Hello again, great to see you all! Joe, Steve, how's it going Toph? Bill, Michelle, Pete, Lyra, Zuko. It would be fantastic if someone reading this was actually named above, but I digress. Last week, we learned about proofs and proof techniques as well as reviewed limits--as in delta-epsilon proofs. The concept of proofs does not intimidate me--nonetheless, I would still like to know the relevance of proofs to programming. Will we create programs that can solve mathematical proofs? This sounds beyond the depth of a first year undergraduate course, however, I could be wrong. This form of communicating truth does remind me of a more philosophical conflict: the argument that everything is subjective.
This perspective of reality has its reasoning--I personally prefer x colour, whilst you might prefer y colour--but when it is expressed mathematically, it is easy to obliterate this idea that life is subjective. For all things (x) in the Universe (U), if it exists in reality or (inclusive) abstractly (E(x)), then it is Subjective (S(x)).
Mathematically:
As a universal statement, all that is needed to prove this statement incorrect is a single counter-example. Ironically, in stating that everything is subjective, the statement itself must be included in this definition. The statement is objective, and thus, the idea that everything is subjective nullifies its own conclusion. The statement is its own counter-example, and everyone who believes that statement needs to reconsider the purpose of their existence. This may have been a philosophical topic of existentialism, but it is still exciting to see how logic intersects these supposedly 'unrelated' fields.
Of course, as this course continues, I hope to return to this "philosophical proof" and reinterpret it entirely within the structure of a mathematical proof. The chain of results was not quite extensive when stated in English--maybe the mathematical proof will be just as brief.
I am certain that a few people would rebel against this logic, others might redefine their idea of subjectivity, and still others might raise their fists in triumph. I hope to hear some feedback.
Until next time. Thank you for reading.
No comments:
Post a Comment