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Aristotle‘s categories are presented as a system relying on logic and syntax instead of on meanings. His square of oppositions is found to be of crucial importance.
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Aristotle‘s categories are presented as a system relying on logic and syntax instead of on meanings. His square of oppositions is found to be of crucial importance.
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The aim of the paper is to reveal the epistemological pretensions and possibilities of the two general approaches to providing understanding of the strange behavior of the quantum objects. The first one is quantum logical, the other is theoretical-and constructive one. It has been shown that quantum logic based on the basic mathematical structure of quantum mechanics, the Hilbert space, demonstrates the empirical adequacy of this first theory about the micro-world. However, quantum logic refers to the empirical level of the behavior of quantum objects. It provides us with knowledge how they behave in different experimental situations, but remains silent about why they behave in this way, and not in another one. The latter knowledge could be principally reached through the theoretic-and-constructive approach. It exploits classical logic, but its results are non-classical theoretical models of quantum objects.
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Problem setting. The paper is the Part II of the large research, dedicated to both revision of the system of basic logical categories and generalization of the modern predicate logic to functional logic. Basic categories of functional logic are the following: an individual, a function, representation, and a sequence. Paper objective. The main task of the paper is to describe every one of the categories in question. The more expansive task of all the paper series is to expose the whole system of functional logic and to prove its advantagies.Recent research and publications analysis. Functional logic was discovered by the author in 1997, and there is no investigation in this field up today except of papers of the autor.Paper main body. An individual is any theoretical object regarded as atomic. Functions are regarded as ambiguous in general case, maybe nullary, and are treated as methods to represent some (any) objects. Most important types of functions are individuals’ functions (for example, arithmetic operations), functionals, and operators. Representation is the ultimate generalization of equality; we treat representation as any specification of an object, as a way to make it present. Fundamentals of the theory of representation are following: any individual can be represented either by itself as a function, or by a nullary function, or via other objects by a function with argument places. The corrected form (with respect to the Paper I) of representation formulas, i. e., atomic formulas of functional logic are involved. The form of terms that represents general names in formal languages of functional logic is present. Both these corrections use the machinery of choice functions, i. e., functions that “elect” one value of any ambiguous function in any case of its use. A sequence treated as a basic nondefinable logical notion. The nondefinability of the notion of a sequence will be proved in another paper. When we operate with individuals, functions, and representation, we structure them in sequences such that every latter has the first element and is discrete (and many of them also have the last element). Conclusions of the research. An individual and a function are relative categories because, first, when we start to talk about a function, it became an individual with the name “such and such a function” and, secondly, when an individual is represented by itself, it became a function. Also, categories of an individual, a function, representation, and a sequence are basic but not universal for logic, i. e., not every logical object is either an individual or a function or representation or a sequence. Say, semantical categories of an expression, a sense, and a denotation are independent of four described above. This means that we described above the field of logic, independent from semantics. The author calls this field (and its theory) logistics.
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The paper focuses on the relationship between the notions of modality and indexicality. First, it is demonstrated, on the one hand, how modalities are indexicalized and made relevant to a particular context and, on the other, how indices are modalized. The indexical expression “there” not only points to a place but also to the place as a desired place, or as a forbidden, or as a possible place, etc. And at the same time the desire, and the prohibition, and the possibility are contextually limited. In this sense, indexicality assures the association of context and modality. Second, the paper distinguishes between two types of indexicality. The first one is contextual indexicality where the indices point to a context. The second type is that of modal indexicality where the indices point to modalities. Finally, the paper shows how modalities can indicate other modalities.
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In Aristotle, substance, being specified in Z17 as cause and principle, is to be understood according to the analogical theory of principles and causes, namely form, matter and privation. These three causes involve potentiality and actuality, since form, privation, and the compound substance are in actuality, while matter is in potentiality. «What a substance is» depends on the connection between these three principles. In order to grasp the meaning of this connection, one has to put the analogical theory of principles back in its context, where previous theories on contraries (Plato’s theory included) are amended. The amendment of previous theories of principles relies on positing a third term, matter, between both opposites, i.e. form and privation. The implied distinction between matter and privation allows an understanding of generation which makes it compatible with substance. While generation removes privation, substance as form gives shape to matter, final matter and shape being identical to one another. Predication of matter by form supplies a relevant pattern for considering the relationship between matter, form and privation. At the same time, predication of matter by form provides both a renovated theory of opposites and a new theory of form as a cause, i.e. a theory of form as actuality.
