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#### On Wright’s Inductive Definition of Coherence Truth for Arithmetic

(Blackwells, 2000)

In “Truth – A Traditional Debate Reviewed” (1999), Crispin Wright proposed an inductive definition of “coherence truth” for arithmetic relative to an arithmetic base theory B. Wright’s definition is in fact a notational ...

#### Can a Many-Valued Language Functionally Represent its own Semantics?

(Blackwells, 2003)

Tarski’s Indefinability Theorem can be generalized so that it applies to many-valued languages. We introduce a notion of strong semantic self-representation applicable to any (sufficiently rich) interpreted many-valued ...

#### A proof of the (strengthened) Liar formula in a semantical extension of Peano Arithmetic

(Blackwells, 2000)

In the Tarskian theory of truth, the strengthened liar sentence is a theorem.
More generally, any formalized truth theory which proves the full, self-applicative scheme True(“f”) f will prove the strengthened liar ...

#### Conservativeness and translation-dependent T-schemes

(Blackwells, 2000)

Certain translational T-schemes of the form True(“f”) « f(f), where f(f) can be almost any translation you like of f, will be a conservative extension of Peano arithmetic. I have an inkling that this means something ...

#### Bueno and Colyvan on Yablo’s Paradox

(Blackwells, 2004)

This is a response to a paper “Paradox without satisfaction”, Analysis 63, 152-6 (2003) by Otavio Bueno and Mark Colyvan on Yablo’s paradox. I argue that this paper makes several substantial mathematical errors which vitiate ...

#### Some More Curious Inferences

(Blackwells, 2005)

The following inference is valid:
There are exactly 101 dalmatians,
There are exactly 100 food bowls,
Each dalmatian uses exactly one food bowl
Hence, at least two dalmatians use the same food bowl.
Here, ...

#### Craig’s Theorem

(Macmillan Reference USA, 2005)

In mathematical logic, Craig’s Theorem (not to be confused with Craig’s
Interpolation Theorem) states that any recursively enumerable theory is recursively
axiomatizable. Its epistemological interest concerns its possible ...

#### Second-Order Logic

(Macmillan Reference USA, 2005)

Second-order logic is the extension of first-order logic obtaining by introducing
quantification of predicate and function variables.

#### Jacquette on Grelling’s Paradox

(Blackwells, 2005)

This discusses a mistake (concerning what a definition is) in “Grelling’s revenge”, Analysis 64, 251-6 (2004), by Dale Jacquette, who claims that the simple theory of types is inconsistent.

#### Hume = Small Hume

(Blackwells, 2002)

We can modify Hume’s Principle in the same manner that George Boolos suggested for modifying Frege’s Basic Law V. This leads to the principle Small Hume. Then, we can show that Small Hume is interderivable with Hume’s Principle.