Abstract
In the nineteenth century, philosophy was at a crossroads. While the natural and technical sciences were develo** in an unprecedented fashion, philosophy seemed to be stalled. Inspired by the progress of the natural sciences, many philosophers attempted to make such progress in philosophy and make philosophy a truly scientific discipline. This effort was also reflected in the philosophy of the Lvov-Warsaw school. While its founder, Kazimierz Twardowski, following his teacher Franz Brentano, promoted psychology as a method of scientific philosophy, one of his first students, Jan Łukasiewicz, was convinced that mathematical logic was such a method. To use mathematical logic as a tool, Łukasiewicz had to, however, argue convincingly that logic is an independent science and hence is not a part of psychology, i.e., arguing for anti-psychologism in logic. He initially adopted the arguments provided by Husserl, then celebrated as a proponent of anti-psychologism, and Frege’s views. When Łukasiewicz developed, however, his systems of many-valued logic, he denied almost all the principles that characterise Husserl and Frege’s anti-psychologism, i.e., the objectivity of the laws of logic, the existence of apodictic propositions, and the distinction between a priori and empirical sciences. He was, however, a proponent of anti-psychologism up to the end of his life. The aim of my paper is to introduce Łukasiewicz’s unique concept of anti-psychologism that significantly affected the views of mathematical logic in the Lvov-Warsaw School, and the views of his colleagues which helped him develop the concept.
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Notes
The addition ‘in logic’ is important as there could also be psychologism (or anti-psychologism) in other philosophical disciplines. (see e.g. Kusch, 1995, p. 105). The terms psychologism and anti-psychologism mean psychologism in logic and anti-psychologism in logic, respectively in this paper.
At the beginning of his academic career, Łukasiewicz spent some time in Berlin contributing to experiments that took part at the Institute of Philosophy. He proposed in his letters to Twardowski that he could cooperate in a similar institute at the University of Lvov (see Łukasiewicz, 1905/1998, pp. 470–471). It was at the time when he already denied psychologism in logic. It seems therefore that he was not entirely sceptical about psychology, although, he aimed to lessen its position in philosophy. Łukasiewicz (1927/1998, pp. 41–42) later, however, explicitly acknowledged mathematical logic as the only method of scientific philosophy.
In Łukasiewicz’s (1907/1961) paper, the precise formulation of arguments slightly differs. Namely, he formulated them as:
the laws of logic are not grounded in laws of psychology.
the laws of logic have a different content than the laws of psychology.
logic as a science does not concern correct reasoning but truth and falsehood.
logical terms differ from psychological terms.
In my formulation, I merged the first two and pointed out another distinction which was important to Łukasiewicz’s formulation of anti-psychologism later. All four points will be developed in further chapters.
Surma (2012, pp. 64–65) pointed out this issue out in his book but did not go into detail as to how Łukasiewicz’s views on psychologism changed.
Using the term ‘proposition’ here, it has to be pointed out that the term is used without any philosophical connotation, i.e., it by no means meant the Fregean propositions that are placed in the third realm. Łukasiewicz and several of his colleagues from the Lvov-Warsaw School opposed the introduction of these entities in logic. The term ‘zdanie’ which would correspond to the English word ‘sentence’, is used in Polish. The term ‘sentence’ has a slightly different meaning in English, however, and cannot be used in logic. This issue is further discussed in the fifth chapter of my paper.
The psychological law of contradiction is false, as Łukasiewicz (1910/1987, pp. 33–35) later emphasized in his book. In the book, Łukasiewicz (1910/1987, p. 9–13) also identified a third meaning of the law of contradiction, namely an ontological one. Its formulation is ‘no object can have and lack a property at the same time’.
It is important to stress that this empirical research concerns by no means psychology. Łukasiewicz (1922/1961) favoured in this respect physics. He did not express clearly, however, which new findings of physics could undermine laws of logic. In contrast, his colleague Tarski (1987, pp. 31–32) and also Quine (1951, p. 40) clearly mentioned quantum mechanics as a possible refutation of certain laws of logic.
Paradoxically, it is also a period when intensional systems of logic began to flourish.
Łukasiewicz did not describe these abstract objects among which he listed cause nor did he intend to do so. Woleński (1989, pp. 54–55) argues that the best candidate for such objects might be certain Platonistic entities, as they are not placed in human minds either in time or in space.
For instance, if electricity is passing through a thin platinum wire (the cause), the wire gets warm (the effect). The fact, that electricity is passing through the wire, implies that the wire gets warm. However, the sole fact that the wire gets warm does not imply the cause, as there might be other causes that affect the wire. In contrast, when the wire is not warm (e.g., the effect is missing), it is the case that electricity is not passing through it (see Łukasiewicz 1906/1961, pp. 26–28).
Łukasiewicz (1910/1987, pp. 13–14) was aware that Meinong also differentiated between two meanings of the term ‘judgement’. Meinong identifies the judgements in the logical meaning with his ‘Objectives’. However, Łukasiewicz’s judgements in the logical meaning are not entirely equal to ‘Objectives’, since Łukasiewicz (1910/1987, p. 14) described them as: “Objectives expressed in words or other symbols”.
It is important, however, to point out that Łukasiewicz was not a nominalist.
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Acknowledgements
Previous versions of the text have been presented at the Philosophical Workshop of the Lvov-Warsaw School Research Center at the University of Warsaw and the Sixteenth International Congress on Logic, Methodology, and Philosophy of Science and Technology in Prague. I am grateful to the audiences at these events for their comments. My colleagues from Tadeusz Ciecierski’s research group and my colleague from Palacký University in Olomouc, Martina Číhalová, reviewed previous versions of the text and suggested several important improvements. I would like to thank them from the bottom of my heart. I am also obliged to unknown reviewers of this paper for their suggestions. The work on this paper was supported by the project “JG_2020_005 Times, Events, and Logical Specification” of Palacký University Olomouc, the Czech Republic.
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I began, therefore, my war with psychology, which, as it seems to me, does not completely justly occupy a so dominant position in philosophy (Łukasiewicz, 1904/1998a, p. 460)
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Rybaříková, Z. Łukasiewicz’s concept of logic and anti-psychologism. Synthese 200, 103 (2022). https://doi.org/10.1007/s11229-022-03479-3
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DOI: https://doi.org/10.1007/s11229-022-03479-3