ИСТИНА

According to Dummett’s theory of truth [1], we can understand truth and falsity in two senses. Dummett based his theory on Frege’s ideas. The latter considered truth and falsehood to be two abstract objects, which are the reference of sentences. Dummett remarked that Frege could not say that by defining Truth and Falsehood as a reference for sentences, he had explained these concepts and how they were used. For Dummett, the purpose of introducing Truth and Falsehood as truth values is to distinguish between the two classes of states of affairs. Each statement, unless it is ambiguous or vague, divides all possible states of affairs into two classes. The first class states of affairs can be characterized by saying that (1) the possibility of detecting them is excluded by the statement; (2) if someone accepts the statement and nevertheless considers this state of affairs as possible, we will consider that he or she is either wrongly understand the meaning of the statements or wants to mislead his or her audience. The second class states of affairs does not rule out by the statement. If first class cases are found, the statement is false. If all actual states of affairs are of the second class, the statement is true. For Dummett, the only thing that matters here is that the truth values allow us to distinguish between the two type of states of affairs. We can call these technical terms of truth values ‘truth-2’ and ‘false-2’. We can also understand truth in a different sense, one that would allow us to introduce the truth value ‘neither true, nor false’. Think about this statement: ‘If it rains now, there is a mud in the street’. All that is guaranteed by this statement is that there is no state of affairs in which there is rain and there is no mud in the street. Imagine that the listener doesn’t know whether it’s raining now or not. However, if there is no rain, it is reasonable to say that the statement is not true or false. At this level, we can talk about ‘truth-1’, ‘false-1’ and ‘neither truth-1, nor false-1’. Conditional statements will be (1) true-2 when they are true-1; (2) false-2 when they are false-1; (3) true-2 when they are not true-1 and not false-1. The point of making these distinctions between different degrees of truth, as Dummett points out, can help us to understand at least one more way of using the terms ‘true’ and ‘false’ in our natural language. Dummett remarked [1, p.11] that in order to give an adequate truth-functional account of the behaviour of negated conditionals it is useful to allow ‘neither truth-1, nor false-1’. Curiously, Dummett’s definition of the negated conditional is very similar to the falsity condition for implication in some connexive logics [2]. In this work we try to reconstruct Dummett’s intuitive understanding of conditional connective in the framework of three-valued logic.