# Introducing Logic  ## Metadata - Author: [[Dan Cryan, Sharron Shatil, Bill Mayblin]] - Full Title: Introducing Logic - Category: #books ## Highlights - Logic is quite simply the study of truth-preserving arguments. ([Location 73](https://readwise.io/to_kindle?action=open&asin=B00KFEK0EM&location=73)) - From just three connectives (and, or, not) we can express every possible logical proposition. ([Location 221](https://readwise.io/to_kindle?action=open&asin=B00KFEK0EM&location=221)) - However, if the string of symbols in question contains a contradiction, the method’s effectiveness breaks down, as anything follows from a contradiction. ([Location 629](https://readwise.io/to_kindle?action=open&asin=B00KFEK0EM&location=629)) - Note: Hacking basis - This means that Gödel’s incompleteness theorem applies to computers. The uncomputable numbers correspond in a way to programs that will never give a result. Gödel’s incompleteness theorem means that there cannot be a program using a finite number of steps to check any program to see whether it will reach a conclusion or halt. This has become known as the “halting problem”. ([Location 727](https://readwise.io/to_kindle?action=open&asin=B00KFEK0EM&location=727)) - The work of the scientist is thus similar to the work of a chemist distilling some substance. By careful use of induction, deduction and elimination of candidates, the scientist eventually retains a few necessary and sufficient conditions for any phenomenon. The more experiments are made, the more the scientist can be sure of finding the correct causes for a certain effect. ([Location 1006](https://readwise.io/to_kindle?action=open&asin=B00KFEK0EM&location=1006)) - This is because to derive the truth or falseness of any statement, we require a host of hidden premises effectively describing the whole of our web of belief. ([Location 1115](https://readwise.io/to_kindle?action=open&asin=B00KFEK0EM&location=1115)) - logic is the study of the presentation of the truth ([Location 1145](https://readwise.io/to_kindle?action=open&asin=B00KFEK0EM&location=1145))