equality and identity

Bulletin of Symbolic Logic 19 (3):255-256 (2013)

Authors
John Corcoran
State University of New York, Buffalo
Abstract
Equality and identity. Bulletin of Symbolic Logic. 19 (2013) 255-6. (Coauthor: Anthony Ramnauth) Also see https://www.academia.edu/s/a6bf02aaab This article uses ‘equals’ [‘is equal to’] and ‘is’ [‘is identical to’, ‘is one and the same as’] as they are used in ordinary exact English. In a logically perfect language the oxymoron ‘the numbers 3 and 2+1 are the same number’ could not be said. Likewise, ‘the number 3 and the number 2+1 are one number’ is just as bad from a logical point of view. In normal English these two sentences are idiomatically taken to express the true proposition that ‘the number 3 is the number 2+1’. Another idiomatic convention that interferes with clarity about equality and identity occurs in discussion of numbers: it is usual to write ‘3 equals 2+1’ when “3 is 2+1” is meant. When ‘3 equals 2+1’ is written there is a suggestion that 3 is not exactly the same number as 2+1 but that they merely have the same value. This becomes clear when we say that two of the sides of a triangle are equal if the two angles they subtend are equal or have the same measure. Acknowledgements: Robert Barnes, Mark Brown, Jack Foran, Ivor Grattan-Guinness, Forest Hansen, David Hitchcock, Spaulding Hoffman, Calvin Jongsma, Justin Legault, Joaquin Miller, Tania Miller, and Wyman Park. ► JOHN CORCORAN AND ANTHONY RAMNAUTH, Equality and identity. Philosophy, University at Buffalo, Buffalo, NY 14260-4150, USA E-mail: corcoran@buffalo.edu The two halves of one line are equal but not identical [one and the same]. Otherwise the line would have only one half! Every line equals infinitely many other lines, but no line is [identical to] any other line—taking ‘identical’ strictly here and below. Knowing that two lines equaling a third are equal is useful; the condition “two lines equaling a third” often holds. In fact any two sides of an equilateral triangle is equal to the remaining side! But could knowing that two lines being [identical to] a third are identical be useful? The antecedent condition “two things identical to a third” never holds, nor does the consequent condition “two things being identical”. If two things were identical to a third, they would be the third and thus not be two things but only one. The plural predicate ‘are equal’ as in ‘All diameters of a given circle are equal’ is useful and natural. ‘Are identical’ as in ‘All centers of a given circle are identical’ is awkward or worse; it suggests that a circle has multiple centers. Substituting equals for equals [replacing one of two equals by the other] makes sense. Substituting identicals for identicals is empty—a thing is identical only to itself; substituting one thing for itself leaves that thing alone, does nothing. There are as many types of equality as magnitudes: angles, lines, planes, solids, times, etc. Each admits unit magnitudes. And each such equality analyzes as identity of magnitude: two lines are equal [in length] if the one’s length is identical to the other’s. Tarski [1] hardly mentioned equality-identity distinctions (pp. 54-63). His discussion begins: Among the logical concepts […], the concept of IDENTITY or EQUALITY […] has the greatest importance. Not until page 62 is there an equality-identity distinction. His only “notion of equality”, if such it is, is geometrical congruence—having the same size and shape—an equivalence relation not admitting any unit. Does anyone but Tarski ever say ‘this triangle is equal to that’ to mean that the first is congruent to that? What would motivate him to say such a thing? This lecture treats the history and philosophy of equality-identity distinctions. [1] ALFRED TARSKI, Introduction to Logic, Dover, New York, 1995. [This is expanded from the printed abstract.]
Keywords LOGIC  MATHEMATICS  FOUNDATIONS OF MATHEMATICS  ANALYTIC PHILOSOPHY  LOGICAL ANALYSIS  SEMANTICS  ALFRED TARSKI  EQUALITY  IDENTITY  GEOMETRY
Categories (categorize this paper)
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Translate to english
Revision history

Download options

Our Archive
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Expressing Set-Size Equality.John Corcoran & Gerald Rising - 2015 - Bulletin of Symbolic Logic 21 (2):239.
Formalizing Euclid’s First Axiom.John Corcoran - 2014 - Bulletin of Symbolic Logic 20 (3):404-405.
The Logic of the Trinity.Einar Duenger Bohn - 2011 - Sophia 50 (3):363-374.
Gender Reflection: Reconciling Feminism and Equality.Laurie Gaughran - 1998 - Philosophy and Social Criticism 24 (5):37-51.
Equality.David Miller - 1989 - Royal Institute of Philosophy Supplement 26:77-98.
¿ De qué hablamos cuando hablamos de igualdad constitucional?Fernando Rey - 2011 - Anales de la Cátedra Francisco Suárez 45:167 - 181.
Consequences of Collapse.Theodore Sider - 2014 - In Donald Baxter & Aaron Cotnoir (eds.), Composition as Identity. Oxford University Press. pp. 211-221.
Distinctness and Non-Identity.David H. Sanford - 2005 - Analysis 65 (4):269–274.
The Identity of Clones.Kathinka Evers - 1999 - Journal of Medicine and Philosophy 24 (1):67 – 76.

Analytics

Added to PP index
2015-07-01

Total views
110 ( #63,948 of 2,325,374 )

Recent downloads (6 months)
9 ( #139,294 of 2,325,374 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature