Bulletin

Issue: April 2006

Research in Action

New concepts for logic in the modern age

La Trobe University philosopher, Dr Ross Brady, is setting out to apply new concepts to logic.

He is not dealing in lofty intellectual concepts. He believes his new approach to rational thinking will have concrete applications.

‘Because we work with valid patterns of argument, we work at an abstract level. Logic is generally a theoretical subject concerning systems of logic, determined using interpretations of basic logical words, like “and”, “not” and “if…then” ‘, says Dr Brady, a Reader and Associate Professor in La Trobe’s Philosophy Program.

‘Logic involves mathematical-style work, but is subject to philosophical disagreements regarding conceptualisation.

‘Despite working at a theoretical level, I believe my project can provide more meaningful and accurate applications of logic in computer science, philosophy and mathematics and will engender an overall smarter use of information,’ he said.

Specialising among other things in relevant logics, para-consistent logics, content semantics, natural deduction, the logical paradoxes, and philosophical logic, Dr Brady has received $105,000 in Australian Research Council funding to conduct his research over three years.

‘I am looking at the application of logic in this modern age. In doing so, I am one of few philosophers questioning the traditional view that truth-preservation is all there is to logical inference.’

What he describes as the traditional view is not that of the founder of logic, the Greek philosopher, Aristotle, but more recent “classical” philosophers like Bertrand Russell and Gottlob Frege.

There are many arguments that show that this traditional view of logic condones inferences that are informally invalid. Indeed, there are classical inferences which no-one in their right mind would ever use. For example: given any two sentences whatsoever, one implies the other.

Dr Brady is different from classical philosophers in that he believes that there must be meaningful connections between the premise and the conclusion of an argument, as opposed to that of classical logic where a conclusion can validly “follow” from premises due to truth-preservation alone. For example: Brothers are female. Therefore, the moon is made of green cheese.

‘I am one of few philosophers in the world who really questions this. Some of my colleagues around the world do ask the question but very few attempt to come up with definite answers. I hope my continuing research will provide many of the answers.’

‘As an example of computational ramifications, instead of calling upon rigid data from a database, you can have a knowledge base of sentences which can then be logically coded. Then, applying logical rules and deducing conclusions, you can establish what was implicit rather than explicit in the original knowledge base,’ he said.

The research would also benefit the teaching of logic in Australia with the development of sharper analytical skills in students. It will also lay the groundwork for a textbook on the new logic.