On Existence, Inconsistency, and Indispensability

Indispensability and Practice

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In Defence of Indispensability

Indispensability arguments for realism about mathematical entitieshave come under serious attack in recent years. To my mind the most profoundattack has come from Penelope Maddy, who argues that scientific/mathematicalpractice doesn't support the key premise of the indispensability argument, thatis, that we ought to have ontological commitment to those entities that are indis-<l...

Structuralism and the Indispensability Argument

I distill the indispensability argument to four general charateristics, which yield six unfortunate consequences, unwelcome characteristics of the objects yielded by the argument. The indispensabilist’s objects are not mathematical, in any traditional sense, but merely empirical posits. Then, I characterize a form of structuralism in the philosophy of mathematics which relies on an indispensabi...

On inconsistency of a pairwise comparison matrix

On Inconsistency Indices and Inconsistency Axioms in Pairwise Comparisons

Pairwise comparisons are an important tool of modern (multiple criteria) decision making. Since human judgments are often inconsistent, many studies focused on the ways how to express and measure this inconsistency, and several inconsistency indices were proposed as an alternative to Saaty’s inconsistency index and inconsistency ratio for reciprocal pairwise comparisons matrices. This paper aim...