Does infinity really come in multiple sizes? According to mathematical orthodoxy, some infinities are bigger than others – but that’s awfully hard to wrap your mind around. So, I’ve asked Dr. Toby Meadows from the University of Queensland to help me out. He specializes in the philosophy of mathematics and set theory.
Why is the world of ideas dominated by male thinkers? Is it because women are discouraged from intellectual life – or is it because women tend to choose other careers?
If we go even deeper: why do women (and men) make the choices they do? Is it because they are influenced by overwhelming societal pressures – or are they acting freely?
These are the questions I’ve asked Dr. Michelle Boulous-Walker, who teaches at the University of Queensland in Brisbane, Australia.
If we choose to argue, have we presupposed an ethical framework? Is “self-ownership” a concept that cannot coherently be doubted?
To help me answer these questions, I’m joined by one of the most prominent supporters of “argumentation ethics” – the theory that says ownership is inescapable, and as soon as we choose to argue, we’re committed to a set of ethical values.
Does consciousness “emerge” from physical phenomena? What does “emerge” even mean? If we grant that consciousness emerges, and that it has a distinct ontological status, doesn’t that imply dualism?
To help me answer these questions, I spoke with Dr. Braddon-Mitchell at the University of Sydney.
Are the foundations of mathematics rock-solid? Are we allowed to doubt them? How central is the concept of “infinity” to modern mathematics – and has the logic of infinity been fully worked out?
To help me answer these questions, I’ve traveled to Sydney, Australia to interview an unorthodox mathematician on the topic.
Dr. Norman Wildberger is also skeptical of the foundations of mathematics – even though he’s a teaching professor at the University of New South Wales – and he has a popular youtube channel where he’s laying out new foundations for the field.
Breakdown of the interview I had with Dr. Patrick Girard about paraconsistent logic. Nothing is both true and false at the same time. Any logical theory that suggests otherwise is catastrophically flawed.
There are no true logical contradictions, and if we get this wrong, we eliminate any chance of internal incoherence in our theories.
Original interview here – Ep. 42 – Truth and Paraconsistent Logic | Dr. Patrick Girard