Modality in Classıial Logic: Explaining the Operations in Modal Propositions and Modal Syllogisms and Representing them with Symbols
Abstract
Expression of propositions with words that express necessity, continuity, possibility and actuality constitutes modal propositions. Modal syllogisms are also obtained by using these propositions in syllogism. The subject of modality is accepted as one of the most important subjects of logic and it has important results in philosophy and theology. The most general concepts related to existence, such as necessity, possibility and impossibility, which form the basis of the subject of modality, became the subjects which discussed at the Islamic philosphy and kalam books under the title of general things (umûr-u âmme) over time. Many philosophical and theological problems are somehow related to these most basic concepts. However, modality is rather concerned with the nature of the judgment given on an issue, that is, the quality of the relationship between the subject and the predicate, or how it is expressed in the proposition. The first of these corresponds to the substance of the proposition and the second to its modality.
Modality is a literal record attached to the predicate of the proposition and indicates the manner in which the predicate in the proposition is attributed to the subject. In this context, all the words that determine the relationship of the predicate with the subject are modalities, and a modal proposition is a new judgment given upon the judgment. In modal propositions, if the modality of the proposition is in accordance with its article, that is, the truth the proposition is true; if its modality does not comply with its article, that is, it does not comply with the truth and the proposition is false.
Logicists make some determinations about the provisions of any modal proposition, such as rotation and contradiction. For example, they say that the contradiction of a mandatory proposition contains possible meaning. When it comes to the rotation it means actuality at some times in the positive ones and means continuation of the essence in the negative ones. They also set some rules for modal syllogisms. For example, the small premise in the first and third figure and both premise in the fourth figure can not be a possible proposition. They talk about many more principles and rules like this. Of course, these rules are not accepted just because logicians say so. Each rule has been elaborated and proved by various methods.
The logicians also have not determined these rules randomly. Naturally, these rules have not been accepted as correct just because logicians deem it appropriate. Each of them has valid, proven reasons. In this article, these results were discussed and explained in their context. The structures of modal propositions, their meanings, their relationships with each other, and the rules regarding their use in syllogisms have been explained. Indeed, some of the mistakes made in thinking have the effect of ignoring the rules regarding which type of syllogisms can yield results in which modality, depending on the modality of the propositions. These rules were carefully created by logicians. For example, in any syllogism, depending on what form this syllogism is and what modality of propositions it consists of, they set principles regarding in which cases the conclusion is the same as the modality of the major proposition and in which cases it is different from it. Understanding these depends on the correct understanding of necessity, continuation and possibility. This is followed by the principles to be relied upon when judging something as necessary or possible and what consequences these will have. In this context, the meanings of necessity, possibility, continuation and act, as well as their types and relationships with each other, are very important. It can be said that the issue of modality really starts after this stage and is quite complex.
In this article, some of these differences and the reasons for this have been pointed out. At the end of the article, tables with detailed explanations showing how the results are obtained in modal syllogism are added. In addition, a general method of representing modal propositions and modal syllogisms with symbols is provided. All of these symbols are specific to this study. This method is also described in detail in the appendix. Thus, it is aimed to better understand the subject of modal propositions and to make the obtaining results in modal syllogisms more understandable and easier. To represent modal syllogisms with this method, symbols related to modal propositions are placed on each proposition to show its modality. In this way, it is possible to understand modal propositions better and to perform comparison operations more easily.
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Klasik Mantıkta Modalite: Modal Önermeler ve Modal Kıyaslardaki İşlemlerin Açıklanması ve Sembollerle Gösterilmesi
Abstract
Önermelerin zorunluluk, devam, imkân ve fiil ifade eden lafızlarla kayıtlanması modal önermeleri oluşturur. Bu önermelerin kıyasta kullanılmasıyla da modal kıyaslar elde edilir. Modalite konusu mantığın en önemli konularından kabul edilir. Mantıkçılar herhangi bir modal önermenin döndürme ve çelişiklik gibi hükümleriyle ilgili birtakım tespitlerde bulunurlar. Örneğin özü bakımından zorunlu bir önermenin çelişiğinin imkân anlamı taşıdığını söylerler. Döndürmesine gelince olumlularında nispetin bazı zamanlardaki fiiliyyetini, olumsuzlarında ise özü bakımından devamı ifade ettiğini belirtirler. Aynı şekilde modal kıyaslar için de bazı kurallar koyarlar. Örneğin birinci ve üçüncü şekilde küçük öncülün, dördüncü şekilde ise her iki öncülün de mümkün bir önerme olamayacağını ifade ederler. Bunlar gibi daha birçok ilke ve kuraldan söz ederler. Bu makalede söz konusu kurallar delilleriyle birlikte ele alınmıştır. Yine mantıkçılar arasında modal önermeler ve bu önermelerin kıyaslarda kullanımı ile ilgili de bazı görüş ayrılıkları da vâkidir. Bu çalışmada söz konusu farklılıkların bir kısmına ve sebeplerine işaret etmekle birlikte müteahhirûn dönemi ve özellikle genel kabul gören isimler ve kurallar benimsenmiştir.
Makalenin sonuna kıyasın dört şeklinde öncüllerin modalitesine göre hangi modalitedeki sonuçların nasıl elde edildiğini gösteren ve her bir modal önerme için ayrıntılı açıklamalar içeren tablolar eklenmiştir. Ayrıca bu çalışmaya özgü olarak modal önermeler ve modal kıyasların sembollerle gösterilmesine ilişkin genel bir yönteme yer verilmiştir. Daha önce “Kıyas Şekillerinin Geometrik Yöntemle İrcâı” başlıklı çalışmada sunulan yöntem ile modal önermelerin sembollerle gösterimine dair yöntemin bir arada etkin bir şekilde kullanılmasını sağlayan genel bir metot önerilmiştir. Böylece modal önermeler konusunun daha iyi anlaşılması ve modal kıyaslardaki işlemlerin daha anlaşılır ve kolay bir şekilde yapılması amaçlanmıştır.
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