Some of you might be interested in articles found at http://www.edge.org/.
At the end of each year, prominent academics are asked for their response to a question. That question in 2005 was:
What do you believe is true even though you cannot prove it?
Here are some of the responses offered:
1. that all human languages have a common origin
2. that extra-terrestrial life exists
3. that consciousness does not survive death
4. that Homo neanderthalensis (Neanderthal Man) became extinct because Homo sapiens (our ancestors) ate them
5. that there is moral progress
6. that some works of art have eternal value
7. that most ideas taught in first-year undergraduate Economics courses are wrong
8. that neuroscience will never fully explain the nature of thought
9. that the Riemann hypothesis is true
10. that animals have feelings
Pick one or two of the items on this list and suggest (a) why it is difficult to establish that they are true, and (b) what methods we might nevertheless try in order to do so.