Philosophy of Logic

AMBIGUITY: LEXICAL AND STRUCTURAL.


An expression with more than one normal sense or meaning is ambiguous. To demonstrate ambiguity it is sufficient to indicate two senses. In the broad sense of ‘animal’, every human is an animal; in the narrow sense, no human is an animal. In the nonexclusive sense of ‘or’, every human is human or human; in the exclusive sense, not even one human is human or human. A human that is human or human, in the exclusive sense, is not both human and human, thus not human. An ambiguous non-compound expression is lexically ambiguous in the narrow sense. A compound expression containing a lexically ambiguous constituent is lexically ambiguous in the broad sense. Consider ‘every animal is not a human’. Reading ‘not’ with broad scope and ‘animal’ in the broad sense, it expresses the true negative proposition “not every animal is a human”. Reading ‘not’ with narrow scope and ‘animal’ again in the broad sense, it expresses the false universal proposition “every animal is a non-human”—which is logically equivalent to “no animal is a human”.  A compound expression is structurally ambiguous in the narrow sense if none of its non-compound constituents are ambiguous but it expresses senses having different logical structures or forms.  The broad sense drops the restriction to non-ambiguous constituents. The last example is structurally and lexically ambiguous in the broad senses. Lexical ambiguity of constituents is sometimes essential to structural ambiguity of compounds. Consider ‘every number but one is positive’. Reading ‘one’ denotationally can yield a false proposition implying that one is not positive. Reading ‘one’ quantificationally can yield a true proposition implying that there is only one number that is not positive—taking ‘number’ to refer to non-negative integers.

This paper looks into what can reasonably be regarded as truth-table devices in one of Boole's late manuscripts, as a way of addressing Boole's relation to modern propositional logic. A careful investigation of the divergences between those table devices and our current conception of truth tables offers an opportunity to reassess the singularity of Boole's logical system, especially concerning the relation between its linguistic and mathematical aspects. The paper explores Boole's conception of the compositional structure of symbolic expressions , the genesis of table devices from his method of development into normal forms, and the non-logical origin of the constants 0 and 1 as dual terms. Boole's system of logic is in this way shown to be chiefly concerned with the problem of the formal interpretability conditions of symbolic expressions, rather than with the truth conditions of logical propositions.

This paper focuses on formal properties of functions satisfying a weak conservativity, a generalisation of classical conservativity, a well known constraint on the denotations of unary determiners. Informally , classically conservative determiners are determiners which are conservative "on the right" whereas weakly conservative determiners can be conservative "on the right" or "on the left". These notions are made precise and it is shown in particular that the constraint of weak con-servativity remains a very strong constraint excluding most type 1, 1 functions and that the Boolean closure of weakly conservative functions equals the set of all type 1, 1 functions.

By logic I mean the subject Aristotle started in Prior Analytics. Logic studies demonstration and everything necessary for demonstration, and also many things that come to mind in the course of such studies—including axiomatic method as described in my short “Axiomatic method”. By young I mean less than about 40 years old. By logicians I mean people who have dedicated their lives to advancing and criticizing logic: to discovering and establishing new additions and also to clarifying and correcting what has or had been accepted. More specifically, my advice is for people who have already embarked on their careers: from fresh PhDs, instructors, and assistant professors to young professors looking forward to reaping the fruits of their long years of study and research. My advice is for people who have mastered logic and who want to improve their mastery.

