A purely topological form of non-Aristotelian logic

1937 ◽  
Vol 2 (3) ◽  
pp. 97-112 ◽  
Author(s):  
Carl G. Hempel
Keyword(s):  
Truth Table ◽  
Aristotelian Logic ◽  
Truth Values ◽  
Symbolic Notation ◽  
Sentential Logic ◽  
New Type ◽  
Points Of View ◽  
Topological Form

1. The problem. The aim of the following considerations is to introduce a new type of non-Aristotelian logic by generalizing the truth-table methods so far employed for establishing non-Aristotelian sentential calculi. We shall expound the intended generalization by applying it to the particular set of pluri-valued systems introduced by J. Łukasiewicz. One will remark that the points of view illustrated by this example may serve to generalize quite analogously any other plurivalued systems, such as those originated by E. L. Post, by H. Reichenbach, and by others.2. J. Łukasiewicz's plurivalued systems of sentential logic. First of all, we consider briefly the structure of the Łukasiewicz systems themselves.As to the symbolic notation in which to represent those systems, we make the following agreements: For representing the expressions of the (two- or plurivalued) calculus of sentences, we make use of the Principia mathematica symbolism; however, we employ brackets instead of dots. We call the small italic letters “p”, “q”, “r”, … sentential variables or elementary sentences, and employ the term “sentence” as a general designation of both elementary sentences and the composites made up of elementary sentences and connective symbols (“~”, “ν” “.”, “⊃” “≡”).Now, the different possible sentences (or, properly speaking, the different possible shapes of sentences, such as “p”, “p∨q”, “~p.(q∨ r)”, etc.) are the objects to which truth-values are ascribed; and just as in every other case one wants a designation for an object in order to be able to speak of it, we want now a system of designations for the sentences with which we are going to deal in our truth-table considerations.

scholarly journals THE TURN OF THE SCREW: HENRY JAMES AS AN AUTHOR AND A CRITIC

2020 ◽  
pp. 55-67
Author(s):  
M.B. Rarenko ◽  
Keyword(s):  
Henry James ◽  
William James ◽  
Absolute Truth ◽  
The Core ◽  
Works Of Art ◽  
Starting Point ◽  
The World ◽  
New Type ◽  
Points Of View ◽  
The Absolute

The article considers the story by Henry James (1843 – 1916) «The Turn of the Screw» (1898 – first edition, 1908 – second edition) in connection with the emergence of a new type of narrator in the writer's late prose. The worldview and creative method of H. James are formed under the influence of the philosophy of pragmatism, which became widespread at the turn of the XIX-XX centuries thanks to the works of the writer's elder brother, the philosopher William James (1842 – 1910). The core of pragmatism is the pluralistic concept of William James based on the assumption that knowledge can be realized from very limited, incomplete, and inadequate «points of view» and this leads to the statement that the absolute truth is essentially unknowable. The epistemological statements of William James's theory is that the content of knowledge is entirely determined by the installation of consciousness, and the content of the truth in this case depends on the goals and experience of the human, i.e. the central starting point is the consciousness of the person. Henry James not only creates works of art, but also sets out in detail the principles of his work both on the pages of fiction works of small and large prose, putting them in the mouths of their characters – representatives of the world of art, and in the prefaces to his works of fiction, as well as in critical works.

Graphing True-False Statements

1969 ◽  
Vol 62 (7) ◽  
pp. 553-556
Author(s):  
Margaret Wiscamb
Keyword(s):  
Truth Table ◽  
Graphic Representation ◽  
Truth Values ◽  
Truth Tables ◽  
True False ◽  
Tedious Process ◽  
Three Components

In elementary logic the construction of truth tables, while not difficult, can be a long and tedious process. In this article I would like to present a simple graphic representation of the truth values of compound statements involving two or three components. The graph gives all the information found in a truth table and pictures the statement as an easily recognizable pattern. By using this graphing procedure, the simplifying of statements is shortened considerably. In fact, for statements involving only two components, with a little practice it can usually be done by inspection. Proving that a statement is a tautology becomes almost trivial.

