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1. The Paideia Archive: Twentieth World Congress of Philosophy: Volume > 8
Salah al-Fadhli Logical Foundation of Logic Programming
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2. The Paideia Archive: Twentieth World Congress of Philosophy: Volume > 8
Jean-Yves Béziau Do Sentences Have Identity?
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We study here equiformity, the standard identity criterion for sentences. This notion was put forward by Lesniewski, mentioned by Tarski and defined explicitly by Presburger. At the practical level this criterion seems workable but if the notion of sentence is taken as a fundamental basis for logic and mathematics, it seems that this principle cannot be maintained without vicious circle. It seems also that equiformity has some semantical features ; maybe this is not so clear for individual signs but sentences are often considered as meaningful combinations of signs. If meaning has to play a role, we are thus maybe in no better position than when dealing with identity criterion for propositions. In formal logic, one speaks rather about well-formed formulas, but closed formulas are called sentences because they are meaningful in the sense that they can be true or false. Formulas look better like mathematical objects than material inscriptions and equiformity does not seem to apply to them. Various congruencies can be considered as identities between formulas and in particular "to have the same logical form". One can say that the objects of study of logic are rather logical forms than sentences conceived as material inscriptions.
3. The Paideia Archive: Twentieth World Congress of Philosophy: Volume > 8
Katalin Bimbó Dual Identity Combinators
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This paper offers an analysis of the effect of the identity combinators in dual systems. The result is based on an easy technical trick, namely, that the identity combinators collapse all the combinators which are dual with respect to them. (Dual combinators were introduced in Dunn & Meyer 1997, a related system, the symmetric l-calculus was introduced by Barbanera & Berardi 1996.) After reviewing dual combinators I consider the possible combinatory systems and l-calculi in which the functions and/or the application operation are bidirectional. The last section of the paper shows the devastating effect the identity combinators have for a dual system: they half trivialize simple combinatory bases, although they are not sufficient to cause real triviality for what cancellative combinators are needed.
4. The Paideia Archive: Twentieth World Congress of Philosophy: Volume > 8
George Boger The Modernity of Aristotle’s Logical Investigations
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Not until the early 1920’s was it possible to distinguish Aristotelian or traditional logic from Aristotle’s own ancient logic. We can now recognize many aspects of his logical investigations that are themselves modern, in the sense that modern logicians are making discoveries that Aristotle had already made or had anticipated. Here we gather five salient features of Aristotle’s logical investigations that reveal a striking philosophical modernity: 1) Aristotle took logic to be that part of epistemology used to establish knowledge of logical consequence; 2) Prior Analytics is a metalogical treatise on the syllogistic deduction system; 3) Aristotle recognized the epistemic efficacy of certain elemental argument patterns, and he explicitly formulated them as rules of natural deduction in corresponding sentences; 4) Prior Analytics is a proof-theoretic treatise in which Aristotle describes a natural deduction system and demonstrates certain of the logical relationships among syllogistic deduction rules (Aristotle modeled his syllogistic logic in a rudimentary way for this purpose and metasystematically established the independence of a set of deduction rules); and finally, 5) Aristotle worked with a notion of substitution sufficient for distinguishing logical syntax and semantics. In this connection he also distinguished validity from deducibility sufficiently well to note the completeness of his logic.
5. The Paideia Archive: Twentieth World Congress of Philosophy: Volume > 8
Andrés Bobenrieth, Orellana Benado Carlos Verdugo Metaphilosophical Pluralism and Paraconsistency: From Orientative to Multi-level Pluralism
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In a famous passage, Kant claimed that controversy and the lack of agreement in metaphysics—here understood as philosophy as a whole—was a ‘scandal.’ Attempting to motivate his critique of pure reason, a project aimed at both ending the scandal and setting philosophy on the ‘secure path of science,’ Kant endorsed the view that for as long as disagreement reigned sovereign in philosophy, there would be little to be learned from it as a science. The success of philosophy begins when controversy ends and culminates when the discipline itself as it has been known disappears. On the other hand, particularly in the second half of the twentieth century, many have despaired of the very possibility of philosophy constituting the search for truth, that is to say, a cognitive human activity, and constituting thus a source of knowledge. This paper seeks to sketch a research program that is motivated by an intuition that opposes both of these views.
6. The Paideia Archive: Twentieth World Congress of Philosophy: Volume > 8
Vladimir Bryushinkin Metapsychologism In The Philosophy Of Logic
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The problem of psychologism in the philosophy of logic and the different solutions of this problem are considered. Both traditional psychologistic and antipsychologistic solutions are shown to be untenable and the need for a new solution is demonstrated. The original program of metapsychologism is advanced as a solution to the problem of psychologism based on deduction-search theory. Two formalized levels of a logical procedure are distinguished: 1) an object-level at which a notion of inference is formalized; 2) a metalevel at which principles of deduction-search are formalized, and a thesis of metapsychologism according to which metalevel processes are formulated. Metapsychologism lifts usual psychologist considerations one level up in the hierarchy of logical procedure, while a nonpsychologist justification of logical relations is kept at the object-level. The application of the thesis of metapsychologism to different concrete logical procedures is considered.
