- It seems that we have knowledge. To know a proposition P0 we must have a reason P1
that supports P0 by providing evidence for it. A proposition, however, is a reason only if there is
a proposition that supports it. This requires that we have a reason P2 that supports P1, and so on.
The resulting sequence of reasons is endless: infinite or circular. We cannot, however, acquire
support by means of endless regresses. Thus we have no knowledge.
That, roughly, is the epistemic regress problem. Some of our core epistemic assumptions
are jointly inconsistent, a paradox. To solve this problem we must understand it. Unfortunately,
the best extant statement of the problem makes unduly strong assumptions and thus does not
The Epistemic Regress Problem, page 2
capture its deepest challenges. Contrary to the received version, the regress paradox is not just a
problem about knowledge and justification, it concerns evidential support, a more basic
- Call a finite or infinite sequence of propositions σ = 〈P0, P1, … Pn (…)〉 implicationordered
(I-ordered) just in case σ has propositions in at least its first two places and every
member of σ is implied by its successor, if it has one. Similarly, call a sequence of propositions σ
support-ordered (S-ordered) just in case σ is I-ordered, the elements of σ are propositions
relevantly accessible to a person at a time, and every member of σ is supported by its successor,
if it has one. So a regress of reasons is an S-ordered sequence of propositions.
An infinite regress of reasons is an S-ordered sequence every component of which has a
successor. There are two kinds of such sequences, however, and I shall refine my terminology to
capture this distinction. First, there are sequences with infinitely many filled places. Sequence σS
= 〈I have three sisters, The number of my sisters = √9, I have three sisters, …〉 and the sequence
σT = 〈I am at least 7 feet tall, I am at least 8 feet tall, I am at least 9 feet tall, …〉 have this
feature. Call such sequences ‘endless.’ An endless regress of reasons, then, is an S-ordered
sequence of propositions every member of which has a successor. Second, there are endless
regresses with infinitely many components. Endless sequence σT has infinitely many
components, unlike endless sequence σS. I reserve ‘infinite’ for sequences with infinitely many
components. An infinite regress of reasons, then, is an S-ordered sequence of propositions σ
with infinitely many components. Every infinite regress of reasons is endless, but not conversely.
I now state the two versions of the regress problem. The constituent propositions are
The Epistemic Regress Problem, page 4
given shorthand names and stated in (philosopher’s) English and in a first-order language. Let
the variables ‘x’, ‘y’, and ‘z’ range over the domain P of propositions relevantly accessible to a
person at a time. Assign the one-place predicate ‘J’ to the members of P that are epistemically
justified: the propositions that it is permissible, virtuous, or otherwise good for the person to
accept at that time. Let the two-place predicate ‘S’ express the relation between members of P
that obtains when the first is supported by the second.
May 9th, 2015
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Jun 26th, 2017
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