Mathematical structuralism | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-01-28

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Structuralism_(philosophy_of_mathematics)


00:01:51 1 Historical motivation
00:05:53 2 Varieties
00:08:28 3 See also



Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.

Learning by listening is a great way to:
- increases imagination and understanding
- improves your listening skills
- improves your own spoken accent
- learn while on the move
- reduce eye strain

Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.

Listen on Google Assistant through Extra Audio:
https://assistant.google.com/services/invoke/uid/0000001a130b3f91
Other Wikipedia audio articles at:
https://www.youtube.com/results?search_query=wikipedia+tts
Upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
Speaking Rate: 0.8308023250240009
Voice name: en-US-Wavenet-B


"I cannot teach anybody anything, I can only make them think."
- Socrates


SUMMARY
=======
Structuralism is a theory in the philosophy of mathematics that holds that mathematical theories describe structures of mathematical objects.  Mathematical objects are exhaustively defined by their place in such structures.  Consequently, structuralism maintains that mathematical objects do not possess any intrinsic properties but are defined by their external relations in a system. For instance, structuralism holds that the integer 1 is exhaustively defined by being the successor of 0 in the structure of the theory of natural numbers. By generalization of this example, any integer is defined by their respective place in this structure of the number line. Other examples of mathematical objects might include lines and planes in geometry, or elements and operations in abstract algebra.
Structuralism is an epistemologically realistic view in that it holds that mathematical statements have an objective truth value. However, its central claim only relates to what kind of entity a mathematical object is, not to what kind of existence mathematical objects or structures have (not, in other words, to their ontology). The kind of existence mathematical objects have would clearly be dependent on that of the structures in which they are embedded; different sub-varieties of structuralism make different ontological claims in this regard.Structuralism in the philosophy of mathematics is particularly associated with Paul Benacerraf, Geoffrey Hellman, Michael Resnik and Stewart Shapiro.