Throughout this paper, we are trying to show how and why our Mathematical frame-work seems inappropriate to solve problems in Theory of Computation. More exactly, the concept of turning back in time in paradoxes causes inconsistency in modeling of the concept of Time in some semantic situations. As we see in the first chapter, by introducing a version of “Unexpected Hanging Paradox”,first we attempt to open a new explanation for some paradoxes. In the second step, by applying this paradox, it (...) is demonstrated that any formalized system for the Theory of Computation based on Classical Logic and Turing Model of Computation leads us to a contradiction. We conclude that our mathematical frame work is inappropriate for Theory of Computation. Furthermore, the result provides us a reason that many problems in Complexity Theory resist to be solved.(This work is completed in 2017 -5- 2, it is in vixra in 2017-5-14, presented in Unilog 2018, Vichy). (shrink)

This paper considers whether universally—for all (known) rational beings—an argument scheme or pattern can go from being cogent (well-reasoned) to fallacious. This question has previously received little attention, despite the centrality of the concepts of cogency, scheme, and fallaciousness. I argue that cogency has vanished in this way for the following scheme, a common type of impersonal means-end reasoning: X is needed as a basic necessity or protection of human lives, therefore, X ought to be secured if possible. As it (...) stands (with no further elaboration), this scheme is committed to the assumption that the greater the number of human lives, the better. Although this assumption may have been indisputable previously, it is clearly disputable now. It is a fallacy or non sequitur to make a clearly disputable assumption without providing any justification. Although this topic raises critical issues for practically every discipline, my primary focus is on logical (as opposed to empirical or ethical) aspects of the case, and on implications for practical and theoretical logic. I conclude that the profile of vanishing cogency of the scheme may be unique and is determined by a peculiar combination of contingent universality and changing conditions. (shrink)

Öz: Frege özel adların (ve diğer dilsel simgelerin) anlamları ve gönderimleri arasında ünlü ayrımını yaptığı “Anlam ve Gönderim Üzerine” (1948) adlı makalesinde, bu ayrımın önemi, gerekliliği ve sonuçları üzerine uzun değerlendirmeler yapar ancak özel adın anlamından tam olarak ne anlaşılması gerektiğinden yalnızca bir dipnotta kısaca söz eder. Örneğin “Aristoteles” özel adının anlamının Platon’un öğrencisi ve Büyük İskender’in öğretmeni ya da Stagira’da doğan Büyük İskender’in öğretmeni olarak alınabileceğini söyler. Burada dikkat çeken nokta örnekteki özel adın olası anlamları olarak gösterilen belirli betimlemelerin (...) de özel ad içeriyor olması. Anlamın Frege için bileşimsel olduğu, bir başka deyişle bir dilsel simgenin anlamının (varsa) parçalarının anlamlarınca belirlendiği düşünülürse, örnekteki belirli betimlemelerin anlamlarının saptanabilmesi için içerdikleri özel adların da anlamları saptanıp betimleme içinde geçtikleri yere konmalıdır. Bu işlem hiçbir özel ad kalmayana kadar sürdürülmelidir. Ancak biraz düşünülünce bir özel adın nesnesini tekil olarak betimleyecek ve içinde özel ad geçmeyecek bir betimleme bulmanın kolay olmadığı görülür. Örneğin yukarıdaki betimlemelerde geçen “Platon”, “Büyük İskender” ve “Stagira” gibi özel adların anlamları olabilecek ancak özel ad içermeyen betimlemeler bulmak pek kolay görünmüyor. Ortaya bir sonsuz gerileme sorunu çıkmış gibi duruyor. Frege’nin anlam-gönderim ayrımını için ciddi sonuçları olabilecek bu sorunu Frege çözebilir mi? Bu yazıda bu sorunun yanıtını arayacağım. Sorunu betimledikten sonra Frege’nin önündeki seçenekleri (örneğin bağlama duyarlı terimlerden (gösterme adılları veya belirteçler) yararlanma veya bağlamı sınırlama gibi) değerlendireceğim. -/- Abstract: In his “Sense and Reference” (1948), Frege makes his famous distinction between the sense and the reference of a proper name (and other signs) and discusses at length the significance, necessity and consequences of the distinction, but he explains how the sense of a proper name should be understood very briefly in a footnote. According to him, for example, the sense of the proper name “Aristotle” can be taken as the pupil of Plato and teacher of Alexander the Great or the teacher of Alexander the Great who was born in Stagira. What is interesting here is that the definite descriptions given as the possible senses of this proper name do themselves contain proper names too. Since the sense is something compositional for Frege, which means the sense of a linguistic sign is determined by its constituents (if there are any), in order to determine the sense of definite descriptions in question, we should first determine the senses of proper names they contain and substitute these senses with the proper names themselves. This process should continue until no proper name remains. However, it does not seem easy to find a definite description which describes the object of a proper name uniquely but contains no proper name itself. For instance, could we find appropriate senses that contain no proper name for “Plato”, “Alexander the Great” and “Stagira”? It does not seem likely. A problem of infinite regress appears to arise. Can Frege solve this problem, which poses a serious threat for his sensereference distinction? I will explore this problem in this paper. After explaining the problem, I will discuss the options (e.g. turning to indexicals or context restriction) Frege can take to deal with it. (shrink)

