The Ontological Status of Mathematical Entities: The Necessity for Modern Physics of an Evaluation of Mathematical Systems

By Kfia, Lilianne Rivka | The Review of Metaphysics, September 1993 | Go to article overview

The Ontological Status of Mathematical Entities: The Necessity for Modern Physics of an Evaluation of Mathematical Systems


Kfia, Lilianne Rivka, The Review of Metaphysics


FAR FROM BEING A PURELY ESOTERIC CONCERN of theoretical mathematicians, the examination of the ontological status of mathematical entities, I submit, has far-reaching implications for a very practical area of knowledge, namely, the method of science in general, and of physics in particular. Although physics and mathematics have since Newton's second derivative been inextricably wedded, modem physics has a particularly mathematical dependence. Physics has moved and continues to move further away from the possibility of direct empirical verification, primarily because of the increasingly complex logistical problems of experimentation within the parameters of the very large and of the very small. As certain areas become more and more theoretical, with developments of this century in astrophysics, cosmology, and quantum mechanics, and more specifically, with the postulation of new hypothetical elementary particles based almost exclusively upon mathematical data, physics is forced to depend increasingly upon mathematics as a method for verifying physical possibility. Typically, a mathematical formulation descriptive of an empirically established phenomenon x is manipulated and made subject to derivation on the assumption that the new formulation will continue to correspond with physical reality, and may even yield new information about the phenomenon's behavior. Why, however, should a coherence between the empirically-defined world and mathematical processes be assumed? This coherence is, above all, dependent upon a hidden metaphysically strong presupposition about the ontological status of mathematical entities and their systems.

That there is a metaphysically strong presupposition of the sort to which I refer is not immediately obvious, and I would like here to address three common refutations of this position initially given. Perhaps the most immediate is the insistence that mathematics serves a purely descriptive function in the sciences, that it acts only as a kind of language. Although this characterization is certainly applicable in some cases, it cannot possibly justify the present use of mathematics to make hypotheses and predictions in physics. It cannot explain the prescriptive use of mathematics to verify and suggest physical possibility.

Assuming the prescriptive use of mathematics, another argument can be made that mathematics is simply logic, in its most absolute, noncontroversial tautological sense. Thus, the use of mathematics in physics simply ensures the same consistency, although in a much more easily manipulatable form, that would occur by our following out the implications of theories using what amounts to common sense reason, for it is obvious that our knowledge of physical reality (physics) must be limited by, or at least not be inconsistent with, our own mental principles of logic. Unfortunately, this tautological view of mathematics too is untenable; for besides its rather narrow view of the role of mathematics, it makes the mistaken assumption that mathematics as used in physics is in fact logical, never mind tautological. One need only think of the prominent use in physics of complex numbers and common surds such as the exponential function and pi to realize how many mathematical inconsistencies have been wholeheartedly embraced without question and with success. The intuitionist school of mathematics, very much concerned with consistency and solid grounding, deems the use of infinity as unacceptably anti-intuitive, yet where would its absence leave calculus, a veritable cornerstone of the foundations of physics? A merely tautological system would severely limit the present scope of the physical and even social sciences.

The final and most common argument against inherent assumptions of mathematical Platonism in physics is simply that of cold pragmatism, which claims that we use the mathematical systems that we use not because we endow them with any real ontological status, but because they are effective. …

The rest of this article is only available to active members of Questia

Sign up now for a free, 1-day trial and receive full access to:

  • Questia's entire collection
  • Automatic bibliography creation
  • More helpful research tools like notes, citations, and highlights
  • A full archive of books and articles related to this one
  • Ad-free environment

Already a member? Log in now.

Notes for this article

Add a new note
If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items

Items saved from this article

This article has been saved
Highlights (0)
Some of your highlights are legacy items.

Highlights saved before July 30, 2012 will not be displayed on their respective source pages.

You can easily re-create the highlights by opening the book page or article, selecting the text, and clicking “Highlight.”

Citations (0)
Some of your citations are legacy items.

Any citation created before July 30, 2012 will labeled as a “Cited page.” New citations will be saved as cited passages, pages or articles.

We also added the ability to view new citations from your projects or the book or article where you created them.

Notes (0)
Bookmarks (0)

You have no saved items from this article

Project items include:
  • Saved book/article
  • Highlights
  • Quotes/citations
  • Notes
  • Bookmarks
Notes
Cite this article

Cited article

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Cited article

The Ontological Status of Mathematical Entities: The Necessity for Modern Physics of an Evaluation of Mathematical Systems
Settings

Settings

Typeface
Text size Smaller Larger Reset View mode
Search within

Search within this article

Look up

Look up a word

  • Dictionary
  • Thesaurus
Please submit a word or phrase above.
Print this page

Print this page

Why can't I print more than one page at a time?

Help
Full screen

matching results for page

    Questia reader help

    How to highlight and cite specific passages

    1. Click or tap the first word you want to select.
    2. Click or tap the last word you want to select, and you’ll see everything in between get selected.
    3. You’ll then get a menu of options like creating a highlight or a citation from that passage of text.

    OK, got it!

    Cited passage

    Style
    Citations are available only to our active members.
    Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

    1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

    Cited passage

    Thanks for trying Questia!

    Please continue trying out our research tools, but please note, full functionality is available only to our active members.

    Your work will be lost once you leave this Web page.

    For full access in an ad-free environment, sign up now for a FREE, 1-day trial.

    Already a member? Log in now.