A transactional approach to the logic of truth

Summary

Abstract. We survey and evaluate recent discussions about axiomatic theories of truth, with special attention to deflationary approaches. Then we propose a new account of the use of truth theories, called a transactional analysis. In this analysis, information is communicated between intelligent agents, which are modeled as individual axiomatic theories. We note the need in the course of communication to distinguish whether or not new information is considered trustworthy.

τò μὲν γὰρ λέγειν τò ὂν μὴ εἶναι ἢ τò μὴ ὂν εἶναι ѱεῦδος, τò δὲ τò ὂν εἶναι ϰαὶ τò μὴ ὂν μὴ εἶναι ἀληϑές, ὥστε ϰαὶ ὁ λέγων εἶναι ἢ μὴ ἀληϑεύσει ἢ ψεύσεται

To say that what is is not, or that what is not is, is false; but to say that what is is, and what is not is not, is true; and therefore also he who says that a thing is or is not will say either what is true or what is false.

– Aristotle, Metaphysics, 1011b

This paper consists of three parts. First is a brief introduction; probably most of it will be very familiar material. Then I will describe and discuss some recent work on axiomatic theories of truth. Finally, I will suggest an alternative way of thinking about axiomatic theories of truth, which I call a transactional approach. The famous quotation from Aristotle (shown above, and chosen in honor of the conference at which this paper was presented) is not really the starting point, but includes one little feature which deserves attention for later reference: the use of the word “say”.