Editing Metaphysics (section)

== <span style="color: #FFFFFF;">Applying</span> ==
'''Formalizing metaphysical claims with modal logic:'''
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# Metaphysics uses modal logic to formalize possibility/necessity claims
# □P = "Necessarily P" (P is true in all possible worlds)
# ◇P = "Possibly P" (P is true in at least one possible world)

# We can simulate possible worlds reasoning computationally

class World:
    """A possible world with specific facts about it."""
    def __init__(self, name: str, facts: dict):
        self.name = name
        self.facts = facts  # {'proposition': bool}
    
    def is_true(self, proposition: str) -> bool:
        return self.facts.get(proposition, False)

class ModalModel:
    """Kripke model for modal logic: worlds + accessibility relation."""
    def __init__(self):
        self.worlds: dict[str, World] = {}
        self.accessibility: dict[str, set[str]] = {}  # w → {accessible worlds}
    
    def add_world(self, world: World, accessible_from: list[str] = None):
        self.worlds[world.name] = world
        self.accessibility[world.name] = set()
        if accessible_from:
            for w in accessible_from:
                if w in self.accessibility:
                    self.accessibility[w].add(world.name)
    
    def necessarily(self, proposition: str, from_world: str) -> bool:
        """□P: true in all accessible worlds."""
        return all(self.worlds[w].is_true(proposition)
                   for w in self.accessibility[from_world]
                   if w in self.worlds)
    
    def possibly(self, proposition: str, from_world: str) -> bool:
        """◇P: true in at least one accessible world."""
        return any(self.worlds[w].is_true(proposition)
                   for w in self.accessibility[from_world]
                   if w in self.worlds)

# Example: Is "water is H₂O" a necessary truth? (Kripke's essential properties)
model = ModalModel()
actual = World("actual", {"water_is_H2O": True, "gold_is_element": True, "I_exist": True})
w1 = World("w1", {"water_is_H2O": True, "gold_is_element": True, "I_exist": False})
w2 = World("w2", {"water_is_H2O": True, "gold_is_element": True, "I_exist": True})
# Note: in w2, 'water' might be a different substance, but it still IS H₂O in our sense

model.worlds["actual"] = actual
model.accessibility["actual"] = {"w1", "w2"}
model.worlds["w1"] = w1
model.worlds["w2"] = w2

print(f"'Water is H₂O' necessarily: {model.necessarily('water_is_H2O', 'actual')}")
# Kripke argues: yes, necessary a posteriori — discovered empirically but true in all worlds
print(f"'I exist' necessarily: {model.necessarily('I_exist', 'actual')}")
# No: there are possible worlds where I don't exist
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; Key metaphysical debates and theorists
: '''Mind-body''' → Descartes (dualism), Smart & Place (identity theory), Putnam (functionalism), Chalmers (hard problem), Dennett (eliminativism)
: '''Universals''' → Plato (Forms), Aristotle (immanent realism), Quine (nominalism), Armstrong (universals as relations)
: '''Causation''' → Hume (regularity), Lewis (counterfactual), Armstrong (necessitation), Mackie (INUS conditions)
: '''Personal identity''' → Locke (memory), Hume (bundle theory), Parfit (''Reasons and Persons''), Olson (animalism)
: '''Modal metaphysics''' → Kripke (''Naming and Necessity''), Lewis (modal realism), Plantinga (ersatz worlds)
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