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Confirmation is a graded notion: evidence can confirm a hypothesis to a greater or lesser degree. There has been debate about how to measure degree of confirmation. Starting from the observation that we would like evidence to be a discriminating indicator of truth, we conduct computer simulations to determine how well the various known measures of confirmation predict the extent to which a given piece of evidence fulfills that role, given a hypothesis of interest. The outcomes show that some measures are markedly better indicators of truth than others.
It has become standard practice in philosophy to follow Richard Foley (1992) in distinguishing between an epistemology of belief and an epistemology of degrees of belief. The former distinguishes among three doxastic attitudes: belief, disbelief (i.e., believing something not to be the case), and suspension of belief. Key to the latter epistemology is the idea that beliefs come in various strengths, where the strength of a belief can be measured on a continuous scale (typically, the unit interval but that is a matter of convention). Many have hoped that because the two epistemologies appear to differ only in assuming a different granularity while looking at the same attitude – that of belief – there must be some way to connect them. Finding one or more bridge principles between these epistemologies seems a worthy endeavor indeed, for given such principles, we might be able to derive truths about the notion of categorical belief from insights about the notion of graded belief, or vice versa.
We talk and think about our beliefs both in qualitative terms – as when we say that we believe A, or disbelieve A, or are agnostic about A – and in quantitative terms, as when we say that we believe A to a certain degree, or are more strongly convinced of A than of B. Traditionally, analytic philosophers, especially epistemologists, have focused on categorical (all-or-nothing) beliefs, to the almost complete neglect of graded beliefs. On the other hand, the Bayesian boom that started in the late 1980s has led many philosophers to concentrate fully on graded beliefs; these philosophers have sometimes rejected talk about categorical beliefs as being unscientific and as therefore having no place in a serious epistemology.
We talk and think about our beliefs both in a categorical (yes/no) and in a graded way. How do the two kinds of belief hang together? The most straightforward answer is that we believe something categorically if we believe it to a high enough degree. But this seemingly obvious, near-platitudinous claim is known to give rise to a paradox commonly known as the 'lottery paradox' – at least when it is coupled with some further seeming near-platitudes about belief. How to resolve that paradox has been a matter of intense philosophical debate for over fifty years. This volume offers a collection of newly commissioned essays on the subject, all of which provide compelling reasons for rethinking many of the fundamentals of the debate.
This paper argues that if epistemological contextualism is correct, then not only have knowledge-ascribing sentences context-sensitive truth conditions, certain comparative and superlative constructions involving ‘know’ have context-sensitive truth conditions as well. But not only is there no evidence for the truth of the latter consequence, the evidence seems to indicate that it is false.
The position I aim to criticize has been defended by, most notably, Stewart Cohen, Keith DeRose, and David Lewis. While the contextualist theories offered by these authors differ in their details, the problem to be presented seems to arise irrespective of these details. And though in most of the illustrations below I rely on Lewis's account, I could have made essentially the same points in terms of any of the other accounts.
The authors argue that group performance depends on the degree to which group members identify with the group as well as on their degree of differentiation. In this commentary, I discuss results from agent-based simulations, suggesting that group performance depends, at least in part, on features orthogonal to agents' caring about group performance or about how they are perceived by other group members.
In Putnam's characterization of metaphysical realism, this position is committed to a correspondence conception of truth as well as to the claim that truth outstrips empirical adequacy. Putnam's model-theoretic argument seeks to refute metaphysical realism by arguing that, on this conception of truth, truth and empirical adequacy must coincide. It has been noted in the literature that the argument involves as an auxiliary premise a thesis sometimes called “semantic naturalism,” according to which semantics is an empirical science like any other. At the time when the model-theoretic argument was presented, semantic naturalism was taken to imply, among other things, that if truth is indeed to be defined in terms of a correspondence relation, then that relation ought to be characterizable in physical terms. This chapter argues that metaphysical realists should reject semantic naturalism as a fundamentally physicalist-reductionist program. It does not follow that they must abandon the view that semantics is to be pursued as an empirical science. This chapter points to some promising approaches to semantics that are scientific without being physicalist and that do not support Putnam's model-theoretic argument.
The model-theoretic argument
Hilary Putnam's (1978, 1980) widely discussed model-theoretic argument (MTA) is directed against metaphysical realism, two key tenets of which – in Putnam's statement of the position – are correspondence truth
(CT) Truth is a matter of correspondence to the facts. and methodological fallibism
(MF) Even an empirically adequate theory – a theory that is predictively accurate and that satisfies any theoretical virtue one may like – may still be false.
The conclusion of the MTA is that MF is false: an epistemically ideal theory is guaranteed to be true.
Despite its somewhat intimidating name, the core of the MTA is quite straightforward, and involves no model theory beyond what is commonly covered in an intermediate logic course. The argument can be usefully split into three parts. The first part starts by assuming that the world is infinite, and then considers an empirically adequate theory that has (also) infinite models but that is otherwise arbitrary. On some interpretations of this theory's language, the theory will no longer be empirically adequate.
