Fallibilism And The Principle Of Closure Under Known Implications

The lottery puzzle stems from the same structure as the lottery paradox, which is a modern paradox credited to Professor Henry E. Kyburg Jr. The lottery puzzle, much like the lottery paradox is episodic, dealing with belief or knowledge. To understand the lottery puzzle, I will analyze the concepts of fallibilism and the principle of closure under known implications. Then I will analyze the plausibility and the strength of the possible solution to the lottery puzzle: the denial of knowledge of ordinary propositions, acceptance of the conclusion, and denial of closure under known implications. The fallibilism principle states that “if it is both highly probable and true that p, then S knows that p”(cite). In order for p to have a high probability
The lottery puzzle is constructed of two propositions, the ordinary and lottery propositions and a conclusion, which is identical to the structure principle of closure under known implications. The principle of closure under known implications states that “if S knows that p and if S knows that p implies q, then S knows that q” (cite). The first proposition, the ordinary proposition would be considered p and states what we already know, such as “my car is parked at the Target parking lot”. The next proposition, the lottery proposition, which would be considered q and states something that is highly likely, but we are not willing to say we know them like “if I know that my car is parked in the Target parking lot, then my car has not been stolen in the last few minutes”. Following the principle of fallabilism, the lottery proposition within the puzzle has a strong chance of being true, but it does not have to be absolutely true, there just needs to be circumstantial evidence of truth. The principle of closure under known implications states this high likelihood of the lottery proposition being true extends from the known truth of the ordinary proposition, but because of its lack of certainty we know that there is still a chance of the lottery proposition being false. This type of argument leads to a conclusion that we are not in a position to know, like for example, the conclusion to the
Acceptance of this solutions would lead to inconsistent assertions; we realize the association between the two propositions by accepting how one relates to the other but we deny knowledge of the second proposition. In order to accept this solution, we would have to reject either the addition closure principle, the equivalence principle or the distribution principle. The addition closure states that if we know p and deduce q from p while retaining knowledge of p then we must know q. The equivalence principle states that you know p is equivalent to q then we are in a position to know q. Lastly, the distribution principle claims that if you both p and q then you know p and you know q. None of these are possible if we accept the principle on which the structure of this lottery paradox rests on. By restricting the principle of closure, we run into even more problems like creating an ad hoc solution, a vague definition of lottery propositions and weak logical principles that do not hold for all propositions. Restriction also brings into question relevance of alternative propositions, which according the objective reading has to do with the possibility of it being realized as relevant and according to the subjective reading relevance is dependent on whether or not the subject, or