OK, so the trouble with logical induction is assuming mathematical realism, where “the claim that the 87,653rd digit of π is a 7” is either true or false even when not yet evaluated by someone, and the paper is discussing a way to assign a reasonable probability to it (e.g. ^{1}⁄_{10} in this case if you know nothing about digits or pi apriori) using the trading market model. In which case the implication condition does not hold ever, (since the chance of making an error in calculating the 87,653rd digit of π is always larger than in calculating 1+1). So they are treating logical uncertainty as environmental then. It makes sense if so.

OK, so the trouble with logical induction is assuming mathematical realism, where “the claim that the 87,653rd digit of π is a 7” is either true or false even when not yet evaluated by someone, and the paper is discussing a way to assign a reasonable probability to it (e.g.

^{1}⁄_{10}in this case if you know nothing about digits or pi apriori) using the trading market model. In which case the implication condition does not hold ever, (since the chance of making an error in calculating the 87,653rd digit of π is always larger than in calculating 1+1). So they are treating logical uncertainty as environmental then. It makes sense if so.