Formal Logic Tutorial

The aim of Sunday’s logic tutorial was to explore what it means for an argument to be valid, focussing on the key issue of consistency. The morning was spent developing an understanding of what logic is – not rationality, as popular understandings may have one believe, but possibility and internal consistency. The students then developed a spectrum in which to categorise the ‘truth-value’ of declarative sentences – from logical truths (tautologies, necessary truths, etc.) at one end, through contingent truths, to logical falsities (contradictions) at the other. After fully grasping what is meant by all of the relevent terms, we moved on to learn ‘the language of logic’. Students had to acquire an understanding of a range of new symbols, so that they could translate ambigous sentences of English into unambigous formulae of ‘Logicese’.

If the afternoon, we set about using our new language to translate arguments, and then to prove whether or not those argument were valid. Using the student’s new understanding of validity – the impossiblity of the simultaneous truth of the premisses and falsity of the conclusion – we used two methods of proof. Firstly, the cumbersome and time-consuming ‘truth-table’ method, which we found frustrating, but intuitive. After verifying the students’ understanding of this method with a series of exercises, we moved on to the more difficult, but more elegant, ‘tableaux’ method.

I was hugely impressed with the ability of the students. They were able to grasp the counter-intuitive elements of logic quickly, and we were able to cover some advanced topics.

Check out the Philosophy Summer School for more workshops like this.

Max Kasriel, Philosophy Tutor