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Aristote est l’inventeur de la notion de matière et de cause matérielle. Mais les passages où il parle d’une matière absolument première sont rares dans le corpus aristotélicien. Le problème, posé depuis longtemps par les interprètes modernes, est le suivant : Aristote croyait‑il à l’existence d’une matière imperceptible, sans forme et sans qualités, en tant que niveau autonome de la réalité, ou envisageait‑il plutôt la matière première comme un objet logique, un pur concept abstrait ? On se propose ici d’analyser le dossier des passages aristotéliciens les plus sensibles sur la question de la matière première et, après un rapide status quaestionis des interprétations antiques et modernes, on avancera une proposition interprétative selon la ligne «traditionnelle», à contre‑courant par rapport à la tendance actuelle.
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Porphyry’s Expositio per interrogationem et responsionem can help us to understand some obscure passages of chapter seven of Aristotle’s Categories, focused on the relative (πρός τι). The Porphyrian analysis of πρός τι presents indeed developments which are both useful for the understanding of the Aristotelian text and very innovative too. First, we can mention the general Porphyrian thesis according to which categories are predicates. This theory fits very well with πρός τι, which are predicates corresponding to properties that subjects only possess because of an observed reciprocal relationship. This brings us to the second novelty of Porphyry’s analysis, really important for modern developments of the notion of relation, namely the difference between σχέσις and πρός τι, which depends on it. Finally, we will mention the important Porphyry’s contribution to the understanding of a particularly obscure issue concerning the relationship between the two definitions of πρός τι that Aristotle provides. Porphyry points out the Platonic origin of the first definition, without dismissing it though: instead, he will just consider it too vast and encompassing the true πρός τι, object of the second definition.
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Problem setting. During the period of expansion of the practice of argumentation in society, thanks to the media, the theory of argumentation is also actively developing. In the process of interdisciplinary research and the influence of irrationalism, the problem of rethinking the rationality of argumentation, the conditions for its rationality to preserve the civilizational orientation of the development of modern society, arises.Recent research and publications analysis. At the present stage of development of the theory of argumentation, differences in the correctness and incorrectness of argumentation and proof are investigated, various concepts of the logic of argumentation, its role in communication, the rationality of the rules in argumentation as a characteristic of human rationality are proposed.Paper objective. The aim of the study is to reveal the reasons for the rationality of argumentation by analyzing the logical rules and values, their relationship in the construction of the structure of argumentation, the differences from the evidence.Paper main body. The rules for the structural elements of argumentation are divided into: rules of the thesis, rules of arguments and rules of demonstration. Arguments as bases in the structure of argumentation are connected with the thesis of causation. The logical rules of truth of implication establish a strict relationship between cause and consequence. Based on a certain rule, it is possible to obtain one or another logical value. It is in the peculiarity of causation that the difference in the argumentation in which it is modified lies. Modified argumentation changes the implicit connections. Logical rules and values are also implicitly related. If the logical meaning of truth in the traditional and classical sense represents the highest level of reason, which is identified with the perfect form, then the different derived values (probabilities, sufficiency, etc.) are associated with different types of rationality. An essential feature of rationality is the ability to justify. Rational reasoning related to speech contexts is crucial for argumentation. Contextual coherence and communicative nature allow us to generally determine the type of rationality of such an argument as discursive rationality. Different types of justification determine different types of rationality. The difference in the logic of argumentation appears as the difference in the conditions of the antecedent in implicit relations. The effectiveness of discursive rationality depends on the strength of judgments. The open nature of the argument means that there is no final rule; the rules are intersubjective; their establishment and choice requires strong-willed efforts and reflection, the involvement of the criteria of truth.Conclusions of the research. Analysis of modern research on the theory of argumentation shows a certain expansion of the possibilities of intelligent human activity in relation to the limited model of perfect pure reason according to the rules. But argumentation in its various forms is a rational activity connected with the logical criteria of truth. In this case, a significant difference between man as an intelligent being is justified through the awareness of rational activity that occurs according to certain rules.
