Cesare Cozzo

The author presents a theory of meaning centred upon the notion of "immediate argumental role", which distinguishes between understandability and correctness of a language. First, the theoretical and quasi-empirical criteria of adequacy and the relevant data for such a theory are described. Then the sense of a word is defined as given by a set of argumentation rules. The immediate argumental role of a sentence is determined by its syntactic structure and by the senses of the component words. The immediate argumental role of a sentence is distinguished from its global argumental role. Different conceptions of truth are compatible with the resulting theory of sense, but the author gives some reasons for preferring an epistemic conception of truth. The possibility of understandable and meaningful paradoxical languages and of many different understandable logics is a consequence of such a view.

Gilbert Harman has written: “Williamson‟s Knowledge and its Limits is the most important philosophical discussion of knowledge in many years. It sets the agenda for epistemology for the next decade and beyond” (Harman 2002, p. 417). Timothy Williamson‟s ground-breaking proposal is that knowing is “merely a state of mind”. In other words, for every proposition p “there is a state of mind being in which is necessary and sufficient for knowing p” (Williamson 2000, p. 21). When first advanced, Williamson‟s view ran contrary to the general trend. The “standard view” (ibidem) was that “believing is merely a state of mind, but..

The compulsion of proofs is an ancient idea, which plays an important role in Plato’s dialogues. The reader perhaps recalls Socrates’ question to the slave boy in the Meno: “If the side of a square A is 2 feet, and the corresponding area is 4, how long is the side of a square whose area is double, i.e. 8?”. The slave answers: “Obviously, Socrates, it will be twice the length” (cf. Me 82-85). A straightforward analogy: if the area is double, the side is double. Nevertheless, the answer is wrong. Socrates wants to lead the slave to the right conclusion. The boy should reach the truth through steps that are all “his own”, performed with full conviction. To this aim, Socrates addresses a series of short pressing questions to the slave boy. Simple questions provoke equally simple replies, though the boy is sometimes puzzled and surprised by the answers he feels compelled to give. In the first part of the exchange the boy is gradually forced to admit that a square B with double side (i.e. side of length 4) has an area which is not double, but four times as big, i. e. 16. In the second part the boy hazards the guess that the square with double area has a side of length 3, since 3 is between 2 and 4. But Socrates easily drives him to acknowledging that if the side is 3, the area of the resulting square C is 9, not 8. The boy can only exclaim: “By Zeus, Socrates, I do not know!”. In the third part, at Socrates’ prompting, the diagonal of the original square A is drawn within the second fourfold square B. Responding to Socrates’ questions, the boy is led to conclude that the square D whose side is the diagonal of A is precisely the required square: its area is 8.

The intuitionistic conception of truth defended by Dummett, Martin Löf and Prawitz, according to which the notion of proof is conceptually prior1 to the notion of truth, is a particular version of the epistemic conception of truth. The paradox of knowability (first published by Frederic Fitch in 1963) has been described by many authors2 as an argument which threatens the epistemic, and the intuitionistic, conception of truth. In order to establish whether this is really so, one has to understand what the epistemic conception of truth really is. So I shall start inpart I with a description of the matter at issue between theepistemic conception of truth and the opposite position, therealistic conception of truth. Inpart II I shall very briefly describe the paradox. Inpart III I shall try to answer the question which appears in the title of this paper: What can we learn from the paradox of knowability?. My conclusion will be that the paradox of knowability is not a refutation of the epistemic conception of truth, but helps us to better formulate (and understand) such a view.