scholarly journals Reconditioning the conditional [Recondicionando o condicional]

2016 ◽  
Vol 23 (40) ◽  
pp. 9-27
Author(s):  
David Miller
Keyword(s):  
Conditional Probability ◽  
Probability Function ◽  
Primary Concern ◽  
Conditional Probabilities ◽  
Indicative Conditional ◽  
Everyday Language ◽  
Conditional Statements ◽  
The Absolute ◽  
Truth Value

Many authors have hoped to understand the indicative conditional construction in everyday language by means of what are usually called conditional probabilities. Other authors have hoped to make sense of conditional probabilities in terms of the absolute probabilities of conditional statements. Although all such hopes were disappointed by the triviality theorems of Lewis (1976), there have been copious subsequent attempts both to rescue CCCP (the conditional construal of conditional probability) and to extend and to intensify the arguments against it. In this paper it will be shown that triviality is avoidable if the probability function is replaced by an alternative generalization of the deducibility relation, the measure of deductive dependence of Miller and Popper (1986). It will be suggested further that this alternative way of orchestrating conditionals is nicely in harmony with the test proposed in Ramsey (1931), and also with the idea that it is not the truth value of a conditionalstatement that is of primary concern but its assertability or acceptability.

The dependence of the majority voting decision-making probabilities on a multi-expert binary system experts number

2020 ◽  
pp. 7-14
Author(s):  
E. D. Avedyan ◽  
Le Thi Trang Linh
Keyword(s):  
Decision Making ◽  
Binary System ◽  
Conditional Probability ◽  
Majority Voting ◽  
Correct Solution ◽  
Conditional Probabilities ◽  
Analytical Results ◽  
Independent Expert ◽  
Mutually Independent

The article presents the analytical results of the decision-making by the majority voting algorithm (MVA). Particular attention is paid to the case of an even number of experts. The conditional probabilities of the MVA for two hypotheses are given for an even number of experts and their properties are investigated depending on the conditional probability of decision-making by independent experts of equal qualifications and on their number. An approach to calculating the probabilities of the correct solution of the MVA with unequal values of the conditional probabilities of accepting hypotheses of each statistically mutually independent expert is proposed. The findings are illustrated by numerical and graphical calculations.

scholarly journals NONCONGLOMERABILITY FOR COUNTABLY ADDITIVE MEASURES THAT ARE NOT κ-ADDITIVE

2016 ◽  
Vol 10 (2) ◽  
pp. 284-300 ◽  
Author(s):  
MARK J. SCHERVISH ◽  
TEDDY SEIDENFELD ◽  
JOSEPH B. KADANE
Keyword(s):  
Conditional Probability ◽  
Inaccessible Cardinal ◽  
Conditional Probabilities ◽  
Uncountable Cardinal ◽  
Additive Probability ◽  
De Finetti ◽  
Additive Measures

AbstractLet κ be an uncountable cardinal. Using the theory of conditional probability associated with de Finetti (1974) and Dubins (1975), subject to several structural assumptions for creating sufficiently many measurable sets, and assuming that κ is not a weakly inaccessible cardinal, we show that each probability that is not κ-additive has conditional probabilities that fail to be conglomerable in a partition of cardinality no greater than κ. This generalizes a result of Schervish, Seidenfeld, & Kadane (1984), which established that each finite but not countably additive probability has conditional probabilities that fail to be conglomerable in some countable partition.

Conditional Probability

2017 ◽  
Author(s):  
Kenny Easwaran
Keyword(s):  
Conditional Probability ◽  
Conditional Probabilities ◽  
Unconditional Probability

Conditional probability has been put to many uses in philosophy, and several proposals have been made regarding its relation to unconditional probability, especially in cases involving infinitely many alternatives that may have probability 0. This chapter briefly summarizes some of the literature connecting conditional probabilities to probabilities of conditionals and to Humphreys' Paradox for chances, and then investigates in greater depth the issues around probability 0. Approaches due to Popper, Rényi, and Kolmogorov are considered. Some of the limitations and alternative formulations of each are discussed, in particular the issues arising around the property of “conglomerability” and the idea that conditional probabilities may depend on a conditioning algebra rather than just an event.

scholarly journals Disintegration and Bayesian inversion via string diagrams

2019 ◽  
Vol 29 (7) ◽  
pp. 938-971 ◽  
Author(s):  
Kenta Cho ◽  
Bart Jacobs
Keyword(s):  
Probability Theory ◽  
Conditional Probability ◽  
Opposite Direction ◽  
Bayesian Inversion ◽  
Conditional Probabilities ◽  
Discrete Probability ◽  
Joint State

AbstractThe notions of disintegration and Bayesian inversion are fundamental in conditional probability theory. They produce channels, as conditional probabilities, from a joint state, or from an already given channel (in opposite direction). These notions exist in the literature, in concrete situations, but are presented here in abstract graphical formulations. The resulting abstract descriptions are used for proving basic results in conditional probability theory. The existence of disintegration and Bayesian inversion is discussed for discrete probability, and also for measure-theoretic probability – via standard Borel spaces and via likelihoods. Finally, the usefulness of disintegration and Bayesian inversion is illustrated in several examples.

Is Kierkegaard’s Absolute Paradox Hume’s Miracle?

