Frege believed that math is analytic, meaning that the definitions of mathematical terms like “2” and “4” guarantee the truth of sentences like “2+2=4”. Frege’s theory explains how we know about math; as long as we can understand what we mean by mathematical terms, and can reason logically, our mathematical knowledge is guaranteed. But in order to work, the theory has to rely on Frege’s definition of a number.
What Is It
At the end of the 19th Century, the German philosopher Gottlob Frege invented a new language, based on mathematics, designed to help people reason more logically. His ideas have had a lasting impact on philosophy, math, computer science, and the study of artificial intelligence. And many of the questions that influenced his thinking are still hotly debated today: How much does language influence the thoughts you can think? Could there be a way of speaking that taps into deep philosophical insights about the nature of reality? What's the relationship between math and logic? Josh and Ray try to make sense of Frege with host emeritus John Perry, author of Frege's Detour: An Essay on Meaning, Reference, and Truth.
In this episode, Josh and Ray examine the work of Gottlob Frege, a German philosopher who created a new system of logic. Although there were plenty of former mathematical frameworks, Ray points out that Frege’s was revolutionary because it involved systematic proofs. Josh questions how Frege checked his own system, to which Ray admits that it was still imperfect and contradictory. Then, Josh questions how Frege’s system makes sense of real world confusions.
The philosophers are joined by John Perry, Professor Emeritus of Philosophy at Stanford University and the co-founder and former co-host of Philosophy Talk. Ray asks about the advances made in Frege’s influential book “The Begriffsschrift,” and John discusses how to apply mathematical ways of thinking about grammar. For instance, Frege favors an object-concept model instead of a subject-predicate structure for sentences. Josh asks about identity puzzles such as the confusion between Clark Kent and Superman, since Frege left that problem unsolved in his first book. John explains how Frege’s solution was to demonstrate that sentences describe the content of people’s thoughts and the world.
In the last segment of the show, Josh, Ray, and John discuss how Frege’s logic differs from that of other philosophers, such as Aristotle, Wittgenstein, and Richard Rorty. Ray asks about the relationship between logic and understanding what goes on inside people’s heads, prompting John to discuss things that happen in the abstract and outside of people’s heads. Josh wonders if Frege’s ideas have influenced computer science, and John describes how Frege’s failures sparked a wave of other scientists working in computing and the philosophy of science.
- Roving Philosophical Report (Seek to 4:32) → Holly J. McDede examines how identity confusion plays out in real life.
- From the Community (Seek to 42:13) → Josh and Ray consider if real life wars could be carried out in virtual reality.
What if we created the perfect logical language?
Would we gain important new insights about mathematics?
Could we find deep connections between ideas just by studying the grammar of sentences?