Tuesday, August 25, 2020

Infinitism in Epistemology


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.

Sunday, August 9, 2020

Foreknowledge and Free Will


Suppose it were known, by someone else, what you are going to choose to do tomorrow. Wouldn’t that entail that tomorrow you must do what it was known in advance that you would do? In spite of your deliberating and planning, in the end, all is futile: you must choose exactly as it was earlier known that you would. The supposed exercise of your free will is ultimately an illusion.

Historically, the tension between foreknowledge and the exercise of free will was addressed in a religious context. According to orthodox views in the West, God was claimed to be omniscient (and hence in possession of perfect foreknowledge) and yet God was supposed to have given humankind free will. Attempts to solve the apparent contradiction often involved attributing to God special properties, for example, being “outside” of time.

However, the trouble with such solutions is that they are generally unsatisfactory on their own terms. Even more serious is the fact that they leave untouched the problem posed not by God’s foreknowledge but that of any human being. Do human beings have foreknowledge? Certainly, of at least some events and behaviors. Thus we have a secular counterpart of the original problem. A human being’s foreknowledge, exactly as would God’s, of another’s choices would seem to preclude the exercise of human free will.

  The Problem of Foreknowledge and Free Will

Moses Maimonides (1135-1204) has set out the problem in the traditional manner:

…”Does God know or does He not know that a certain individual will be good or bad? If thou sayest ‘He knows’, then it necessarily follows that [that] man is compelled to act as God knew beforehand he would act, otherwise God’s knowledge would be imperfect.…” (1966, pp. 99-100)

The argument can be extended. The thrust of the argument does not apply only to doing good or ill, but indeed to every human act, from the most mundane to the most significant. The argument could just as well read:

“Does God know or does He not know that a certain individual (let’s say the Prime Minister of Canada), on Feb. 3, 2081, will put on brown shoes when dressing in the morning? If thou sayest ‘He knows’, then it necessarily follows that the Prime Minister is compelled to act (that is, to put on brown shoes) as God knew beforehand he/she would, otherwise God’s knowledge would be imperfect. …”

The argument for the seeming impossibility of both God’s having foreknowledge and our having free will has troubled religious thinkers, philosophers, and jurists for centuries.

It is clear why theologians are troubled by the challenge of foreknowledge and free will. For most religions insist that God has given human beings free will and thus human beings can choose right from wrong, and that (in some religions at least) wrongful acts are sinful and worthy of divine punishment, while good acts are righteous and worthy of divine reward. But many of these same religions will also insist that God is omniscient, that is, God knows everything (and thus has perfect foreknowledge).[1] To deny either of these claims – that human beings have free will or that God is omniscient – amounts to heresy. Yet, on the face of it, each of these two claims appears to contradict the other.

But why should secular philosophers and jurists also be concerned with this conundrum? For two reasons.

First is that many, perhaps most, contemporary philosophers and jurists are keen to preserve the viability of the concept of free will. Our legal institutions, our very sense of what is praiseworthy and what is blameworthy, turn on the notion of free will. It is at the conceptual bedrock of our civilization that persons are creatures having the capacity of deliberation, that we have the ability to recognize right from wrong, that we have the ability to choose (to a large extent) what we do (and what we do not do), and – most especially – we are responsible for what we choose to do (and responsible for what we choose not to do).

Second is that the challenge to the existence of free will is posed not just by God’s foreknowledge but by any foreknowledge whatsoever. The religious version of the puzzle arises because God is said to have omniscience, that is, knowledge of everything. But the problem would arise if anyone at all (that is, anyone whatsoever) were to have knowledge of our future actions. This generalized version of the problem has come to be known as the problem of Epistemic Determinism (“epistemic” because it involves knowledge; see Epistemology). For example, if my wife were to know today that I would choose tea (rather than coffee) for my breakfast tomorrow, then one could argue (paralleling Maimonides’s argument) that it would be impossible for me not to choose tea tomorrow at breakfast.

The two concepts – (i) foreknowledge and (ii) human freedom – seem to be utterly incompatible. The challenge, then, (that is, the problem posed by epistemic determinism) is to find a way to show that

either  (1)       foreknowledge (of human beings’ future actions) does not exist;
or        (2)       free will does not exist;
or        (3)       the alleged logical relation between foreknowledge and the
exercise of free will is mistaken (that is, foreknowledge is not incompatible with the exercise of free will).
Historically, some theologians have tried to solve the puzzle by invoking unique properties of God. For example, some have argued that God is ‘outside of time’ (or that ‘His knowledge is timeless’) and thus His knowledge is not foreknowledge at all, that is, God’s knowledge does not occur before (or during, or after, for that matter) any events in the world. The trouble with such solutions is (a) they leave non-theistic versions of the puzzle untouched (for example, my wife’s knowing that I will drink tea tomorrow), and (b) we can construct a revised version of the puzzle explicitly invoking God’s timelessness, for example:

God is omniscient and His knowledge is timeless—that is, God knows timelessly all that has happened, is happening, and will happen. Therefore, if He knows timelessly that a person will perform such-and-such an action, then it is impossible for that person not to perform that action.

Some other theologians have argued that God has a ‘special way’ of knowing. Unlike human beings (and other sentient creatures) who must causally interact with the world (for example, read a report, see an event, examine evidence [such as ashes, skid marks, etc.]), God is said to “know directly“—that is, without the need of sensory data or of physical interaction with the world. Such a notion of ‘direct knowledge’ is problematic in itself; but more importantly, it is hard to see how it solves the problem at hand, indeed how it even addresses the problem. For, again, as was the case with arguing that God’s knowledge is outside of time, the same two objections can be raised to this putative solution: (a’) this latter attempted solution leaves the non-theistic version of the puzzle untouched; and (b’) we can construct a revised version of the puzzle explicitly invoking God’s “direct knowledge,” for example:

God knows directly (that is, without sensory data) all that has happened, is happening, and will happen. Therefore, if He knows directly that a person will perform such-and-such an action, then it is impossible for that person not to perform that action.

Contemporary philosophers, especially secular ones, seek a solution elsewhere. We are disinclined to pursue solutions that call upon special properties of God, especially since any such solution leaves the ‘secular’ version of the problem untouched.

The focus of attention has shifted dramatically. Secular philosophers argue that the supposed incompatibility arises out of a very subtle but seductive logical fallacy. So unobvious is this fallacy that it escaped detection by Maimonides and hundreds (perhaps even countless thousands) of other persons. The error has come to bear the name “The Modal Fallacy.”