Abstract
This is a critical discussion of Nino B. Cocchiarella’s book “Formal Ontology and Conceptual Realism.” It focuses on paradoxes of hyperintensionality that may arise in formal systems of intensional logic.
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Notes
Quoted from Russell (1901), p. 62.
See Coccharella (2009).
A very accessible introduction may be found in Cocchiarella and Freund (2008).
Cocchiarella (1980).
A type symbol of simple type theory is defined recursively as follows:
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1.
o is an type symbol.
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2.
If \( {\text{t}}_{ 1} , \ldots ,{\text{t}}_{n} \) are type symbols, then \( \left( {{\text{t}}_{ 1} , \ldots ,{\text{t}}_{n}} \right) \) is an type symbol.
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3.
There are no other type symbols.
If F is an n-placed predicate letter and \( \alpha_{1}^{{{\text{ t}}_{1} }} , \ldots , \alpha_{n}^{{{\text{t}}_{n} }} \) are terms, then \( {\text{F}}^{{\left( {{\text{t}}_{1} , \ldots ,{\text{t}}_{n} } \right)}} \left( {\alpha_{1}^{{{\text{ t}}_{1} }} , \ldots , \alpha_{n}^{{{\text{t}}_{n} }} } \right) \) is an atomic well-formed formula of the simple-type stratified language. The well-formed formulas are then the smallest set K containing the atomic formulas and such that \( \varphi \to \psi \), \( \neg \varphi \), and \( \left( {\forall x^{\text{t}} } \right)\varphi \) are in K if φ and ψ are in K.
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1.
In Cocchiarella’s HST*λ, the principle of λ-conversion is accordingly restricted.
Cocchiarella (1986).
Frege uses the sign “x ∩ y”.
A sister theory is the free logic of Cocchiarella’s HST*λ. This allows the formulation of concepts that are not homogeneously stratified. Paradox is blocked by employing the free logic of the theory to treat such singular predicate terms as non-referential.
What Cocchiarella calls “Va” is actually “Vb”.
References
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Landini, G. Cocchiarella’s Formal Ontology and the Paradoxes of Hyperintensionality. Axiomathes 19, 115–142 (2009). https://doi.org/10.1007/s10516-009-9062-7
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DOI: https://doi.org/10.1007/s10516-009-9062-7