Numbers as Quantitative Relations and the Traditional Theory of Measurement
Bibliographic Data
| ID | 8399409 |
|---|---|
| Authors | Joel Michell (0000-0002-6827-4783, The University of Sydney, corresponding author) |
| Year | 1994 |
| Volume | 45 |
| Issue | 2 |
| Pages | 389-406 |
| Publication date | 1994-06-01 |
| Peer Reviewed | Yes |
| Open Access | No |
| Type | ARTICLE |
| Venue | The British Journal for the Philosophy of Science (JOURNAL) |
| Journal identifiers | ISSN: 0007-0882 • E-ISSN: 1464-3537 |
| Publisher | Oxford University Press (PUBLISHER • GB) |
| DOI | 10.1093/bjps/45.2.389 |
| OpenAlex | W2027705786 |
| Language | EN |
| Citations received | 18 |
| References cited | 14 |
The thesis that numbers are ratios of quantities has recently been advanced by a number of philosophers. While adequate as a definition of the natural numbers, it is not clear that this view suffices for our understanding of the reals. These require continuous quantity and relative to any such quantity an infinite number of additive relations exist. Hence, for any two magnitudes of a continuous quantity there exists no unique ratio. This problem is overcome by defining ratios, and hence real numbers, as binary relations between infinite standard sequences. This definition leads smoothly into a new definition of measurement consonant with the traditional view of measurement as the discovery or estimation of numerical relations. The traditional view is further strengthened by allowing that the additive relations internal to a quantity are distinct from relations observed in the behaviour of objects manifesting quantities. In this way the traditional theory can accommodate the theory of conjoint measurement. This is worth doing because the traditional theory has one great strength lacked by its rivals: measurement statements and quantitative laws are able to be understood literally.
Arithmetic · Binary number · Binary relation · Calculus (dental) · Discrete mathematics · Law of large numbers · Mathematical economics · Natural (archaeology) · Natural number · Random variable · Sequence (biology) · Statistics · Computer Science · History and Theory of Mathematics · Mathematics · Philosophy and History of Science · Philosophy and Theoretical Science
Quantitative science and the definition of measurement in psychology
Rules to Infinity
Measurement Theory
Measures without Measurement
Mathematics, Measurement, Metaphor and Metaphysics I
Classification of Psychopathology
Qualitative research meets the ghost of Pythagoras
Mathematics, Measurement, Metaphor and Metaphysics II
The Quantitative Imperative
Representational measurement theory
Les fondements
Bertrand Russell's 1897 Critique of the Traditional Theory of Measurement
How Accurate Is the Standard Second
Controversy and the Rasch Model
On Absolute Units
Old and New Problems in Philosophy of Measurement
On the Distribution of Measurements in Units that are not Arbitrary
Epistemology of Measurement
| Unique citing works | 18 |
|---|---|
| Citations per year | 0,62 |
| Citation span | 1997 - 2025 (29) |
| Citation velocity | recent |
| Highly cited | No |
| Citation types | Neutral: 17 |