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With the advent of algorithm-based decisions, generated in the “black boxes” of deep learning ensembles and their controversially discussed ethical and legal implications, the fact that human legal decision-making is to a large degree not based on rational choices, and thus also neither deducible nor predictable, tends to be neglected in legal discussion. This article intends to provide an overview on heuristic patterns in human legal decision-making by pointing out their flaws and benefits, and also provides some advice on how to hedge its risks in legal practice.
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To say that a philosophical dispute is ‘merely verbal’ seems to be an important diagnosis. If that diagnosis is correct for a particular dispute, then the right thing to do would be to declare that dispute to be over. The topic of what the disputing parties were fighting over was just a pseudo-problem (thus not really a problem), or at least – if there is a sense in which also merely verbal disputes indicate some problem, for example, insufficient clarity of terminology – this problem is not substantial, or not as substantial as the disputing parties believed their problem initially to be. In this paper I will try to clarify what it means if we diagnose that two arguing parties are having a merely verbal dispute.
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We frequently find ourselves in intractable disagreements about the morality of abortion, euthanasia, restrictions to freedom, or eating meat for fun. An adequate reaction to a disagreement requires knowing which type of disagreements we are confronted with. The main aim of my paper is to explain the source of moral disagreements and clarify their nature. I will argue that some moral disagreements are deep conceptual disagreements that similarly to disagreements in logic or ontology, are not resolvable, as the resolution of the disagreement requires the disputants to adopt perspectives that are conceptually unavailable to them. I will suggest four possible sources of moral disagreements: incommensurable fundamental values, different concepts of the good life, different motivating reasons and different concepts of morality.
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Scholars have long recognized the existence of myriad widespread deep disagreements on values, justice, morality, and ethics. In order to come to terms with such deep disagreements, resistant to rational solution, this article asserts the need for developing an ethics of disagreement. The reality that theoretical disagreements often turn into practical conflicts is a major justification for why such an ethics is necessary. This paper outlines an ethics of deep disagreement that is primarily conceived of as a form of virtue ethics. Such an ethics asks opposing parties in moral and intellectual conflicts to acknowledge that (a) deep disagreements exist, (b) opposing positions should be recognized as worthy of respect, and that (c) one should seek dialogue and mutual understanding. This ethical approach conceives of toleration as a moral and political virtue and presents an argument for toleration based on deep disagreements.
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Cognitive scientists used to deem reasoning either as a higher cognitive process based on the manipulation of abstract rules or as a higher cognitive process that is stochastic rather than involving abstract rules. I maintain that these different perspectives are closely intertwined with a theoretical and methodological endorsement of either cognitivism or connectionism. Cognitivism and connectionism represent two prevailing and opposed paradigms in cognitive science. I aim to extoll the virtues of connectionist models of enthymematic reasoning by the following means: (1) via the phenomenon of creative enthymeme, viz. the inference where one cannot even articulate the missing premise, I introduce a connectionist mechanism of pattern recognition as underlying expertise; (2) via Gestalt switch or Gestalt click, I demonstrate how differences in pattern recognition of an expert and a novice can be construed as qualitatively different, and not merely a matter of faster reasoning.
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Martin Gardner's two-children paradox posits two scenarios, in one we know that of two children one is a girl, and in the other we know that of two children the older one is a girl. The chances of the other child being a girl is not the same in these two scenarios, in the first being 1 in 3 while in the second they are 1 in 2. Gardner himself believed that the problem of this paradox lies in the ambiguous way the scenarios are articulated. However, it is possible to show that the original version of the paradox provides sufficient content for a meaningful explanation of these unexpected results. Inspired by comments by Leonard Mlodinow, we attempt to provide a comprehensible explanation for this counterintuitive change with help of Bertrand Russell's theory of descriptions. The difference between the two scenarios then boils down to the difference between indefinite and definite descriptions.