1998 ◽  
pp. 119-125 ◽  
Author(s):  
Jyrki Kivelä
Keyword(s):  
Human Being ◽  
Historical Events ◽  
The Absolute ◽  
Truth Value

I clarify Hume's concept of miracle with Kierkegaard's concept of absolute paradox. I argue that absolute paradox is like that miracle which, according to Hume, allows a human being to believe Christianity against the principles of his understanding. I draw such a conclusion on the basis that Kierkegaard does not think Christianity is a doctrine with a truth value and, furthermore, he holds that all historical events (such as miracles) are doubtful. Kierkegaard emphasizes the absolute paradox as the condition of faith in such a way that it becomes close to Hume's idea of personal miracle which causes the subversion of the believer's principles of understanding. Hence, the absolute paradox cannot be a possible supporting event (Hume's first miracle) for the credibility of Christianity. Absolute paradox more closely approximates Hume's second miracle insofar as it makes persons believe contrary to their custom and experience.

RAMSEY’S TEST, ADAMS’ THESIS, AND LEFT-NESTED CONDITIONALS

2010 ◽  
Vol 3 (3) ◽  
pp. 467-484 ◽  
Author(s):  
RICHARD DIETZ ◽  
IGOR DOUVEN
Keyword(s):  
Conditional Probability ◽  
Van Fraassen ◽  
Indicative Conditional ◽  
Ramsey’S Test

Adams famously suggested that the acceptability of any indicative conditional whose antecedent and consequent are both factive sentences amounts to the subjective conditional probability of the consequent given the antecedent. The received view has it that this thesis offers an adequate partial explication of Ramsey’s test, which characterizes graded acceptability for conditionals in terms of hypothetical updates on the antecedent. Some results in van Fraassen (1976) may raise hope that this explicatory approach to Ramsey’s test is extendible to left-nested conditionals, that is, conditionals whose antecedent is itself conditional in form. We argue that this interpretation of van Fraassen’s results is to be rejected. Specifically, we provide an argument from material inadequacy against a generalization of Adams’ thesis for left-nested conditionals.

scholarly journals Discussion of ``V-Matrix Method of Solving Statistical Inference Problems" by Vlamidir Vapnik and Rauf Izmailov

2018 ◽  
Author(s):  
Niharika Gauraha
Keyword(s):  
Conditional Probability ◽  
Optimization Problem ◽  
Probability Function ◽  
Future Research ◽  
Short Discussion ◽  
Quadratic Optimization Problem ◽  
Inference Problems ◽  
Consistent Solution ◽  
Constrained Quadratic Optimization ◽  
Conditional Probability Function

We would like to begin by stating that we have not fully understood the formulation of V-matrix conceptually. However, We are fascinated by the idea of estimation of conditional probability function without assuming any probabilistic model. In this short discussion, we would like to present that the proposed constrained quadratic optimization problem for conditional probability estimation using v-matrix based method may not have a consistent solution always. We are sure that the paper will stimulate a deeper exploration of V-matrix based methods for inference in high-dimensional problems in future research.

scholarly journals N-gram probability effects in a cloze task

2014 ◽  
Vol 9 (3) ◽  
pp. 437-472 ◽  
Author(s):  
Cyrus Shaoul ◽  
R. Harald Baayen ◽  
Chris F. Westbury
Keyword(s):  
Conditional Probability ◽  
Language Processing ◽  
Implicit Knowledge ◽  
Empirical Measure ◽  
Word Choice ◽  
Conditional Probabilities ◽  
Linguistic Context ◽  
Specific Context ◽  
Probabilistic Information ◽  
N Gram

What knowledge influences our choice of words when we write or speak? Predicting which word a person will produce next is not easy, even when the linguistic context is known. One task that has been used to assess context dependent word choice is the fill-in-the-blank task, also called the cloze task. The cloze probability of specific context is an empirical measure found by asking many people to fill in the blank. In this paper we harness the power of large corpora to look at the influence of corpus-derived probabilistic information from a word’s micro-context on word choice. We asked young adults to complete short phrases called n-grams with up to 20 responses per phrase. The probability of the responded word and the conditional probability of the response given the context were predictive of the frequency with which each response was produced. Furthermore the order in which the participants generated multiple completions of the same context was predicted by the conditional probability as well. These results suggest that word choice in cloze tasks taps into implicit knowledge of a person’s past experience with that word in various contexts. Furthermore, the importance of n-gram conditional probabilities in our analysis is further evidence of implicit knowledge about multi-word sequences and support theories of language processing that involve anticipating or predicting based on context.

Causal and noncausal conditionals: An integrated model of interpretation and reasoning

2005 ◽  
Vol 58 (8) ◽  
pp. 1479-1513 ◽  
Author(s):  
Andrea Weidenfeld ◽  
Klaus Oberauer ◽  
Robin Hörnig
Keyword(s):  
Conditional Probability ◽  
Causal Link ◽  
Integrated Model ◽  
Path Model ◽  
Willingness To Accept ◽  
Indirect Pathway ◽  
Degree Of Belief ◽  
Direct Pathway ◽  
Conditional Statements ◽  
Causal Path

We present an integrated model for the understanding of and the reasoning from conditional statements. Central assumptions from several approaches are integrated into a causal path model. According to the model, the cognitive availability of exceptions to a conditional reduces the subjective conditional probability of the consequent, given the antecedent. This conditional probability determines people's degree of belief in the conditional, which in turn affects their willingness to accept logically valid inferences. In addition to this indirect pathway, the model contains a direct pathway: Availability of exceptional situations directly reduces the endorsement of valid inferences. We tested the integrated model with three experiments using conditional statements embedded in pseudonaturalistic cover stories. An explicitly mentioned causal link between antecedent and consequent was either present (causal conditionals) or absent (arbitrary conditionals). The model was supported for the causal but not for the arbitrary conditional statements.

Sign in / Sign up

Export Citation Format

Share Document