My inner positivist: "You must be kidding! Such frivolous activities will waste your mind."
My inner neopragmatist: "Come on, inner positivist. Some frivolity is not necessarily a bad thing. Would you rather have us watch 'Dark Knight Rises'?"
My inner positivist: "Well... I'm not taking part in this, anyway."
My inner neopragmatist: "I'd rather have us write some poetry, but I'm not gonna spend this evening alone. Bring out your toys, inner anti-anti-realist."
Reality is indexical
My inner anti-anti-realist claims that the following is roughly right, although it might require corrections.
- Objects of mathematical nontrivial theories are some of the processes: their processuality is the way in which they are constructed from the corresponding theories. Constructivists are invited to consider only constructive mathematics. Other processes are similar in that they are not "standalone", but are parts of systems.
- Finitists are encouraged to share their mathematics with constructivists and read below about what mathematical objects are real.
- We divide processes into two disjoint groups: platonic processes and physical processes. Platonic processes are mostly mathematical objects, but also qualia are platonic processes too; if the reader does not wish to think that qualia are real, then mathematical objects might suffice; if the reader has a bent towards humanities, then even literary characters can qualify as platonic processes. Platonic processes are "not fully individuated". Physical processes are "fully individuated". They are mostly the processes which could in principle have the reader as a necessary cause, and other processes like that. Even if the reader participates in a creative process, the platonic deed is "discovered", is a cause of the physical creative process.
- It is allowed for physical processes to in some sense be mathematical objects.
- A metaphysical system consists of a triple: a separation of processes into platonic and physical ones, a distinguished process (the index), and a ternary relation among processes, called causation.
- A metaphysical system serves as a formalization of the philosophical concept of reality.
- We call a direct cause the antecedent, first term of a causation relation, we call direct effect the consequent, second term of a causation relation, and we call the third term of a causation relation the individuation.
- A single process cannot have two direct effects with the same individuation.
- You can think of individuation as fixing of parameters or fixing of the reference frame.
- We are speaking in terms of necessary causes, not of sufficient causes.
- A process can have many direct causes and effects.
- We call a cause and an effect the antecedent and consequent of the transitive closure of the causality relation, ignoring the individuation term.
- When we talk about cause and effect but require the existence of individuation, it is a shorthand for talking about direct cause and direct effect.
- We define past reality as all causes of the distinguished process:
- The distinguished process is past-real.
- A cause of a past-real process is past-real.
- No other processes are past-real.
- If a process correlates with an object of mathematical theory, that object is one its causes.
- I have not yet established, how causation among mathematical objects, i.e. platonic processes, looks like.
- A platonic process cannot have a physical cause. But see the following point.
- If a physical process A has platonic cause B with individuation X, process B has platonic effect C, and physical process D has platonic cause C with the same individuation X, then A has effect D.
- Arbitrary one of the physical processes that correspond to the unity of the consciousness of the reader is the distinguished process (the index).
- Here the use of physicality forbids the "leakage" of reality, where only an abstraction of the reader is taken as an index.
- Every information flow is a causal flow.
- New information cannot appear from nothing: a non-decomposable process adds information by combining causes. There has to be sufficient number of processes to account for all information.
- We define necessity inductively:
- The distinguished process is necessary.
- A cause of a necessary process is necessary.
- For a process P that has at least one direct cause that is necessary and is not an effect of P, take S to be the set of all processes that are both a cause and an effect of P (possibly indirect). If all causes of all processes in S are either necessary or in S, then P is necessary (and therefore S are necessary).
- No other processes are necessary.
- We call real all necessary physical processes and their causes.
- A possible universe is a set of processes U that is closed under necessity, i.e.:
- A cause of a process in U is in U.
- For a process P that has at least one direct cause that is in U and is not an effect of P, take S to be the set of all processes that are both a cause and an effect of P (possibly indirect). If all causes of all processes in S are either in U or in S, then P is in U (and therefore S is contained in U).
- A set S is a sufficient set of causes for a process C, if all causes of C can be traced back to S, i.e. if every possible universe that contains S also contains C.
- A possible universe whose all processes are platonic is called a platonic universe.
- A simulation of a platonic universe U is a set of physical processes S, such that there is an individuation X, that for every platonic process B in U there is a process A in S such that B is a cause of A with individuation X.
- A synonym for "simulation" is "a physical correlate".
- When two simulations simulate the same platonic universe, we call one an emulation of the other.
- All necessary physical processes and their causes are real.
- An embedded metaphysics differs from a metaphysical system only in that point 11 does not hold for it.
- An embedded metaphysics A is valid with respect to a metaphysical system B via a homomorphism of causality h, if for every process P that is real in A, process h(P) is real in B.
- An embedded metaphysics A is possible with respect to a metaphysical system B via a homomorphism of causality h, if for every process P that is real in A, process h(P) is necessary in B.
- Materialism: were a real platonic process to differ, the physical processes over which it supervenes would differ as well.
- More generally: if only a subprocess of a process is essential for its effect, only the subprocess is a necessary cause of the effect.
Would the platonic "Permutation City" be real according to the physical characters of the book, if they used the presented metaphysics?