Peircean Graphs for Prepositional Logic

1996 ◽  
Author(s):  
Eric Hammer
Keyword(s):  
Predicate Logic ◽  
Propositional Calculus ◽  
Compound Structure ◽  
History Of Logic ◽  
Subsequent Work ◽  
History Of ◽  
Science Community ◽  
Modern Analysis ◽  
Graphical System ◽  
As If

The contributions of C.S. Peirce to the early history of prepositional and predicate logic are well known. Much less well known, however, is Peirce’s subsequent work (for more than ten years) on diagrammatic versions of prepositional and predicate logic. This work was considered by Peirce himself to be his most important contribution to logic. From his experience with chemistry and other parts of science, Peirce had become convinced that logic needed a more visually perspicuous notation, a notation that displayed the compound structure of propositions the way chemical diagrams displayed the compound structure of molecules. Peirce’s graphs for prepositional sentences are built up from sentence letters by the operations of enclosing a graph within a closed figure (interpreted as its negation) and juxtaposing two or more graphs on separate parts of the page (interpreted as their conjunction). For example, a graph like would be interpreted as “If A and B, then C” or “It is false that A and B and not-CV’ A graph such as would be read as “If A then B, but not C.” This chapter gives a modern analysis of Peirce’s diagrammatic version of the propositional calculus from the ground up. In particular, it is an investigation of just what is involved in formulating precisely the syntax, semantics, and proof theory of Peirce’s graphical approach to propositional logic. The project is interesting for several reasons. First, given Peirce’s importance in the history of .logic and his own opinion of the value of his work on graphs, it seems of historical interest to see to what his suggestions amounted. Second, Peirce’s work has gained a following in the computer science community, due especially to the work of Sowa [1984], whose system of conceptual graphs is modeled after Peirce’s work on diagrammatic approaches to prepositional and predicate logic. Third, in reconstructing Peirce’s graphical system we will confront a number of features characteristic of “visual” or “diagrammatic” inference, that is, inference that employs various forms of graphical representations in addition to, or in place of, sentences.

Polish logic

2018 ◽  
Author(s):  
Jan Zygmunt
Keyword(s):  
Set Theory ◽  
Quantifier Elimination ◽  
History Of Logic ◽  
Modern Logic ◽  
Truth Theory ◽  
Subsequent Work ◽  
Consequence Operation ◽  
The Matrix ◽  
History Of ◽  
Logical Research

The term ‘Polish logic’ was coined by McCall to signal the important contributions to modern logic by logicians from Poland between the wars. There were several centres of research, of which the Warsaw school, which grew out of the earlier Lwów–Warsaw philosophical movement, was the most significant. Its development was closely connected with the Warsaw school of mathematics, which gave it its characteristic mathematical bent. Polish logic took as its point of departure the main trends in logical research of the time and it has influenced both subsequent logical research and subsequent work in the Western analytic tradition of philosophy. Its chief contributions were: (1) an enrichment of existing logical theory (including work on Boolean algebras, the sentential calculus, set theory, the theory of types); (2) new logical theories (for example, Leśniewski’s systems, Łukasiewicz’s many-valued logics, Tarski’s theory of truth, theory of the consequence operation and the calculus of systems); (3) new methods and tools as well as improvements of existing methods (for example, the matrix method of constructing sentential calculi, axiomatizability of logical matrices, algebraic and topological interpretations of deductive systems, permutation models for set theory, the application of quantifier elimination to decidability and definability problems); and (4) the application of formal methods to the study of the history of logic, resulting in a new understanding of the logics of Aristotle, the Stoics and the medievals.

Kant and a Philosophical History of Logic

2018 ◽  
Author(s):  
Huaping Lu-Adler
Keyword(s):  
Eighteenth Century ◽  
Historical Narrative ◽  
History Of Logic ◽  
Philosophical Discourse ◽  
Systematic Philosophy ◽  
History Of ◽  
Early Eighteenth Century ◽  
Kantian Theory

This chapter discusses certain exegetical challenges posed by Kant’s logic corpus, which comprises the Logic compiled by Jäsche, Kant’s notes on logic, transcripts of his logic lectures, and remarks about logic in his own publications. It argues for a “history of philosophical problems” method by which to reconstruct a Kantian theory of logic that is maximally coherent, philosophically interesting, and historically significant. To ensure a principled application of this method, the chapter considers Kant’s conception of history against the background of the controversy between eclecticism and systematic philosophy that shaped the German philosophical discourse during the early eighteenth century. It thereby looks for an angle to make educated decisions about how to select materials from each of the periods considered in the book and builds a historical narrative that can best inform our understanding of Kant’s theory of logic.

Figurines

2020 ◽  
Keyword(s):  
Art History ◽  
Greco Roman ◽  
Roman Culture ◽  
History Of ◽  
Relationship Of ◽  
Material Concept ◽  
As If

This book concerns figurines from cultures that have no direct links with each other. It explores the category of the figurine as a key material concept in the art history of antiquity through comparative juxtaposition of papers drawn from Chinese, pre-Columbian, and Greco-Roman culture. It extends the study of figurines beyond prehistory into ancient art-historical contexts. At stake are issues of figuration and anthropomorphism, miniaturization and portability, one-off production and replication, substitution and scale. Crucially, figurines are objects of handling by their users as well as their makers—so that, as touchable objects, they engage the viewer in different ways from flat art. Unlike the voyeuristic relationship of viewing a neatly framed pictorial narrative, as if from the outside, the viewer as handler is always potentially and without protection within the narrative of figurines. This is why they have had potential for a potent, even animated, agency in relation to those who use them.

