Grounds and limits: Reichenbach and foundationalist epistemology

Abstract

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.

The Solvability of Probabilistic Regresses. A Reply to Frederik Herzberg

“…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].…”

The Maxim of Probabilism, with special regard to Reichenbach

“…Hence, because of the lack of an explicit semantics and its clear separation from syntax, for a logician, Reichenbach's axiomatization was too much informal mathematics; for a practicing mathematician, the formal logic involved in the axiomatization separated it too much from mainstream mathematics to be useful; and for a physicist interested in applying probability theory, Reichenbach's axiomatization was too much logic, mathematics and philosophy altogether. For philosophers the axiomatization offered a target for philosophical criticism, which it received indeed (see section 5 in Eberhardt and Glymour's paper Eberhardt and Glymour (2009) for a review of the main philosophical criticisms, and Peijnenburg and Atkinson (2011) for a defense of Reichenbach against a specific objection raised by C.I. Lewis).…”

The dialectics of infinitism and coherentism: inferential justification versus holism and coherence

“…[44, p. 173] (emphasis inserted by this author) (For a discussion of some historical aspects of infinitism, cf. Peijnenburg and Atkinson [51,52].) In addition, the said consistency theorem can be used to counter more recent arguments to infinitism as well (cf.…”

“…The last inequality is, of course, equivalent to the formula P (E|F ) > P (E| F ) 6 which in the terminology of Peijnenburg [50] or Peijnenburg and Atkinson [51,52] is expressed as F probabilistically supports E.…”

“…The treatment of regresses of inferential justification in Peijnenburg [50] as well as Peijnenburg and Atkinson [51,52] suggests that at least the necessity part of a principle like (BPIJ) is not seen as extraordinarily controversial, neither by infinitists nor foundationalists that subscribe to some kind of probabilism.…”