Arman Besler

The standard inferential scheme of traditional assertoric syllogistic, based on the initial chapters of Aristotle’s Prior Analytics, employs single-premissed deductions, i.e., principles of immediate inference, in the reduction of imperfect valid moods to perfect moods. G. W. Leibniz has attempted to replace this scheme with his own version of syllogistic reduction, in which the principles of immediate inference themselves are modelled as valid syllogisms. This paper examines the place of this modelling, i.e. syllogistic expansion, of immediate inferences in Leibniz’s scheme of syllogistic reduction, and shows through this examination that the tenability of the whole scheme actually hinges on the interpretation to be given for the categorical propositional forms. Geleneksel asertorik tasım kuramının, Aristoteles’in Birinci Çözümlemeler’inin ilk bölümlerine dayanan standart çıkarım planı, eksik geçerli kipleri tam/mükemmel kiplere indirgemek için bazı tek öncüllü dedüktif çıkarımları, yani dolaysız çıkarım ilkelerini kullanır. G. W. Leibniz, bu planın yerine, özü itibariyle yine Aristoteles’in tasımsal dönüştürme hakkındaki gözlemlerine dayanan, kendi tasımsal indirgeme örneğini koymaya girişenlerden birisidir. Leibniz’in indirgeme planında, dolaysız çıkarım ilkelerinin kendileri, geçerli tasımlar olarak modellenir. Bu çalışma, dolaysız çıkarımların bu modellemesinin, yani tasımsal genleştirmenin, Leibniz’in tasımsal indirgeme planındaki yerini incelemekte ve bu inceleme yoluyla bütün bir indirgeme planının savunulabilirliğinin, aslında, kategorik önerme biçimleri için verilecek yoruma bağlı olduğunu göstermektedir.

The main doctrines of the traditional logic of terms (logica termini) are standardly organized according to the formation structure of syllogistic inferences. A syllogistic inference is analyzed into propositions, and propositions, in the last instance, to terms; the logic of terms, in line with this formation structure, is partitioned into the doctrines, respectively, of terms (terminorum), of propositions (propositionum) or judgments (judiciorum), and of immediate and mediate inferences or followings (consequentiarum immediatarum/mediatarum). This structure communicates the idea that a given doctrine could be treated, to a certain extent, independently of the next one to come, so that propositions, for instance, could be examined, at least to a certain extent, independently of syllogistic inferences. Some classical philosophers such as Immanuel Kant have developed approaches that break in part this order of analysis which finds its clearest expression in the Port-Royal logic (Arnauld & Nicole’s Logic or the Art of Thinking). In Kant’s case the order is changed in favor of the doctrine of judgements. This paper examines the French philosopher Jules Lachelier’s (1832-1918) approach which similarly breaks the same doctrinal order, and which, more specifically, refines the typification of propositions according to the roles to be played by propositions in syllogisms. What lies at the core of this approach is the identification of the semantic values of categorical propositions (or, as Lachelier calls them, of propositions of inherence) in terms of modal statuses which are to determine these roles. Lachelier seems to use the set of values he assigns to the categorical forms as a tool for testing logical implication among types of predication, that is, as some sort of semantic theory in the modern sense. Lachelier also discusses the three-figured categorical syllogistic along with a method, effectively used by G. W. Leibniz, of transforming syllogistic moods into each other, and tries to confirm his semantic theory in terms of such syllogistic. This paper explains Lachelier’s analysis of meaning by treating it as a non-formal semantics of predication, and tries to make some modern sense of Lachelier’s general approach to syllogistic.

