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The theory of Dempster-Shafer (DS) belief functions (Dempster 1968, Shafer 1976) rejects the claim that degrees of belief can be measured by the epistemic agent’s betting behavior. A particular version of the theory of DS belief functions is the transferable belief model (Smets & Kennes 1994). It distinguishes between two mental levels: the credal level, where one entertains and quantifies various beliefs, and the pignistic level, where one uses those beliefs for decision making. Its twofold thesis is that (fair) betting ratios should indeed... |
When epistemologists say that knowledge implies belief (see the entry on epistemology), they use a qualitative notion of belief that does not admit of degrees (except in the trivial sense that there is belief, disbelief, and suspension of judgment). The same is true for philosophers of language when they say that a normal speaker, on reflection, sincerely asserts ‘[ltr][size=18]AA[/ltr]’ only if she believes that [ltr] |
In subjective probability theory complete ignorance of the ideal doxastic agent with respect to a particular proposition [ltr][size=18]AA[/ltr] is modeled by the agent’s having a subjective probability of .5 for [ltr]AA[/ltr] as well as its complement [ltr]W∖AW∖A[/ltr]. More generally, an agent with subjective probability Pr is said to be ignorant with respect to the partition [ltr] |
The theory of subjective probabilities is not an adequate description of people’s doxastic states (Kahneman & Slovic & Tversky 1982). It is a normative theory that tells us how an ideal doxastic agent’s degrees of belief should behave. The thesis that an ideal doxastic agent’s degrees of belief should obey the probability calculus is known as probabilism. So, why should such an agent’s degrees of belief obey the probability calculus?
The Dutch Book Argument provides... |
Subjective probability theory is the best developed account of degrees of belief. As a consequence, there is much more material to be presented here than in the case of other accounts. This section is structured into six subsections. The topics of these subsections will also be discussed in the sections on Dempster-Shafer theory, possibility theory, ranking theory, belief revision theory, and nonmonotonic reasoning. However, as there is less (philosophical) literature about these latter accounts, there will not be separate subsections there. |
Epistemology is the study of knowledge and justified belief. Belief is thus central to epistemology. It comes in a qualitative form, as when Sophia believes that Vienna is the capital of Austria, and a quantitative form, as when Sophia’s degree of belief that Vienna is the capital of Austria is at least twice her degree of belief that tomorrow it will be sunny in Vienna. Formal epistemology, as opposed to mainstream epistemology (Hendricks 2006), is epistemology done in a formal way, that is, by employing tools from logic and mathematics. The goal... |
Syllogistic logic reached the height of its development in Buridan and for the next two hundred years, little was said about it. Buridan's younger associates at Paris, Albert of Saxony and Marsilius of Inghen, were both competent logicians, but neither made any substantive additions to the theory developed by their master. Paul of Venice was a well-known early fifteenth-century logician, but he had little to say about the theory of the syllogism. In the late fifteenth and sixteenth centuries, several very good logicians wrote books on logic, perhaps... |
John Buridan (c. 1300–1361) was the foremost logician of the later Middle Ages and in his hands the theory of the syllogism was reworked and developed well beyond anything seen before in the history of logic. His two most important logical works are the Treatise on Consequence and theSummulae de Dialectica. The presentation here is primarily based on the Treatise (for further discussion, see Lagerlund 2000, Chapter 5, and Zupko 2003, Chapters 5–6).
In the Treatise,... |
An important figure in the history of syllogistic logic is Richard of Campsall (c. 1280/90–1350/60). Sometime before 1308 he wrote his Questions on the Books of the Prior Analytics(Questiones super librum Priorum Analeticorum), a commentary on the first book of the Prior Analytics that devotes 14 of its 20 questions to modal syllogistic. He seems to think that there is nothing to add to the theory of assertoric syllogistic and his presentation of it is fairly standard, but he has lots of interesting things to say about modal... |
The first known commentary on the Prior Analytics in the Latin West is an anonymous work that has recently been edited (Thomsen Thörnqvist 2015) but is not yet fully studied (see Thomsen Thörnqvist 2010 and 2013 for more details). The author has been called Anonymous Aurelianensis III by Sten Ebbesen, who studied parts of the work (Ebbesen 1981). He dates it to c. 1160–80. The theory of the assertoric syllogism was repeated and summarized in almost all logic works from this time, but there are no other major Latin commentaries that we know... |
Arabic logic begins in the middle of the eighth century. As with logic in the Latin tradition, it has its foundation in Ancient Greek logic, primarily in Aristotelian logic and syllogistics. The Syriac Christians adopted a teaching tradition in logic that included Porphyry’s Isagoge in addition to Aristotle's Categories, De interpretatione and the first seven chapters of the Prior Analytics. This teaching tradition was adopted and spread through the Arab conquest. During the Abbasid Caliphate (750-1258), there was a... |
The medieval tradition of logic is generally thought to have begun with Boethius (c. 475–526), who ambitiously tried to preserve what was left of philosophical learning from the declining culture of late antiquity. In fact, however, he was only able to save parts of ancient logic, primarily Aristotelian logic (see Lee 1984 for a discussion of Aristotle's syllogistic in late ancient thought). He wrote extensively on the theory of the syllogism, producing a Latin translation of the Prior Analytics, though it was not used very much before the... |
Aristotle's theory of the syllogism played an important role in the Western and Near Eastern intellectual traditions for more than two thousand years, but it was during the Middle Ages that it became the dominant model of correct argumentation.