Sentences in mathematical English such as E below, expressing propositions about [natural] numbers, are routinely translated into sentences such as F below of an interpreted first-order language. E: Every number x is either zero or the successor of some number y.
F: Ax (x = o --> Ey x = sy).
The English quantifier phrases every number x and some number y correspond to the symbolic quantifier phrases Ax and Ey. However, there is disagreement among mathematical logicians concerning symbolic "location" of the meaning of the sortal [substantive] number. Some logicians, the majority, take the meaning of number to be elliptically absorbed into the variable so that x means, in effect, number x. Others take it to be absorbed into the quantifier so that A means, in effect, every number. The former, the sortal variable approach, treats the quantifier as a logical symbol but, contrary to tradition, treats the variable as non-logical. The latter, the sortal quantifier approach, treats the variable as logical, but, contrary to tradition, treats the quantifier as non-logical. This paper traces the disagreement to Frege, who did not recognize universes of discourse, whose individual variables ranged over "the universe", and whose suppressed sortal was object (or individual), which is naturally taken to be logical. This paper favors a third alternative, the suppressed sortal approach, in effect, that Ax and Ey are elliptical for ANx and ENy, where N is a sortal, or symbolic [common] noun, a category useful for understanding how number-theoretic propositions can be fully expressed in first-order. According to this approach, the quantifier and the variable are both logical and the content of the quantifier phrase, Ax or Ey, is carried by the suppressed non-logical sortal N.

Este trabajo pretende trazar las líneas generales del programa (en el sentido de Lakatos) absolutista en filosofía de la lógica. Sostiene que las tesis principales de dicho programa se encuentran el el proyecto de Leibniz para la construcción de una Characterica universalis, y que Frege retoma en su obra Conceptografía. En este sentido, el proyecto logicista en filosofía de las matemáticas (según el cual es posible derivar los principios de la matemática clásica a partir de un conjunto reducido de principios y conceptos lógico) aparece como la materialización de dicho proyecto leibniciano. Sostiene además que la filosofía del Tractatus de Wittgenstein se encuentra inmersa en dicho programa, de modo que las crítica que este dirige a Frege y a Russell se comprenden mejor si se consideran como críticas a partir de los rasgos absolutistas de la lógica, y no como crítica externas a dicho programa.

The Talking-Tree or Palaver Tree (Arbre à palabres) is a designated location (originally a large ancestral tree such as the baobab, but is also can be a grave) in many African traditions where the community comes together to discuss in a peaceful and constructive manner, issues of common interest. It is conceived as an open gathering space of interactive communication lead by the stance that finding a compromise or common solution is the best way to consolidate a community. At times the interchange taking place at a Talking-Tree, may also transform into conflict management. Conflict management unfolds into several specific patterns of argumentation including those that aim at deciding if some given accusation is or not justified.
The main aim of our paper is to study, within the Baule tradition of Talking-Tree debates involving accusations of wrongdoing, the meaning explanation underlying proverbs (nyanndra), which constitute the most fundamental elements of these debates. More precisely our study, based on a pragmatic approach to meaning, will focus on the distinction drawn by the linguist J. Kouadio, Yao. (2012) between ascertainment, (epistemo)logical and moral Baule proverbs by distinguishing their different role in a Talking-Tree debate.
One of the main results of our approach is that it makes it patent that drawing a conclusion of a Talking-Tree debate is grounded on contentual functional links, rather than on the analysis of logical constants. This research should set the basis for a larger epistemological research on the structure of argumentation patterns born and developed in Africa, where meaning and knowledge are constituted during dialogical interaction. The dialogical system underlying such form of argumentation, that we call Dialogues of functional reasoning by proverbs, we think provides a general instrument for the study of patterns of argumentation beyond the African tradition.

A string theory is a mathematical science whose universe is the set of strings of characters from a fixed finite alphabet. Tarski and Hermes axiomatized string theories in the 1930s [3]. String-theoretic concepts include "string", "concatenation", and "occurrence"-not "token", "type", or other concepts presupposing material, or concrete, objects pertaining to applications. Applications of string theories involve concrete inscriptions, utterances, or other human artifacts, but string theories per se don't. The relationships between string theories and their applications are analogous to those between other abstract mathematical theories and their respective concrete applications. We apply a string theory by correlating concrete physical artifacts with abstract strings. The relational concepts "is-the-type-of" and "is-a-token-of" pertain. When we correlate several concrete perceptible artifacts such as printings of a certain word with a certain string, each of the former is-a-token-of the latter and the latter is-the-type-of each of the former.
Please post you frank objections and comments.
Acknowledgements: Mark Brown, James Cargile, Richard Grandy, Idris Samawi Hamid, Joaquin Miller, Frango Nabrasa, Albert Visser, and others.

