Ancient Indian Logic and Analogy

B.K.Matilal, and earlier J.F.Staal, have suggested a reading of the `Nyaya five limb schema' (also sometimes referred to as the Indian Schema or Hindu Syllogism) from Gotama's Nyaya-Sutra in terms of a binary occurrence relation. In this paper we provide a rational justification of a version of this reading as Analogical Reasoning within the framework of Polyadic Pure Inductive Logic

An inequality concerning the expected values of row-sum and column-sum products in Boolean matrices

We give a proof of a matrix inequality and indicate how it can be applied to establish a natural analogy principle in Pure Inductive Logic

The Twin Continua of Inductive Methods

After dominating the subject of Inductive Logic for over 50 years Carnap's Continuum of Inductive Methods has in the past decade had its monopoly challenged by a second continuum of inductive methods, the NP-Continuum, which is also based on arguably rational principles. Does this mean there are (at least) two distinct notions of rational or logical probability? We describe the bases and key properties of both continua

Combining Analogical Support in Pure Inductive Logic

We investigate the relative probabilistic support afforded by the combination of two analogies based on possibly different, structural similarity (as opposed to e.g. shared predicates) within the context of Pure Inductive Logic and under the assumption of Language Invariance. We show that whilst repeated analogies grounded on the same structural similarity only strengthen the probabilistic support this need not be the case when combining analogies based on different structural similarities. That is, two analogies may provide less support than each would individually

Pure Inductive Logic

A self-contained guide to pure inductive logic, the study of rational probability treated as a branch of mathematical logic

There is a reason for everything (probably): On the application of maxent to induction

In this paper we show how the maxent paradigm may be used to produce an inductive method (in the sense of Carnap) applicable to a wide class of problems in inductive logic. A surprising consequence of this method is that the answers it gives are consistent with, or explicable by, the existence of underlying reasons for the given knowledge base, even when no such reasons are explicitly present. We would conjecture that the same result holds for the full class of problems of this type

An examination of the SEP Candidate Analogical Inference Rule within Pure Inductive Logic

Within the framework of (Unary) Pure Inductive Logic we investigate four possible formulations of a probabilistic principle of analogy based on a template considered by Paul Bartha in the Stanford Encyclopedia of Philosophy and give some characterizations of the probability functions which satisfy them. In addition we investigate an alternative interpretation of analogical support, also considered by Bartha, based not on the enhancement of probability but on the creation of possibility

Some limit theorems for ME, MD and CM#infinity#

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