Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A. N. Prior in [9] has suggested an approach towards a second order logic of existence where, following medieval logicians,  distinguish "beten predicates (like 'is red', 'is hard', etc.) which entail existence, and predicates (like 'is thought to be red', 'is thought of', etc.) which do not."2 Let us refer to attributes (including relational attributes) which are designated by the former kind of predicate as existence attributes, or for brevity, e-attributes. It is suggested then that 'x exists' be defined as 'there is some e-attribute which x possesses'. In what follows, this approach regarding the concept of existence is formalized semantically as ll as syntactically, and a completeness theorem is established corresponding to the completeness (in a secondary sense, i.e., as including normal, nonstandard models) of standard second order logic (as formulated, for example, in Church [1]). In [2] (cf. the abstracts [3] and [4]), the present author formalized a complete first order logic (with identity) of actual and possible objects which was there used in the formulation of a complete first order tense logic.3 The observation, which will be proved here, was made by Prior that in a second order logic with e-attributes quantification over actual objects can be appropriately defined so that every theorem of the first order logic of actual and possible objects becomes a theorem of second order logic with e-attributes.4 In effect, the definition (where q is a formula, a is an individual variable, and vr is a 1-place predicate variable) is e e
['Nino B. Cocchiarella']
I am writing a research paper on a idea A SECOND ORDER LOGIC OF EXISTENCE
[{"from": "human", "value": "I am writing a research paper on a idea A SECOND ORDER LOGIC OF EXISTENCE"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A. N. Prior in [9] has suggested an approach towards a second order logic of existence where, following medieval logicians,  distinguish \"beten predicates (like 'is red', 'is hard', etc.) which entail existence, and predicates (like 'is thought to be red', 'is thought of', etc.) which do not.\"2 Let us refer to attributes (including relational attributes) which are designated by the former kind of predicate as existence attributes, or for brevity, e-attributes. It is suggested then that 'x exists' be defined as 'there is some e-attribute which x possesses'. In what follows, this approach regarding the concept of existence is formalized semantically as ll as syntactically, and a completeness theorem is established corresponding to the completeness (in a secondary sense, i.e., as including normal, nonstandard models) of standard second order logic (as formulated, for example, in Church [1]). In [2] (cf. the abstracts [3] and [4]), the present author formalized a complete first order logic (with identity) of actual and possible objects which was there used in the formulation of a complete first order tense logic.3 The observation, which will be proved here, was made by Prior that in a second order logic with e-attributes quantification over actual objects can be appropriately defined so that every theorem of the first order logic of actual and possible objects becomes a theorem of second order logic with e-attributes.4 In effect, the definition (where q is a formula, a is an individual variable, and vr is a 1-place predicate variable) is e e"}]