Logic

La descrizione generica delle condotte e degli stati di cose ai quali si applicano le norme risulta particolarmente
rilevante per valutare la completezza o l’incompletezza nonché la coerenza o l’incoerenza dei
sistemi giuridici. Il presente articolo intende discutere queste due questioni centrali della teoria del
diritto e le implicazioni di tale genericità. Si comincerà dall’analisi della struttura della norma in generale,
concentrandosi in particolare sulla genericità dell’antecedente. In seguito, dopo aver illustrato le
principali caratteristiche di tale proprietà, si valuterà il concetto di genericità come criterio per distinguere
tra regole e principi. Si passerà poi alla valutazione di tutte le norme in base alle rispettive condizioni,
sia per quanto riguarda l’(in)coerenza sia per quanto riguarda l’(in)completezza dei sistemi
giuridici. Confutata la chiusura logica dei sistemi, si illustrerà il ruolo fondamentale della rappresentazione
generica delle condotte da parte del sistema giuridico, come strumento per riferirsi (in maniera
contingente) a tutte le condotte concepibili. Infine, si illustreranno i punti di forza e di debolezza della
tesi dell’equivalenza pragmatica tra le non proibizioni e i permessi, in caso di silenzio del sistema. Anche
per quanto riguarda questo punto la genericità sembra ricoprire un ruolo importante. L’ammissibilità di
un’equivalenza pragmatica si tradurrà sempre nella regolazione più generica possibile, con implicazioni
sulla (e relative spiegazioni della) debolezza dei permessi da questa risultanti.

Analyzing the position of two philosophers whose views are recognizably divergent, W. O. Quine and M. Dummett, we intend to support a striking point of agreement between them: the idea that our logical principles constitute our principles about what there is, and therefore, that logic is metaphysics.

New computer languages have permitted formal verification of much of Mathematics(1,2). I asked to verify informal demonstrations such as in the natural and social sciences, where false conclusions sometimes propagate(4,5). I announce a program for crowd sourced formal verification of informal rational demonstration. TruthSift addresses a critical problem, deciding truth and publishing a transparent proof, for which the world has not previously had a good solution outside of mathematics. I prove: Theorem 1: In the limit where members bring to bear all
their pertinent knowledge, a statement will be rated TE by TruthSift if and only if there is an established proof of it to which no member has a remaining challenge. If it is not rated TE, there is an established proof of a disproof of it, or of every proof of
it. I predict crowd-sourced verification will lead to progress on wicked problems(3).

In this thesis, we will study the * embedding of classical first-order logic in first-order S4, which is based on the * translation, originally introduced in Fitting (1970). The initial, main part is dedicated to a detailed modeltheoretic proof of the soundness of the embedding. This will follow the proof sketch in Fitting (1970). We will then outline a proof procedure for a proof-theoretic replication of the soundness result. Afterwards, a potential proof of faithfulness of the * embedding, read in terms of soundness and completeness, will be discussed. We will particularly highlight the many difficulties coming with it. In the final section, we will relate this discussion to the debate on notational variance in French (2019). We will do this by showing how a weaker version of French's notion of 'expressive equivalence' conforms to the model-theoretic soundness result. We will then conclude that the soundness result without completeness might contain rather little overall insight by relating it to the extensibility of classical logic to S4.

Metalogik der Aussagenlogik 74 2.1 Objektebene vs. Metaebene 74 2.2 Logische Wahrheit . . 78 a) Definition 78 b) Das Substitutionstheorem 85 2.3 Logische Falschheit 87 2.4 Logische Folgerung 92 a) Synthetische Definition, analytische Definition, Explikation 92 b) ...

A \emph{standard formalization} of a scientific theory is a system of axioms for that theory in a first-order language (possibly many-sorted; possibly with the membership primitive $\in$). Patrick Suppes (\cite{sup92}) expressed skepticism about whether there is a ``simple or elegant method'' for presenting mathematicized scientific theories in such a standard formalization, because they ``assume a great deal of mathematics as part of their substructure''.