Antoine Arnauld ile Pierre Nicole’ün Mantık veya Düşünme Sanatı – daha iyi bilinen takma adıyla Port-Royal Mantığı – kitabı, geleneksel terim mantığının gelişim tarihinde en az iki bakımdan önemli bir aşamayı temsil etmektedir. Birincisi, bu kitap, “eski” mantığı, René Descartes’ın bilgi ve varlık anlayışınca belirlenmiş olan modern felsefeye ayarlı hale getirmekte ve sonraki dönemlerin mantıkçıları için terim mantığının terminolojisini bir dereceye kadar yeniden tanımlamaktadır. İkincisi ve daha önemlisi, bu kitap, kategorik tasım kuramında geçerlilik denetimi/saptaması için kullanılan ve Aristoteles’e dayanan standart kanıtkuramsal yaklaşım yerine, Ortaçağlarda geliştirilmiş, daha çok semantik yönelimli olduğu söylenebilecek alternatif bir yaklaşımı ana öğreti olarak sunmaktadır. Bu yaklaşımda, geçerli tasım biçimleri, kategorik önermelerde geçen terimlerin semantik bir özelliği olan dağıtım fikrini merkeze alan az sayıda kural yoluyla tespit edilir. Bu yazının asıl amacı semantik yönelimli bu yaklaşımın özünü Port-Royal örneği üzerinden aydınlatmaktır. Öncelikle, Port-Royal mantıkçılarının ilgili kuralları geçerli tasımsal biçimleri saptamak için nasıl uyguladıkları, bağlantılı bazı kavramların ve sorunların ışığında, ayrıntılı olarak açıklanmaktadır. Sonra da Port-Royal mantıkçılarının altık tasım biçimlerini eleyişlerinin, semantik yönelimli yaklaşımın ruhuna uygun olmayan bir tutum oluşturduğu, dolayısıyla da Port-Royal Mantığı’nın bu yaklaşımın arı olmayan bir örneklemesi olarak görülmesi gerektiği savunulmaktadır.

Aristotle’s categorical syllogistic is the first formal deductive system in the history of formal sciences. Most parts or elements of the system are validated by modern (first-order) mathematical logic, but the system is quite limited in scope, as it is incapable of analyzing inferences other than the ‘figure syllogisms’ consisting of a couple of_ a-e-i-o_ premises and an _a-e-i-o_ conclusion, containing three ‘moderately’ universal terms – terms that express neither a highest genus nor a lowest species – each of which is common to a different couple of propositions out of the three. Logicians in the following ages dealt with various questions concerning the addition of various (novel) logical forms into this limited system, among which are singular predications, i.e. categorical propositions with a singular term as subject, and the most common choice has been interpreting singular predications as _universal _predications. This paper tries to take a strictly formal perspective on the system of categorical syllogisms, and argues in detail for a much simpler and fairly effective assimilation or translation scheme for singular predications. The key to the proposed scheme is the preservation of the supposed inferential relation between opposite singular predications, namely _contradiction_. It is argued that the resulting _singularized _syllogistic moods, which are also validated by first-order logic (under its standard renderings of _a-e-i-o_ and singular predications), promote in turn the mentioned type of treatment, since they call for the employment of two of the four subaltern moods of the system, disregarded by Aristotle, which are _formally _there.

The idea and the actual exercises of logical analysis as a philosophical method are at the heart of the emergence of analytic philosophy in the beginning of the 20th century. Although analytic philosophy is most commonly said to emerge with the critique devised by G. E. Moore and Bertrand Russell of the then-dominant idealist currents of philosophy in Britain, the central conception of analysis at work in this process is not the dominant traditional conception of analysis as decomposition of concepts, but a fairly new, distinctive conception which we find to be exemplified exclusively in Frege’s and Russell’s works (specifically Frege 1879, 1893 and Russell 1905). This distincive conception has been specified under a few various rubrics, such as paraphrastic or transformative-interpretive analysis, to separate it not only from the decompositional but the regressive conception as well, the latter characterizing the analysis-synthesis method of ancient Greek geometry. The present paper first locates logical analysis (as a philosophical method) in this picture, by proposing to define it as a definite kind of paraphrastic (or transformative/interpretive) analysis, the kind where the language in the analysans position is a logical language. The paper highlights the fact that the whole point of analyzing natural language forms by means of translating them into a logical language is essentially solving problems of inference – i.e. determining whether certain natural language sentence types follow from/contradict with/entail certain others, and shows that this particular conception of analysis is not as self-consistent a notion as it may first seem to be. The key to the argument is the undeniable connection between the meaning (at large) of a sentence form and the principal inferential relations that the sentence form is supposed (pre-analytically) to enter into with other related forms. The argument employs as a clear example the common modern logical analysis of the so-called problem of existential import of traditional categorical forms in order to problematize the viability of logical analysis, and concludes that one of the necessary conditions of the self-consistency (viability, possibility) of logical analysis is the acceptance of a certain negative thesis about meaning.