S C I E N T I F I C J O U R N A L Published by the decision of the Scientific Council of Khachatur Abovian Armenian State Pedagogical University Department of Philosophy and Logic named after Academician Georg Brutian W I S D O M 3(16), 2020 WISDOM is covered in Clarivate Analytics‟ Emerging Sources Citation Index service YEREVAN – 2020 Robert DJIDJIAN, Hasmik HOVHANNISYAN DOI: 10.24234/wisdom.v16i3.395 Robert DJIDJIAN, Hasmik HOVHANNISYAN AXIOMS OF PHILOSOPHY IN ARISTOTLE‟S METAPHYSICS Abstract The goal of this article is to study Aristotle‟s concept of philosophical principles. Metaphysics re- quired from a philosopher to reveal the axioms of his teaching. It declared the law of contradiction as the most certain of all principles and axioms. This article proves that the Aristotelian definition of truth makes it necessary to accept the ontological formulations of all the three main laws of thought as axioms of first philosophy. This article points out the absence of any reference in Metaphysics on Categorias and vice versa. This circumstance questions if could Aristotle be the author of both works? Authors of this article underline that the modern trend of meta-philosophical studies requires investigating the possibility of building the system of axiomatic philosophy. EPISTEMOLOGY, PHILOSOPHY OF SCIENCE, METAPHILOSOPHY, ARGUMENTATION, COMMUNICATION Keywords: axiom, the axiom of philosophy, the choice of an axiom, the set of axioms, the priority of ontology. Introduction ments and its rigorous proofs did not yet come to light. Developing the theory of syllogisms and Axioms – the most valuable acquisition in revealing that his theory was based on the gen- the treasury of scientific knowledge – have been eral syllogisms of the first figure, Aristotle called highly appreciated from the time of Aristotle. them perfect syllogisms and never qualified them They were rightly regarded as the unshakable as axioms. These two general syllogisms of the foundation of the colossal temple of demonstra- first figure in medieval logic were denoted as tive scientific knowledge. The clearest concept of Barbara and Celarent and were called “dictum the function of axioms was presented in Posteri- de omni et de nullo”. And only much later, in the or analytics (chapter 10 of the book I). Moreo- frame of traditional formal logic the principle ver, Jan Lukasiewich proved that Aristotelian “dictum” started to be called “the axiom of syllo- syllogistics was the first axiomatic theory in the gism” though in the traditional formal logic this history of sciences (Lukasiewicz, 1951). axiom was not used in the theory of syllogisms. Yet the axiomatic method of building scien- Axioms of fundamental natural sciences tific theories by introducing a set of axioms and could be called the highest principles of the natu- deducing all other statements of the theory from ral world. Albert Einstein devoted the last dec- axioms and definitions with the help of rules of ades of his life to the study of the general theory valid inferences was not yet put into scientific of the field. If Einstein had succeeded in his great practice by the days of Aristotle. Euclid‟s Ele- endeavour, then the physical science could claim WISDOM 3(16), 2020 6 7 7 Robert DJIDJIAN, Hasmik HOVHANNISYAN that it has revealed the ultimate essence of exist- Principia Mathematica. Its famous laws of me- ence, the first principles and the highest causes chanics can serve as illustrating analogues for the of the physical world. Now substituting in this “set of axioms of a theory”. Each modern edu- formulation the concept “physical world” by Ar- cated man is able to learn and remember these istotelian “being as being” we‟ll get the task of there laws. On the contrary, the task “creating a the first philosophy – to reveal the first principles complete axiomatic theory” means proving the and the highest causes of being as being. Thus entire body of the statements of Newtonian me- we come to an understanding that in essence the chanics, and this task is out of reach of any mod- Aristotelian first philosophy could be viewed as ern educated man if he is not helped by New- the most basic level of physical science, a true ton‟s famous work. meta-physics, the most valuable knowledge of In short, the task of “setting out of axioms of natural science, and in the latter sense – the high- a theory” means suggesting a number of state- est and ultimate knowledge of all the existence – ments that presumably could serve a basis for the the true meta-physics. theory. While “creating a complete axiomatiza- Commentaries on Metaphysics are traced tion” means building the theory as a whole, pre- back by historians to Alexander Aphrodisias, and senting a proof of its every statement based on its their number is constantly growing in our days axioms and definitions. and times to come (Fraser, 2002; Wedin, 2002; “The most certain axiom” of the first phi- 2009; Sharples, 