*David M. Armstrong*

- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199590612
- eISBN:
- 9780191723391
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199590612.003.0003
- Subject:
- Philosophy, Philosophy of Mind, Metaphysics/Epistemology

Following Bertrand Russell, properties are seen as the monadic case with the dyadic, triadic, etc. cases constituting the relations. A Principle of Instantial Invariance, that a relation that is a ...
More

Following Bertrand Russell, properties are seen as the monadic case with the dyadic, triadic, etc. cases constituting the relations. A Principle of Instantial Invariance, that a relation that is a universal has always the same number of terms in each instantiation, is argued for, against Fraser MacBride A distinction is drawn between internal and external relations and it is argued that the internal relations do no more than supervene.Less

Following Bertrand Russell, properties are seen as the monadic case with the dyadic, triadic, etc. cases constituting the relations. A Principle of Instantial Invariance, that a relation that is a universal has always the same number of terms in each instantiation, is argued for, against Fraser MacBride A distinction is drawn between internal and external relations and it is argued that the internal relations do no more than supervene.

*Shoutir Kishore Chatterjee*

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198525318
- eISBN:
- 9780191711657
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198525318.001.0001
- Subject:
- Mathematics, Probability / Statistics

The book examines the distinguishing features of the various contending approaches to statistical inference (including decision-making) that are currently available in statistical literature, and ...
More

The book examines the distinguishing features of the various contending approaches to statistical inference (including decision-making) that are currently available in statistical literature, and traces the historical evolution of the concepts underlying these approaches and their applications. The first part entitled, Perspective, shows that statistical inference is really a prolongation of the philosophical problem of induction, and in it, probability is involved both in the input (in the form of model) and the output (for quantifying uncertainty). Four different approaches (behavioural, instantial, pro-subjective Bayesian, and purely subjective) to such statistical induction arise due to the invocation of different conceptions of probability (objective and subjective) at the two stages of the process. The comparative characteristics, advantages, and disadvantages of the different approaches are considered, and it is concluded that each is appropriate in its natural setting. The second part entitled, History, discusses how the different types of probability originated and evolved, and how their application to statistical induction gave rise to the variety of concepts and principles associated with the different approaches. After some reference to pre-history, the developments made by the principal contributors to probability and statistics during 17th-20th centuries (from Cardano, Pascal, Fermat, Huygens, and James Bernoulli through to Daniel Bernoulli, Bayes, Laplace, Gauss, to Galton, Karl Pearon, Fisher, Jeffreys, de Finetti, Neyman, E. S. Pearson, Wald, and their successors) are delineated.Less

The book examines the distinguishing features of the various contending approaches to statistical inference (including decision-making) that are currently available in statistical literature, and traces the historical evolution of the concepts underlying these approaches and their applications. The first part entitled, *Perspective*, shows that statistical inference is really a prolongation of the philosophical problem of induction, and in it, probability is involved both in the input (in the form of model) and the output (for quantifying uncertainty). Four different approaches (behavioural, instantial, pro-subjective Bayesian, and purely subjective) to such statistical induction arise due to the invocation of different conceptions of probability (objective and subjective) at the two stages of the process. The comparative characteristics, advantages, and disadvantages of the different approaches are considered, and it is concluded that each is appropriate in its natural setting. The second part entitled, *History*, discusses how the different types of probability originated and evolved, and how their application to statistical induction gave rise to the variety of concepts and principles associated with the different approaches. After some reference to pre-history, the developments made by the principal contributors to probability and statistics during 17th-20th centuries (from Cardano, Pascal, Fermat, Huygens, and James Bernoulli through to Daniel Bernoulli, Bayes, Laplace, Gauss, to Galton, Karl Pearon, Fisher, Jeffreys, de Finetti, Neyman, E. S. Pearson, Wald, and their successors) are delineated.

*Shoutir Kishore Chatterjee*

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198525318
- eISBN:
- 9780191711657
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198525318.003.0004
- Subject:
- Mathematics, Probability / Statistics

Objective statistical induction may be behavioural, instantial, or pro-subjective (Bayesian), depending on the form of judging inferential uncertainty. In the behavioral case, the unknown parameters ...
More

Objective statistical induction may be behavioural, instantial, or pro-subjective (Bayesian), depending on the form of judging inferential uncertainty. In the behavioral case, the unknown parameters are fixed and uncertainty is judged by measures of procedural trustworthiness (like significance and confidence levels, power and risk functions), interpreted through repeated conceptual experimentation. Various principles are invoked for optimizing the procedure in different problems. The instantial approach (likelihood inference, P-value testing, and fiducial inference) remains pegged to the instance at hand without visualizing repetition, and weighs uncertainty in non-standard ways, although often like the behavioural approach, it also has to appeal to sampling theory. In the pro-subjective Bayesian approach, the unknown parameters are subjectively random with a known prior distribution, and inference is based on their posterior distribution. Various kinds of priors (improper/proper, impersonal/personal) fit in different tastes and situations. The subjective approach, based on a fully known subjective probability model, ‘previses’ about future observables, conditionally fixing the observations, often assuming exchangeability to simplify the process. Comparison of the different approaches shows that each has a natural setting in which it is advantageous.Less

Objective statistical induction may be behavioural, instantial, or pro-subjective (Bayesian), depending on the form of judging inferential uncertainty. In the behavioral case, the unknown parameters are fixed and uncertainty is judged by measures of procedural trustworthiness (like significance and confidence levels, power and risk functions), interpreted through repeated conceptual experimentation. Various principles are invoked for optimizing the procedure in different problems. The instantial approach (likelihood inference, P-value testing, and fiducial inference) remains pegged to the instance at hand without visualizing repetition, and weighs uncertainty in non-standard ways, although often like the behavioural approach, it also has to appeal to sampling theory. In the pro-subjective Bayesian approach, the unknown parameters are subjectively random with a known prior distribution, and inference is based on their posterior distribution. Various kinds of priors (improper/proper, impersonal/personal) fit in different tastes and situations. The subjective approach, based on a fully known subjective probability model, ‘previses’ about future observables, conditionally fixing the observations, often assuming exchangeability to simplify the process. Comparison of the different approaches shows that each has a natural setting in which it is advantageous.

*Jr. Henry E. Kyburg*

- Published in print:
- 1991
- Published Online:
- October 2011
- ISBN:
- 9780195062533
- eISBN:
- 9780199853038
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195062533.003.0004
- Subject:
- Philosophy, Philosophy of Science

Induction is the inference from a sample to a population, regardless of the possible existence of exceptions. Induction is used in the practice of science and engineering based on knowledge that can ...
More

Induction is the inference from a sample to a population, regardless of the possible existence of exceptions. Induction is used in the practice of science and engineering based on knowledge that can be accepted as evidence. There are two bodies of knowledge: evidential corpus, a set of propositions acceptable as evidence in a certain context; and practical corpus, a set of propositions counting as “practically certain” in that context. There are five kinds of induction described: statistical, universal, nomic, theoretical, and instantial.Less

Induction is the inference from a sample to a population, regardless of the possible existence of exceptions. Induction is used in the practice of science and engineering based on knowledge that can be accepted as evidence. There are two bodies of knowledge: evidential corpus, a set of propositions acceptable as evidence in a certain context; and practical corpus, a set of propositions counting as “practically certain” in that context. There are five kinds of induction described: statistical, universal, nomic, theoretical, and instantial.