Frege demonstrated in Begriffsschrift that predication is irreducibly asymmetric: the function-argument structure cannot be collapsed into identity without loss of inferential power.
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A relation between an object and itself, expressed as an atomic formula (a=a), subject to the same existence-entailment conditions as other atomic predicates under GSA
Inferential power(reasoning and logic)
The ability to draw conclusions and make new deductions from existing information.
asymmetric(as used in logic and epistemology)
When two things are treated differently or unequally, rather than being balanced or fair—like giving one side of an argument more weight than the other.
predication(Soames treats predication as a primitive notion that underlies but does not reduce to belief.)
A primitive mental act whereby an agent represents an object as having a property — for example, representing o as red via perception, thought, or nonlinguistic perceptual belief.