Editing Philosophy of Mathematics (section)

== <span style="color: #FFFFFF;">Applying</span> ==
'''Modeling 'Mathematical Truth' (The Formalist Game):'''
<syntaxhighlight lang="python">
def is_chess_legal(move):
    """
    To a Formalist, Math is like Chess rules.
    """
    rules = {"Pawn": "Forward", "Knight": "L-Shape"}
    if move in rules:
        return "TRUE: Valid within the rules of the game."
    else:
        return "FALSE: This is a 'move' that the rules don't allow."

# Testing 'Knight: Jump'
print(is_chess_legal("Knight"))
# Formalists argue that '1+1=2' is true for the same 
# reason a Knight moves in an L-shape: because we 
# agreed it does.
</syntaxhighlight>

; Mathematical Paradoxes
: '''Russell's Paradox''' → The set of all sets that don't contain themselves (Breaking the foundations of logic).
: '''Banach-Tarski Paradox''' → A mathematical proof that says you can cut a ball into 5 pieces and put them back together to make two identical balls (Challenge to our intuition of reality).
: '''The Skolem Paradox''' → The fact that "Uncountable" infinities can be modeled using "Countable" sets.
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