7. The Paideia Archive: Twentieth World Congress of Philosophy: Volume > 8
Mustafa M. Dagli Modus Ponens, Modus Tollens, and Likeness
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Modus Ponens (MP) and Modus Tollens (MT) are taught as basic rules of inference related to conditional statements in introductory logic courses. In ordinary reasoning, MP and MT can have important roles in modes of argumentation. However, one can also distinguish counter-examples to such reasoning patterns when considered as ‘strictly’ valid rules (i.e., McGee’s counterattacks for MP, and Adams’ criticisms of MT). I suggest that this problem can be resolved if we revise MP and MT as basic tools of logic, assuming the above-mentioned counter-cases are valid, on the basis of nonmonotonicity. If the only thing that we know is ‘Tweety is a bird,’ we say ‘Tweety flies.’ But, after learning ‘Tweety is an ostrich,’ we (change our minds and) say, ‘Tweety does not fly.’ In actual life, we use ‘rules of logic’ in a limited sense; when we learn new facts, we change some of our beliefs sometimes. The question arises, ‘In which situation, which exception does not violate which rule?’ When reasoning about something, we use some semantic patterns in order to make inferences, or for the sake of argumentation. Two reasoning patterns employed in ordinary life scenes concerning conditional statements will be identified as MP-like and MT-like. These will be exemplified and discussed. The general idea guiding this tableau will be stated as likeness.
8. The Paideia Archive: Twentieth World Congress of Philosophy: Volume > 8
Don Faust Conflict without Contradiction: Noncontradiction as a Scientific Modus Operandi
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We explicate the view that our ignorance of the nature of the real world R, more so than a lack of ingenuity or sufficient time to have deduced the truth from what is so far known, accounts for the inadequacies of our theories of truth and systems of logic. Because of these inadequacies, advocacy of substantial correctness of such theories and systems is certainly not right and should be replaced with a perspective of Explorationism which is the broadest possible investigation of potential theories and systems along with the realization that all such theories and systems are partial and tentative. For example, the position of classical logic is clearly untenable from the perspective of explorationism. Due to ignorance regarding R and, consequently, the partial and evidential nature of our knowledge about R, an explorationist foundational logical framework should contain machinery which goes beyond that of classical logic in the direction of allowing for the handling of confirmatory and refutatory evidential knowledge. Such a foundational framework (which I call Evidence Logic) is described and analysed in terms of its ability to tolerate substantial evidential conflict while not allowing contraditions.
9. The Paideia Archive: Twentieth World Congress of Philosophy: Volume > 8
Saul Fisher ‘Probabilist’ Deductive Inference in Gassendi’s Logic
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In his Logic, Pierre Gassendi proposes that our inductive inferences lack the information we would need to be certain of the claims that they suggest. Not even deductivist inference can insure certainty about empirical claims because the experientially attained premises with which we adduce support for such claims are no greater than probable. While something is surely amiss in calling deductivist inference "probabilistic," it seems Gassendi has hit upon a now-familiar, sensible point—namely, the use of deductive reasoning in empirical contexts, while providing certain formal guarantees, does not insulate empirical arguments from judgment by the measure of belief which we invest in their premises. The more general point, which distinguishes Gassendi among his contemporaries, is that the strength shared by all empirical claims consists in the warrant from experience for those claims we introduce in their support.
10. The Paideia Archive: Twentieth World Congress of Philosophy: Volume > 8
Joseph Grunfeld Haack On Fuzzy Logic
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Much of the progress in modern logic beyond Aristotle is due to the invention of a precise and powerful formalism, and this is why Haack is reluctant to weaken it. What motivates her to regard deviant and fuzzy logic as extensions rather than rivals of classical logic is its demonstrated capacity for refinement and progress. Thus she sharply distinguishes between a logic dealing with fuzzy concepts (she accepts), and one which is itself fuzzy, i.e., where "true" and "false" cease to be precise concepts (she rejects). While it is often more convenient to retain as much as possible of classical logic because of its simplicity and familiarity, there is nothing in the hermeneutical view of logic to render it immune from revision. Yet to treat logic as a canon of interpretation conflicts with Haack's idea of what logic is and does.
