The question stated in the title of the article splits into two other questions. One is historical: why did Alfred Tarski choose physical objects as truth-bearers in his famous article „On the notion of truth in languages of deductive sciences”? The second is philosophical: are there general reasons for choosing physical objects to play the role of truth-bearers? In the article the thesis put forward by H. Field and J. McDowell, that it is physicalism of Vienna Circle which had led Tarski to his choice, is rejected. Instead, it is argued that the source of Tarski's choice was Brentanian tradition.
In the article a historical and systematical presentation of pros and cons of different theories of truth-bearers is contained. Different definitions of truth-bearers are presented. In author's opinion, in the Brentanian tradition metaphysical rather than epistemological arguments for the objectivity of truth are typical.
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