore fiorentino, esplicitandone le inferenze tramite la logica proposizionale, le sue regole e i suoi teoremi. Nello specifico, gli schemi logici utilizzati, che si provano a rintracciare all'interno del dettato machiavelliano, sono quelli della riduzione all'assurdo e del dilemma costruttivo in alcune sue varianti. Le parti paradigmatiche degli scritti del fiorentino, che vengono utilizzate per estrapolarne alcuni luoghi del suo pensiero, sono il Capitolo XXV de Il Principe e il Libro III, Capitolo 9 dei Discorsi sopra la prima decade di Tito Livio.

1972. Weak and Strong Completeness in Sentential Logic, Logique et Analyse 59/60, 429–34.  MR0337476 (49 #2245)

This is another study illustrating the fruitfulness of thinking of “logics” as three-part systems composed of a language, a semantics [or model theory] and a deductive system [or proof theory]. For simplicity we take a fixed language for sentential logic [or propositional logics] with a fixed standard two-valued semantics, but we “vary” deductive systems. In the 1960s when this paper was written, it was still widely assumed that a “logic” was “determined” by its theorems, by what it could “prove”. The vague assumption was that once the theorems were fixed, it was somehow automatic which conclusions were derivable from given premises.
The purpose of this paper is to give a method which weakens deriving power of a sentential logic while leaving proving power unchanged. In particular if the method is applied to a strongly complete logic the resultant will not have strong completeness but it will retain weak completeness. Moreover, because of the nature of the method two added facts obtain.
First, weak completeness of the resultant is always an obvious corollary to weak completeness of the operand, so that no new completeness proof need be constructed. Second, failure of strong completeness in the resultant is always obvious, so no multi-valued matrices need be constructed. The method applies to all sentential logics formulated using only axiom schemes and schematically statable rules. These results reaffirm, generalize, and simplify a result of Hiz [Journal of Symbolic Logic, 24 (1959), pp. 193-202].

Resumen La siguiente charla pretende ser una introducción al concepto de "paradoja", su problemática, y, su relevancia en lógica y distintas áreas afines. Nos centraremos en analizar en las paradojas autorreferenciales y su papel en lógica, especialmente se abordará si es condición suficiente o necesaria la presencia de autorreferencia para la paradojicidad.

In this paper, I examine anti-realist remarks made by Wittgenstein in the begin- ning of the 1930s on the nature of contradictions. An anti-realist view of logic rejects the paradigm of correspondence to facts and an independent reality to deal with important logical notions such as logical connectives and contradic- tions. In the 1930s,1 the so-called Middle Wittgenstein discussed the nature of language, logic, and mathematics based on the notion of rules with mem- bers of the Vienna Circle at the close of his influential, but highly problematic, Tractarianproject.2 Inspiredbythesediscussions,Isuggestaphilosophicalac- count using the notion of rules and normativity to understand the philosoph- ical meaning of contradictions in paraconsistent logic. I defend, pace (middle) Wittgenstein and Frege, that contradictions should be taken as conflicting rules in practices rather than as dialetheia, that is, as corresponding to some peculiar but real contradictory entity or state of affairs in the world.

Resumo

Resumo: a abordagem de ?A Lógica da História faz com que seja possível concretizar a dialética do natural (incluindo o biológico) e o social. O desenvolvimento criativo do método de investigação científica foi possível revelar a interligação interna sistemática das leis e categorias da teoria social que refletem a estrutura da sociedade desenvolvida, mas também tornou possível delinear a periodização teórica da história humana (as leis objetivas de sua ?subida desde o início, o surgimento, a formação, até a maturidade) por meio de um prisma de interconexões de fatores naturais e sociais. As fases do processo de desenvolvimento são analisadas aqui: como a unidade do natural (incluindo o biológico) e o social, como um processo de emergência do social que surge do natural, como a transformação do natural pelo social.
Palavras-chave: Lógica da história. Materialismo Histórico. Método. Dialética. Desenvolvimento.

By the thematic division of Wittgenstein works, brought into account at this thesis, we may distinguish all possible philosophical orientations of Wittgenstein's thoughts. Therefore, we shall investigate Wittgenstein's remarks concerning the parallel language-musicality from his works.

Nel presente lavoro si andranno ad analizzare i possibili punti di contatto tra le
cornici teoriche di Matte-Blanco e di Fonagy e colleghi.
Passando in rassegna i punti chiave della bi-logica (Matte-Blanco 1975; 1988) e
del concetto di mentalizzazione (Fonagy et al., 2002), con i loro risvolti evolutivi
e confrontandole con altre prospettive presenti in letteratura, si tenterà di
raggiungere un duplice obiettivo: da un lato reinterpretare in termini bi-logici
alcune delle proposte di Fonagy e colleghi, soprattutto per quel che riguarda la
nascita di una teoria della mente, la deviazione del suo percorso di sviluppo da
un tracciato “normale”, ed il significato del disturbo borderline di personalità;
dall’altro verrà fornita una prospettiva evolutiva all’impostazione
matteblanchiana, così da riempirne un vuoto teorico, ed in particolare verrà
esaminata la nascita della bi-logica nel contesto interpersonale primario
rispecchiante.
La conclusione principale è che il rispecchiamento materno sia garante dello
sviluppo di una funzione asimmetrizzante, ed anche della logica asimmetrica in
generale. Il Sé sarà un costrutto fondamentale in questo lavoro, ed il suo
sviluppo si presupporrà seguire quello della bi-logica, passando da una sua forma
più passiva simmetrica ad una più attiva asimmetrica (in compresenza con la
prima), intrecciandosi con lo sviluppo di una teoria della mente.

Computational and information-theoretic research in philosophy has become increasingly fertile and pervasive, giving rise to a wealth of interest-ing results. In consequence, a new and vitally important field has emerged, the philosophy of information (PI). This essay is the first attempt to analyse the nature of PI systematically. PI is defined as the philosophical field concerned with the critical investigation of the conceptual nature and basic principles of information,including its dynamics, utilisation, and sciences, and the elaboration and application of information-theoretic and computational methodologies to philosophical problems. I argue that PI is a mature discipline for three reasons: it represents an autonomous field of research; it provides an innovative approach to both traditional and new philosophical topics; and it can stand beside other branches of philosophy, offering a systematic treatment of the conceptual foundations of the world of information and the information society.

Abstracts for 20 papers to be discussed at a symposium on  Wittgenstein: Lectures, Cambridge 1930-1933, From the Notes of G. E Moore, edited by David Stern, Brian Rogers, and Gabriel Citron.  The symposium will be held at the University of Iowa, May 18-22, 2015.