This is an overview of infinitism in epistemology. Infinitism is a
family of views in epistemology about the structure of knowledge and epistemic
justification. It contrasts naturally with coherentism and foundationalism. All
three views agree that knowledge or justification requires an appropriately
structured chain of reasons. What form may such a chain take? Foundationalists
opt for non-repeating finite chains. Coherentists (at least linear
coherentists) opt for repeating finite chains. Infinitists opt for
non-repeating infinite chains. Appreciable interest in infinitism as a genuine
competitor to coherentism and foundationalism developed only in the early
twenty-first century.
Introduces infinitism by explaining its intuitive motivations and the
context in which they arise. Next it discusses the history of infinitism, which
is mostly one of neglect, punctuated by brief moments of hostile dismissal.
Then there is a survey of arguments for and against infinitism.
For the most part, philosophers have assumed that knowledge requires
justified belief. That is, for some proposition (statement, claim or sentence)
P, if you know that P, then you have a justified belief that P. Knowledge that
P thus inherits its structure from the structure of the constituent justified
belief that P. If the justified belief is inferential, then so is the
knowledge. If the justified belief is “basic,” then so is the knowledge.
Introduction
We often provide reasons for the things we believe in order to justify holding the beliefs. But what about the reasons? Do we need reasons for holding those reasons? And if so, do we need reasons for holding those reasons that were offered as reasons for our beliefs? We’re left to wonder:
Does this regress ever end?
Infinitism is designed to answer that question. Given that one of the
goals of reasoning is to enhance the justification of a belief, Q, infinitism
holds that there are two necessary (but not jointly sufficient) conditions for
a reason in a chain to be capable of enhancing the justification of Q:
No reason can be Q itself, or equivalent to a conjunction containing Q
as a conjunct. That is, circular reasoning is excluded.
No reason is sufficiently justified in the absence of a further reason.
That is, there are no foundational reasons.
If both (1) and (2) are true, then the chain of reasons for any belief
is potentially infinite, that is, potentially unlimited.
The reason for accepting (1), and thereby rejecting circular reasoning
as probative, that is, as tending to prove, is that reasoning ought to be able
to improve the justificatory status of a belief. But if the propositional
content of a belief is offered as a reason for holding the belief, then no
additional justification could arise. Put more bluntly, circular reasoning begs
the question by positing the very propositional content of the belief whose
justificatory status the reasoning is designed to enhance.
Condition (1) is generally accepted, although some coherentists seem to
condone the sort of circular reasoning that it proscribes (for example, Lehrer
1997). However, these coherentists might not actually be denying (1). Rather,
they might instead be claiming that it is epistemically permissible to offer a
deliverance of a cognitive faculty as a reason for believing that the faculty
produces justified beliefs. On this alternative reading, these coherentists
don’t deny (1), because (1) concerns the structure, not the source, of
probative reasons. For example, suppose you employ beliefs produced by perception
as reasons for believing that perception is reliable. This need not involve
employing the proposition “perception is reliable” as one of the reasons.
Condition (2) is much more controversial. Indeed, denying (2) is a
component of the dominant view in epistemology: foundationalism. Many
foundationalists claim that there are beliefs, so-called “basic beliefs” or
“foundational beliefs,” which do not require further reasons in order to
function effectively as reasons for “non-basic” or “non-foundational” beliefs.
Basic beliefs are taken to be sufficiently justified to serve as, at least,
prima facie reasons for further beliefs in virtue of possessing some property
that doesn’t arise from, or depend on, being supported by further reasons. For
example, the relevant foundationalist property could be that the belief merely
reports the contents of sensations or memories; or it could be that the belief
is produced by a reliable cognitive faculty. The general foundationalist
picture of epistemic justification is that foundational beliefs are justified
to such an extent that they can be used as reasons for further beliefs, and
that no reasons for the foundational beliefs are needed in order for the
foundational beliefs to be justified.
Infinitists accept (2) and so deny that there are foundational beliefs
of the sort that foundationalists champion. The motivation for accepting (2) is
the specter of arbitrariness. Infinitists grant that in fact every actually
cited chain of reasons ends; but infinitists deny that there is any reason
which is immune to further legitimate challenge. And once a reason is
challenged, then on pain of arbitrariness, a further reason must be produced in
order for the challenged reason to serve as a good reason for a belief.
In addition to denying the existence of so-called basic beliefs,
infinitism takes reasoning to be a process that generates an important type of
justification — call it “reason-enhanced justification.” In opposition to
foundationalism, reasoning is not depicted as merely a tool for transferring
justification from the reasons to the beliefs. Instead, a belief’s
justification is enhanced when sufficiently good reasons are offered on its
behalf. Such enhancement can occur even when the reasons offered have not yet
been reason-enhanced themselves. That is, citing R as a reason for Q can make
one’s belief that Q reason-enhanced, even though R, itself, might not yet have
been reason-enhanced.
As mentioned above, infinitists reject the form of coherentism –
sometimes called “linear coherentism” – that endorses question-begging,
circular reasoning. But by allowing that reasoning can generate epistemic
justification, infinitists partly align themselves with another, more common
form of coherentism – often called “holistic coherentism.” Holistic coherentism
also accepts that reasoning can generate reason-enhanced justification (see
BonJour 1985, Kvanvig 2007). As the name “holistic coherentism” indicates,
epistemic justification is taken to be a property of entire sets of beliefs, rather
than a property of individual beliefs. Holistic coherentism holds that
individual beliefs are justified only in virtue of their membership in a
coherent set of beliefs. On this view, justification does not transfer from one
belief to another, as foundationalists or linear coherentists would claim;
rather, the inferential relationships among beliefs in a set of propositions
generates a justified set of beliefs; individual beliefs are justified merely
in virtue of being members of such a set. Sosa (1991, chapter 9) raises serious
questions about whether holistic coherentism is ultimately merely just a
disguised version of foundationalism; and if Sosa is correct, then some of the
objections to foundationalism would apply to holistic coherentism as well.