Bu çalışma Nietzsche’nin dilin ve mantığın bazı kabul, ilke ve kurallarının insanca saiklerle ortaya çıktıkları yönündeki kanaatinden hareketle, Nietzsche’nin dil ile mantık arasında nasıl bir ilişki varsaydığını ortaya koymayı amaçlamaktadır.

در این مقاله به تبارشناسی مفاهیم حکم، گزاره و جمله-نشانه و نحوه موضوعیت یابی آنها در منطق در خلال دو جریان اصلی مطالعات منطقی در قرن نوزدهم میلادی می پردازیم. این دو جریان را می توان سنت جبری، که منطق را نوعی از جبر و حساب قلمداد می کند، و سنت نظریه استنتاجی، که استنتاج را جدا از جبر و بنیادی تر از آن می داند، نامید. ما در این مقاله از کانت آغاز می کنیم که تلاش او برای تفکیک منطق از متافیزیک نقش عمده ای بر هر دو جریان داشته است و همچنین پژوهش های او در مورد حکم و انواع آن را می توان نقطه شروع نظریه سنت استنتاجی دانست. نشان می دهیم که چگونه در یک سنت منطقی مفهوم حکم و در قدم بعدی گزاره مفاهیم مرکزی منطق قلمداد می شوند و در سنتی دیگر مفهوم جمله و به تبع آن مفهوم فرمول درست¬ساخت و قواعد معطوف به آن محور مطالعات منطقی را شکل می دهد. سیر این تحولات را درآرای کانت، بولتزانو، بول و فرگه پی خواهیم گرفت و نهایتا به تحلیل دیدگاه پدیده شناسانه هوسرل از ماهیت مفاهیم مذکور و نسبت آنان با منطق خواهیم پرداخت.

CORCORAN & SWINIARSKI ADMIRE OCKHAM’S SUPPOSITION THEORY

1978. Logical Structures of Ockham's Theory of Supposition, Franciscan Studies 38, 161–83
This article is a defense of Ockham against a baseless charge of error, which, if left unanswered, might tend to diminish Ockham's reputation as a technically competent logician. Study of the sources of the charge reveal that two recent commentaries each attribute ingenious and interesting logical structures to Ockham's thought on supposition. Comparison of these two structures with each other and with Ockham's writings yields three results: first, that the two structures, though separately consistent, are inconsistent with each other; second, that neither of them square with Ockham's own statements and, third, that Ockham's thought does have a logical structure which, in several respects, is even more ingenious. This article articulates the logical structure of Ockham's theory of supposition and compares it with the two others.

Preprint to a chapter of the book Dialog Systems. A Perspective from Language, Logic and Computation, edited by Teresa Lopez Soto
. Nowadays, there is a quite considerable amount of literature on the use of analogy or more generally of inferences by parallel reasoning in contemporary legal reasoning, and particularly so within Common Law. These studies are often motivated by researches in artificial intelligence seeking to develop suitable software-support for legal reasoning. Recently; Rahman/Iqbal/Soufi (2020) developed a dialogical approach in the framework of Constructive Type Theory to what in Islamic Jurisprudence was called qiyās or correlational inferences. In their last chapter the authors suggested that such an approach contributes to the study of patterns of reasoning by precedent cases within contemporary common Law. In the present paper we will further motivate the deployment within Civil and Common Law of the dialogical framework developed in Rahman/Iqbal/Soufi (2020). After a presentation of Scott Brewer's take on analogy within Common Law, that has striking structural similarities to reasoning by precedent case rooted in ratio legis (known in Islamic Jurisprudence as qiyās al-'illa or correlational inference by the occasioning factor), we will illustrate the implementation of the framework with a brief discussion of some cases of legal reasoning based in Spanish Civil Law but where the accent is put in the emerging ruling rather than in the existing of a case as in Common Law. Moreover; quite surprisingly, the case under study suggests that even cases of Law-interpretation fit the argumentation pattern of qiyās al-'illa. A caveat: in the present paper we will focus mainly in discussing the dynamics of the meaning constitution involved rather than in setting the rules of the underlying dialogical framework, the latter is the subject of a follow-up paper.