If oneness and manyness are second-order properties applying to how we carve the world conceptually, the Parmenidean deductions conflate levels of predication, invalidating the synthesis.
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(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.
second-order properties(as applied to oneness and manyness)
Characteristics that describe how we think about or organize things, rather than properties of the things themselves. For example, 'being organized into categories' is second-order, while 'being red' is first-order.