This document discusses several common paradoxes and their possible solutions. It begins by defining a paradox as a self-contradictory statement that may nonetheless be true. Examples of paradoxes explored include the Barber Paradox, the Liar Paradox, and the Ship of Theseus. For each, potential resolutions are examined, such as proposing multiple barbers or that the original ship shares a relevant history with any replacement. Overall, the document analyzes how paradoxes pose seemingly logical problems without obvious answers and can provoke philosophical thinking.

1. Paradox
John Galvin

2. Driving Question:
• The Driving Question for my project is “Can
paradoxes be solved, and if so, what are there
solutions?”

3. What is a paradox?
• A paradox is a statement that, despite
apparently being logical and reasonable,
contradicts its self, without necessarily being
untrue.

4. Examples and possible solutions

5. • The Barber Paradox: The Barber shaves
everyone in town that does not shave himself.
Who shaves the barber?
• Depending on how the paradox is phrased,
there could be more than one barber.

6. • The Epimenides Paradox: Epimenides the
Cretan says “All Cretans are liars.”
• Not all Cretans are liars, but Epimenides is.

7. • The Liar Paradox: This Sentence is
false.
• The sentence “ This sentence is false,”
is either both true and false at the
same time, or neither at all.

8. • Irresistible Force Paradox: What would
happen if an unstoppable force hit an
immovable object?
• Irresistible Force: If an unstoppable force hit
an immovable object, they would pass
through each other.

9. • Ship of Theseus: You can replace any part of a
ship and it will still be the same ship, but if
you replace all of them and then use the
original parts to make another ship you will
have two of the same ship. Which one is the
ship of theseus?
• There are many proposed solutions, but one is
that is that the ship of Theseus is any ship that
shares a relevant history with the original ship.

10. • Sorites Paradox: If you remove a grain of sand
from a heap, you will still have a heap. If you
keep removing sand you will no longer have a
heap. At what point does it cease to be a
heap?
• The word “heap” is too vague to have a
definite point where it ceases to be a heap. If
a definite number of sand grains defined it as
a heap, then there would be no paradox.

11. • Grelling-Nelson Paradox: Is the word
heterological, meaning not applicable to its
self, heterological?
• No, a collection of all collection is not a
member of its self.

12. Paradoxes are interesting because they are
seemingly logical questions with no clear
answer. They can have philosophical
implications, and change the way people
think.