The argument pattern for infinitism employs the epistemic regress
argument and, thus, infinitists defend their view in a manner similar to the
way in which foundationalism and coherentism have been defended. This is the
pattern:
There are three possible, non-skeptical solutions to the regress
problem: foundationalism, coherentism and infinitism.
There are insurmountable difficulties with two of the solutions (in this
case, foundationalism and coherentism).
The third view (in this case, infinitism) faces no insurmountable
difficulties.
Therefore, the third view (in this case, infinitism) is the best
non-skeptical solution to the regress problem.
Historical Discussion of
Infinitism
The term ‘epistemic infinitism’ was used by Paul Moser in 1984, and the
phrase “infinitist’s claim” was used by John Post in 1987. Both philosophers
rejected infinitism.
Infinitism was well known by the time of Aristotle – and he rejected the
view. The empiricist and rationalist philosophers of the 17th and 18th
centuries rejected the view. Contemporary foundationalists and coherentists
reject the view.
Indeed, it is fair to say that the history of infinitism is primarily a
tale of neglect or rejection, with the possible exception of Charles Pierce
(Aikin 2011, pp. 80–90; see also “Some Questions Concerning Certain Faculties
Claimed for Man” in Peirce 1965, v. 5, bk. 2, pp. 135–155, esp. pp. 152–3). Some
have questioned whether Peirce was defending infinitism (BonJour 1985, p. 232,
n. 10; Klein 1999, pp. 320–1, n. 32). There has been some recent interest in
infinitism, beginning when Peter Klein published the first in a series of
articles defending infinitism (Klein 1998). But it clearly remains in the early
21st century a distinctly minority view about the structure of reasons.
Ever since Aristotle proposed objections to infinitism and defended
foundationalism, various forms of foundationalism have dominated Western
epistemology. For example, consider the epistemologies of the seventeenth and
eighteenth centuries; this is the formative period in which modern philosophy
shaped the issues addressed by contemporary epistemologists. Both the
empiricists and rationalists were foundationalists, although they clearly
disagreed about the nature of foundational reasons.
Consider this passage from Descartes’s Meditation One, where he explains
his method of radical doubt:
“But in as much as reason already persuades me that I ought no less
carefully to withhold my assent from matters which are not entirely certain and
indubitable than from those which appear to me manifestly to be false, if I am
able to find in each one some reason to doubt, this will suffice to justify
rejecting the whole. And for that end it will not be requisite that I should
examine each in particular, which would be an endless undertaking; for owing to
the fact that the destruction of the foundations of necessity brings with it
the downfall of the rest of the edifice, I shall only in the first place attach
those principles upon which all my former opinions rest.” (Descartes 1955
[1641], p. 145)
After producing a “powerful” reason for doubting all of his former
beliefs based on his senses, Descartes begins his search anew for a
foundational belief that is beyond all doubt and writes in Meditation Two:
Archimedes, in order that he might draw the terrestrial globe out of its
place, and transport it elsewhere demanded only that one point should be fixed
and unmovable; in the same way I shall have the right to conceive high hopes if
I am happy enough to discover one thing only which is certain. (Descartes 1955
[1641], p. 149)
He then happily produces what he takes—at least at that point in the
Meditations – to be that one, foundational proposition:
“So that after having reflected well and carefully examined all things
we must come to the definite conclusion that this proposition: I am, I exist,
is necessarily true each time I pronounce it, or that I mentally conceive it.”
(Descartes 1955 [1641], p. 150)
Regardless of the success or failure of his arguments, the point here is
that Descartes clearly takes it as given that both he and the empiricist, his
intended foil, will accept that knowledge is foundational and that the first
tasks are to identify the foundational proposition(s) and to uncover the
correct account of the nature of the foundational proposition(s). Once that is
accomplished, the second task is to move beyond it (or them) to other beliefs by
means of truth-preserving inferences. The Meditations presupposes a
foundationalist model of reasons without any hint of argument for
foundationalism.
Now consider this passage from Hume:
“In a word, if we proceed not upon some fact present to the memory or
senses, our reasonings would be merely hypothetical; and however the particular
links might be connected with each other the whole chain of inferences would
have nothing to support it, nor could we ever, by its means arrive at the
knowledge of any real existence. If I ask you why you believe a particular
matter of fact which you relate, you must tell me some reason; and this reason
will be some other fact connected with it. But as you cannot proceed after this
manner in infinitum, you must at last terminate with some fact which is present
to your memory or senses or must allow that your belief is entirely without
foundation.” (Hume 1955 [1748], pp. 59–60)
Setting aside an evaluation of the steps in Hume‘s argument for
foundationalism, notice that he too simply discards infinitism with the stroke
of a pen: “But as you cannot proceed in this manner in infinitum …”. To Hume,
infinitism seemed so obviously mistaken that no argument against it was needed.
So why did infinitism come to be so easily and so often rejected?
The short answer is: Aristotle. His arguments against infinitism and for
foundationalism were so seemingly powerful that nothing else needed to be said.
We can divide Aristotle’s objections to infinitism into three types. Each
pertains to the infinitist solution to the regress problem.
·
Misdescription
Objection: Infinitism does not correctly describe our epistemic practices; but
foundationalism does.
·
Finite
Mind Objection: Our finite minds are not capable of producing or grasping an
infinite set of reasons.
·
Unexplained
Origin Objection: Infinitism does not provide a good account of how
justification is generated and transferred by good reasoning; but
foundationalism does.
