Editing Epistemology (section)

== <span style="color: #FFFFFF;">Applying</span> ==
'''Working with epistemological frameworks — practical analysis:'''
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# Epistemology is primarily a philosophical discipline worked through argumentation,
# but we can illustrate its concepts through formal modeling.

# Modeling a belief network (Bayesian epistemology)
# Bayesian epistemology uses probability to formalize degrees of belief (credences)
# and rational updating via Bayes' theorem

from fractions import Fraction

def bayes_update(prior: float, likelihood_given_h: float, likelihood_given_not_h: float) -> float:
    """
    Update belief in hypothesis H given new evidence E.
    
    Prior P(H), P(E|H), P(E|¬H) → Posterior P(H|E)
    
    This formalizes the epistemological claim: rational belief revision
    requires updating proportionally to how much evidence was expected.
    """
    p_e = likelihood_given_h * prior + likelihood_given_not_h * (1 - prior)
    posterior = (likelihood_given_h * prior) / p_e
    return posterior

# Example: I believe it is raining (P=0.3 prior).
# I look outside and see wet pavement (E).
# P(wet pavement | raining) = 0.9
# P(wet pavement | not raining) = 0.2
posterior = bayes_update(0.3, 0.9, 0.2)
print(f"Posterior probability of rain given wet pavement: {posterior:.2f}")
# ≈ 0.66 — evidence significantly updates belief

# Modeling Gettier-type cases
class Belief:
    def __init__(self, content, is_true, is_justified, causal_connection=True):
        self.content = content
        self.is_true = is_true
        self.is_justified = is_justified
        self.causal_connection = causal_connection  # Externalist add-on
    
    @property
    def is_jtb_knowledge(self):
        """Classical justified true belief — Gettier shows this is insufficient."""
        return self.is_true and self.is_justified
    
    @property
    def is_causal_knowledge(self):
        """Causal theory: belief must be causally produced by the fact that makes it true."""
        return self.is_true and self.is_justified and self.causal_connection
    
    def __repr__(self):
        return (f"Belief: '{self.content}' | True: {self.is_true} | "
                f"Justified: {self.is_justified} | JTB: {self.is_jtb_knowledge} | "
                f"Causal: {self.is_causal_knowledge}")

# Classic Gettier case
gettier_case = Belief(
    content="There is a sheep in the field",
    is_true=True,           # There IS a hidden sheep
    is_justified=True,      # You saw what looked like a sheep (actually a dog)
    causal_connection=False # Your belief was caused by the dog, not the actual sheep
)
print(gettier_case)
# JTB: True (fails as knowledge!) | Causal: False (correctly excluded)
</syntaxhighlight>

; Key epistemological positions and theorists
: '''Rationalism''' → Descartes (''Meditations''), Leibniz, Spinoza, Plato
: '''Empiricism''' → Locke (''Essay Concerning Human Understanding''), Hume (''Enquiry''), Berkeley
: '''Kantian synthesis''' → Kant (''Critique of Pure Reason'') — a priori structures of experience
: '''Reliabilism''' → Alvin Goldman — knowledge requires reliable belief-forming processes
: '''Virtue epistemology''' → Ernest Sosa, Linda Zagzebski — knowledge through intellectual virtues
: '''Social epistemology''' → Miranda Fricker (''Epistemic Injustice''), Alvin Goldman
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