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.

 

Infinitism maybe explained by its intuitive motivations and the context in which they arise. 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.

 

. 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