Felsefi Düşün Issue:7 – Mantık / October 2016
Issue Editor: Yücel YÜKSEL (İstanbul Üniversitesi)
Please click on the name of any article for abstract and keywords
Abdurrahman ALİY (İstanbul Üniversitesi)
Abdülkadir ÇÜÇEN (Uludağ Üniversitesi)
Uğur EKREN (İstanbul Üniversitesi)
Mehmet GÜNENÇ (İstanbul Üniversitesi)
M. Ertan KARDEŞ (İstanbul Üniversitesi)
Cüneyt KAYA (İstanbul Üniversitesi)
Gamze KESKİN YURDAKURBAN (Kırklareli Üniversitesi)
Zekiye KUTLUSOY (Maltepe Üniversitesi)
Murad OMAY (İstanbul Üniversitesi)
Enver ORMAN (İstanbul Üniversitesi)
Güncel ÖNKAL (Maltepe Üniversitesi)
Cahid ŞENEL (İstanbul Üniversitesi)
İskender TAŞDELEN (Anadolu Üniversitesi)
Ahu TUNÇEL ÖNKAL (Maltepe Üniversitesi)
Reconsideration of Kantian Geometry Perspective After the Rise of Non-Euclidean Geometries
Kant claimed that geometric judgements are synthetic a priori judgements in his Critique of Pure Reason and Prolegomena. As is known that, Kant’s all references to geometry are rest on Euclidean Geometry. According to Kant, Euclidean Geometry is the only valid geometry when human experience is considered. This is because Euclidean Geometry is a structural feature of human reason. With the proof of the existence and consistency of Non-Euclidean Geometries in the nineteenth century, the truth and validity of Euclidean Geometry, which is the only valid geometry for approximately two thousand years, has been questioned. This questioning has a broad repercussion in not only mathematics but also in philosophy. Especially analytic philosophers considered the proof of the existence and consistency of Non-Euclidean Geometries as a counter argument for the Kantian Geometry Perspective. In fact, according to them Non-Euclidean Geometries has destroyed the legitimacy of Kant’s argument. In this article firstly I will focus on Kant’s special use of synthetic a priori judgements and then I will focus on the relation between object and space with respect to Euclidean and Non-Euclidean objects. By this way, I will try to show that there is no contradiction between the Non-Euclidean Geometries and the claim of Kant that is ‘geometric judgements are synthetic a priori.’
Keywords: Kant, Euclidean space, non-Euclidean Geometries, non-Euclidean Spaces, synthetic a priori judgements.
Systems of Strict Implication
The aim of this article is investigate to Clearence Irwing Lewis’ ‘systems of strict implication’. For this purpose, developments which play role for the emergence of the system (S1, S2, S3, S4 ve S5) offered by Lewis are examined. To do this, firstly, it will be notified an explanation with truth condition of ‘material implication’ which is passed in Principia Mathematica writen by Alfred North Whitehead and Bertrand Russell. Subsequently, the relation between ‘the systems of strict implication’ which is passed in Symbolic Logic written by Lewis and Cooper H. Langford and ‘material implication’ will be analyzed ligthing history of modal logic. Secondly, ‘systems of strict implication’ which is presented as an alternative instead of ‘material implication’ by Lewis, will be addressed as syntactic. In the conclusion third part, the focus moves on the interpretation offered by Lewis and its effects on history of modal logic. Thereby, the bond between ‘systems of strict implication’ and ‘material implication’ will arise. In the last instance, the point that the idea of Symbolic Logic brings us will be highlighted by showing how syntactic developments in the field of symbolic logic interoperability with modal logic via Lewis’ criticism of Principia Mathematica.
Keywords: modal logic, lewis, strict implication, material implication, syntax
‘Infinite Names’ in Aristotle Logic
To categorize of names or concepts in formal logic, especially of positive and negative concepts, bring about a major problem. A fundamental ontological structure of Aristotelian logic or still be connected to Aristotle’s metaphysics is an important factor. Because, when the name receives negative words in some language, whether it is a negative name or not, there is not fully understood. In addition, there is another problem about negated names since we can’t know whether these names contradictory or contrary terms. For example, ‘tree’ (ağaç) is a positive name in Turkish and when asked to negation, whether this should be ‘non tree’ (ağaç-olmayan) or ‘not tree’ (ağaç değil) that is unknown. Here, in On Interpretation Aristotle suggest to solution on this problem. So, Aristotle has called and categorized the word like ‘ağaç-olmayan’ as ‘infinite names’ and as a result he has created two kind of names: name and infinite name. As a Peripatetic one, Avicenna and Thomas Aquinas using contextual and formal criteria have called ‘privative name’ for the word like ‘blind, spotless, lazy’. Privative names signify an absence and these names are different from the other.
