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Steps Toward a Computational Metaphysics
 JOURNAL OF PHILOSOPHICAL LOGIC
, 2007
"... In this paper, the authors describe their initial investigations in computational metaphysics. Our method is to implement axiomatic metaphysics in an automated reasoning system. In this objects is implemented in prover9 (a firstorder automated reasoning system which is the successor to otter). Afte ..."
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Cited by 8 (5 self)
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In this paper, the authors describe their initial investigations in computational metaphysics. Our method is to implement axiomatic metaphysics in an automated reasoning system. In this objects is implemented in prover9 (a firstorder automated reasoning system which is the successor to otter). After reviewing the secondorder, axiomatic theory of abstract objects, we show (1) how to represent a fragment of that theory in prover9’s firstorder syntax, and (2) how prover9 then finds proofs of interesting theorems of metaphysics, such as that every possible world is maximal. We conclude the paper by discussing some issues for further research.
Relations versus functions at the foundations of . . .
 FORTHCOMING IN THE JOURNAL OF LOGIC AND COMPUTATION
"... Though Frege was interested primarily in reducing mathematics to logic, he succeeded in reducing an important part of logic to mathematics by defining relations in terms of functions. By contrast, Whitehead & Russell reduced an important part of mathematics to logic by defining functions in term ..."
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Though Frege was interested primarily in reducing mathematics to logic, he succeeded in reducing an important part of logic to mathematics by defining relations in terms of functions. By contrast, Whitehead & Russell reduced an important part of mathematics to logic by defining functions in terms of relations (using the definite description operator). We argue that there is a reason to prefer Whitehead & Russell’s reduction of functions to relations over Frege’s reduction of relations to functions. There is an interesting system having a logic that can be properly characterized in relational but not in functional type theory. This shows that relational type theory is more general than functional type theory. The simplification offered by Church in his functional type theory is an oversimplification: one can’t assimilate predication to functional application.
On the Distinction between Relational and Functional Type Theory
"... It is commonly believed that it makes no difference whether one starts with relational types or functional types in formulating type theory, since one can either start with relations as primitive and represent functions as relations or start with functions as primitive and represent relations as fun ..."
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It is commonly believed that it makes no difference whether one starts with relational types or functional types in formulating type theory, since one can either start with relations as primitive and represent functions as relations or start with functions as primitive and represent relations as functions. It is also commonly believed that the formulabased logic of relational type theory is equivalent to the termbased logic of functional type theory. However, in this paper, the authors argue that there are systems with logics that can be properly characterized in relational type theory, but not in functional type theory. We investigate an important difference between relational type theories (RTTs) and functional type theories (FTTs). It is often thought that for each RTT, there is an FTT which is a mere variant (or vice versa), since relations and functions are interdefinable. It is often concluded,
University of California–Berkeley and
"... In this paper, the authors describe their initial investigations in computational metaphysics. Our method is to implement axiomatic metaphysics in an automated reasoning system. In this objects is implemented in prover9 (a firstorder automated reasoning system which is the successor to otter). Afte ..."
Abstract
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In this paper, the authors describe their initial investigations in computational metaphysics. Our method is to implement axiomatic metaphysics in an automated reasoning system. In this objects is implemented in prover9 (a firstorder automated reasoning system which is the successor to otter). After reviewing the secondorder, axiomatic theory of abstract objects, we show (1)howtorepresentafragmentofthattheoryinprover9’s firstorder syntax, and (2) how prover9 then finds proofs of interesting theorems of metaphysics, such as that every possible world is maximal. We conclude the paper by discussing some issues for further research. 1.
and
"... In this paper, the authors argue that there is a version of actualist realism about possible worlds and possible individuals that is immune to the difficulties raised for this view in Divers 2002. We show that object theory, as a form of actualist realism, provides a general theory of modality that ..."
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In this paper, the authors argue that there is a version of actualist realism about possible worlds and possible individuals that is immune to the difficulties raised for this view in Divers 2002. We show that object theory, as a form of actualist realism, provides a general theory of modality that is at least as good as genuine realism but without the commitment to possible worlds in David Lewis’s sense. 1.