scholarly journals Cooperation-Controlled Learning for Explicit Class Structure in Self-Organizing Maps

2014 ◽  
Vol 2014 ◽  
pp. 1-24 ◽  
Author(s):  
Ryotaro Kamimura
Keyword(s):  
Cooperative Networks ◽  
Class Structure ◽  
Small Individual ◽  
Self Organizing Maps ◽  
Information Theoretic ◽  
New Type ◽  
Points Of View ◽  
Information Theoretic Method ◽  
Self Organizing

We attempt to demonstrate the effectiveness of multiple points of view toward neural networks. By restricting ourselves to two points of view of a neuron, we propose a new type of information-theoretic method called “cooperation-controlled learning.” In this method, individual and collective neurons are distinguished from one another, and we suppose that the characteristics of individual and collective neurons are different. To implement individual and collective neurons, we prepare two networks, namely, cooperative and uncooperative networks. The roles of these networks and the roles of individual and collective neurons are controlled by the cooperation parameter. As the parameter is increased, the role of cooperative networks becomes more important in learning, and the characteristics of collective neurons become more dominant. On the other hand, when the parameter is small, individual neurons play a more important role. We applied the method to the automobile and housing data from the machine learning database and examined whether explicit class boundaries could be obtained. Experimental results showed that cooperation-controlled learning, in particular taking into account information on input units, could be used to produce clearer class structure than conventional self-organizing maps.

scholarly journals HYBRID WAR AS A MODERN FORM OF VIOLENCE

2021 ◽  
Vol 1 (48) ◽  
pp. 133-145
Author(s):  
Володимир Вікторович Чалапко
Keyword(s):  
Careful Analysis ◽  
Scientific Concept ◽  
Main Body ◽  
Hybrid Warfare ◽  
Public Consciousness ◽  
New Type ◽  
Points Of View ◽  
Hybrid War ◽  
The Military ◽  
Modern Form

Problem setting. One of the modern forms of violence that requires careful analysis is hybrid war. The events of recent decades have shown that hybrid war is not only a scientific concept, but also a reality today. The phenomenon of hybrid war requires a comprehensive study from both theoretical and practical points of view. Recent research and publications analysis. The problem of hybrid wars is reflected in the scientific works of both foreign and domestic scientists. Among foreign scientists, research in this direction was carried out by R. Glenn, D. Lasik, M. McLuhan, F. Hoffman, who focused on determining the characteristics of hybrid wars in comparison with classical wars, analyzed the strategies and tactical algorithms for conducting such wars, and focused on poly-straightness and multimodality of this type of violence. On the other hand, domestic scientists, in particular V. Kravchenko, focus on the fact that hybrid war is not an absolutely new phenomenon in world history and gives a number of examples of manifestations of "hybridity" in wars of the past. In turn, M. Senchenko, analyzing hybrid war as an integral phenomenon, defines its information component as the main one which the strategy of this type of war is built around. Paper objective. The purpose of this work is to define the essential characteristics of hybrid war as a new form of violence. Paper main body. The understanding of the essence and content of hybrid warfare in the scientific literature is presented by a number of points of view that complement the understanding of this complex and little-studied phenomenon. As you know, the concept of "hybrid war" was introduced into scientific circulation by the American scientist M. McLuhan. Domestic scientists generally understand hybrid war as military actions that are carried out by combining militaristic, quasi-militaristic, diplomatic, informational, economic and other means in order to achieve strategic political goals. The specificity of this combination lies in the fact that each of the military and non-military methods of conducting a hybrid conflict is used for military purposes and is used as a weapon. The researchers note that hybrid warfare is not a fundamentally new type of violence, and its elements have been used by opponents in wars throughout the entire existence of mankind. "Hybridity" in this sense is understood as the complex application of various means and strategies of warfare – from information-psychological to purely military ones. Conclusions of the research.  Thus, hybrid war as a modern form of violence is aimed primarily not at the seizure of territories, but at mastering the public consciousness of the target country and at dominating its information and cultural field. The victory on the "information and cultural front" provides further economic and political dividends for the initiator of the hybrid war.

