Plato claimed that numbers exist in some mind-independent abstract heaven. Nominalists claim that there is no such heaven. Clearly, we can't see, hear, taste or feel numbers.
What is it
A paradox is a persuasive argument that something, which we judge must be false, is true. Zeno's Paradox, for example, is a convincing argument that it's impossible to move. Paradoxes are valuable in philosophy because they help us become aware of forms of argument that are deceptively convincing yet logically fallacious. John and Ken are joined by Roy Sorensen from Dartmouth College, author of A Brief History of the Paradox, to consider what we can learn from paradoxes.
What is a paradox? People use the word 'paradox' in many ways, for example to denote something very surprising. But these aren't genuine "philosophical" paradoxes. In a genuine paradox, one starts with seemingly true premises, performs reasoning thought to generate true conclusions from true premises, and ultimately derives a conclusion that's apparently false. Here are four paradoxes:
With guest Roy Sorensen of Dartmouth College, John and Ken discuss these paradoxes and others. Are they irresolvable, or do they disappear once one thinks about them deeply enough? And either way, do they have theoretical or practical significance, or are they just plain mind-blowing fun?
- Roving Philosophical Report (seek to 5:55): Zoe Corneli interviews Palo Mancuso of UC Berkeley about the history of Russell's paradox, sketched in (4) above. The story revolves around Gottlob Frege, an unpopular and ambitious German mathematician who in the late nineteenth century tried to reduce all of mathematics to logic, and Bertrand Russell, a young and aristocratic English philosopher who discovered a fatal flaw in Frege's attempted reduction.
- 60-Second Philosopher (seek to 49:35): In this peek at the "paradox philosophy" of Joe Hunt, Ian Scholls shows just how distorted popular notions of paradox can get. Hunt, once the ringleader of a famous Ponzi scheme called the Billionaire Boys Club and now serving a life sentence for murder, held that what something is depends on how you look at it, and that nothing is real except what you want. After "accidentally" killing a con artist who allegedly swindled millions from the Club, Hunt even went so far as to deny that the man was dead! Paradoxical? You decide.