Philosophical Logic

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.

Bu çalışmada, önermeler mantığı dizgeleri ile bu dizgelerin anlambilimsel
(semantik) yorumlamalarında eksiksizlik teoremlerive
bu teoremlerin meta-mantıksal yorumlamaları incelenecektir.İlk
bölümde, önermeler mantığı dizgesini oluşturan dil, bu
dile ait yapısal kurallar ve çıkarım kurallar ortaya konulacaktır.
Ardından sağlamlık ve tutarlılık teoremlerine geçilerek, türetilebilirlik
vegeçerlilik arasındaki ilişkiye değinilecektir. İkinci
bölümde, önermeler mantığı dizgeleri içerisinde eksiksizlik teoremleri
sunulacak ve ardından bu teoremlerin meta mantıksal
yorumlamalarına değinilecektir.

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?

Monografia  si  kladie  za  cieľ  kriticky  zmapovať chápanie pojmu možných svetov. V historicky ladenej prvej kapitole opisuje formovanie sémantiky možných svetov, spolu s naznačením niektorých problémov, ktoré so sebou prináša, a ktoré prenikavým spôsobom odhaľoval predovšetkým W. V. O. Quine.
V ďalších dvoch kapitolách sa zameriava na modernejšie názory na povahu možných svetov, pričom hlavná pozornosť je venovaná dichotómii medzi posibilistickým a aktualistickým prístupom k otázke modalít, popri ktorom je nevyhnutné posúdiť aj iné rozlíšenia (esencializmus - antiesencializmus, realizmus - redukcionizmus, príp. erzacizmus či fikcionalizmus, naturalizmus - nenaturalizmus a pod.). Zvýšená pozornosť je venovaná koncepciám D. Lewisa, S. Kripkeho, A. Plantingu, R. M. Adamsa, N. Reschera a D. Armstronga.
Neštandardný prístup k problematike možných svetov je zachytený vo štvrtej kapitole. Táto kapitola je predovšetkým venovaná významnej koncepcii J. Hintikku, ktorá pracuje s pojmom epistemických možných svetov a dokumentuje  príklon  k modifikácii  a  relativizácii  modálneho diskurzu.
V monografii sú objasnené niektoré reprezentatívne koncepcie možných svetov, resp. možných indivíduí a je v nej naznačený celkový postup od posudzovania možných svetov ako ideálnych logických konštruktov, cez ich relativizáciu prostredníctvom oddelených oblastí indivíduí pre jednotlivé svety a ďalej prostredníctvom vzťahu dosiahnuteľnosti až k fikčným, nemožným a neštandardným možným svetom.

Revision sequences were introduced in 1982 by Herzberger and Gupta (independently) as a mathematical tool in  formalising their respective theories of truth. Since then, revision has developed in a method of analysis of  theoretical concepts with several applications in other areas of logic and philosophy. Revision sequences are usually formalised as ordinal-length sequences of objects of some sort. A common idea of revision process is shared by all revision theories but specific proposals can differ in the so called limit rule, namely the way they handle the limit stages of the process. The limit rules proposed by Herzberger and by Belnap show different mathematical properties, called periodicity and reflexivity, respectively. In this paper we isolate a notion of cofinally dependent limit rule, encompassing both Herzberger’s and Belnap’s ones, to study periodicity and reflexivity in a common framework and to contrast them both from a philosophical and from a mathematical point of view. We establish the equivalence of weak versions of these properties with the revision-theoretic notion of recurrent hypothesis and draw from this
fact some observations about the problem of chosing the "right” limit rule when performing a revision-theoretic analysis.

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).

Alternative models of idealized scientific inquiry are investigated and compared. Particular attention is devoted to paradigms in which a scientist is required to determine the truth of a given sentence in the structure giving rise to his data.

Philosophical paradigms are principles in which is used to view the world. In this paper I aim to use the philosophical paradigms: Phenomenology, Hermeneutics, Logical positivism, Critical rationalism, The Systems Theory and Ubuntu to view and help the people in need.

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.

In this piece, we will discuss what is posthuman in the writings of Kafka, and how his writing compares to that of the other writers classified under the title Posthumanism. The issue is whether Kafka's short story, A Report to an Academy (1988), is a posthumanist piece or not.

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

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.

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].

There are several difficulties in understanding the concept of modal realism in our philosophical context. The author shows various types of modal realism as a theory. The analyses of the main theories of modal worlds and modal individuals show the problems of identity and identification as the fundamental questions. One of the key problems is the place of individuals in modals worlds.

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.

ABSTRACT: Minimalists about truth contend that traditional inflationary theories systematically fail to explain certain facts about truth, and that this failure licenses a 'reversal of explanatory direction'. Once reversed, they purport that their own minimal theory adequately explains all of the facts involving truth. But minimalists' main objection to inflationism seems to misfire, and the subsequent reversal of explanatory direction, if it can be made sense of, leaves minimalism in no better explanatory position; and even if the objection were serviceable and the reversal legitimate, minimalists' adequacy thesis is still implausible.