The major difficulties amount to these. First, as the theories of interest are \emph{mathematicized}, one must specify the underlying \emph{applied mathematics base theory}, which the physical axioms live on top of. Second, such theories are typically \emph{geometric}, concerning quantities or trajectories in space/time: so, one must specify the underlying \emph{physical geometry}. Third, the differential equations involved generally refer to \emph{coordinate representations} of these physical quantities with respect to some implicit coordinate chart, not to the original quantities.

These issues may be resolved. Once this is done, constructing standard formalizations is not so difficult---at least for the theories where the mathematics has been worked out rigorously. Here we give what may be claimed to be a simple and elegant means of doing that. This is for mathematicized scientific theories comprising differential equations for $\R$-valued quantities $Q$ (that is, scalar fields), defined on $n$ (``spatial'' or ``temporal'') dimensions, taken to be isomorphic to the usual Euclidean space $\R^n$. For illustration, I give standard (in a sense, ``text-book'') formalizations: for the simple harmonic oscillator equation in one-dimension and for the Laplace equation in two dimensions.

The evidence, which has been studied in this dissertation, is one of the essential instruments of criminal justice. The issue was limited to obtaining evidence, and the problems concerning to this issue have been specified and some suggestions for these problems have been offered.
Once the law of TCP (The Act of Turkish Criminal Procedure – 2005) 5271 numbered came into use and it provided some novelty to the evidence system in criminal justice. Thanks to the scientific and technical progress, lots of methods of collecting evidence such as biological evidence from living body and molecular genetics examines, recording private communication, observation by technical devices and secret investigation methods have been included in TCP. Some regulations were legislated for rules of evidence collection and they were made effective. The role of the public prosecutors in the criminal investigations became more effective to maintain fair trail and protect the rights of suspect.
The rule of rejecting indictment aims at collecting evidence in the prosecution stage faster and more effectively. And collecting methods of evidence have become more significant by the rule of cross examination.
However, still some evidence rules are existing in the other codes and this violates the unity of evidence rules. And the rule of “crime scene investigation” has not been identified completely in TCP. Despite some novelties brought by TCP, the constructions of prosecution and law enforcement units should be strengthened to apply this law efficiently.

Key Words: Evidence, Obtaining Evidence, Proofing, Criminal Evidence, the Law of Evidence.

ÖZET Bu makalede, klasik mantığın dayandığı temel sayılan ve akıl ilkeleri olarak bilinen özdeşlik, çelişmezlik ve üçüncü halin imkânsızlığının Platon'un eserlerindeki anlamı ve kullanımı analiz edilmektedir. Platon, özcü varlık anlayışından hareket eden, bu sayede doğru bilginin imkânını savunan bir filozof olarak, öğrencisi ve mantığın kurucusu Aristoteles'ten önce bu ilkeleri tanımlamış ve kullanmıştır. İdealar ve görüngüler âlemi olarak ayırdığı varlıkta, hakikati ideaların bir özelliği kabul eden Platon, özdeşliği bu aşkın varlıklardan hareketle temellendirmiş, sonrasında çelişmezlik ve üçüncü halin imkânsızlığı ilkeleriyle görüngüler âleminde var olan değişim problemine çözüm üretmeye çalışmıştır. Filozofun sisteminde idealar ve görüngüler arasındaki ontik ayrılık, yeniden hatırlama teorisiyle birleştirilerek, akıl ilkelerinin elde edilmesini ve uygulanmasını içine alan bütün epistemik süreçler tutarlı bir şekilde temellendirilmiştir. Bu çalışmada, öncelikle bu ilkelerin mahiyeti ve tanımı, Aristoteles ile kıyaslamalar yapılarak, ontolojik ve epistemik açıdan incelenmekte, sonrasında ise Platon'un eserlerindeki uygulamalarıyla örneklendirilerek ele alınmaktadır. ABSTRACT In this article, the principles of logic, identity, non-contradiction and the excluded middle, regarded as the grounds of classical logic, are analysed in the philosophy of Plato. As a philosopher, Plato, accepting the possibility of true knowledge from an essentialist ontology, both identified and used these principles before his student, Aristotle, namely the founder of classical logic. 

