The Pioneering Proving Methods as Applied in the Warsaw School of Logic – Their Historical and Contemporary Significance

Abstract

Justification of theorems plays a vital role in any rational human activity. It is indispensable in science. The deductive method of justifying theorems is used in all sciences and it is the only method of justifying theorems in deductive disciplines. It is based on the notion of proof, thus it is a method of proving theorems. In the Warsaw School of Logic (WSL) – the famous branch of the Lvov-Warsaw School (LWS) – two types of the method: axiomatic deduction method and natural deduction method were developed and practiced. In this paper, both of these methods are briefly discussed with an emphasis on their historical, groundbreaking significance for logic. The axiomatic method by means of rejection (proposed by Jan Łukasiewicz – a co-creator of the WSL), which is the method of the so-called rejection proof (rejection/refutation method) in logical systems and the proving method of generalized natural deduction, which is a hybrid deduction–refutation method of proving theorems, are also outlined in the paper. The author discusses their historical significance. This paper also contains a brief mention of the most significant results which the application of the discussed methods introduced into contemporary scientific research, not only logical one.

Keywords:

• History of logic
• justification of theorems
• proving methods used in the Warsaw School of Logic
• axiomatic deduction method
• natural deduction method
• rejection method
• generalized natural deduction
• historical significance of proving methods

Acknowledgments

I would like to express my gratitude the Referees for their comments, remarks and suggestions which allowed me to complete and improve some fragments of my paper.