11. The Paideia Archive: Twentieth World Congress of Philosophy: Volume > 8
Arkadiusz Gut Two Types of Philosophical Analysis
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The aim of this paper is a comparative analysis of the Lvov-Warsaw School and Frege-Russell's tradition. The Comparison of these is made on the grounds of the analysis of existence. Choosing "existence" as the object of the analysis is very essential. It is so because understanding of the category of existence is strongly connected with the whole system. Thus, while analyzing the category, one can make a reconstruction of the concept scheme (in both traditions); show their functioning; and compare them to each other. It is easy to notice that in both these systems: a) analyzing is strongly connected with the way of expressing existence in a language, b) the essential problem is to which category existence belongs, c) the main question is whether existence is a predicate. Since the problem of analyzing—especially the problem of applying logic in philosophy—played an essential role both in Frege-Russell's system and Twardowski's school, the author of this paper wants to show how this was understood there (especially application of logic to some philosophical problems).
12. The Paideia Archive: Twentieth World Congress of Philosophy: Volume > 8
John Howes Faithful and Fruitful Logic
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Appropriate for a conference relating philosophy and education, we seek ways more faithful than the truth-functional (TF) hook to understand and represent that ordinary-language conditional which we use in, e.g., modus ponens, and that conditional’s remote and counterfactual counterparts, and also the proper negations of all three. Such a logic might obviate the paradoxes caused by T-F representation, and be educationally fruitful. William and Martha Kneale and Gilbert Ryle assist us: "In the hypothetical case in which p, it is inferable, on the basis that p and at least in the given context, that q." "Inferable" is explained. This paraphrase is the foundation of the logic of hypothetical inferability ("HI logic"). It generates the negative but non-TF device "hib" (= "there is a hypothetical-inferability bar against the conjoint proposition that"), followed by a bracketed conjunction. This is an enriched negative: "hib (p . -q)" is stronger than "-(p . -q)," and "-hib" ("dash hib" = "there is no h-i bar...") offers us "-hib (p . -q)," weaker than "p . -q." Thus equipped, we can test deductive arguments by the CI ("Compatible-orincompatible?") method explained, and explode paradoxes. The paraphrase, "hib," and the CI method are fruitful in training students to understand this conditional, and to demonstrate genuine validity or invalidity.
13. The Paideia Archive: Twentieth World Congress of Philosophy: Volume > 8
E.F. Karavaev Logic and Moral Dilemmas
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Logic is of great importance for the philosophy of education. In particular, logic provides a rational and critical approach in ethics, helping us understand the nature of moral dilemmas. Some suggest that all moral dilemmas result from some kind of inconsistency in the moral rules. Unsolvable moral situations simply reflect implicit inconsistencies in our existing moral code. If we are to remain moral as well as logical, then we must restore consistency to our code. This is accomplished by adding exception clauses to current principles, and giving priorities to some principles over others, or by some other device. I argue that we must accept moral dilemmas as an essential part of real-life reality on the grounds that some moral statements concern values. According to Moore's "axiological thesis," whether these statements are true depends on two factors: the set of alternatives from which we make an evaluation, and the scale of values with which we rate them. Also, it is possible that a given alternative is no better than another in some respect. Furthermore, there is no respect in which they are equally good or equally bad (the so-called "Condorcet's effect"). Thus, we must accept moral dilemmas as real rather than apparent.
14. The Paideia Archive: Twentieth World Congress of Philosophy: Volume > 8
S. L. Katretchko Between Logic and Heuristic
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This article aims to construct a new type of logical calculilogical heuristic calculus which contains the means of reducing complete search. Such a heuristic component of calculus is reached with the help of meta-level means. The principal means for reducing search is structural information about information about contrary literals of formula.
15. The Paideia Archive: Twentieth World Congress of Philosophy: Volume > 8
John Kearns Logic: An Empirical Study of A Priori Truths
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I distinguish a priori knowledge from a priori truths or statements. A priori knowledge either is evident or is derived from evident premisses by means of correct reasoning. An a priori statement is one that reflects features of the conceptual framework within which it is placed. The statement either describes semantic relations between concepts of the framework or it characterizes the application of the framework to experience and the world. An a priori statement is not necessarily part of anyone’s a priori knowledge. I also distinguish empirical knowledge from empirical statements. Both statements and theories are empirical if they are designed to characterize features of experience and the world. Knowledge is empirical if it fits experience; thus, one must check to see whether it fits. We do not obtain knowledge of logical systems by rational insight of evident truths and careful deductions from evident truths. Adequate logical systems are developed by trial and error. Logical knowledge is empirical knowledge that is not generally a priori. It is empirical knowledge of (some) a priori truths and principles of our conceptual systems. Logical systems are empirical theories of these truths and principles.
