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But what is a presupposition of a proposition is not the logical consequence of the proposition. It is true that a proposition can never be true if either its presupposition or its entailment is false. But if what is entailed is false the proposition is not true and when a presupposition is false the proposition is neither true nor false or, in other words, there is a truth-value gap.²² This is because the entailment of a proposition is in a sense a part of the content of the proposition. But a presupposition is never a part of the content of the proposition.

The final point to be raised against Dretske is that though PDJ is a presupposition of Gettier's counterexamples, many Gettier like counterexamples may be constructed which do not presuppo­se the PDJ principle as we shall see later on. So even if we show the invalidity of the PDJ principle we cannot overcome Gettier's principal charge against the traditional definition.

Irving Thalberg, however, questions not only the PDJ principle but also the Gettier counterexamples. In fact his attack against PDJ principle is indirect, i.e., via the counterexamples. His principal concern was to challenge the genuineness of Gettier counter­examples, though thereby he undermines the principle also.

Thalberg believes that the PDJ principle has been applied by Gettier at two stages: (a) in the transition from (1) "Jones will get the job" and (2) "Jones has ten coins in his pocket" to (3) "Jones will get the job and Jones has ten coins in his pocket", and (b) in the passage from (3) to (4) "The man who will get the job has ten coins in his pocket".

He questions the transition from (1) and (2) to (3) by referring to the principle of probability. He declares that the probability of a conjunctive proposition is always less than the probability of each of the conjuncts. To quote him:

Then the most elementary theory of probability indicates that Smith's prospects of being right on both (1) and (2) namely, of being right on (3) are bound to be less favourable than his prospects of being right on either (1) or (2).²³

In this respect he draws an. analogy between risk-taking and believing. The point of comparison seems to be that just as a person wants to win as many bets as possible, so also he wants to get his beliefs correct as often as possible.

His principal charge, however, is against the passage from proposition (3) to proposition (4). From the manner in which he argues, it seems that he takes (4) to be a general and perhaps a universal proposition. He translates the proposition "The man who will get the job has ten coins in his pocket" as "Whoever will get the job has ten coins in his pocket". He argues that from (3) which is a singular proposition the passage to a universal proposition is not justified. Smith would have been justified in believing the universal proposition if Smith were told by the chairman of the company that only those who possess ten coins in their pockets would be selected for the job or if Smith would have found out that the company always chooses candidates who carry ten coins in their pockets. What Thalberg says about the first counterexample may be made more intellilgible if we bring in Keith Donellan's distinction between the purely referential use and the attributive use of what is called a definite description.²⁴

The subject term in (4), viz., "The man who will get the job" is a definite description. If we take this definite description as a referring expression, then we may interpret it either in a purely referential sense or in an attributive sense. If it is used in a purely referential sense then its reference will be 'Jones' because here Smith actually wants 1o talk about Jones. In this case, the proposi­tion "The man who will get the job has ten coins in his pocket" will turn out to be "Jones has ten coins in his pocket". But in that case this will be a case of knowledge and will not be treated as a counterexample. If, however, it is taken in an attributive sense the move from (3) to (4) will not be justified, because (4) in that case will be a universal proposition. Hence, either it will be a case of knowledge and therefore not a counterexample or it will lack one of the conditions of traditional definition and in that case too it will no longer be a counterexample.

When Thalberg comes to consider Gettier's second counter­example, he lays stress on the normal conditions under which a disjunctive assertion is made. In his second counterexample Gettier considers the disjunctive proposition "Either Jones owns "a Ford or Brown is in Barcelona".

Normally when we make a disjunctive assertion, we assume that if the first disjunct turns out to be false the second is most likely to be true. But this is not the case here. There is no likelihood of the second disjunct's being true under the circumstances under which the first disjunct is false. If Smith would have known that Jones likes only Ford cars then he would have been justified in believing the disjunctive proposition "Either Jones owns a Ford or he does not own any car". Again if Smith knew that Jones' second preference is Ferrari, then he would have been justified in believing the disjunctive proposition "Jones owns a Ford or a Ferrari". Thalberg thus rejects both of Gettier's counter­examples.

Thalberg, however, makes certain mistakes in his argument against Gettier. For example, he fails to realise that there is no application of the PDJ principle in the move from (1) and (2) to (3), for from (1) alone (3) cannot be derived, i.e., (1) alone does not entail (3) and from (2) alone (3) cannot be derived. But PDJ allows the transmission of justification from a proposition to its entailments alone. To quote Michael K. Hooker:

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