#wip

A sketch of Metaplatonism

Introduction

Assume an infinite-dimensional-abstract-space (this means that it is analogous but not identical to material or other kinds of spaces, we can see it as space in a metaphorical way) that is constituted by all the possible mental objects (abstracted and recursively meta-abstracted from actual mental objects). This includes things like statements (discrete thoughts, for example, all sets) and qualia, and combinations and abstractions of them (note that this also includes statements which are not true and qualia that might not correspond to any actual real-world experience).

It might seem strange that the space includes both statements and qualia. But note that statements are just one specific kind of quale, characterised by being, in some sense, a semantic claim. All those mental and experiential objects will be called metaplatonic objects, idea-objects, ideas, mental-objects, mental experiences or any reasonable similar o derivative term, and they will be referred to by ℰ. There is a sub-set of ℰ that is characterised as the set of all statements (all ℰ that are a semantic claim).

All ℰ (be them simple or complex) live inside this space. We will call it the Idea-space or the Meta-Platonic space and we will refer to it as Μ (uppercase-µ). It is called metaplatonic because it takes the Platonic theory of forms and abstracts it to strip objects of unnecessary teleology and theologic and metaphysical assumptions. The theory or model might be called Metaplatonism or the Meta-Platonic model (MP).

Μ is not limited by any means. It is not limited by existing qualia domains. It is not limited by logical constraints. This might seem completely unreasonable, but we are describing a model that includes logic inside of it, not a model that needs logic to be sustained. This will be explained in detail below.

The World of Wittgenstein is defined as constituted by all true facts^[1], we will refer to it as @W. @W lives inside Μ. That means that there is a sub-region of it that is bounded by a number of true-statements: metaphysical (the ones that configure the physical —for example, matter, space, time—, they are not given by logic, but constrained by logic, and logic is also constrained by them), logical, mathematical, physical statements, and so on. The necessary-versus-contingent characterisations of a true-statement are a spectrum and not a binary division. Metaphysical truths are more necessary than Physical ones, but both are usually considered non-contingent. Fairy-tale, fantasy and fiction worlds all share some truth-layers, but not all of them, with our world. We call this kinds of layers context-layers. Then, a plausible definition of truth is such "all ℰ that live in Μ and are bound by all the context-planes that accord with our reality". Note that this doesn't mean that our World lives inside Μ, but that the set of all true facts does (as facts are true statements and all statements live inside Μ). In a sense, @W is a complete description of our World.

It may seem impossible to state that any model works without assuming the rules of logic, as for ex contradictione quodlibet, it would seem that it couldn't possibly be described by language (as language assumes logic). But we must make a differentiation of looking at the model from inside @W versus looking at the model just by itself.

Logic is a language, id est, a syntactic system to encode semantics of some particular ontology . Logic might be thought of as the first level of such languages. We are familiar with @W-logic, as we are with @W-physics. It is easier to imagine non-@W-physical facts than non-@W-logical facts, but they are (seem to be) just as impossible inside @W. Each logic is a description of its particular ontology, and @W-logic will not necessarily work outside @W. This doesn't mean Μ is not governed by any logic, because each logic is a description of a particular ontology. The totality of Μ itself can be described by a logic that completely lacks a semantic concept of negation, and it is able to be formalised just like ours. The following formula illustrates it easily:

Ex contradictione quodlibet is the intended result. With "the totality of Μ itself" we mean only the totality of it, and not necessarily its sub-regions (for example, our subregion (@W) is governed by a logic that does include a semantic negation, @W doesn't (seem, at least, to) allow for logical contradictions).

MP's explanatory power and applications in different areas of philosophy (examples)

Logic

The model already solves and explains the Russell Paradox (admittedly rejecting @W-logic). The set of sets that do not contain itself is both contained in itself and not contained in itself. This statement is not inside @W, as it doesn't agree with the logical rule of excluded middle. Naïve Set Theory exists comfortably inside Μ, but it is not complete inside @W.

Language

When one thinks or utters a thought, one is expressing or referring to a specific ℰ. The first goal of spoken and written language is to replicate one ℰ from one's mind to another mind or system, this is a definition of communication. The language elements themselves are only signifiers of the ℰ in question. This explains very well what people mean when they say "I know but I don't know how to explain", they have the pertinent ℰ in their mind but don't know how to translate it into words for the other person to understand. A complete ℰ in someone's mind is usually extraordinary complex and includes all (closely and distantly) related concepts, this is why it is difficult to communicate with people with whom one share less context, as language is designed to communicate only the relevant fraction of the meaning intended, and the rest of it is not needed to be communicated as it is already shared context.

