Lessons in Paradoxes
A paradox is an apparently sound argument with an apparently
The existence of a paradox implies a lack of understanding, so we try
to dissolve the paradox by employing one of the following resolutions:
- Deny that the reasoning is valid
- Deny that the premises are true
- Realize that the conclusion is true
Paradoxes are caused by allowing an unfounded assumption to slip by.
We can learn some valuable lessons by looking at the nature of this assumption.
Don't confuse two different levels that appear similar
Anselm's Ontological Argument
Self-referential statements may have no truth value
In general, be careful with the math
Zeno's Paradox of Motion
Achilles and the Tortoise
Logic cannot operate on undefined terms
Arbitrarily large does not imply infinite
Zeno's Paradox of Plurality
If the universe is deterministic, then thought is too
English is not so great for logic
- Most philosophical debates are caused by two people assuming different definitions for the same term. The issue arises often because each person may think that their definition is self-evident and so they forget to check for consistency with the other person's definition.