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1.4 The second presupposition

Gettier's second presupposition proceeds in the following man­ner: If S is justified in believing p and if p entails q and S deduces q from p and accepts q as a result of this deduction then S is justified in believing q. To put it briefly, justification is transmissible to the known logical consequences of the justified proposition. This principle has come to be known as the principle of deducibility for justification or, in abbreviation, simply as PDJ.

Fred Dretske did not deny that Gettier's application of this principle to his counterexamples is correct but he rejects the principle itself. He argues that though Gettier's application of the principle to his proposed counterexample is unobjectionable, the principle itself is not true. Dretske holds that it is possible to be justified in believing a proposition without being justified in believing the known logical consequences of the proposition. To support this assertion, he puts forward a number of examples. It is possible, for example, to be justified in believing that the apple is rotten without being justified in believing that it is the apple which is rotten, though the latter proposition is a known logical consequence of the former. The apple is believed to be rotten because it is all brown and mushy, This is enough to justify someone's belief that the apple is rotten but this does not justify one to believe that what is rotten is an apple. Similarly, one may be justified in believing that the church is empty without being justified in believing that it is the church which is empty. The former belief was generated and supported by a thorough search or inspection of the building. But this search does not help us to be justified in believing that the building is a church. In fact 'being justified in believing that', according to Dretske, is a semi-penetra­ting operator. Dretske distinguishes between three kind s of opera­tors, viz., the fully penetrating operator, the non-penetrating operator and the semi-penetrating operator.

An operator (sentential operator) is such that when affixed to a sentence or statement, it operates on it to generate another sentence or statement. Affixes like 'it is necessary that', 'it is possible that', 'it is a fact that' are called penetrating operators or fully penetrating operators. If we let 'O' stand for the operator and O(p) for the statement that is generated by affixing the operator 'O: to a statement p and if p entails q then if O(p) entails O(q) then 'O' is a fully penetrating operator. When 'O' is a fully penetrating operator it penetrates to every logical consequence of 'p' which is the sentence to which 'O' is affixed. An operator is non-penetrating if the fact is that p entails q and O(p) does not entail O(q). Operators like 'it is strange that', 'it is a mistake that' arc non-penetrating operators. It may be strange that Robert married Susan but it is not at all strange that Susan got married. It may be a mistake that Susan married Robert but it is not at all a mistake that Susan got married. Semi-penetrating operators fall in between the fully penetrating operators and what are called non-penetrating operators. As Dretske comments:
We have, then, two ends of the spectrum with examples from both ends. Anything that falls between these two extremes I shall call a semi-penetrating operator.¹⁹

Semi-penetrating operators have a degree of penetration that is missing in the non-penetrating operators. According to Dretske, in a trivial sense it penetrates to the logical consequences of a proposition though he docs not believe that in a significant sense it penetrates to the known logical consequences of a proposition. That is why he regards this as a semi-penetrating operator. Epistemic operators, it is usually thought, penetrate to the known logical consequences of a proposition. But Dretske contests that epistemic operators penetrate to the known logical consequences of a proposition. In other words, he is contesting the PDJ principle. The proposition "The widow is limping" entails "It is the widow who is limping" and one knows that the first sentence entails the second, yet one may be justified in believing the first but may not be justified in believing the second. The reason why we believe that the widow is limping, Dretske argues, is that we see it. But this cannot be the reason why we believe that it is the widow who is limping. We are justified in believing that the coffee is boiling because we have seen vapours coming out but this does not justify us in believing that it is the coffee which is boiling.

Here we have to make a number of comments some of which may be construed as criticisms of Dretske's point of view. First of all, it is indeed clever of Dretske to have noticed that the justification for the proposition "The apple is rotten" need not be the same as the justification for the proposition "It is the apple which is rotten"— in the first the emphasis is on something's being rotten, while in the second the emphasis is on something's being an apple. But in his eagerness to pursue this point he has failed to note that we have to lake into consideration what the exact content of the belief is. If the belief is of the form "The apple is rotten" then admittedly it does entail "It is the apple which is rotten". But then we do not see why we should not be justified in believing the second, if we are justified in believing the first proposition. It, however, we are justified in having the belief of the form "It is rotten", then of course we are not justified in believing "It is the apple which is rotten" on its basis. But in that case nor is the proposition "It is the apple which is rotten" entailed by the belief of the form "It is rotten".²⁰ Dretske cannot have it both ways. He cannot have the cake and eat it. Secondly, in what sense is, "It is the apple which is rotten" a logical consequ­ence of "The apple is rotten?" What would be the symbolized form of the valid inference corresponding to this entailment? None that can depict the passage involved in the inference seems to be forthcoming. Another point to be noticed is that Dretske confuses between the concepts of presupposition and of logical consequence. In his eagerness to show that in some cases we may not be justified in believing the logical consequence of a proposi­tion though we may be justified in believing the proposition itself, he goes to the extreme of asserting that this happens in those uses where the consequence is a presupposition of the proposition. In fact, Dretske says this in so many words. To quote: ...there are certain presuppositions associated with a state­ment. These presuppositions, although their truth is entailed by the truth of the statement, are not part of what is operated on when we operate on the statement with one of our epistemic operators. The epistemic operators do not pene­trate to these presuppositions.²¹

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