Infinitism Regained

2008

Stud Logica

Self Cite

Section: The Objections Refutedmentioning

confidence: 99%

Probabilistic Justification and the Regress Problem

2008

Stud Logica

Self Cite

“…From this it follows that P(¬E 0 ) = 0 and thus that P(E 0 ) = 1. 4 Far from supporting Turri's hope that his infinite chain can serve the foundationalist's purpose, the above reasoning has provided ammunition for an infinitist new-style (see Peijnenburg 2007). For, in complete accordance with the Weltanschauung of the latter, we have here a proposition that is entailed (up to measure zero) by an infinite chain of conditional probabilities.…”

Section: Limits As Grounds?mentioning

confidence: 84%

Grounds and limits: Reichenbach and foundationalist epistemology

2009

Synthese

Self Cite

From 1929 onwards, C. I. Lewis defended the foundationalist claim that judgements of the form 'x is probable' only make sense if one assumes there to be a ground y that is certain (where x and y may be beliefs, propositions, or events). Without this assumption, Lewis argues, the probability of x could not be anything other than zero. Hans Reichenbach repeatedly contested Lewis's idea, calling it "a remnant of rationalism". The last move in this debate was a challenge by Lewis, defying Reichenbach to produce a regress of probability values that yields a number other than zero. Reichenbach never took up the challenge, but we will meet it on his behalf, as it were. By presenting a series converging to a limit, we demonstrate that x can have a definite and computable probability, even if its justification consists of an infinite number of steps. Next we show the invalidity of a recent riposte of foundationalists that this limit of the series can be the ground of justification. Finally we discuss the question where justification can come from if not from a ground.

“…In several papers we have given counterexamples to this claim. That is, we have demonstrated that a proposition can have a well-defined nonzero probability, even though its probabilistic justification is forever postponed [1], [2], [3], [4].…”

mentioning

confidence: 89%

The Solvability of Probabilistic Regresses. A Reply to Frederik Herzberg

2010

Stud Logica

Self Cite

We have earlier shown by construction that a proposition can have a well-defined nonzero probability, even if it is justified by an infinite probabilistic regress. We thought this to be an adequate rebuttal of foundationalist claims that probabilistic regresses must lead either to an indeterminate, or to a determinate but zero probability. In a comment, Frederik Herzberg has argued that our counterexamples are of a special kind, being what he calls 'solvable'. In the present reaction we investigate what Herzberg means by solvability. We discuss the advantages and disadvantages of making solvability a sine qua non, and we ventilate our misgivings about Herzberg's suggestion that the notion of solvability might help the foundationalist.We further show that the canonical series arising from an infinite chain of conditional probabilities always converges, and also that the sum is equal to the required unconditional probability if a certain infinite product of conditional probabilities vanishes.