scholarly journals The Pivotal Meaning and Its Relationship with Derivation Al Tahqiq fe AlQuran Al-Kareem. A Sample (Scrutinizing Words in Glorious Quran: A Sample)

2018 ◽  
Vol 212 (1) ◽  
pp. 211-240
Author(s):  
Assist. Prof. Dr. Khamis Abdullah Al-Timimy. ◽  
Dr. Haider Shnawa Faisal Al-zaidi.
Keyword(s):  
New Type ◽  
Points Of View ◽  
The Difference ◽  
Central Meaning ◽  
Relationship Of ◽  
The Relationship

The Paper has tackled the pivotal meaning, its relationship with derivation, and its types. The paper starts with defining the pivotal meaning and the ways of its formation, then mentioning the difference between the pivotal meaning and central meaning with revealing the most significant points of view anciently and recently. The researcher has defined derivation mentioning the essential views that have said about it with providing on adequate exposure to Mustafawi's remarks concerning derivation and hid unique achievement in this field i.e. adding a new type of derivation which he calls "extractive derivation". The researcher has also tackled about the relationship of the pivotal meaning with types of derivation represented by: small, big, the biggest, and magnificent. Keeping in mind that derivation is a linguistic procedure which cannot be restricted in specific limits in addition to the fact that its relation with the pivotal meaning is divergent depending on the type of derivation. 

A test for the existence of tautologies according to many-valued truth-tables

1950 ◽  
Vol 15 (3) ◽  
pp. 182-184 ◽  
Author(s):  
Jan Kalicki
Keyword(s):  
Finite Number ◽  
Truth Table ◽  
Effective Procedure ◽  
Single Variable ◽  
Truth Values ◽  
Contraction Process ◽  
The One ◽  
Image Position ◽  
Truth Tables

Theorem. There is an effective procedure to decide whether the set of tautologies determined by a given truth-table with a finite number of elements is empty or not.Proof. Let W(P) be a w.f.f. with a single variable P and n a given n-valued truth-table with elements (values)Substitute 1, 2, 3, …, n in succession for P. By the usual contraction process let W(P) assume the truth-values w1, w2, w3, …, wn respectively. The sequencewill be called the value sequence of W(P).Value sequences consisting of designated elements of exclusively will be called designated; others will be called undesignated.All the W(P)'s will be classified in the following way:(a) to the first class CL1 of W(P)'s there belongs the one element P,(b) to the (t + 1)th class CLt + 1 belong all the w.f.f. which can be built up by means of one generating connective from constituent w.f.f. of which one is an element of CLt and all the others (if any) are elements of CLn ≤ t.For example, if N and C are the connectives described by a truth-table etc.Let ∣CLn∣ stand for the set of value sequences of the elements of CLn.

A theorem about infinite-valued sentential logic

1951 ◽  
Vol 16 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Robert McNaughton
Keyword(s):  
Logical Formula ◽  
Real Numbers ◽  
The Real ◽  
Truth Values ◽  
Sentential Logic ◽  
Usual Manner ◽  
Image Position

