scholarly journals Solving a Paradox of Evidential Equivalence

Mind ◽  
2020 ◽  
Author(s):  
Cian Dorr ◽  
John Hawthorne ◽  
Yoaav Isaacs
Keyword(s):  
Infinite Collection ◽  
Conditional Credence

Abstract David Builes presents a paradox concerning how confident you should be that any given member of an infinite collection of fair coins landed heads, conditional on the information that they were all flipped and only finitely many of them landed heads. We argue that if you should have any conditional credence at all, it should be 1/2.

The Bayesian Transition Theory

2020 ◽  
pp. 101-154
Author(s):  
Scott Sturgeon
Keyword(s):  
Contact Point ◽  
Modus Ponens ◽  
Transition Theory ◽  
Jeffrey’S Rule ◽  
Natural Conception ◽  
Rational Inference ◽  
Conditional Credence ◽  
The Way

Chapter 4 discusses the Bayesian transition theory. The distinction is drawn between dynamics and kinematics, and it’s argued that the theory of rational inference belongs to the former rather than the latter. It’s shown that Jeffrey’s rule is thus not a rule of rational inference. Credence lent to a conditional is explained and compared to conditional credence. Two problems for Bayesian kinematics then come into focus: conditional credence is never changing in the model, nor is it ever the contact-point of rational shift-in-view. A natural conception of conditional commitment is then put forward and used to solve both these problems. Along the way it’s argued that modus-ponens-style arguments do not function in thought as logical syllogisms, since modus-ponens-style arguments specify obligatory paths forward in thought.

scholarly journals The Kolmogorov equation in the stochastic fragmentation theory and branching processes with infinite collection of particle types

2006 ◽  
Vol 2006 ◽  
pp. 1-10
Author(s):  
R. Ye. Brodskii ◽  
Yu. P. Virchenko
Keyword(s):  
Stochastic Model ◽  
Basic Equation ◽  
Branching Process ◽  
Branching Processes ◽  
Fragmentation Process ◽  
Kolmogorov Equation ◽  
Infinite Collection ◽  
Kolmogorov Theory

The stochastic model for the description of the so-called fragmentation process in frameworks of Kolmogorov approach is proposed. This model is represented as the branching process with continuum set(0,∞)of particle types. Each typer∈(0,∞)corresponds to the set of fragments having the sizer. It is proved that the branching condition of this process represents the basic equation of the Kolmogorov theory.

Fluctuation theory for systems of signed and unsigned particles with interaction mechanisms based on intersection local times

1989 ◽  
Vol 21 (2) ◽  
pp. 334-356 ◽  
Author(s):  
Robert J. Adler
Keyword(s):  
Field Theory ◽  
Interaction Mechanism ◽  
Particle Systems ◽  
Fluctuation Theory ◽  
Local Times ◽  
Quantum Field ◽  
First Case ◽  
Infinite Collection ◽  
Euclidean Quantum Field Theory ◽  
Intersection Local Times

We consider two distinct models of particle systems. In the first we have an infinite collection of identical Markov processes starting at random throughout Euclidean space. In the second a random sign is associated with each process. An interaction mechanism is introduced in each case via intersection local times, and the fluctuation theory of the systems studied as the processes become dense in space. In the first case the fluctuation theory always turns out to be Gaussian, regardless of the order of the intersections taken to introduce the interaction mechanism. In the second case, an interaction mechanism based on kth order intersections leads to a fluctuation theory akin to a :φ k: Euclidean quantum field theory. We consider the consequences of these results and relate them to different models previously studied in the literature.

scholarly journals Type Inference with Inequalities

1990 ◽  
Vol 19 (336) ◽  
Author(s):  
Michael I. Schwartzbach
Keyword(s):  
General Result ◽  
Existence Of Solutions ◽  
Finite Automata ◽  
Minimal Solution ◽  
Type Inference ◽  
Constraint Solving ◽  
Multiple Inheritance ◽  
Exponential Time ◽  
Systems Of Inequalities ◽  
Infinite Collection

Type inference can be phrased as constraint-solving over types. We consider an implicitly typed language equipped with recursive types, multiple inheritance, 1st order parametric polymorphism, and assignments. Type correctness is expressed as satisfiability of a possibly infinite collection of (monotonic) inequalities on the types of variables and expressions. A general result about systems of inequalities over semilattices yields a solvable form. We distinguish between deciding <em>typability</em> (the existence of solutions) and <em>type inference</em> (the computation of a minimal solution). In our case, both can be solved by means of nondeterministic finite automata; unusually, the two problems have different complexities: polynomial vs. exponential time.

