Mathematicians have the concept of rigorous proof, which leads to knowing something with complete certainty. Consider the extent to which complete certainty might be achievable in mathematics and at least one other area of knowledge.
In Theory of Knowledge, the course divides into two core subjects which are the Ways of Knowing and Areas of Knowing. Based on the title, there is an extent to which the areas and ways of knowledge may elucidate the question. The title discusses the concept of mathematical rigorous proof which involves the process of uncertainties and contradictions, if none are available then the proof exists on complete certainty.
The question, in this case, is, are proofs completely certain and reliable to act as a general statement? Aren’t proofs based on a structure of logic and rely on a certain depth of axiom? All proofs in mathematics have a range of fundamental laws which are based on known axioms. Expressions which are false and considered to be true, then used as the main subject of logic such as mathematics, are the reasons that prevent proofs from being absolutely certain. A number of mathematicians claim that axioms are self-evident and that the truth behind them can be recognized, understood and reflected upon. In the end there is a definite possibility of that axioms being wrong, contradicting the issue of absolute truth in that proof.
Logic is frequently used by mathematicians; historians etc. to support and justify their subjects in arguments. But what is logic? For humans, it’s an everyday use in our lives. For instance, suppose you were to travel for a business conference on Sunday and Today is Wednesday, and you had to get your clothes from the dry cleaner which you know will take an hour. So you ask yourself, when is the best time to get it? First, you know that you’ll be away for the weekend with your family, so that leaves out Friday and Saturday. You also distinguish that you have a date... [continues]
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