 (ii) The distinction between exemplifying and encoding is a primitive one and is represented in the theory by two atomic formulas: \(F^nx_1\ldots x_n\) \((x_1,\ldots ,x_n\) exemplify \(F^n\)) and \(xF^1\) \((x\) encodes \(F^1).\) While both ordinary and abstract objects exemplify properties, only abstract objects encode  properties;[10]  it is axiomatic that ordinary objects necessarily fail to encode properties \((O!x \to \Box \neg \exists FxF).\) Zalta’s proposal can be seen a positive metaphysical proposal distinct from all the others we have considered; a positive proposal that uses encoding as a key notion to characterize abstract objects. On this reading, the definitions and axioms of the theory convey what is meant by encoding and how it works. Intuitively, an abstract object encodes the properties by which we define or conceive of it, but exemplifies some properties contingently and others necessarily. Thus, the number 1 of Dedekind-Peano number theory encodes all and only its number-theoretic properties, and whereas it contingently exemplifies the property being thought about by Peano, it necessarily exemplifies properties such as being abstract, not having a shape, not being a building, etc. The distinction between exemplifying and encoding a property is also used to define identity: ordinary objects are identical whenever they necessarily exemplify the same properties while abstract objects are identical whenever they necessarily encode the same properties.