2010; Yu, 2003; Bell, 2004; Gill, losophy is clearly stated in the book IV of Meta- 2005; Gill, 2006; Anagnostopoulos, 2009; Per- physics: “the same attribute cannot at the same amatzis, 2011; Kotwick, 2016; van Inwagen, & time belong and not belong to the same subject Sullivan, 2018). Our study is an element in this and in the same respect” (Metaphysics, 1005b huge domain of research in first philosophy ded- 20). In the following sentence, Aristotle under- icated to a quite narrow branch of axioms of Me- lines that this “is the most certain of all princi- taphysics that, as we hope, could become a sig- ples” and then suggests another formulation for nificant trend in modern philosophy. the first axiom of his philosophical system: “it Preparing this article for publication, we is impossible that contrary attributes should be- have revealed that some current time philoso- long at the same time to the same subject” (natu- phers even those who are involved in neo-Aristo- rally, this both formulations of the first axiom of telian research do not understand the significant the first philosophy are accompanied by traditi- difference between the concepts “axioms of a onal precautions against possible “dialectical ob- theory” and “axiomatic theory”. One of them jections” by pointing out that they are considered even stated proudly: “I didn‟t distinguish clearly “in the same respect”, “at the same time”, and enough between setting out axioms and creating other “usual qualifications”). a complete axiomatization”. We hope that the following simple example The Law of Contradiction as the will be helpful to understand clearly the huge Axiom of the First Philosophy difference between “set of axioms of a theory” and “creating a complete axiomatic theory”. Let It is quite evident that the law of contradic- us consider Newton‟s Philosophiae Naturalis tion is formulated in Metaphysics as a principle WISDOM 3(16), 2020 8 8 Axioms of Philosophy in Aristotle’s Metaphysics that it has revealed the ultimate essence of exist- Principia Mathematica. Its famous laws of me- of ontology since both formulations of the axiom the same subject”) unite for further analysis of ence, the first principles and the highest causes chanics can serve as illustrating analogues for the speak about things and subjects, about “existing the axioms of philosophy in the following formu- of the physical world. Now substituting in this “set of axioms of a theory”. Each modern edu- things qua existing” aimed to reveal the most lation: “It is impossible that the same attribute formulation the concept “physical world” by Ar- cated man is able to learn and remember these certain principles of “all things”. belong and not belong to the same subject at the istotelian “being as being” we‟ll get the task of there laws. On the contrary, the task “creating a On the other hand, the law of contradiction same time and in the same respect” (1). This the first philosophy – to reveal the first principles complete axiomatic theory” means proving the is much wider recognized in the language of sci- formulation we‟ll call ontological formulation of and the highest causes of being as being. Thus entire body of the statements of Newtonian me- ence as the main law of human thought rather the law of contradiction (the first axiom of Aris- we come to an understanding that in essence the chanics, and this task is out of reach of any mod- than the first axiom of the first philosophy deal- totle‟s first philosophy). Respectively, we‟ll call Aristotelian first philosophy could be viewed as ern educated man if he is not helped by New- ing with the most certain principles of “all logical-cognitional the law of contradiction of the most basic level of physical science, a true ton‟s famous work. things”. Unavoidably, this twofold nature of the traditional logic: “It is forbidden to assert and meta-physics, the most valuable knowledge of In short, the task of “setting out of axioms of law of contradiction raises the question of “prior- simultaneously to negate the same property of natural science, and in the latter sense – the high- a theory” means suggesting a number of state- ity”: which one of these two natures of the law of the same subject” (2). The most laconic wording est and ultimate knowledge of all the existence – ments that presumably could serve a basis for the contradiction is the primary? In its turn, a con- of the logical-cognitional formulation is given in the true meta-physics. theory. While “creating a complete axiomatiza- vincing answer to this principle question could the first book of Posterior Analytics: “it is im- Commentaries on Metaphysics are traced tion” means building the theory as a whole, pre- have a decisive impact in evaluating Aristotle‟s possible to affirm and deny simultaneously the back by historians to Alexander Aphrodisias, and senting a proof of its every statement based on its refutation of Plato‟s idealism.