The Bayesian Model

2020 ◽  
pp. 19-60
Author(s):  
Scott Sturgeon
Keyword(s):  
Bayesian Model ◽  
Mental States ◽  
Probability Functions ◽  
Venn Diagrams ◽  
Mathematical Properties ◽  
The Absolute ◽  
Conditional Credence ◽  
Truth Tables

Chapter 2 introduces the Bayesian Model of rational credence. The mathematical properties of classic probability are explained—their linearity, cardinality, and so on—as well as the use of probability functions to model mental states. A game with balls is created and diagrammed to make visually vivid how probability works. Venn diagrams and truth-tables are used to illustrate everything for the absolute beginner. Conditional Credence is explained with intuitive examples, and the standard ratio formula is introduced. A game with marbles is then created and diagrammed to pump intuition about change of probability, which leads directly to Jeffrey-style kinematics. The chapter closes by describing a notionally possible agent, Creda, whose psychology matches the Bayesian Model.

The Bayesian Theory of States

2020 ◽  
pp. 61-100
Author(s):  
Scott Sturgeon
Keyword(s):  
Bayesian Model ◽  
Critical Discussion ◽  
Bayesian Theory ◽  
Point Of View ◽  
Probability Functions ◽  
Fundamental Part ◽  
Way Of Thinking ◽  
Conditional Credence ◽  
Extended Discussion

Chapter 3 is a critical discussion of the Bayesian theory of states. It argues that our psychology includes many more types of confidence than Bayesian credence. There is an extended discussion of the missing types of confidence—from both a functionalist and intuitive point of view. Conditional credence is discussed and it’s shown that the Bayesian way of thinking of it—baked into the formalism—is wrong. It is argued that conditional credence is a fundamental part of our rational psychology. Three attempts are then considered to generalize the Bayesian model: one uses midpoints of mathematical intervals, one uses midpoints along with 3-place psychological attitudes, and one uses richly membered sets of probability functions. It is argued that none of the generalizations work very well.

Time and Metaphysics: Kant and McTaggart on the Reality of Time

Kant Yearbook ◽  
2010 ◽  
Vol 2 (1) ◽  
pp. 175-194
Author(s):  
Matthew Rukgaber
Keyword(s):  
A Priori ◽  
Mental States ◽  
Infinite Regress ◽  
First Person ◽  
Main Argument ◽  
Person Perspective ◽  
The World ◽  
First Person Perspective ◽  
The Absolute ◽  
Mctaggart’S Argument

Abstract The paper examines Kant’s theory of time in light of McTaggart’s argument that time is unreal. First, it presents McTaggart’s theory of time and his argument that a contradiction inevitably emerges in time’s analysis, leading either to an infinite regress of times or the denial that time is real. The paper then shows that Kant rejects the absolute notion of time, the idea that there are eternal coordinates that are experienced by us as being in time. It argues against subjectivist or psychological interpretations of Kant’s theory of time. The main argument is that Kant’s notion of a priori intuition, rather than being the flow of mental states in consciousness, is the subject’s self-intuition as being temporally present, and, moreover, that the present acts as a temporal metric, specifying a first-person perspective in the world and designating a temporal simple.

scholarly journals Measuring the Magnitude of Health Inequality Between 2 Population Subgroup Proportions

2020 ◽  
Vol 189 (9) ◽  
pp. 987-996
Author(s):  
Makram Talih ◽  
Ramal Moonesinghe ◽  
David T Huang
Keyword(s):  
Health Disparities ◽  
Absolute Difference ◽  
Measurement Unit ◽  
Z Score ◽  
Underlying Distribution ◽  
Standard Measurement ◽  
Mathematical Properties ◽  
Population Subgroup ◽  
The Absolute ◽  
Measures Of Inequality

Abstract In this paper, we evaluate 11 measures of inequality, d(p1, p2), between 2 proportions p1 and p2, some of which are new to the health disparities literature. These measures are selected because they are continuous, nonnegative, equal to 0 if and only if |p1 − p2| = 0, and maximal when |p1 − p2| = 1. They are also symmetrical [d(p1, p2) = d(p2, p1)] and complement-invariant [d(p1, p2) = d(1 − p2, 1 − p1)]. To study intermeasure agreement, 5 of the 11 measures, including the absolute difference, are retained, because they remain finite and are maximal if and only if |p1 − p2| = 1. Even when the 2 proportions are assumed to be drawn at random from a shared distribution—interpreted as the absence of an avoidable difference—the expected value of d(p1, p2) depends on the shape of the distribution (and the choice of d) and can be quite large. To allow for direct comparisons among measures, we propose a standard measurement unit akin to a z score. For skewed underlying beta distributions, 4 of the 5 retained measures, once standardized, offer more conservative assessments of the magnitude of inequality than the absolute difference. We conclude that, even for measures that share the highlighted mathematical properties, magnitude comparisons are most usefully assessed relative to an elicited or estimated underlying distribution for the 2 proportions.

Internalism to the Rescue?