Indicative conditionals

2018 ◽  
Author(s):  
Sarah Moss
Keyword(s):  
Conditional Probability ◽  
Inference Rules ◽  
Indicative Conditionals ◽  
Valid Inference ◽  
Logical Operators ◽  
Context Sensitive ◽  
Probabilistic Semantics ◽  
Truth Conditional ◽  
Conditional Credence

This chapter defends a probabilistic semantics for indicative conditionals and other logical operators. This semantics is motivated in part by the observation that indicative conditionals are context sensitive, and that there are contexts in which the probability of a conditional does not match the conditional probability of its consequent given its antecedent. For example, there are contexts in which you believe the content of ‘it is probable that if Jill jumps from this building, she will die’ without having high conditional credence that Jill will die if she jumps. This observation is at odds with many existing non-truth-conditional semantic theories of conditionals, whereas it is explained by the semantics for conditionals defended in this chapter. The chapter concludes by diagnosing several apparent counterexamples to classically valid inference rules embedding epistemic vocabulary.

Zeno of Elea (fl. c.450 BC)

2018 ◽  
Author(s):  
Stephen Makin
Keyword(s):  
Opposite Direction ◽  
Infinite Number ◽  
The Other ◽  
Fellow Citizen ◽  
Greek Philosopher ◽  
Moving Body ◽  
The World ◽  
Infinite Collection ◽  
Catch Up ◽  
Moving Bodies

The Greek philosopher Zeno of Elea was celebrated for his paradoxes. Aristotle called him the ‘founder of dialectic’. He wrote in order to defend the Eleatic metaphysics of his fellow citizen and friend Parmenides, according to whom reality is single, changeless and homogeneous. Zeno’s strength was the production of intriguing arguments which seem to show that apparently straightforward features of the world – most notably plurality and motion – are riddled with contradiction. At the very least he succeeded in establishing that hard thought is required to make sense of plurality and motion. His paradoxes stimulated the atomists, Aristotle and numerous philosophers since to reflect on unity, infinity, continuity and the structure of space and time. Although Zeno wrote a book full of arguments, very few of his actual words have survived. Secondary reports (some from Plato and Aristotle) probably preserve accurately the essence of Zeno’s arguments. Even so, we know only a fraction of the total. According to Plato the arguments in Zeno’s book were of this form: if there are many things, then the same things are both F and not-F; since the same things cannot be both F and not-F, there cannot be many things. Two instances of this form have been preserved: if there were many things, then the same things would be both limited and unlimited; and the same things would be both large (that is, of infinite size) and small (that is, of no size). Quite how the components of these arguments work is not clear. Things are limited (in number), Zeno says, because they are just so many, rather than more or less, while they are unlimited (in number) because any two of them must have a third between them, which separates them and makes them two. Things are of infinite size because anything that exists must have some size: yet anything that has size is divisible into parts which themselves have some size, so that each and every thing will contain an infinite number of extended parts. On the other hand, each thing has no size: for if there are to be many things there have to be some things which are single, unitary things, and these will have no size since anything with size would be a collection of parts. Zeno’s arguments concerning motion have a different form. Aristotle reports four arguments. According to the Dichotomy, motion is impossible because in order to cover any distance it is necessary first to cover half the distance, then half the remainder, and so on without limit. The Achilles is a variant of this: the speedy Achilles will never overtake a tortoise once he has allowed it a head start because Achilles has an endless series of tasks to perform, and each time Achilles sets off to catch up with the tortoise it will turn out that, by the time Achilles arrives at where the tortoise was when he set off, the tortoise has moved on slightly. Another argument, the Arrow, purports to show that an arrow apparently in motion is in fact stationary at each instant of its ‘flight’, since at each instant it occupies a region of space equal in size to itself. The Moving Rows describes three rows (or streams) of equal-sized bodies, one stationary and the other two moving at equal speeds in opposite directions. If each body is one metre long, then the time taken for a body to cover two metres equals the time taken for it to cover four metres (since a moving body will pass two stationary bodies while passing four bodies moving in the opposite direction), and that might be thought impossible. Zeno’s arguments must be resolvable, since the world obviously does contain a plurality of things in motion. There is little agreement, however, on how they should be resolved. Some points can be identified which may have misled Zeno. It is not true, for example, that the sum of an infinite collection of parts, each of which has size, must itself be of an infinite size (it will be false if the parts are of proportionally decreasing size); and something in motion will pass stationary bodies and moving bodies at different velocities. In many other cases, however, there is no general agreement as to the fallacy, if any exists, of Zeno’s argument.

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