scholarly journals Triviality Results for Probabilistic Modals

2017 ◽  
Vol 99 (1) ◽  
pp. 188-222
Author(s):  
Simon Goldstein
Keyword(s):  
Triviality Results

Two Interpretations of the Ramsey Test

2017 ◽  
Author(s):  
R.A. Briggs
Keyword(s):  
Conditional Probability ◽  
Ramsey Test ◽  
Triviality Results

According to Adams’ thesis the probability of a conditional is the conditional probability of the consequent given the antecedent. According to Stalnaker semantics, a conditional is true at a world just in case its consequent is true at all closest antecedent worlds to the original world. The chapter argues that Adams’ thesis and Stalnaker semantics are ways of cashing out the same ‘Ramsey test’ idea. Unfortunately, a well-known class of triviality theorems shows that Adams’ thesis and Stalnaker semantics are incompatible. Stefan Kaufmann has proposed (for reasons largely independent of the triviality theorems) a revised version of Adams’ thesis, which the chapter calls Kaufmann’s thesis. The chapter proves that combining Kaufmann’s thesis with Stalnaker semantics leads to ‘local triviality’ results, which seem just as absurd as the original triviality results for Adams’ thesis.

PLACING PROBABILITIES OF CONDITIONALS IN CONTEXT

2014 ◽  
Vol 7 (3) ◽  
pp. 415-438
Author(s):  
RONNIE HERMENS
Keyword(s):  
Conditional Probability ◽  
Modus Ponens ◽  
Bayes Rule ◽  
Context Sensitive ◽  
Intuitive Rules ◽  
Triviality Results

AbstractIn this paper I defend the tenability of the Thesis that the probability of a conditional equals the conditional probability of the consequent given the antecedent. This is done by adopting the view that the interpretation of a conditional may differ from context to context. Several triviality results are (re-)evaluated in this view as providing natural constraints on probabilities for conditionals and admissible changes in the interpretation. The context-sensitive approach is also used to re-interpret some of the intuitive rules for conditionals and probabilities such as Bayes’ rule,Import-Export, and Modus Ponens. I will show that, contrary to consensus, the Thesis is in fact compatible with these re-interpreted rules.

Conditional Commitment and the Ramsey Test

2020 ◽  
pp. 197-218
Author(s):  
Scott Sturgeon
Keyword(s):  
Bayesian Model ◽  
David Lewis ◽  
Critical Discussion ◽  
Transition Theory ◽  
Impossibility Theorem ◽  
Ramsey Test ◽  
Place Theory ◽  
Belief Model ◽  
Triviality Results

Chapter 7 is a critical discussion of conditional commitment in both the Bayesian and the Belief model. Both use their treatment of conditional commitment as something to connect their theory of states with their respective transition theory. In doing so both models are immediately hit with technical difficulties. The Belief Model generates the ‘impossibility theorem’ first proved by Peter Gärdenfors, and the Bayesian model generates ‘triviality results’ first proved by David Lewis. Each of these technical areas is explained from scratch and diagnosed philosophically. It is argued that the bombshells discussed are best seen as showing that the Binary-Attitude Assumption is false when it comes to conditional commitment, and that there is no essential tie between conditional commitment and rational shift-in-view. Throughout the discussion the 3-place theory of conditionality is related back to Chapter 4’s restricted-vision approach to conditionality.

Variations on the Ramsey test: More triviality results

Studia Logica ◽  
1987 ◽  
Vol 46 (4) ◽  
pp. 321-327 ◽  
Author(s):  
Peter G�rdenfors
Keyword(s):  
Ramsey Test ◽  
Triviality Results

scholarly journals Preservation, Commutativity and Modus Ponens: Two Recent Triviality Results

Mind ◽  
2016 ◽  
Vol 126 (502) ◽  
pp. 579-602 ◽  
Author(s):  
Jake Chandler
Keyword(s):  
Modus Ponens ◽  
Triviality Results

scholarly journals Triviality Results and the Relationship between Logical and Natural Languages

Mind ◽  
2018 ◽  
Vol 128 (510) ◽  
pp. 485-526 ◽  
Author(s):  
Justin Khoo ◽  
Matthew Mandelkern
Keyword(s):  
Natural Languages ◽  
The Relationship ◽  
Triviality Results

Geometry of warped product pointwise semi-slant submanifolds of cosymplectic manifolds and its applications

2017 ◽  
Vol 14 (03) ◽  
pp. 1750042 ◽  
Author(s):  
Akram Ali ◽  
Cenap Ozel
Keyword(s):  
Warped Product ◽  
Second Fundamental Form ◽  
Gauss Equation ◽  
Space Forms ◽  
Equality Case ◽  
Slant Submanifolds ◽  
The Second Fundamental Form ◽  
Cosymplectic Manifolds ◽  
Potential Applications ◽  
Triviality Results

It is known from [K. Yano and M. Kon, Structures on Manifolds (World Scientific, 1984)] that the integration of the Laplacian of a smooth function defined on a compact orientable Riemannian manifold without boundary vanishes with respect to the volume element. In this paper, we find out the some potential applications of this notion, and study the concept of warped product pointwise semi-slant submanifolds in cosymplectic manifolds as a generalization of contact CR-warped product submanifolds. Then, we prove the existence of warped product pointwise semi-slant submanifolds by their characterizations, and give an example supporting to this idea. Further, we obtain an interesting inequality in terms of the second fundamental form and the scalar curvature using Gauss equation and then, derive some applications of it with considering the equality case. We provide many trivial results for the warped product pointwise semi-slant submanifolds in cosymplectic space forms in various mathematical and physical terms such as Hessian, Hamiltonian and kinetic energy, and generalize the triviality results for contact CR-warped products as well.

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