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. (shrink)

This paper critically evaluates the regress argument for infinitism. The dialectic is essentially this. Peter Klein argues that only an infinitist can, without being dogmatic, enhance the credibility of a questioned non-evident proposition. In response, I demonstrate that a foundationalist can do this equally well. Furthermore, I explain how foundationalism can provide for infinite chains of justification. I conclude that the regress argument for infinitism should not convince us.

Foundationalist, Coherentist. Skeptic etc., have all been united in one respect—all accept epistemic justification cannot result from an unending, and non‐repeating. chain of reasons. Peter Klein has recently challenged this minimal consensus with a defense of what he calls “Intinitism”—the position that justification can result from such a regress. Klein provides surprisingly convincing responses to most of the common objections to Infinitism, but I will argue that he fails to address a venerable metaphysical concern about a certain type of regress. (...) My conclusion will be that until Klein answers these metaphysical worries he will not have restored Infinitism as a viable option in epistemology. (shrink)

We have earlier shown by construction that a proposition can have a welldefined 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. (shrink)

We discuss two objections that foundationalists have raised against infinite chains of probabilistic justification. We demonstrate that neither of the objections can be maintained.

Foundationalist, Coherentist, Skeptic etc., have all been united in one respect--all accept epistemic justification cannot result from an unending, and non-repeating, chain of reasons. Peter Klein has recently challenged this minimal consensus with a defense of what he calls "Infinitism"--the position that justification can result from such a regress. Klein provides surprisingly convincing responses to most of the common objections to Infinitism, but I will argue that he fails to address a venerable metaphysical concern about a certain type of regress. (...) My conclusion will be that until Klein answers these metaphysical worries he will not have restored Infinitism as a viable option in epistemology. (shrink)

The purpose of this paper is to explain how infinitism—the view that reasons are endless and non-repeating—solves the epistemic regress problem and to defend that solution against some objections. The first step is to explain what the epistemic regress problem is and, equally important, what it is not. Second, I will discuss the foundationalist and coherentist responses to the regress problem and offer some reasons for thinking that neither response can solve the problem, no matter how they are tweaked. Then, (...) I want to present the infinitist solution to the problem and defend it against some of the well known objections to it. (shrink)

In Metaepistemology and Skepticism (Rowman & Littlefield:\n1995), Richard Fumerton defends foundationalism. As part of\nthe defense he rejects infinitism--the view that holds that\nthe solution to the problem of the regress of justificatory\nreasons is that the reasons are infinitely many and\nnonrepeating. I examine some of those arguments and attempt\nto show that they are not really telling against (at least\nsome versions of) infinitism. Along the way I present some\nobjections to his account of inferential justification.

In an earlier paper I argued that there are cases in which an infinite probabilistic chain can be completed. According to Jeremy Gwiazda, however, I have merely shown that the chain in question can be computed, not that it can be completed. Gwiazda thereby discriminates between two terms that I used as synonyms. In the present paper I discuss to what extent computability and completability can be meaningfully distinguished.

Consider the following process of epistemic justification: proposition $E_{0}$ is made probable by $E_{1}$ which in turn is made probable by $E_{2}$ , which is made probable by $E_{3}$ , and so on. Can this process go on indefinitely? Foundationalists, coherentists, and sceptics claim that it cannot. I argue that it can: there are many infinite regresses of probabilistic reasoning that can be completed. This leads to a new form of epistemic infinitism.

We prove, in ZFC,the existence of a definable, countably saturated elementary extension of the reals.

In a recent paper, Jeanne Peijnenburg and David Atkinson [ Studia Logica, 89:333-341 ] have challenged the foundationalist rejection of infinitism by giving an example of an infinite, yet explicitly solvable regress of probabilistic justification. So far, however, there has been no criterion for the consistency of infinite probabilistic regresses, and in particular, foundationalists might still question the consistency of the solvable regress proposed by Peijnenburg and Atkinson.

Łoś's theorem for bounded D -ultrapowers, D being the ultrafilter introduced by Kanovei and Shelah [4], is established.

This article establishes the existence of a definable , countably saturated nonstandard enlargement of the superstructure over the reals. This nonstandard universe is obtained as the union of an inductive chain of bounded ultrapowers . The underlying ultrafilter is the one constructed by Kanovei and Shelah [10].

We prove, in ZFC, the existence of a definable, countably saturated elementary extension of the reals.