Philosophers like G.H. von Wright and D. Makinson have pointed to serious challenges regarding the foundations of deontic logic. In this paper, I suggest that to deal successfully with these challenges a reconsideration of the research program of the discipline is useful. Some problems that have troubled this particular field of logical study for decades may disappear or appear more tractable if we view them from the perspective of a language game introduced by D. Lewis involving three characters: the Master, (...) the Slave and the Kibitzer. The adoption of this perspective opens a natural approach to a new layout of the domain of deontic studies. I propose dividing deontic logic into six sub-areas which are distinguished by their focus on the different idioms typical of the individual players, by conceiving the language game as either being static or as dynamic and by the aims of the logical inquiry. What kind of insights the proposed perspective provides is illustrated by an analysis of the so-called Ross paradox—a problem that has troubled deontic logic since its origins and, though it was many times pronounced solved, still keeps coming back ‘alive and kicking’. (shrink)

On the face of it, normative conflicts are commonplace. Yet standard deontic logic declares them to be logically impossible. That prompts the question, What are the proper principles of normative reasoning if such conflicts are possible? This paper examines several alternatives that have been proposed for a logic of 'ought' that can accommodate normative conflicts, and finds all of them unsatisfactory as measured against three criteria of adequacy. It then introduces a new logic that does meet all three criteria, and (...) so allows for the possibility of genuine normative conflicts. (shrink)

RESUMO De acordo com a teoria das funções de verdade, a verdade/falsidade de uma proposição é computável a partir da verdade/falsidade das suas proposições “internas”: para cada proposição há uma função entre valores de verdade. Aplicada a proposições modais, origina a semântica dos mundos possíveis e, aplicada a proposições normativas, origina uma semântica que reduz os conceitos normativos aos conceitos modais, a semântica modal. Esta redução fica posta em questão com a existência dos chamados ‘paradoxos da lógica deôntica’. Estes não (...) podem ser vistos como meras anomalias, mas devem ser vistos como indícios da incorreção da semântica modal. Em todos eles, a regra da necessitação, assim como o axioma da distribuição, “não batem certo”. Não obstante, o cumprimento/incumprimento das normas já é computável a partir da verdade/falsidade das proposições que expressam os estados de coisas devidos. ABSTRACT According to the theory of truth-functions the truth/falsehood of a proposition is computable from the truth/falsehood of its “internal” propositions: for each proposition there is a function between truth values. Possible world semantics arises from the application of that theory to modal propositions; modal semantics - the reduction of normative concepts to modal concepts - arises from its application to normative propositions. But the ‘paradoxes of deontic logic’, as they are called, undermine such reduction: they cannot be seen as mere anomalies but instead as evidence for the wrongness of modal semantics. In all these paradoxes, the necessitation rule, as well as the distribution axiom, fail. Nevertheless, the fulfillment/nonfulfillment of norms is computable from the truth/falsehood of the propositions which express the required states of affairs. (shrink)