Keywords: name, Aristotle, infinite name, contradictory, negative, privative name, On Interpretatione
Pure Intuition, Formal System, Turing Machine and Frege’s Concept-writing
The aim of this investigation is a consideration, in a historical context, of the first phase of Gottlob Frege’s Project of reducing arithmetic to logic, that is, the development of an ideography to represent number in the ordinal sense. In this article, to provide a context for interpreting this phase of Frege’s project, two separate investigations are carried out: firstly, Immanuel Kant’s view of pure intuition and his project of constructing mathematical objects in pure intuition are evaluated; secondly, the project of a number of mathematicians and philosophers of developing formal systems as a sequel to Frege’s concept-writing to represent mathematical proofs in a rigorous manner is presented. A positioning of Frege’s project in view of its predecessors and pursuers provides us grounds to make a critical assessment. The initial phase of Frege’s project of reducing arithmetic to logic comprises the construction of a formal system within which the concept of ordering (in a sequence) can be rigorously represented. Frege desires in this way to constitute a medium into which nothing intuitive penetrates in an unnoticed manner. Nevertheless, since the constitution of such a medium requires the treatment of units successively, the existence of a relation of succession or subordination should be assumed at the outset. That is to say, a formal system relies on subordination of its elements for its proper constitution. Therefore, Kant seems to be right when he claims that the number (the schema of number) should be presupposed in each and every activity of quantitative construction. In a way Frege’s project of reducing arithmetic to logic seems to work at its outward appearance involves some circularity. A formal system constructed to represent all the true propositions of arithmetic rests on number itself and its order in an ontological sense. In other words Frege’s system is subject to an ontological circularity.
Keywords: Kant, Frege, Hilbert, pure intuition, formal system, concept-writing, Turing Machine.
Logic and Logical Space in The Critique of Pure Reason
The present paper addresses how the relationship, which is established between logic and ontology throughout the history of philosophy, is responded by Kant, and how it is radically transformed during the period of the Critique of Pure Reason. In pre-critical period, Kant adheres to the Leibnizian version of the conception which considers the principles of being and the principles of logic together and on the same level. In this version, the principle of non-contradiction and the principle of sufficient reason were considered not only as the supreme principles of thought but also of being. In the pre-critical period, when Kant talks about ‘allness’ and ‘totality’ he addresses them as being in itself, in the sense that being has real connections with God. In the Critique of Pure Reason, this perspective totally changed. In his conception of transcendental logic, Kant disconnects the strong link that the traditional metaphysics established between logic and ontology by reframing the ‘unconditional’ and ‘totality’ in the reason and allness (or ‘logical space’) in the understanding. Kant states that when he talks about totality of the facts he does not talk about reality in itself but about the way, the reason conceives reality. To talk about ‘totality of facts’ at this level is to talk about them at the transcendental level. When we talk about ‘totality of facts’ in terms of general logic, falling in antinomies is inevitable. In sum, to talk about ‘totality of facts’ is not talking on the facts, it is talking about the ‘I’ and the acts of the reason. It is here the whole critique of ‘the metaphysics of presence’ is embedded.
Keywords: Kant, totality, allness, logical space, God, transcendental logic.
Basic Debates In Philosophy of Logic
The target of this paper is an inquiry on philosophy of logic. Despite having an exact execution, in the field of logic there are deep philosophical problems concerning epistemology and ontology. In this paper, it is first aimed to exhibit the scope and the extent of philosophy of logic. Related with this aim, logic is divided into three periods. First period is the intrinsic logic period, second one is the primitive logic period and the third one is the systematized logic period. In the systematized logic period, logic appeared as an independent and whole discipline. Most of the discussions within philosophy of logic are held at his period. After historical aspects of logic, common philosophical debates about logic are expressed. Definition of logic is such philosophical debate on logic. It is shown in the paper that there are several conception of logics. Then, other disputes about logic are expressed as conceptions of ‘reasoning’, ‘validity’ and foundation of principles of logic. Finally, the theories of truth are stated regarding their criticism.
