Logic + Reason in the Context of Arguments

The structure of any logical argument begins with a number of ‘factual’ statements, (for our purposes we’ll only be using 2 although in real life there are usually a couple of statements) which we are going to refer to as the premises of the argument as they are the statistics, facts or rules that any logical argument is built from. The conclusion of the argument is their stance on the matter, e.g. pro-life or pro-choice and the validity is whether their line of reasoning seems logical and you can clearly see where they have drawn off their original premises if you can’t follow their reasoning or it simply doesn’t match up then their argument is invalid.

The trivial part of this concept is that two people can start with the different yet equally factual and true premises and both follow a logical line of reasoning leading to a valid argument but their logic results in contrasting conclusions. For example on the topic of abortion someone who is pro-life might have the premises that murdering people is wrong and abortion is murder which would lead them to the conclusion that abortion is wrong, which is a valid argument, on the other hand, someone who is pro-choice may have the premises that murder is wrong except in self-defence and abortion is self-defence leading them to a valid conclusion of abortion not being wrong. They are both equally valid arguments yet completely contrasting which is the difficulty here, if you are faced with two equally valid arguments how do you choose one over the other? Personally, I feel that I would go with the one already supports my view of the topic which is a way of placing my own bias onto what is supposed to be a decision made solely on reason and logic. This is how legal systems and really the politics of most countries operate with the big decisions being made in this way which begs the question: how far can logic and reason take us in reality?

Maths Conceptual Understandings

Maths seeks to prove theorems explaining the world of mathematics through a process of deduction and induction.

To keep Maths as close to the ‘truth’ as we can we aim to prove every theorem and new discovery by tracing it back to the core axioms that we hold as certain (note not truth), if there is a clear process leading to the formulae/theorem that clearly follows the laws and axioms of mathematics then we can hold this as certain. The mathematical process of getting from our core axioms to this new formulae or theorem is a process of deduction (especially in the cases of finding a value etc.) and occasionally induction which is simply the process of using different ideas and facts to draw a conclusion which in a mathematical sense could be applying axioms etc.

Maths is a surprisingly social/ collaborative subject yet maintains the individual and solitary subject we stereotypically view it as.

As we saw in the video played to us in class many many mathematical discoveries could simply have never been reached without fellow mathematicians collaborating and publishing their work. In the video Wiles would have never been able to find a solution to Fermat’s last theorem without the research papers and work of mathematicians worldwide (e.g. the Japanese mathematicians) and his fellow colleagues at Cambridge, yet the fact that he isolated himself and worked in secret for 7 years shows the solitary, closed off nature we tend to associate with mathematics and mathematicians.

Although it is not typically seen as one Mathematics has the potential to be an emotional subject with revelations and highs and lows of its own.

People rarely view Mathematics as an emotional subject or one requiring creativity, however, as we saw last class for those who are dedicated and passionate about mathematics it can be a very emotional experience. It was quite a shock to see words such as revelation as this word has religious or at least philosophical connotations when many see mathematics as a subject that should be and mostly is devoid of emotion, much as the sciences are.