16. The Paideia Archive: Twentieth World Congress of Philosophy: Volume > 8
Patricia Morey, Sandra Vi Sokolskis Una Aparente Violacion del Principio de No Contradiccion: El Caso de Los Azande Nuevas Perspectivas
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The Principle of Non-Contradiction is one of the fundamental rules in the framework of rationality. As rational agents who avoid contradictions and logic, human beings follow this rule as a basic principle. The study of inconsistencies in natural, scientific and formal reasoning have threatened this view in the recent past, with the danger that relativism will lead to incommensurable, parochial and local knowledge. Evans-Pritchard's studies on magic, oracle and witchcraft among the Azande has prompted perennial discussion on the limits of the universality of classical logic. In this paper, we propose that with the aid of non-deductive logics — non-monotonic and logic of partial structures — it is possible to reformulate a rationality that more precisely describes natural reasoning.
17. The Paideia Archive: Twentieth World Congress of Philosophy: Volume > 8
Volodymyr Navrotsky Interval Description of Change
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This paper concerns a description of change in the framework of tense interval logic. The main goal is to present an approach to the construction of tense paraconsistent logic. Recent investigations show that moments are inapplicable to the study of the phenomenal continuums: for many kinds of the quality changes, any subdivision of existence time of an object does not separate clearly the state before change from the state after it. It is not possible to determine the last moment of the prior state and the first moment of the posterior one. So, the predicates of natural language are not valued relatively to the moment of time. I consider change as that occupying an interval of time which has fuzzy boundaries. The description of change consists in the conjunction of the descriptions of those states which overlap an interval of change. As a result such description contains inconsistent statements.
18. The Paideia Archive: Twentieth World Congress of Philosophy: Volume > 8
Sergey Pavlov Sentential Falsehood Logic FL4
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In some philosophical conceptions, statements are valued as true, false, senseless (neither true nor false), or inconsistent. Falsehood logic FL4 makes it possible to operate correctly by such statements. Logic with falsehood operator FL4 is formulated. For FL4 metatheorems of consistency, deduction and completeness are fulfilled. Correlation between falsehood logic FL4 and four-valued Belnap’s logic and von Wright’s truth logic T"LM is considered. In FL4, the implication for Belnap’s logic is defined so that the truth-valued matrix of it is characterized for logic of tautological consequences Efde. Correlation between three-valued falsehood sublogic FL3N of FL4 and three-valued Kleene’s logic and Lukasiewicz’s logic is considered. Lukasiewicz’s three-valued logic is functionally equivalent to FL3N logic. Correlation between three-valued falsehood sublogic FL3B of FL4 and three-valued paraconsistent Priest’s logic is also considered.
19. The Paideia Archive: Twentieth World Congress of Philosophy: Volume > 8
Leonid G. Kreidik, George P. Shpenkov Philosophy and the Language of Dialectics and the Algebra of Dialectical Judgements
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Subjective science, as a pattern of an objective science, is based on a dialectical triad: language-logic-philosophy, which is the language of dialectics. The first level of language is its grammar, whose basis constitutes lexemes (name-words) and lexas (relation-words). Dialectical logical factor sets (logical parts of speech) are the basis of dialectical logic and logical morphology. They form the second level of the language of dialectics. The logical factor sets are represented by dialectical forms of thinking, reflecting the contradictory nature of reality. In the first approximation, any face of a state or a phenomenon of nature has at least two sides of comparison. All variety of these sides are joined together by the common name oppositi. Dialectical philosophy is the third generalized level of language. The main qualitative postulates of dialectical philosophy constitute two postulates: a postulate of existence and a postulate of evolution. A simple description of an object of thought usually contains a statement and a judgment. In this paper, we consider the simplest meanings of judgments, namely, some dialectical combinations-judgments of Yes and No. Judgments are postulated on the basis of a material-ideal dialectical field.
20. The Paideia Archive: Twentieth World Congress of Philosophy: Volume > 8
R. Rodrigo Soberano Disarming Stove’s Paradox: In Defence of Formal Logic
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The argument (d) ("All arguments with true premises and false conclusions are invalid.") is an argument with true premises and false conclusion. Therefore "(d) is invalid" seems to be formally valid. Thus presumably formal logic has to admit it as valid. But then formal logic finds itself in a bind. For the above argument is problematic and even paradoxical since it involves an internal logical contradiction. The paradox, aptly termed "Stove's paradox," is fully realized by demonstrating with the help of symbolic logic the contradiction within the argument. Then as the main part of this essays shows, the paradox is attacked by exposing the paradox's genesis. It is shown that by appeal to some not so obvious logical considerations regarding sound linguistic construction and usage, the above argument could not have been legitimately construction. For its construction must have involved either equivocation or hiatus of meaningfulness in the use of the symbol (d).