Keywords: Logic, Philosophy of Logic, validity, Principles of Logic, truth.
Explication of Charles Sanders Peirce’s First Paper on The Logic of Relatives
Charles Sanders Peirce who is one of the most original and productive logicians of the nineteenth century is the founder of logic of relations. Two volumes of his Collected Papers which was gathered after his death consists of his writings on logic. In this work we tried to explicate his first paper on the logic of relations which was written in 1870 and which takes place in volume 3 of his Collected Papers. Peirce, first of all, introduces De Morgan’s notation and states that this notation can be used outside the logic of absolute terms. Then after emphasizing that the relation of inclusion is a transitive relation he gives definitions and properties of equality, addition and multiplication operations. Here Peirce distinguishes between normal multiplication and the multiplication of functions. He also defines exponentiation, subtraction, division, taking root and logarithm. He says that there are three kinds of terms in the logic of relations which are individual terms, infinitesimal relatives and elementary relatives. Afterwards he gives the general formulas about the logic of relations. Eventually he classifies elementary relatives in different ways. Since Peirce had created many new terms in his essay we gave these terms and their Turkish equivalents in a vocabulary at the end of this work.
Keywords: Charles Sanders Peirce, Augustus De Morgen, logic of relations, relative.
Anti-Althusser or On Idealism In Marx’s Grundrisse
The purpose of this study is to illustrate that Marx’s conception of method is different from the traditional understandings of method in empricism and emprical science, and that it is beyond these, and that, in fact, in the strict meaning of the term its origins can be found in Hegel’ concept of the speculative logical method and also in Hegel’s philosophical system as such. The basic mistake of the traditional Marxism in the approach to Hegel springs from the attempt to differentiate Hegel’s speculative logical method from his philosophical system. What is aimed at or intended by means of this differentiation is to liberate the dialectical logical method from its so-called idealistic fetters and to establish a dialectical method which has powerful relations with philosophical materialism. If it is understood as is due, it will be seen that the famous inversion of Hegel ‘on his feet’ does not automatically lead to ‘dialectical materialism’ by replacing ‘matter’ with ‘idea’ as the subject-matter of dialectical method. Rather, by doing so, it will be understood that the critique of political economy results in the justification of the ‘Idea’ or Hegel’s speculative logical method.
Keywords: method, logic, speculative logical method, dialectical method, Idealism, Materialism.
‘Critique’ of Principles of Formal Logic and Contradiction
Thinking that, with Kant, metaphysics has entered into the process of changing into logic, Hegel tries to develop a new logic which includes categories which are the determinations of thought as well as of being. He regards dialectic as an indispensable moment of this logic and thus gives contradiction an important role in his logic. This appears as an attempt which is impossible to reconcile with the formal logic, just because the principles of identity, non-contradiction and the excluded middle, which are the principles of formal logic, are formulated for eliminating contradiction itself. Hegel in fact attacks these principles of the formal logic in some respects and it seems as if he denied their truth. However, Hegel’s position in this topic cannot be considered as mere denial or mere affirmation by nature of his dialectical logic. This article will try to show on which grounds Hegel criticizes the principles of the formal logic and why he gives contradiction an important place in his logic. Furthermore, we will shortly stress on the connection between Hegel’s conception of dialectic and his absolute idealism.
Keywords: Principles of formal logic, Hegel, dialectic, contradiction, method.
Stumpf and Husserl on State of Affairs (Sachverhalt): In The Wake of Brentano’s Theory of Judgment
‘State of affairs’ makes its first appearance as a philosophical concept in the Austro-German world of the 19th century. Rooted in the thoughts of Franz Brentano and Bernard Bolzano, as it might seem at the start, a closer inspection can show, however, that its origin goes way back to Aristotle and Latin Law tradition. The first section of the present article dwells briefly on this historical background of the concept. In the subsequent section, then, Carl Stumpf’s approach to ‘state of affairs’ is examined, since it was Stumpf’s usage of the term which made a considerable impact on the younger philosophers of the generation. It will be argued that Stumpf’s view is deeply connected with Brentanian premises. That there is a serious paralellism between Brentano’s understanding of ‘content of judgment’ and Stumpf’s understanding of ‘state of affairs’ will also be shown in this second section. One important consequence to be drawn from this paralellism would be that for both philosophers ‘a state of affairs’ can be considered to be a mind-immanent object or an abstract concept. The third section concerns Husserl’s objectivist interpretation of ‘state of affairs’ and presents it as an alternative to the subjectivist direction taken by Brentano and Stumpf. Contrary to Brentano and Stumpf, by ‘state of affairs’ Husserl means the ‘objective correlate’, and not the ‘content’ of judgment.’ From this it follows that Husserl here makes use of a novel distinction ignored by Brentano and Stumpf, namely the distinction between i- “proposition as the sense of the expression” and ii- “state of affairs as the reference of the expression”. Nevertheless, contrary to the established philosophical custom, Husserl also defends the thesis that something can be ‘objectively’ referred to not only on the nominal, but also on the propositional level, and he names the propositional reference ‘state of affairs’.