Our personal study of this topic cannot begin to satisfy the need.  We hope that is encourages others to begin their own eventful pilgrimages in this direction.  It is the blood of Christ, not our perfection of doctrine that saves us.  Be One.  Be well.

Page 1. A Parallel Genetic Algorithm for Rule Discovery in Large Databases Dieferson Luis Alves de Araujo' , Heitor S. Lopes', Alex A. Freitas2 CEFET-PR - Centro Federal de EducaGBo Tecnol6gica do Paranh CPGEI - Curso ...

We argue for a compositional semantics grounded in a strongly typed ontology that reflects our commonsense view of the world and the way we talk about it. Assuming such a structure we show that the semantics of various natural language phenomena may become nearly trivial.

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.

Andrzej Kisielewicz w książce Logika i argumentacja. Praktyczny kurs kry-tycznego myślenia proponuje, abyśmy radykalnie zmienili sposób nauczania logiki praktycznej. To nie podstawy rachunku zdań oraz rachunku kwantyfikatorów (w tym tradycyjne sylogizmy) powinny być wykładane w trakcie elementarnych kursów z logiki i myślenia krytycznego. Rachunki te są ważne, ale w matematyce i naukach pokrewnych. Ich powszechne wykorzystanie w dydaktyce to wielka pomyłka i wedle Kisielewicza ślepa uliczka. Powinniśmy uczyć logiki, która jest wyczerpującą analizą rozsądnych możliwości: wniosek wynika z przesłanek, jeśli nie ma innej rozsądnej możliwości. Powinniśmy myśleć możliwościami, a nie syn-taktycznymi regułami i schematami. Poniżej przedstawiam pięć komentarzy do książki Kisielewicza: 1. Przedstawiona wizja zmiany sposobu nauczania logiki praktycznej jest dobrym kierunkiem rozwoju logiki praktycznej. 2. Możliwościowe ujęcie logiki praktycznej jest de facto ontologizacją logiki. 3. Nauczanie logiki i myślenia krytycznego wymaga uzupełnienia technikami myślenia twórczego. 4. Krytyka logiki tradycyjnej i logiki formalnej przedstawiona przez Andrzeja Kisielewicza jest zbyt surowa. 5. Zdrowy rozsądek jest zwodniczy i utrwala myślowe koleiny, co nie sprzyja porządnemu myśleniu.

In this paper I comment on the theses presented in Andrzej Kisielewicz’s book entitled Logic and Argumentation. A Practical Course in Critical Thinking. The author argues that the current way of teaching practical logic is not good, because it is too much based on formal logic. It should be replaced by a  comprehensive analysis of reasonable possibilities. I demonstrate that Kisielewicz’s vision of changing the way in which practical logic is taught is a good one. I claim that
Kisielewicz proposed a kind of ontologization of logic. I argue that teaching logic and critical thinking need to be complemented by creative thinking techniques. I do not agree with the criticism of traditional logic and formal logic made by Kisielewicz and point out that common sense — so highly valued by Kisielewicz— is deceptive and does not encourage critical thinking.

This paper introduces and discusses three models of the linguistic representation of Future: a determinist model, a stochastic model and the model of True Prophetic knowledge. All three models coexist in natural languages and are represented both in their grammatical systems as well as in the text-building / discourse strategies speakers and authors apply to.

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.

Which is the relation between logic and philosophy of mind? This work tries to answer that question by shortly examining, first, the place that is assigned to logic in three current views of the mind: Computationalism, Interpretativism and Naive Naturalism. Secondly, the classical debate between psychologism and antipsychologism is reviewed –the question about whether logic is or not a part of psychology- and it is indicated in which place of such debate the three mentioned conceptions of mind are located.