2019 ◽  
pp. 24-48
Author(s):  
Mark Richard
Keyword(s):  
Mental States ◽  
Theoretical Interest ◽  
David Chalmers ◽  
The Individual ◽  
Conditional Credence

If meanings are interestingly like species, meanings are multitudes and what our words mean isn’t up to us. This chapter doesn’t deny that one finds things that can reasonably be labeled ‘meanings’ at the level of the individual, or that these are of theoretical interest. It does deny that internalist theorizing about meaning provides a way to resuscitate the notion of analyticity. It also argues that meanings turn out to be much like diachronic ensembles of mental states related by analogs of descent—i.e. analogous to species. The first half of this chapter discusses a popular response to ‘Two Dogmas’ and demonstrates that this response requires an untenable picture of meaning. The second half takes up an internalist response to Quine due to David Chalmers, who suggests we think of conceptual constancy only in the intrapersonal case, identifying it with constancy of conditional credence. Chalmers’ proposal is worth serious consideration. But even from an internalist perspective, it’s unacceptable.

scholarly journals Truth Diagrams Versus Extant Notations for Propositional Logic

2019 ◽  
Vol 29 (2) ◽  
pp. 121-161
Author(s):  
Peter C.-H. Cheng
Keyword(s):  
Propositional Logic ◽  
Graphical Representation ◽  
Venn Diagrams ◽  
Partial Coverage ◽  
Linear Formula ◽  
Specific Interpretation ◽  
Truth Tables

Abstract Truth diagrams (TDs) are introduced as a novel graphical representation for propositional logic (PL). To demonstrate their epistemic efficacy a set of 28 concepts are proposed that any comprehensive representation for PL should encompass. TDs address all the criteria whereas seven other existing representations for PL only provide partial coverage. These existing representations are: the linear formula notation, truth tables, a PL specific interpretation of Venn Diagrams, Frege’s conceptual notation, diagrams from Wittgenstein’s Tractatus, Pierce’s alpha graphs and Gardner’s shuttle diagrams. The comparison of the representations succeeds in distinguishing ideas that are fundamental to PL from features of common PL representations that are somewhat arbitrary.

scholarly journals Radiocarbon Evidence from the Middle Bronze Age Settlement At Portella (Aeolian Islands, Italy): Chronological and Archaeological Implications

Radiocarbon ◽  
2011 ◽  
Vol 53 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Gianmarco Alberti
Keyword(s):  
Bronze Age ◽  
Bayesian Model ◽  
Aeolian Islands ◽  
Middle Bronze Age ◽  
Absolute Dating ◽  
The Absolute ◽  
Aeolian Archipelago

This paper deals with radiocarbon determinations from the Middle Bronze Age site of Portella on the island of Salina (Aeolian Archipelago, Italy). The available14C evidence is taken into account, in a simple Bayesian model, in order to explore the issue of the absolute chronology of both the settlement and the stage of the local cultural sequence to which Portella belongs. A high date is proposed for the start of the Aeolian (and Sicilian) Middle Bronze Age: 1556–1422 cal BC (95.4% confidence), with a a most likely (modal) date of about 1450 cal BC. Further, the analysis suggests that the Portella phase is likely to have been a very short one, with a span of 0–65 yr (68.2%) or 0–131 yr (95.4%). The archaeological implications are explored. The relation of these results to the evidence of ceramic phasing is also considered. Since Aegean datable ceramic imports are documented in Aeolian/Sicilian Middle Bronze Age contexts, the connection between Portella's chronology and the absolute dating of one of the Aegean phases (namely, Late Helladic IIIA1) is also investigated.

Radiocarbon Dating Khirbet Qeiyafa and the Iron I–IIA Phases in the Shephelah: Methodological Comments and a Bayesian Model

Radiocarbon ◽  
2015 ◽  
Vol 57 (5) ◽  
pp. 891-907 ◽  
Author(s):  
Israel Finkelstein ◽  
Eli Piasetzky
Keyword(s):  
Bayesian Model ◽  
Radiocarbon Dating ◽  
Methodological Issues ◽  
Close Proximity ◽  
The Absolute ◽  
Ceramic Typology ◽  
The One ◽  
Neighboring Sites

This article discusses methodological issues related to the radiocarbon dating of Khirbet Qeiyafa, mainly the question of whether the site should be dated solely according to samples retrieved there or dated as part of a regional sequence of stratigraphically based ceramic typology phases. For the latter, we deploy the large number of 14C determinations now available for several sites in the Shephelah, which are located in close proximity to each other, in order to establish a Bayesian model for the absolute chronology of the Iron I–IIA phases in the region. We argue that the information assembled from six neighboring sites in the Shephelah pushes forward the date of Qeiyafa to the 10th century, a date later than the one the excavators estimated based on the more limited 14C information from the site alone.

Bulk standards for low-temperature biological x-ray microanalysis

1984 ◽  
Vol 42 ◽  
pp. 282-283
Author(s):  
P. Echlin ◽  
M. McKoon ◽  
E.S. Taylor ◽  
C.E. Thomas ◽  
K.L. Maloney ◽  
...  
Keyword(s):  
Phase Separation ◽  
Low Temperature ◽  
Analytical Method ◽  
Salt Solutions ◽  
Absolute Concentration ◽  
Cooling Process ◽  
X Ray ◽  
The Absolute ◽  
Analytical Procedures ◽  
Electrical Conductors

Although sections of frozen salt solutions have been used as standards for x-ray microanalysis, such solutions are less useful when analysed in the bulk form. They are poor thermal and electrical conductors and severe phase separation occurs during the cooling process. Following a suggestion by Whitecross et al we have made up a series of salt solutions containing a small amount of graphite to improve the sample conductivity. In addition, we have incorporated a polymer to ensure the formation of microcrystalline ice and a consequent homogenity of salt dispersion within the frozen matrix. The mixtures have been used to standardize the analytical procedures applied to frozen hydrated bulk specimens based on the peak/background analytical method and to measure the absolute concentration of elements in developing roots.

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