Logic

A Blaricum Topology for Brouwer by Dirk van Dalen

By Dirk van Dalen

Does your place of birth have any mathematical vacationer sights resembling statues, plaques, graves, the cafd the place the recognized conjecture used to be made, the table the place the recognized initials are scratched, birthplaces, homes, or memorials? have you ever encountered a mathematical sight in your travels? if that is so, we invite you to undergo this column an image, an outline of its mathematical value, and both a map or instructions in order that others could persist with on your tracks.

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Assuming that mathematics is a body of truths leads to an inextricable muddle, which results in self-defeating statements such as: It is legitimate “to argue from ‘this theory has properties we like’ to ‘this theory is true’” 72. On this basis Frege could have argued that, since his ideography had the property he liked of reducing arithmetic to logic, his ideography was true, only to be belied by Russell’s paradox. That mathematics is not a body of truths does not mean that it has no objective content.

I would add only that to a lesser extent the mathematician is an inventor too, especially when he invents new concepts. But every discoverer has to be, to a certain extent, an inventor too. For instance, if a sailor wants to get to places which other A Socratic Dialogue on Mathematics 11 sailors before him were unable to reach, he has to build a ship that is better than the ships other sailors used. The new concepts invented by the mathematicians are like new ships which carry the discoverer farther on the great sea of thought.

The woman protested and swore to Artemis and Aphrodite that she was innocent, that she never loved anyone but her husband, and that her husband was killed by pirates. Many people were called as witnesses. Some said that the woman was guilty, others said that she was innocent. It was impossible to find out what really happened. HIPPOCRATES Are you mocking me again? First you confused me completely, and now instead of helping me to find the truth you tell me such stories. SOCRATES Do not be angry, my friend, I have serious reasons for speaking about this woman whose guilt it was impossible to ascertain.

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