We’ve looked at various aspects of turning English sentences into logical statements, and modifying them by negation, converse, and so on. Let’s finish by looking at some questions about standard rules of inference, such as Modus Ponens and the Law of Syllogism.
(An archive question of the week) Usually when we discuss converses (and inverses and contrapositives) we use clear, idealized examples. But statements in real life — even in real math — are not quite so straightforward. The difficulty is not merely in the language, but in the complexity of our statements. A question in the …
This is the third post in a series on logic, with a focus on how it is expressed in English. We’ve looked at basic ideas of translating between English and logical symbols, and in particular at negation (stating the opposite). Now we are ready to consider how to change a given statement into one of …
Last time, I started a series exploring aspects of the translation of English statements to or from formal logical terms and symbols, which will lead to discussions of converse and contrapositive, and eventually of logical arguments. We’ve looked at how to translate concepts of “or” (disjunction) and “if” (conditional); but our goals will also require …
The next few posts will examine aspects of logic, both symbolic logic, and how we talk about theorems in general. We’ll start here with issues in interpreting the wording of logic, and some of the semantic difficulties we face. English isn’t logical. (Well, I suppose humans in general aren’t logical.)
(A new question of the week) I want to look at a question that came in recently that is, in one sense, very simple, but at the same time is quite challenging. It was given to a 12-year-old whose father asked us about it, and requires some skill in thinking about non-routine problems.
Last time we looked at the question of why we have to have postulates, which are not proved, rather than being able to prove everything. Often, this question is mixed together with a different question: Why do different texts give different lists of postulates, so that what one calls a postulate, another calls a theorem? …
Early in our history, we answered many questions about geometric proofs, particularly the “two-column” variety. Many of these were collected into a FAQ page. I want to briefly survey just some of what we have said about the big picture – an overall view of how to approach a proof, and how to work your …