As I understand the term “acceptability,” it designates justified or rational believability. To say that a given proposition is acceptable for a person is to say that it is epistemically all right for the person to adopt that proposition as a belief. In Section 3.2, it was already mentioned that the term “acceptability” is used both in a categorical and in a graded sense. Both the categorical and the graded notion of acceptability play a vital role in our epistemic life; we go routinely back and forth between thinking and speaking about what we deem acceptable and about the degrees to which we deem various things acceptable. Neither mode is to be dismissed off-hand as being loose talking and thinking, nor is it even clear on what grounds one mode could be said to be inferior or subservient to the other. Accordingly, many philosophers hold that we need both an epistemology of belief and an epistemology of degrees of belief.
It would seem that we can have both the attitude of deeming categorically acceptable and the attitude of deeming acceptable to a certain degree vis-à-vis conditionals as well. That, at any rate, is what a number of authors have been supposing in their work on either the categorical acceptability conditions of conditionals or their graded acceptability conditions (or both). It was noted in Section 1.1 that the issue of the acceptability of conditionals is one of the rare topics on which philosophers tend to agree. In the previous chapter, we saw that most philosophers agree – wrongly, as was argued – on what the probabilities of conditionals cannot be, whereas the question of what these probabilities are is a matter of ongoing debate. With respect to the issue of acceptability, the agreement is more substantial. Many philosophers agree on what the graded acceptability conditions of conditionals are, and there is also a good deal of agreement on the categorical acceptability conditions.
Thus one might think that if a whole chapter of this book is to be devoted at all to issues – graded and categorical acceptability of conditionals – on which virtually everyone agrees, the chapter will be a short one. Instead, this chapter is the longest in the book. The reason for this is that I believe the near-consensus on both issues to be misguided, and arguing against the mainstream requires proper backing.
I am not under the illusion that I have been able to settle once and for all any of the questions that were listed at the beginning of this book. But nothing of that order was promised or could have reasonably been expected. At the same time, I do believe that some progress has been made in becoming clearer on a number of those questions.
Until very recently, the epistemology of conditionals was, for the most part, a tale of two theses: Stalnaker's Hypothesis (SH) and Adams’ Thesis (AT). That the former is false and that the latter is true seemed to be the only two certainties in a sea of uncertainties and controversies. Neither “certainty” was backed by empirical evidence, and neither seemed to need such backing: the falsity of SH seemed to follow from indubitable formal results, and the truth of AT seemed a matter of course. It is more than ironic that, as we saw in Chapters 3 and 4, recent empirical results suggest that philosophers have gotten things wrong with respect to both claims: SH has been experimentally confirmed several times over, and in one experiment AT was refuted (which is refutation enough).
More specifically, and as explained in Chapter 3, whereas the data apparently in favor of SH might betray a systematic error in how people judge the probabilities of conditionals, or in how they determine conditional probabilities, or in both, further empirical research was seen to support a more charitable interpretation of those data, one that seeks fault rather with an assumption underlying the formal results that had been thought to undermine SH. Still more specifically, the presented results on the generalized version of SH lend credibility to a thesis that thus far many had considered to be no more than an interesting theoretical possibility, to wit, that the interpretation of the conditional-forming operator may vary from one belief state to another. Thus, the answer to the question of what the probabilities of conditionals are may be as simple as was believed before Lewis presented his triviality results: probabilities of conditionals equal conditional probabilities.
[T]he understanding of “if ” is not a narrow academic concern, but a matter of central importance in the understanding of what makes human intelligence special and distinctive.
Jonathan Evans and David Over, If (p. 153)
Conditionals are sentences of the forms “If φ, [then] ψ” and “ψ if φ,” such as
a. If the village is flooded, then the dam must have broken.
b. If Henry had come to the party, Sue would have come too.
c. Paul would have bought the house if it hadn't been so expensive.
One may also classify as conditionals sentences that can be naturally put in the above forms, such as
a. They will leave in an hour, unless John changes his mind.
b. No guts, no glory.
c. Give Louis a toy and he'll ruin it.
which can be rephrased as, respectively, (1.3a), (1.3b), and (1.3c):
a. If John does not change his mind, they will leave in an hour.
b. If a person lacks courage, there will be no glory for him or her.
c. If one gives Louis a toy, he ruins it.
In “If φ, then ψ,” φ is called the “antecedent” and ψ the “consequent.”
Conditionals are special. They are special for a number of reasons, but probably most conspicuously for the heated controversy that they have generated, and continue to generate. Not that controversy is anything out of the ordinary in philosophy. But even in philosophy, controversies commonly take place against a shared background of basic assumptions. For instance, while there is ongoing controversy about the concept of knowledge, there is at the same time broad (if not universal) agreement on many core issues surrounding that concept. Few dispute that knowledge is factive; that it requires belief as well as justification; that justified true belief is not sufficient for knowledge, however; that coherence amongst one's beliefs is not enough to elevate these to the status of knowledge; that we can gain knowledge from testimony; and so on and so forth. Not so in the case of conditionals. For almost any claim about conditionals that is not downright trivial, it will be exceedingly hard to find a majority, or even a sizable minority, of philosophers who adhere to it.