Keywords: state of affairs, fact, judgment, sense, reference, proposition, Franz Brentano, Carl Stumpf, Edmund Husserl.
An Epistemological Objection Against Induction
Induction is known as a problem, a logic method, or a way of reasoning that attracts the attention of philosophers and scientists. It means making inferences from the facts, which we have experienced; for the facts, which we have not experienced yet. Induction is mostly accepted as inferences that do not include any skepticism by philosophers and scientists; and its epistemological position is controversial. In this study, induction will be examined in the scope of David Hume’s philosophy because of its epistemological position, not in the scope of the principles of logic.
Hume has been thought as a radical skeptic about induction in the history of philosophy. In the background of this idea, there is an argument that we have no reason in justification of inductive inferences and of beliefs with regard to them, or inductive inferences have no foundation. This argument of Hume reveals that induction has no epistemic value. This result is a skeptic result, and it shows that Hume deals with induction in a skeptical and epistemological way. In this study, after the epistemological objection of Hume about induction is examined, it will be claimed that this objection is in fact a skeptical objection. This claim will be supported with the ideas of Hume on inductive inferences and the nature of these beliefs.
Keywords: Hume, induction, reasoning, probability, belief.
Hans Reichenbach’s Probability Logic
Hans Reichenbach has been one of the founders of logical positivism and also one of the most seminal figures in the philosophy of science of the twentieth century. Reichenbach’s works on probabilistic logic, in particular, adress the issue of the application of probability statements to reality, as well as the relationship between probability and causality. Also these works have been at the core of his research throughout his life. After having put forward his views on probability logic, Reichenbach had to face a lot of difficulties and criticism from defenders of two valued logic. Regardless of all of that criticism, Reichenbach’s foresight about this new logic proved to be true and probabilistic logic played a functional role in Quantum mechanics. Especially after the developments in Quantum mechanics, Reichenbach took a very important step in regards to the testability of scientific statements and he made substantial contribution to this field because of his own rules of probability logic. Reichenbach made a correlation between Heisenberg indeterminacy principle and the view that probabilities have upper limits. This article outlines the main traits of Reichenbach’s views on probability logic, with special reference to his books Philosophic Foundations of Quantum Mechanics and The Theory of Probability.
Keywords: Hans Reichenbach, Probabilistic Logic, induction, causality, Heisenberg Indeterminacy Principle.
In our previous study called as “Some Determinations on Truth Tables”, we have comprehensively studied truth tables and validity examination method which are applicable by the assistance of the truth tables that is not seen as a research subject and lectured in an almost standardized order by many of the logicians. We have also suggested a few propositions which provide simplicity in the application of these processes. In this study, we have planned to share new determinations which ease the processes on the same subject. But first of all, we are going to repeat some of our suggestion in the mentioned article as a brief, and then we will mention new processes, is built on the suggestions in our previous study in order to clarify the understanding on the subject. For this we should follow this path: First of all, we will show the contingent truth conditions and the new spelling format which we suggest in order to express these more simply. Afterwards we will suggest a formula by which we can determine the truth column of any proposition in a universe of discourse (provided that the array number is known) independent of the truth columns of other propositions. In the last part of the essay we will explain how the truth table method which is used for testing the validity and consistency of propositions can be used in a universe of discourse with ‘n’ number of propositions; we will do this with the help of arithmetical operations used only in two-valued logic but which we designated from arithmetical operations used in multi-valued logics.
Anahtar Kelimeler: truth tables, fundamental truth series, multi-valued logic, arithmetical operations for two-valued logic, simulation operations..
Turkish translation of “ New Operations on Truth Tables”