In this paper we shall use a logic with truth values ranging over all the real numbers x such that 0 ≦ x ≦ 1.1 will be “complete truth” and 0 will be “complete falsity.” The primitive sentential connectives are ‘⊃’ and ‘∼’; other connectives are ‘∨’ and ‘·’. Assume that ‘p’ and ‘q’ are sentential variables, whose truth values are respectively x and y. Then1.1. ‘p ⊃ q’ has the value min(1 − x + y, 1),1.2. ‘∼p’ has the value 1 − x,1.3. ‘p∨q’ has the value max(x, y), and1.4. ‘p·q’ has the value min (x, y).‘∨’ and ‘·’ can be defined as follows:It is the purpose of this paper to prove a theorem which will be stated in the next section. The following symbolism and convention will be used throughout the paper:S is a logical formula.ν (S) is the value of S.‘p’, ‘pi1, ’p2, …, ‘q’, are sentential variables.ν(p) = x and ν(x1) = x1, etc.ν(S) = σ and ν(S1) = σ1, etc.If S contains the sentential variables ‘p1’, ‘p2’, …, then we write for S, S(p1, P2, …). Also ν{S(p1, p2, …)) = σ(x1, x2, …).A logical formula is defined in the usual manner. 1. A sentential variable is a logical formula; 2. if S is a logical formula then ·S is a logical formula; and 3. if S and S′ are logical formulae then (S ⊃ S′) is a logical formula.

scholarly journals Observation of a New Type of Flare

1957 ◽  
Vol 10 (2) ◽  
pp. 319 ◽  
Author(s):  
RJ Bray ◽  
RE Loughhead ◽  
VR Burges ◽  
Marie K McCabe
Keyword(s):  
Maximum Intensity ◽  
Line Of Sight ◽  
The Sun ◽  
Observational Material ◽  
New Type ◽  
Points Of View

The importance of chromospheric flares from both the astrophysical and geophysical points of view is now generally recognized, but, in spite of the extensive observational material collected by Ellison, Dodson, and others, it must be admitted that the mechanism of their origin is still little understood. In this paper we present observations of a hitherto unobserved phenomenon, namely, the ejection of a mass of very bright material from a flare some 28� from the limb of the Sun. The ejection occurred several minutes before flare maximum. It was approximately 10,000 by 30,000 km in size and moved outwards with a velocity across the line-of-sight of 300 km/sec. As it did so, it brightened appreciably, reaching maximum intensity 3� min after expulsion, its height then being 25,000 km. The ejection was quite unlike the dark surge prominences often emitted from flares, and in fact, except for its motion, possessed all the properties of a small flare.

scholarly journals Imaginary World of Post-Byzantine Chronicle-Writing (The Case of the Ekthesis Chronica from the First Half of the Sixteenth Century)

2020 ◽  
Vol 48 ◽  
pp. 172-188
Author(s):  
Lev V. Lukhovitskiy ◽  
Keyword(s):  
Sixteenth Century ◽  
Distinctive Feature ◽  
Contemporary History ◽  
Imaginary World ◽  
Ottoman History ◽  
New Type ◽  
Points Of View ◽  
Chivalric Romances ◽  
The City

This paper addresses the Ekthesis Chronica (Ἔκθεσις χρονική), a Greek chronicle compiled by an anonymous cleric of the Patriarchate of Constantinople in the first half of the sixteenthcentury, which encompassed the events of the Late Byzantine and Early Ottoman history. Its distinctive feature is a recurrent alternation of seemingly mutually excluding points of view. Its neighboring chapters comply with the demands of different genres, accepting the set of values associated with them. The imaginary world of the chapters dealing with the events prior to 1453 reminds the reader of the heroic world of chivalric romances. The chapters describing the fall of Constantinople are may be read as a prosaic lamentation of the loss of the city which embodied the Byzantine civilization as a whole. In the post-Byzantine section, there appeared three approaches to the Ottoman rule over the Greeks. Whenever the chronicle-writer switches to the apocalyptic mode, the sultan becomes an infidel murderer of Christians. If, by contrast, he adopts the aretalogic (hagiographic) mode, the same sultan transforms into a philosopher on the throne. Finally, the pragmatic mode makes him a self-serving albeit sympathetic moderator in the conflicts inside the Patriarchate of Constantinople. The closer is the author to contemporary history, the more unfitting he feels the generic forms inherited from the age of the fall of Constantinople. Eventually, the chronicle-writer makes an attempt to create a new type of narrative with the characters on the foreground, which will allow his reader to feel empathy for them notwithstanding their language and faith.

Sign in / Sign up

Export Citation Format

Share Document