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paradox in the case of inconsistent descriptions. This is achieved by adopting Lam-
bert's Law
∀
y
(
y
=
i
x
ϕ
x
↔
∀
x
(
ϕ
x
↔
x
=
y
)) as a basic principle of Free description
theory. In terms of the semantics for definite descriptions, the following clause is
added to the foregoing specification of a Free logic interpretation:
(v) if
∀
x
(
ϕ
x
↔
x
=
c
) is true, where
c
is an individual constant, then
f
(
i
x
ϕ
x
)
=
f
(
c
), and if
D
o
\
D
i
, and
where the interpretation function
f
on the set of individual constants must be
surjective with respect to
D
o
.
The nominalism of the Buddhist view indicates that the predicate extensions given by
the interpretation function
f
and the attendant set membership conditions used in the
formal definition of truth for atomic formulas should
not
be seen as reflecting some
literal correspondence theory of truth. Instead, they simply encode the internalized
discourse conventions of the speaker's linguistic community. In this manner it is poss-
ible to provide the basics of a formal semantics for natural language that models the
apoha
view, and hence provides a structure that can reflect the conventional truth
conditions for sentences involving non-denoting terms.
¬
∃
x
(
∀
y
ϕ
y ↔ y = x), then
f
(
i
x
ϕ
x
) =
e
, where
e
∈
References
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2.
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3.
Lambert, K.: Free Logic: Selected Essays. CUP, Cambridge (2003)
4.
Lambert, K.: Existential Import Revisited. Notre Dame Journal of Formal Logic 4,
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5.
Russell, B., Whitehead, A.: Principia Mathematica. CUP, Cambridge (1910)
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11.
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Siderits, M.: Śrughna by Dusk. In: Siderits, M., Tillemans, T., Chakrabarti, A. (eds.)
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Press, New York (2011)
16.
Tillemans, T.: Dharmakīrti. In: E. Zalta (ed.) The Stanford Encyclopedia of Philosophy
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http://plato.stanford.edu/archives/spr2014/entries/
dharmakiirti/
