What You See Is What You Get

Paris, Jeffrey

doi:10.3390/e16116186

Cited by 19 publications

(15 citation statements)

References 21 publications

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“…It is well-established and accepted [8,20] that inferences have to depend in some way on the underlying language. However, the number of possible worlds depends on the agent's evidence and thus the dependence of inferences on the underlying language is rooted in the agent's epistemic state and not in the agent's whimsicality.…”

Section: The Role Of Languagementioning

confidence: 99%

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Invariant Equivocation

Landes

Masterton

2016

Erkenn

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Objective Bayesians hold that degrees of belief ought to be chosen in the set of probability functions calibrated with one's evidence. The particular choice of degrees of belief is via some objective, i.e., not agentdependent, inference process that, in general, selects the most equivocal probabilities from among those compatible with one's evidence. Maximising entropy is what drives these inference processes in recent works by Williamson and Masterton though they disagree as to what should have its entropy maximised. With regard to the probability function one should adopt as one's belief function, Williamson advocates selecting the probability function with greatest entropy compatible with one's evidence while Masterton advocates selecting the expected probability function relative to the density function with greatest entropy compatible with one's evidence. In this paper we discuss the significant relative strengths of these two positions. In particular, Masterton's original proposal is further developed and investigated to reveal its significant properties; including its equivalence to the centre of mass inference process and its ability to accommodate higher order evidence.Keywords: Maximum Entropy, Objective Bayesianism, Inference Process, Centre of Mass, Language Invariance 1 Introduction "How should one form graded beliefs?" is a question that has long fascinated philosophers. The answer to this question is highly relevant throughout science, law, operational research and policy-making. Intuitively, it is obvious that one's evidence ought to matter when forming beliefs, whether graded or binary. The best way of caching out this ubiquitous intuition is, however, a matter of lively disagreement. The main philosophical protagonists in this debate are: the subjective Bayesians, who can be further subdivided into the radical (de Finetti This paper is concerned with objective Bayesianism. Objective Bayesians, like their subjective brethren, hold that one's degrees of belief ought to be consistent with one's evidence. However, in cases where the evidential constraints are satisfied by more than one probability function the objective Bayesians differ from the subjective Bayesians in holding that the choice of a particular probability function from those consistent with the evidential constraints ought to made 1 in an objective-i.e., agent-independent-manner. Typically, such a choice is made by applying an inference process that picks from among the probability functions consistent with the evidential constraints that function which is, in some sense, maximally equivocal. 1 Objective Bayesianism is (still!) a minority view with a relatively small but dedicated group of advocates. Even in this relatively small group there are disagreements. One such recent disagreement is that between Williamson [27] and Masterton [16] on how to understand maximal equivocation.We shall herein first rehearse Williamson's account in Section 2.1 and 2.2. Then we improve on Masterton's approach by reformulating it, Section 2...

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Section: The Role Of Languagementioning

confidence: 99%

“…The answer, invariably, depends on the exact nature of our normative enterprise. If our goal is to set subjective common-sensical probabilities as does Jeff Paris in [20]:…”

Section: The Right Inference Process?mentioning

confidence: 99%

Invariant Equivocation

Landes

Masterton

2016

Erkenn

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“…Jeff Paris, in his paper [1], defends MaxEnt against the charge of language dependence and warns against mistaking subjective degrees of belief for estimates of objective probabilities and mis-applying the Principle of Insufficient Reason.…”

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confidence: 99%

“…Patryk Dziurosz-Serafinowicz investigates Maximum Relative Entropy (MRE) updating and the value of learning theorem [4]. His analysis of the Judy Benjamin problem highlights the language dependence of MaxEnt discussed by Jeff Paris in [1]. In [5], Stefan Lukits shows MaxEnt generalises both Jeffrey conditioning and Wagner conditioning.…”

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confidence: 99%

Maximum Entropy Applied to Inductive Logic and Reasoning

Landes

Williamson

2015

Entropy

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This editorial explains the scope of the special issue and provides a thematic introduction to the contributed papers.Keywords: entropy; MaxEnt; inductive logic; reasoning With this special issue, we wanted to provide a platform for practitioners, proponents and opponents of Maximum Entropy methods (MaxEnt) applied to inductive logic and reasoning. Unfortunately, we received no papers arguing against MaxEnt. However, we did receive an exciting array of positive contributions, which are described below.There has been much debate in the inductive logic and reasoning literature on the justificatory status of MaxEnt. Jeff Paris, in his paper [1], defends MaxEnt against the charge of language dependence and warns against mistaking subjective degrees of belief for estimates of objective probabilities and mis-applying the Principle of Insufficient Reason.The other contributed papers focus on extensions of the standard framework for MaxEnt in inductive logic and reasoning. The standard framework considers a single agent equipped with a finite propositional language (or a finite domain of propositions) and a propositional knowledge base, seeking to determine probabilities from these ingredients. Papers in this volume extend the standard framework in four different directions: the multi-agent setting, the dynamic setting, more elaborate knowledge bases, and richer underlying languages.

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“…For a knowledge base R consisting of a set of propositional conditionals, P is a model of R if P satisfies each conditional in R. The principle of maximum entropy (ME principle) is a well-established concept for choosing the uniquely determined model of R having maximum entropy. This model is the most unbiased model of R in the sense that it completes the knowledge given by R inductively but adds as little additional information as possible [3][4][5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Relational Probabilistic Conditionals and Their Instantiations under Maximum Entropy Semantics for First-Order Knowledge Bases

Beierle

Finthammer

Kern-Isberner

2015

Entropy

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For conditional probabilistic knowledge bases with conditionals based on propositional logic, the principle of maximum entropy (ME) is well-established, determining a unique model inductively completing the explicitly given knowledge. On the other hand, there is no general agreement on how to extend the ME principle to relational conditionals containing free variables. In this paper, we focus on two approaches to ME semantics that have been developed for first-order knowledge bases: aggregating semantics and a grounding semantics. Since they use different variants of conditionals, we define the logic PCI, which covers both approaches as special cases and provides a framework where the effects of both approaches can be studied in detail. While the ME models under PCI-grounding and PCI-aggregating semantics are different in general, we point out that parametric uniformity of a knowledge base ensures that both semantics coincide. Using some concrete knowledge bases, we illustrate the differences and common features of both approaches, looking in particular at the ground instances of the given conditionals.

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What You See Is What You Get

Abstract: This paper corrects three widely held misunderstandings about Maxent when used in common sense reasoning: That it is language dependent; That it produces objective facts; That it subsumes, and so is at least as untenable as, the paradox-ridden Principle of Insufficient Reason.

Cited by 19 publications

References 21 publications

Invariant Equivocation

Invariant Equivocation

Maximum Entropy Applied to Inductive Logic and Reasoning

Relational Probabilistic Conditionals and Their Instantiations under Maximum Entropy Semantics for First-Order Knowledge Bases

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