A telling example of the utility of this [metaplatonic] framework in language is the interpretation and conceptualisation of the issue of baptism in different denominations of the Christian religion. Baptism is a ritual of acceptance into the Christian community which a person is submerged in or sprinkled with water "in the name of the Father, the Son and the Holy Spirit" (as instructed by the Holy Scriptures of Christianity). The Roman Catholic Church accepts as valid the baptism of some denominations (like most Protestants, and Eastern Orthodox), but doesn't consider valid the baptism of the Church of Jesus Christ of Latter-Day Saints, also known as Mormons. Mormons are baptised in the same outer way as the other groups, but the Roman Catholic Church notes that their vision of God is different. The ℰ that everyone has in their mind while taking part in a Mormon baptism is not the trinitarian God, but a unitarian God that is not of the of the same essence as Jesus-Christ and the Holy Spirit (you can consult a book on Christian theology or read about the doctrine of the Trinity). So, saying the same, the meaning is not the same. It has to be emphasised that this would be an issue even if the Christian Trinitarian or Mormon God (or any God, for the matter) would not exist (this is not an essay about trinitarian theology, certainly if some Christian God exists this is a more important problem than if no Christian God exists, but if no Christian God exists this is still a genuine problem in philosophy of language). "The Father, the Son and the Holy Spirit" does not mean the same whether a Mormon or Catholic says it. Certainly people are pointing at something when they mean the words, and this is irrespective of that something even existing. If this is rejected (like, for instance, Russell does), in a very curious way, you need substantially more metaphysics: to understand correctly whether there is or not a disagreement between Mormon and Catholic baptisms, you would have to know if any kind of Christian God exists in the first place. This matter can be understood more satisfactorily using the MP-framework.

Philosophy of mathematics

The formalist vs. platonist definition of mathematics is surprisingly dissolved by MP. According to the metaplatonic interpretation of this problem, mathematics is, at the same time, both. The subspace of mathematics includes @W-Mathematics and non-@W-mathematics. We work at @W-Mathematics and adjacent (this means easily analogisable; for example, in going from three spacial dimensions to four, etc.) mathematical spaces. We define the scope (the metaplatonic limits of the space) —this is the formalist point— and then we find what does the space have within that definition —this is the platonist point—.

Theology

Aristotle defined of God as Pure Actuality. Μ seems to be Pure Potentiality.

Another interesting idea (not so much for the model in itself, but for the move of rejecting the absolute necessity of @W-logic outside @W) is the question about where does logic come from as a worthwhile theological question. Assuming logic predates God is not satisfactory; this is another way of saying that the traditional definition of omnipotence is not satisfactory; one can formalise a kind of Eythyphrōn's dilemma, but with logic taking the place of ethics. In the same sense that an omnipotent creator-of-all God is outside Time, creates Time and then chooses to inhabits Time; so God is outside the bounds of logic, creates logic and then chooses to inhabit logic.

Similarities and differences with existing philosophical ideas

This section is in a very sketch-like phase. It will be substantially expanded before publication.

A very interesting fact about MP is that it includes inside it the following models, and retains the usefulness of them while expanding it.

Meinong objects

In a sense, all humanly-accessible $ℰ\notin @W$ are Meinoing objects. But Μ includes also not-humanly-accessible ℰ (for example, from qualia-domains not like the ones we have access through the senses). There is no actual reason why we should stop at Menoing objects, unless we only care about explaining human intentionality, MP goes beyond that (MP talks about preexisting ℰ, which presupposes the need for some ℰ to not be thought by any human in the history of the world —think about Napoleon not being called Napoleon but rather some other collection of sounds that nobody has ever thought before; think about what hypothetical aliens with different available qualia-domains-of-perception could perceive).

Modal Realism

MP is not necessarily realist (see below). All modal worlds are worlds in Μ, and are characterised as such because they are easily analogisable through @W parameters (for example, they share logical and physical rules). However, modal realism talks only about possible worlds, not possible ideas; and it relies on a specific definition of the contingency spectrum (see above), MP allows the same with a higher degree of flexibility.

Ontological status of Μ

In the same way that the laws of nature are useful to scientists and philosophers debate their ontological status, so might this model work (with the little caveat that here is the job of the philosophers to both analyse the explanatory power and debate the ontology). We do note that the actual material world doesn't seem to allow for logical contradictions, which would render the metaplatonic space outside (and in some sense incompatible with) actual material existence; this is self-evident. We make no claim on the actual ontological status of the Μ, this subject is left to metaphysical speculation. Maybe some philosophical pragmatist will allow it to be thought of as existing in some (pragmatist?) way.

We note that this is just a sketch (and currently it is in active progress), meant to give an idea of the model and its interests, and not a comprehensive overview.