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The goal of this paper is to introduce the reader to the distinction between intensional and extensional as a distinction between different approaches to meaning. We will argue that despite the common belief, intensional aspects of mathematical notions can be, and in fact have been successfully described in mathematics. One that is for us particularly interesting is the notion of deduction as depicted in general proof theory. Our considerations result in defending a) the importance of a rule-based semantical approach and b) the position according to which non-reductive and somewhat circular explanations play an essential role in describing intensionality in mathematics.
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While the traditional logic reflected the structure of proposition assuming separation and persistence of concepts of subject and predicate, Hegel, by his conception of a speculative proposition, has allowed philosophy to grasp a dialectical nature of the relation of those concepts. The author considers the radical change that happens in the logical reflection of the essence of the proposition in the light of the crucial requirement of the whole Hegel’s philosophy to think and express the Absolute as the subject. After the introductory comments on the groundbreaking epochs in the history of philosophical thinking due to which the logical problem of proposition became one of the central ontological issues, the birthplace of Hegel’s theory of speculative proposition is found within his early critique of philosophies of the first principle such as Fichte’s. In the central part of the text, the theory of the speculative proposition is thematized considering Hegel’s insight into the difference between a philosophical proposition and propositions and knowledge that originate from the other spheres of spirituality. After that, the proposition that expresses the Absolute as the subject from the Preface of Phenomenology of Spirit is interpreted as the manifestation of the speculative nature of the philosophical proposition, because, from the other side, the speculative proposition could be interpreted as the expression and the way the Absolute exists, too. As the speculative proposition, however, the proposition “the Absolute is subject” reveals reasons why the philosophical system, not the isolated proposition, has to be understood as the true element of existence of truth in Hegel’s thought.
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In the wake of hundredth anniversary of Wittgenstein`s famous literary-philosophical debut, the world once again seems to be deeply occupied with the medical issues of planetary significance: therapeutic role of the Tractatus (also hinted by "New Wittgensteinian" interpretations) was, however, primarily concerned with the purification of human language by means of "ascendence" from logical to mystical view of experience − while it`s function in the latter writings is transfered to more extensive process of "detoxication" of human life itself, precisely from cummulative theoretic "side effects" of occidental "pharmakon" in the form of philosophy. After the exposition of central notions from both early and latter phase of Wittgenstein`s (anti-)philosophy, the focus will be shifted towards a sketch of possible interpretation which could complement the wittgenstanian "pharmacology of detoxication" with more positive vision of theory − which would, contrary to the relience on "self-regulating" power of opaque "forms of life", accentuate "self-transcending" capacity of reflexive language, particularly as an examplary mode of externalization of the dynamics of human life in the full scope of its complexity and creativity.
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Overall attitude towards the problem of language acquisition determines the choice linguistic research as such makes regarding the type of paradigmatic banner it will continue under. Before each science it is the logical itself that moves forward as the vanguard of scientific constitution, as the seed that will give rise to all the methodological dissemination within a given science. Therefore it is paramount to acquire clear and comprehensive insight concerning the core of this problem – inside the framework of linguistics. Author aims at isolating the very logical structure of language acquisition problem. Somewhat overlapping ways in which throughout literature the logical problem is being split asunder seem somewhat problematic.Confronted with such hardship author finds the synthesis for the nucleus of the problem’s structure – in the unavoidable circumstance of grammatically ambiguous positive evidence.
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In this research, the author tries to examine the role of Aristotle's Organon in the theological teachings of the Cappadocian Fathers. The aim of this paper is to show that the Cappadocian Fathers used Aristotle's notions of the first and second substance, in order to defend the original teachings of the church from the opposit teachings that were considered heretical. Even though Cappadocian theologians use philosophical notions in their work, this does not mean that they alienate from the original Christian teaching.
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