Can we say true and false things about Harry Potter? If so, does that mean he exists? If not, then how can we talk about a non-existing thing?
I've gotten different answers to these questions in my interviews so far. Here are some of my thoughts on the topic.
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 Stephan Kinsella, who is one of the most prominent supporters of "argumentation ethics." He claims that ownership is inescapable.
Don't take my word for it, but the experts might not be so expert...
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.
I grew up in a Christian Evangelical household. This is my experience with religious fundamentalism.
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 modern 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.
You can find his youtube channel here: https://www.youtube.com/njwildberger
There are no infinite things - no infinite sets, magnitudes, densities, shapes, distances, or anything else.
Every thing is exactly the way it is. It has boundaries and is therefore finite.
If this is true, then we have a great amount of work ahead of us, re-founding modern mathematics on a more solid logical ground.
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.
How to replace one theory with another. You must accomplish three things:
1) Explain where the dominant theory is wrong.
2) Explain why your theory solves the problem in #1, while preserving its explanatory power.
3) Explain why the incorrect theory still had predictive power.
Do those three, and you've made a compelling case for a paradigm shift.