In Knowledge and the Philosophy of Number, Hossack proposes a Platonist logicist framework where:

• __Knowledge is fundamentally about structures.
• These structures are logical, necessary, and eternal.
• What we call “data” are simply points on these structures.
• With sufficient points, we could map those structures.

“What is true of numbers is true of all logical structures: they are not invented, they are discovered.”
— Hossack

This view is ontological realism about data:

• Data is not reducible to sensory experience or probabilistic signal.
• Rather, data is the formal embodiment of necessary truths, often mathematical or logical.
• Data exists independently of observation, like the Pythagorean theorem or the concept of function.

Concept	Shannon	Hossack
What is data?	A symbol that reduces uncertainty in communication	A representation of a truth in a logical structure
Origin	Emerges from transmission and encoding	Exists eternally in abstract ontology
Truth	Not relevant; Shannon’s model ignores meaning	Central; data expresses necessary truths
Meaning	Extrinsic to the data	Intrinsic to the structure
Observer’s role	Crucial – data needs a channel, noise, receiver	Secondary – truths exist whether or not anyone observes them

Shannon’s framework is syntactic and signal-based, while Hossack's is semantic and formal.

In Hossack’s ontology:

• Data ≈ instantiations of logical relations.
• Numbers are not collections of strokes or sounds, but places in a structure.

A dataset, then, is a mapping between structures: between observed quantities and formal mathematical relationships.

So, to "generate data" in this view is not to create something new, but to bring into our cognitive grasp something that already exists necessarily.

This philosophical view implies:

• Not all data is empirical
  • Some data (especially in mathematics and logic) is a priori.
• Data science must distinguish between data from measurement and data from formal derivation.

Algorithms that rely solely on pattern recognition (like neural networks) may miss deep structure unless guided by logical form.

Though they seem opposed, one might argue:

• Shannon's data is concerned with how we access information.
• Hossack's data is concerned with what information fundamentally___is___.

Shannon explains how data travels. Hossack explains how data is.