“Whoa! It’s like Spotify but for academic articles.”

Instant Access to Thousands of Journals for just $40/month

Try 2 weeks free now

Objects and Processes in Mathematical Practice



In this paper it is argued that the fundamental difference of the formal and the informal position in the philosophy of mathematics results from the collision of an object and a process centric perspective towards mathematics. This collision can be overcome by means of dialectical analysis, which shows that both perspectives essentially depend on each other. This is illustrated by the example of mathematical proof and its formal and informal nature. A short overview of the employed materialist dialectical approach is given that rationalises mathematical development as a process of model production. It aims at placing more emphasis on the application aspects of mathematical results. Moreover, it is shown how such production realises subjective capacities as well as objective conditions, where the latter are mediated by mathematical formalism. The approach is further sustained by Polanyi’s theory of problem solving and Stegmaier’s philosophy of orientation. In particular, the tool and application perspective illuminates which role computer-based proofs can play in mathematics.



Foundations of ScienceSpringer Journals

Published: Nov 1, 2011

DOI: 10.1007/s10699-010-9202-y

Free Preview of First Page

Loading next page...

You’re reading a free preview. Subscribe to read the entire article.

DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy unlimited access and
personalized recommendations from
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $40/month

Try 2 weeks free now

Explore the DeepDyve Library

How DeepDyve Works

Spend time researching, not time worrying you’re buying articles that might not be useful.

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from Springer, Elsevier, Nature, IEEE, Wiley-Blackwell and more.

All the latest content is available, no embargo periods.

See the journals in your area

Simple and Affordable Pricing

14-day free trial. Cancel anytime, with a 30-day money-back guarantee.

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches


Best Deal — 25% off

Annual Plan

  • All the features of the Professional Plan, but for 25% off!
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.

billed annually