A Brief Look at Paradoxes
I appologize for not posting a piece in a while, I have been busy. I am currently writing my own history of philosophy and religion. I understand this is a massive undertaking, but I at least want to complete the timeline, which I am close to doing. Also, for some reason my profile will not update in the views category. I know people have viewed it from new computors, I even looked at it from a computor that had previously not seen my blog and it still did not update. If anyone can help me fix this the assistance is appreicated.
But now for some new subject matter.
I would like to discuss my reasoning on paradoxes. My own definition has a flaw in it so I would like to use the definition from www.wikipedia.org, the english editionA paradox is an apparently true statement or group of statements that seems to lead to a contradiction or to a situation that defies intuition. Typically, either the statements in question do not really imply the contradiction, the puzzling result is not really a contradiction, or the premises themselves are not all really true (or, cannot all be true together). The recognition of ambiguities, equivocations, and unstated assumptions underlying known paradoxes has led to significant advances in science, philosophy and mathematics.
Note again this is not my definition, this is the wikipedia definition. Regardless it is a lucid definition. I would like the classify paradoxes into three categories. The first of these are questions that are puzzling but with logic and reasoning an answer can be found where an answer can be found. Another is when logic and reasoning is applied, it turns out that this is indeed a paradox, and cannot be solved. There is no clear logic that can find an answer for this, or remove its impossibility. The third type is the paradox where an answer cannot be found, and it is impossible to determine an which type of paradox this is. Ideally these types of paradoxes would not exist, but Godel proved that these indeed do exist. An example of the third type is the Riemann Hypothesis.
While paradoxes are intruiging there are not many practical applications for them. The greatest of these is the aformetioned Riemann Hypothesis where if solved it may spell the end of e-commerce. This is not close to being done, but I had an urge to post something. Thank you for reading and this post will be extended.
But now for some new subject matter.
I would like to discuss my reasoning on paradoxes. My own definition has a flaw in it so I would like to use the definition from www.wikipedia.org, the english editionA paradox is an apparently true statement or group of statements that seems to lead to a contradiction or to a situation that defies intuition. Typically, either the statements in question do not really imply the contradiction, the puzzling result is not really a contradiction, or the premises themselves are not all really true (or, cannot all be true together). The recognition of ambiguities, equivocations, and unstated assumptions underlying known paradoxes has led to significant advances in science, philosophy and mathematics.
Note again this is not my definition, this is the wikipedia definition. Regardless it is a lucid definition. I would like the classify paradoxes into three categories. The first of these are questions that are puzzling but with logic and reasoning an answer can be found where an answer can be found. Another is when logic and reasoning is applied, it turns out that this is indeed a paradox, and cannot be solved. There is no clear logic that can find an answer for this, or remove its impossibility. The third type is the paradox where an answer cannot be found, and it is impossible to determine an which type of paradox this is. Ideally these types of paradoxes would not exist, but Godel proved that these indeed do exist. An example of the third type is the Riemann Hypothesis.
While paradoxes are intruiging there are not many practical applications for them. The greatest of these is the aformetioned Riemann Hypothesis where if solved it may spell the end of e-commerce. This is not close to being done, but I had an urge to post something. Thank you for reading and this post will be extended.
posted by Brian Hillman at 12:07 PM
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