Okay. So, I was asked if Gettier, in his paper Is Justified True Belief Knowledge, uses deduction in his Case II?
I noticed that in Case 2, Gettier lays out a disjunction. Basicallly, as far as I can see, Gettier lays out the propostion (f) that Jones owns a Ford, and propositions (g), (h), and (i) as 'tack on' statements.
The article says that Jones owns a Ford:
Smith's evidence might be that Jones has at all times in the past within Smith's memory owned a car, and always a Ford, and that Jones has just offered Smith a ride while driving a Ford. Let us imagine, now, that Smith has another friend, Brown, of whose whereabouts he is totally ignorant. Smith selects three place names quite at random and constructs the following three propositions:
Either Jones owns a Ford, or Brown is in Boston.
Either Jones owns a Ford, or Brown is in Barcelona.
Either Jones owns a Ford, or Brown is in Brest-Litovsk.
Each of these propositions is entailed by (f). Imagine that Smith realizes the entailment of each of these propositions he has constructed by (f), and proceeds to accept (g), (h), and (i) on the basis of (f). Smith has correctly inferred (g), (h), and (i) from a proposition for which be has strong evidence. Smith is therefore completely justified in believing each of these three propositions, Smith, of course, has no idea where Brown is.
But imagine now that two further conditions hold. First Jones does not own a Ford, but is at present driving a rented car. And secondly, by the sheerest coincidence, and entirely unknown to Smith, the place mentioned in proposition (h) happens really to be the place where Brown is. If these two conditions hold, then Smith does not know that (h) is true, even though (i) (h) is true, (ii) Smith does believe that (h) is true, and (iii) Smith is justified in believing that (h) is true.
So, according to the rule of disjunctions, only one half of the disjunction has to be true for the whole thing to be true. It doesn't matter that Smith is wrong in (f) that Jones owns a Ford, becasue by luck, Brown happens to be in Barcelona. That being said, is there a deduction at play?
I thought not. I thought that there is a deduction in the case 1, obviously. But, the more I look at this, the more I think that possibly Smith IS using deduction. The deduction rule, as Gettier outlines earlier:
for any proposition P, if S is justified in believing P, and 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.
(i) Smith is justified in believing that ((f) v (h))
(ii) (f) Jones owns a Ford entails ((f) v (h))
(iii) Smith deduces ((f) v (h)) from (f) Jones owns a Ford
(iv) Smith believes ((f) v (h)) as a result of this deduction
Is ^ correct, to any philo wizards out there? Is Smith/Gettier using a deduction in the Gettier case? I need help my peeps!