Historically, medieval logic is divided into the old logic (logica vetus), the tradition stretching from Boethius (c. 480–525) until Abelard (1079–1142), and the new logic (logica nova), from the late twelfth century until the Renaissance. The division reflects the availability of ancient... |
The discussion of the past few sections has focused on the views and arguments of select figures within NE. The rationale for this focus has been twofold: first, because the positions and figures and in question have been at the forefront of recent discussions of NE; and second, because the general epistemological affinity between Kornblith and Goldman in particular (i.e., their common adherence to reliabilism) has allowed us to isolate and appreciate both the central challenges to NE and some of the major points of difference among its advocates.... |
Given that his moderate naturalism has him (agreeing and) disagreeing with certain elements both of TE and more “radical” naturalisms, it is not surprising that his position has come in for criticism from both sides. Thus, for example, Feldman (1999, 2012) and BonJour (1994) voice doubts about whether more modest forms of NE are both interesting and correct—whether, that is, plausible instances of the relevance of (e.g.) psychology to epistemology aren’t already accommodated by TE, and whether any genuinely newsworthy bearing of (e.g.) psychology... |
As the passage just quoted suggests, Goldman sees conceptual analysis and appeals to intuition as playing an ineliminable role within epistemological practice.[size=12][19] While, as noted above, within TE such an analysis has standardly taken the form of a search for necessary and sufficient conditions, Goldman is dubious of that specific approach (e.g., 1986: 38–39, 2015, 2007: 23 and papers... |
Unlike Quine, Kornblith retains knowledge as a central epistemological notion. However, his position departs dramatically from TE in how the nature of epistemological investigation is understood. Here, in both its proper target and its methods, epistemology is held not to be as TE and its practitioners portray them. As to the first, recall (Section 1.3) that a, if not the, central task of analytic... |
Various responses to the preceding objections have been suggested. Addressing the first will give us occasion to clarify typical current naturalists’ motivations, as well as—and relatedly—to get a better sense of what is, and is not, central to NE. Addressing the fourth and fifth will carry us beyond Quine and into the heart of current disagreements with, and within, NE.
(1) Recall, first, the non sequitur objection, according to which Quine falsely equates TE... |
Just as very few proponents of TE endorse Descartes’ own epistemological views, very few advocates of NE endorse the position presented—or seemingly presented —in the paper that forms the starting point of contemporary discussions of NE, Quine’s “Epistemology Naturalized” (1969b). However, because of its undeniable historical importance, and because it will serve to introduce some of the principal objections to NE, it can hardly be ignored.
Like Descartes, Quine takes epistemology to... |
And so too for those who favor NE: Naturalists join in rejecting one or more of the above features of traditional (non-naturalistic) epistemology. But different theories and theorists within NE reject—to varying extents, in different ways, and for different reasons—different combinations of these features, and so differ in how much distance is put between their specific view and traditional epistemologies.[size=12][ |
Naturalism in epistemology, as elsewhere, has a long history. But it is only relatively recently that it has gone by just that name and received so much focused attention. As in other areas of philosophy, questions concerning naturalism’s merits are central to recent epistemological debate. While many epistemological theories and positions are agreed by all to exemplify, or to run counter to, naturalistic epistemology (NE), it is difficult to characterize precisely, since “naturalism” is used to refer to a range of positions, commitments, and so... |
http://plato.stanford.edu/new.htmlA number of authors have argued that practical reason has available to it the resources to accommodate value incommensurability in ways that would appear to address the concern raised by Regan.
Charles Taylor outlines two such sets of resources. First, we are able to appeal to “constitutive goods that lie behind the life goods” our sense of which is “fleshed out, and passed on, in a whole range of media: stories, legends, portraits of exemplary figures and their actions and passions,... |
Value incommensurability has also been invoked to make sense of a central feature of supposed moral dilemmas—namely, that no matter which alternative the agent chooses, she fails to do something she ought to do. Although moral dilemmas involve choices between concrete bearers of value, the apparent value conflicts involved in these choices have led some philosophers to relate moral dilemmas to the incommensurability of values. Henry Richardson, for example, takes the situation confronting Sophie in the novel Sophie’s Choice—that one of her... |
After determining what incommensurability and incomparability are, the next step is to assess the arguments for and against these possibilities. That is the task of this section.
The most direct argument against the possibility that values are incommensurable is based on value monism (e.g., Mill 1979 and Sidgwick 1981). Donald Regan, for example, argues that “given any two items (objects, experiences, states of affairs, whatever) sufficiently well specified so that it is apposite to... |
Rather than focus on commensurability between abstract values, a number of authors focus on the comparability between concrete bearers of value, often in the context of choice (Broome 1997, 2000; Chang 1997, 2002; Griffin 1986; Raz 1986). Bearers of value sometimes appear incomparable in cases like Joseph Raz’s example of the choice between careers (described above in subsection 1.2).
The case for incomparability in such examples relies in part on what Ruth Chang calls the “Small Improvement... | |
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