Suppose the universe consists of facts.
Each fact can be a thought. Therefore can be represented buy a proposition. And each proposition consists of one or more atomic propositions. Atomic proposition cannot consist two or more propositions, but only one.
Consider inside a room - a room in a house, all the facts inside it are represented by a set of atomic propositions. Consider a proposition about a pedestal lamp is inserted, we can imagine a room without a pedestal lamp now converted to one with a pedestal lamp. Like that facts can be added or removed.
A room is a space. It is a subset of the space of universe. Room should be represented by a single big composite proposition that show every aspect of the room. This proposition will be the conjunction of many atomic prepositions.
The universe is represented by the universal set of all possible atomic propositions.
Any possible proposition is a conjunction of -(set of elements consisting of) atomic propositions.
Then logically the room can be represented by a subset of universal propositions. Wrong! Why?
Consider a proposition that represent Mount Everest. It cannot go into a room. Therefore any subset of the universal set of propositions won't fit a room. We might lead to think it is because of size, but no, Mount Everest cannot be moved to Pacific Ocean. This is an impossibility. Can American Declaration of Independence be inside this room? No. Though the physical size permits, practically it is an impossibility. So factors involved can be unlimited. If it is my room an expensive chair be in the room is illogical. But if the room is of a millionaire it may be possible. But further, a photograph of painting of Mount Everest can be in my room. So not all but some propositions regarding Mount Everest will be acceptable to represent my room.
It means that any subset of the universal set do not represent a subspace of reality.
A subset of the universal set is any number of elements of it taken together.
Room is a subset of universe. But it will not be a subset in respect of conjunction of propositions.
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