Extended Abstract

Introduction

The article examines the ontological issues embedded in the Classical Predicate Logic. While this logic is celebrated for its analytical power and success in formal reasoning, it carries significant ontological commitments that create philosophical problems. These commitments often conflict with linguistic intuitions and common sense. These commitments are the product of the fusion of predicate logic with ontology. Previously, articles and books have addressed the problems that this fusion has created for ontology. In this article, we focus on the problems that this fusion has created for logic.

Ontological Difficulties in Predicate Logic

The article identifies eleven major issues in the Classical Predicate Logic:

1. Past Entities: Classical predicate logic struggles to handle past entities. For instance, how should a sentence like "Nader Shah existed" be analyzed when Nader Shah no longer exists? While intuitively true, such sentences pose a challenge for formal interpretation.

2. Fictional Names: Names like "Rostam" create problems in the Classical Predicate Logic. A statement like "Rostam does not exist" is challenging to formalize, as the logic assumes all names refer to existing entities. Therefore, these names must be removed or any sentences containing them must be considered false, which conflicts with our common sense.

3. Ambiguous Objects: Objects like shadows or holes, which are neither fully present nor absent, challenge the Classical Logic. Quantifiers in the logic may implicitly commit to the existence of these ambiguous entities, which can lead to unnecessary or unwanted ontological commitments.

4. Issues in Modal Logic: Classical Predicate Logic, with its common ontological bias, cannot be extended to modal statements involving necessity and possibility. For example, analyzing the sentence "The morning star is the same as the evening star" in modal logic leads to strange ontological commitments.

5. Unwanted Ontological Commitments in Everyday Language: Everyday phrases like "something scared me in my dream" may lead to dubious or unnecessary ontological commitments when analyzed through the predicate logic.

6. Sentences with Propositional Attitudes: Sentences like "I want to write a better article" involve propositional attitudes and create complex ontological commitments that classical logic cannot handle effectively.

7. Higher-Order Predicate Logic: Quantifiers in higher-order predicate logic lead to commitments to sets or properties or propositions, raising issues about ontological commitment to abstract entities.

8. Quine’s Criterion of Ontological Commitment: Quine’s ontological criterion, "to be is to be the value of a bound variable," often fails to distinguish between real and apparent ontological commitments and therefore it is redundant.

9. Loss of Neutrality: Due to the existential interpretation of quantifiers, the Classical Predicate Logic has lost its neutrality, distancing itself from natural language and from the expectation of formality of logic.

10. Ambiguities in the Use of Consecutive Quantifier without a Predicate: Some sentences require the use of multiple quantifier, which leads to ambiguity in the use of quantifier. For example, the sentence "everything exists" demands distinct quantifiers for "everything" and "exists", which can make the semantic analysis of the quantifiers ambiguous and complicated.

11. Ontological Commitments of the Universal quantifier: Although universal propositions in the Classical Predicate Logic lack ontological commitments, universal quantifier does not. For, since “∀x Fx” implies “∃x Fx”, and since the latter represents the existence of objects of the type F, then the former must also represents. And this again burdens the ontological commitments of the Classical Logic.

Proposed Solutions

To address these problems, the article proposes four main strategies:

1. Paraphrase: This strategy involves reformulating sentences syntactically to reduce ontological commitments. For instance, instead of proper names, descriptive phrases can be used. While effective in reducing ontological commitments, this approach may compromise the neutrality and formal simplicity of logic. It is also sometimes inconsistent with the natural intuitions of language.

2. Naturalism: This strategy limits ontological commitments to empirically verifiable entities. By confining quantifiers to the domain of natural sciences, unnecessary philosophical assumptions are avoided. However, this approach may not handle natural language effectively.

3. Substitutional Interpretation: Instead of interpreting quantifiers existentially, this strategy uses linguistic substitutions in the domain of quantifier. For example, rather than assuming the existence of objects in the domain of quantifier, we can assume a linguistic substitution, for example a name in the domain of quantifier. This approach preserves neutrality but might struggle with complex sentences.

4. Meinongianism: This approach extends the domain of quantifier to include nonexistent entities, such as "Rostam" or "the golden mountain." While it resolves many ontological issues, it introduces significant ontological complexity, conflicting with principle of simplicity.

Conclusion

The article concludes that each of these strategies has its advantages and limitations. Paraphrase and substitutional interpretation are more cost-effective but may be limited in their ability to analyze natural language. In contrast, Meinongianism resolves many problems but is unpopular due to its complexity and heavy ontological commitments. Ultimately, the article emphasizes that rethinking the ontological assumptions of predicate logic is essential to its continued relevance and adaptability. Such reconsideration can align predicate logic more closely with linguistic intuitions and enable more precise and comprehensive interpretations. This reflection not only mitigates ontological challenges but also enhances the applicability of predicate logic in philosophy and science, reinforcing its role as a powerful analytical tool.