LOGIC time true and at another false A sentence such as ‘Theaetetus is sitting’, which is true when Theaetetus is sitting, and false at another time, would on this view be said to express a diVerent proposition at diVerent times, so that at one time it expresses a true proposition, and at another time a false one And a sentence asserting that ‘Theaetetus is sitting’ was true at time t is commonly treated as asserting that the proposition that ascribes sitting at time t to Theaetetus is true timelessly On this account, no proposition is signiWcantly tensed, but any proposition expressed by a tensed sentence contains an implicit reference to time and is itself timelessly true or false Aristotle nowhere puts forward such a theory according to which tensed sentences are incompletely explicit expressions of timeless propositions For him uttered sentences indeed express something other than themselves, namely thoughts in the mind; but thoughts change their truth-values just as sentences (Cat 4a26–8).7 For Aristotle, a sentence or proposition such as ‘Theaetetus is sitting’ is signiWcantly tensed, and is at some times true and at others false It becomes true whenever Theaetetus sits down, and becomes false whenever Theaetetus ceases to sit There is, for Aristotle, nothing in the nature of the proposition as such that prevents it from changing its truth-value: but there may be something about the content of a particular proposition that entails that its truthvalue must remain Wxed Logicians in later ages regularly distinguished between propositions that can, and propositions that cannot, change their truth-value, calling the former contingent and the latter necessary propositions The roots of this distinction are to be found in Aristotle, but he speaks by preference of predicates, or properties, necessarily or contingently belonging to their subjects In both the de Interpretatione and the Categories he discusses propositions such as ‘A must be B’ and ‘A can be not B’: propositions later called by logicians ‘modal propositions’ In the de Interpretatione he introduces the topic of modal propositions by saying that whereas ‘A is not B’ is the negation of ‘A is B’, ‘A can be not B’ is not the negation of ‘A can be B’ A piece of cloth, for instance, has the possibility of being cut, but it also has the possibility of being uncut However, contradictories cannot be true together Hence the negation of ‘A can be B’ is not ‘A can be not B’ but rather ‘A cannot be B’ In the The truth-value of a proposition is its truth or its falsity, as the case may be 130