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Alfred North Whitehead's theory of propositions is a fundamental aspect of his process philosophy, particularly his understanding of how reality is experienced and constituted. In Whitehead's view, propositions play a crucial role in the functioning of experience and reality.

Nature of Propositions: According to Whitehead, propositions are not mere linguistic or logical constructs; they are complex entities that involve a potentiality. A proposition is a potential fact; it proposes a particular way the world might be. It involves a synthesis of multiple potentialities, integrating diverse elements into a coherent potential whole.
Role in Experience: Propositions function primarily as "lures for feeling," influencing the process of becoming in actual entities. They guide the subjective aim of an actual occasion (an instance of experience) and contribute to the realization of potentialities in the concrete world.
Existence and Subjects: Regarding their existence independent of subjects prehending them, Whitehead's philosophy suggests a nuanced view. Propositions, in his framework, exist as potentialities and are not dependent on any single subject for their existence. However, their significance and role in shaping reality become active only when they are prehended (grasped or incorporated) by a subject in the process of experience. This prehension is a selective process, where a subject integrates a proposition into its own becoming, giving it relevance and actuality in a particular context.
Relation to Reality: In Whitehead's process-relational ontology, the actual world is composed of a network of interrelated actual occasions, each prehending and being prehended by others. Propositions play a key role in this relational process, offering possibilities that are actualized in the concrete experiences of these occasions.
Beyond Human Consciousness: Whitehead's theory extends the concept of propositions beyond human language and consciousness. Propositions are considered relevant in the wider process of reality, influencing and being influenced by the ongoing creative advance of the universe.

In summary, while propositions in Whitehead's philosophy have a kind of existence as potentialities independent of any particular subject, their role, significance, and actualization are intrinsically connected to the subjects that prehend them within the process of reality. His view represents a departure from traditional notions of propositions in both logic and linguistics, embedding them deeply into the fabric of his process-relational cosmology.