► JOHN CORCORAN, What syllogisms are: three views, eight centuries.
Philosophy, University at Buffalo, Buffalo, NY 14260-4150, USA
E-mail: [email protected]
  At issue is the nature of “the syllogisms” in Prior Analytics [1]. For centuries from the 1200s, the dominant view was enshrined in the medieval mnemonic “Barbara-Celarent” [2]: syllogisms are certain valid premise-conclusion arguments commonly mislabeled “inferences”.  In the mid-1900s many modern logicians adopted a contrary view credited to Jan Łukasiewicz [3]: syllogisms are certain true universal propositions informally called “implications”. A fruitful two-sided debate ensued producing evidence weakening the Łukasiewicz case.
  Toward the last quarter of the 1900s, a third contender appeared. Independently, John Corcoran [4] and Timothy Smiley [5] took the class of syllogisms to exclude propositions while including not only the valid arguments recognized as syllogisms in medieval times but also deductions establishing validity. A deduction contains, over and above premises and conclusion of an argument, a chain of reasoning showing that the conclusion’s information is contained in that of the premises. The debate became three-sided for twenty years or more.
  The Łukasiewicz view lacks current defenders leaving the debate to the medieval and Corcoran-Smiley views.
  This study details all three views—emphasizing their differences. For example, the medieval syllogisms are valid but ‘true’ does not apply to them, though their premises and conclusions are all true or false. The Łukasiewicz syllogisms are all true but the term ‘valid’ as applied to arguments is inappropriate. The Corcoran-Smiley syllogisms cannot be said to be true in the sense applicable to propositions but they are all valid in the sense that their conclusions follow from their premises. Moreover, many of them containing chains of reasoning are “cogent” [6] in an epistemic sense not applicable either to the Łukasiewicz or to the medieval syllogisms.
  [1] ROBIN SMITH, Aristotle’s Prior Analytics, Hackett, 1989. 
  [2] JOHN CORCORAN, DANIEL NOVOTNÝ, AND KEVIN TRACY,  Deductions and Reductions Decoding Syllogistic Mnemonics, Entelekya Logico-Metaphysical Review,  vol.2 (2018), pp. 5–39.
  [3] JAN ŁUKASIEWICZ, Aristotle’s syllogistic, Oxford UP, 1951.
  [4] JOHN CORCORAN, Aristotle’s Prototype Rule-based Underlying Logic, Logica Universalis, vol. 2 (2018) pp. 9-35.
  [5] TIMOTHY SMILEY, What is a Syllogism?, Journal of Philosophical Logic,
vol. 2 (1973) pp. 136–154.
[6] JOHN CORCORAN, Argumentations and logic, Argumentation, vol. 3 (1989), pp. 17–43.

Abstract. The hexagon of opposition is an improvement of the square
of opposition due to Robert Blanch´e. After a short presentation of the
square and its various interpretations, we discuss two important problems
related with the square: the problem of the I-corner and the problem of
the O-corner. The meaning of the notion described by the I-corner does
not correspond to the name used for it. In the case of the O-corner, the
problem is not a wrong-name problem but a no-name problem and it
is not clear what is the intuitive notion corresponding to it. We explain
then that the triangle of contrariety proposed by different people such
as Vasiliev and Jespersen solves these problems, but that we don’t need
to reject the square. It can be reconstructed from this triangle of contrariety,
by considering a dual triangle of subcontrariety. This is the main
idea of Blanch´e’s hexagon. We then give different examples of hexagons
to show how this framework can be useful to conceptual analysis in many
different fields such as economy, music, semiotics, identity theory, philosophy,
metalogic and the metatheory of the hexagon itself. We finish by
discussing the abstract structure of the hexagon and by showing how we
can swing from sense to non-sense thinking with the hexagon.

The paper presents Hegel's view on the link between logic and metaphysics. Hegel criticizes, not unlike Kant, the pre-Kantian dogmatic meaning of “metaphysics”, but explicitly defends an ancient and specifically Aristotelian view. In particular, I show that Hegel aims at both tracing metaphysics back to its logical roots and logic back to its metaphysical roots, thus developing the idea of an interplay between the two disciplines. My claim is that this idea is the main reason of Hegel’s importance for contemporary debates in philosophical logic and metaphysics.

The aim of this research paper is to clarify the concept and the doctrine of Natural Justice and its apparatus in the judicial, quasi-judicial, and regulatory frameworks is not new. It appears to be as matured as the framework of the dispensation of equity itself. It has by presently accepted the significance of being, so to say, "an essential inbuilt component" of the component, through which the decision-making process passes, within the things touching the rights and freedom of the individuals. It is no question, a procedural requirement but it guarantees a solid safeguard against any Legal or authoritative; arrange or action, antagonistically influencing the substantive rights of the people. 'Natural Justice' is an expression of English common law. This hypothesis has also been created with the significant help of a few logicians. Afterward, when the equitable circumstance has kept up there in various nations, such standards ought to be overseen to back this democracy. In this paper, I attempt to investigate the concept of characteristic equity, the root of common.

Negative theology developed by Pseudo-Dionysius the Areopagite is hardly considered as a consistent doctrine. The aim of this paper is to provide a coherent and extensive interpretation of its claims. I shall argue that the theory of negative theology consist in four theses concerning God’s positive and negative properties and his unknowability. Afterwards I will propose and discuss three consistent logical interpretations of that theory.  Only one of these interpretations covers all the theses of negative theology and therefore is a preferable one.

This book analyzes metaphysical consequences of the quantum theory of many particles with respect to the fundamental notions of identity, individuality and discernibility. The main focus is on the proper interpretation of the quantum formalism in relation to the role of permutation invariance and the adequate representation of the properties of individual subsystems. Two main approaches to the issue of the individuation of quantum particles are distinguished and thoroughly discussed.  These approaches differ radically with respect to their metaphysical consequences – while one of them implies the complete indiscernibility of quantum particles of the same kind, the other one restores the possibility of discerning individual particles by their properties. We connect the problem of quantum individuation and discernibility with an analysis of the concept of quantum entanglement, and we also discuss identity over time and in counterfactual scenarios.

Manual concebido para un curso semestral de teoría de los argumentos. Abarca tanto la analítica como la crítica, La analítica trata de las cuestiones relativas a la naturaleza, estructura y tipología de los argumentos, mientras que la crítica trata de los  estándares y criterios y tipos de evaluación y/o crítica.