A DEFENSE OF THE CAROLINGIAN “DEFENSE OF MEDICINE”: INTRODUCTION, TRANSLATION, AND NOTES

Traditio ◽  
2020 ◽  
Vol 75 ◽  
pp. 87-125
Author(s):  
JOEL L. GAMBLE
Keyword(s):  
Content Analysis ◽  
English Translation ◽  
Natural Sciences ◽  
History Of Ideas ◽  
Christian Faith ◽  
Medical Texts ◽  
The Poor ◽  
Imitation Of Christ ◽  
History Of ◽  
As If

The “Defense of Medicine” prefaces the Codex Bambergensis Medicinalis 1, a Carolingian collection of medical texts. Some scholars have dismissed the Defense as an incoherent patchwork of quotations. Yet, missing from the literature is an adequate assessment of the Defense's arguments. This present study includes the first English translation accompanied by a complete source commentary, a prerequisite for valid content analysis. When read systematically and with attention to the author's use of sources, the Defense is limpid and cogent. Its first purpose is to defend the compatibility of Christian faith and secular medicine. Key propositions include the following: God made nature good, so the natural sciences are reconcilable with divine learning; scripture respects medicine; God expects the sick to avail of physicians and deserves honor for healings done through physicians. Counter-arguments used by the Defense's opponents, who rejected medicine on principle, can also be reconstructed from the text. Two further purposes of the Defense have hitherto been explored insufficiently. After justifying medicine, the Defense addresses sick patients. It encourages them that illness can be spiritually healthful, an instrument for curing their souls. The Defense then addresses caregivers. It tells them why they should succor the sick, even the poor: not for gain or fame, but in imitation of Christ and as if treating Christ himself, whose image the sick bear. The Defense thus contributes to the history of ideas on medicine, health, sickness, and the ethics of altruistic care.

Robert M. Young's Mind, Brain and Adaptation revisited

2021 ◽  
pp. 1-17
Author(s):  
Christopher Lawrence
Keyword(s):  
Nineteenth Century ◽  
Philosophy Of Science ◽  
Experimental Psychology ◽  
Social Reform ◽  
Victorian Britain ◽  
Unique Character ◽  
Philosophy Department ◽  
History Of ◽  
Science Community ◽  
Scientific Ideas

Abstract Robert Maxwell Young's first book Mind, Brain and Adaptation in the Nineteenth Century (1970), written from 1960 to 1965, still merits reading as a study of the naturalization of mind and its relation to social thought in Victorian Britain. I examine the book from two perspectives that give the volume its unique character: first, Young's interest in psychology, which he considered should be used to inform humane professional practices and be the basis of social reform; second, new approaches to the history of scientific ideas. I trace Young's intellectual interests to the Yale Philosophy Department, the Cambridge Department of Experimental Psychology and a new history and philosophy of science community. Although Young changed his political outlook and historiography radically after 1965, he always remained faithful to ideas about thought and practice described in Mind, Brain.

Wyclif and the wheel of time

1997 ◽  
Vol 33 ◽  
pp. 177-193 ◽  
Author(s):  
Michael Wilks
Keyword(s):  
Time Factor ◽  
Spiritual Power ◽  
Christian Church ◽  
Political Situation ◽  
Ecclesiastical Authority ◽  
Wide Range ◽  
History Of ◽  
Right Relationship ◽  
The Right ◽  
As If

During the 1370s Wyclif wrote to defend a monarchy which made extensive use of bishops and other clergy in the royal administration and yet was faced with aristocratic factions encouraged by bishops like Wykeham and Courtenay who espoused papal supremacy, if not out of conviction, at least as a very convenient weapon to support their independence against royal absolutism. At first sight Wyclifs attempts to define the right relationship between royal and episcopal, temporal and spiritual, power seem as confused as the contemporary political situation. His works contain such a wide range of theories from orthodox two swords dualism to a radical rejection of ecclesiastical authority well beyond that of Marsilius and Ockham that it seems as if his only interest was in collecting every anti-hierocratic idea available for use against the papacy. The purpose of this paper is to suggest that a much more coherent view of episcopal power can be detected beneath his tirades if it is appreciated that his continual demand for a great reform, a reformatio regni et ecclesiae, is inseparably linked to his understanding of the history of the Christian Church, and that in this way Wyclif anticipates Montesquieu in requiring a time factor as a necessary ingredient in constitutional arrangements.

Is God Really in History?

1979 ◽  
Vol 15 (3) ◽  
pp. 379-390
Author(s):  
Frederick Sontag
Keyword(s):  
Nineteenth Century ◽  
Human Life ◽  
History Of ◽  
The Relationship ◽  
As If ◽  
The Way

For some time it seemed as if Christianity itself required us to say that ‘God is in history’. Of course, even to speak of ‘history’ is to reveal a bias for eighteenth- and nineteenth-century forms of thought. But the justification for talking about the Christian God in this way is the doctrine of the incarnation. The centre of the Christian claim is that Jesus is God's representation in history, although we need not go all the way to a full trinitarian interpretation of the relationship between God and Jesus. Thus, the issue is not so much whether God can appear or has appeared within, or entered into, human life as it is a question of what categories we use to represent this. To what degree is God related to the sphere of human events? Whatever our answer, we need periodically to re-examine the way we speak about God to be sure the forms we use have not become misleading.

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