The Solution to All Philosophical Problems
An introduction to a new science of knowledge
The following is a brief overview of a new book, The Shape of Knowledge: An Introduction to Paraphilosophy.
The Structure of Concepts
Philosophical problems can be approached from a subjective and an objective perspective, and thus our discourse is divided into subjectivistic and objectivistic theories. If one of these perspectives is false, then our perception of duality does not mirror reality, and if both of them are true, then reality is in some sense dualistic.
Complementarity provides a way to explain opposing perspectives such that each side reflects a reciprocal and mutually dependent aspect of a whole, rather than as two entirely independent domains.
In analytic psychology, a principle of complementarity was utilised by Carl Jung to explain the relationship between opposed psychological functions, the relative expression of each being the relative repression of the other.
Four of Jung’s functions — a duality within a duality — can be used to characterise temperaments in philosophy:
- Extraversion looks to the outside;
- Introversion looks inside;
- Thinking seeks distinctions;
- Feeling finds connections.
What we find is that philosophical perspectives on given problems can be defined by this structure. Four classes describe all of the possible forms of knowledge; all of the possible forms of being; and value; and socio-political right; as well as all of the theories of which these perspectives form the foundation:
We can therefore talk about philosophical theories as being emergent from a basic and uniform structure, and we can talk about the various expressions of the four quadrants of this structure in terms of different worldviews:
The objectivist worldview aligns with the synthetic a posteriori, the concrete particular, the subjective relative, and the libertarian individual — or empiricism, materialism, moral relativism, and anarcho-capitalism.
The subjectivist worldview aligns with the analytic a priori, the abstract universal, the objective absolute, and the authoritarian collective — or analytic rationalism, idealism, moral objectivism, and state-socialism.
The third worldview (abjectivist) is neither objectivist nor subjectivist, and aligns with the synthetic a priori, the abstract particular, the objective relative, and the authoritarian individual — or synthetic rationalism, some form of neutral monism, value pluralism, and state-capitalism.
Finally, there is a hypothetical fourth worldview (superjectivist) which is simultaneously subjectivist and objectivist, and this aligns with the analytic a posteriori, the concrete universal, the subjective absolute, and the libertarian collective. These notions are commonly considered to be self-refuting, oxymoronic, or otherwise normatively circular. This matter is of crucial importance and shall be returned to at a later stage.
The Paradox of Self-Reference
Classical logic is grounded in four key logical laws:
- The law of excluded middle states that contradictory propositions cannot both be false — one must be true;
- The law of non-contradiction states that contradictory propositions cannot both be true — one must be false.
- The principle of implosion states that a tautology is entailed by anything.
- The principle of explosion states that everything is entailed by a contradiction.
From the start of the 20th century, mathematical logic was confronted with a number of logical paradoxes, all essentially of the same basic structure.
The paradox is most simply expressed as the liar paradox, which asserts:
This sentence is false.
If the liar sentence is true, then it is false; and if it is false, then it is true.
The hope for mathematical logic was that we could devise a system of axioms that could produce every true proposition and no false ones, but attempts to circumvent the paradoxes eventually proved futile.
In the 1920s, Kurt Gödel showed that any consistent logical system could produce a proposition analogous to “This proposition is unprovable,” which cannot be false, for if it were false that it was unprovable, then it would be provable.
The proposition is therefore true but unprovably so, revealing a distinction between truth and provability.
The problem that Gödel’s theorems present for the philosophy of mathematics is that they entail that a satisfactory account of the notion of truth is inconsistent with any consistent logical system.
However, if e were to alter classical logic we may again achieve an equivalence between truth and provability, and the alternative ways that we can interpret logical consequence can be characterised by the same quadripartite structure as all other philosophical notions.
If we assert that the fact we cannot prove the Gödel sentence means it cannot be considered true, then we must assert that it is neither true nor false, since if it were false it would be provable. This is the paracomplete perspective.
And if we assert that the fact we can see the Gödel sentence is true by necessity means that it must be provable, then we assert that it is both true and false, for if it is true and provable then it is unprovable and false. This is the paraconsistent perspective.
Both options require abandoning one of the laws of thought on which classical logic is built. The paracomplete approach requires violating the law of excluded middle, for not all sentences are true or false, and the paraconsistent approach requires violating the law of non-contradiction, for not all sentences are not true and false. The two perspectives are duals of each other, so one could not discriminate between them on the basis of the logic alone.
Again, non-classical perspectives on logical consequence can be defined by the same structure, and in the same way, as all other philosophical notions. We can represent this on the quadrant system as four fundamental logical rules:
We can represent this as the four elements of theoremhood — provability, nonprovability, disprovability, and non-disprovability:
And, if we are taking truth to be bound to proof, we can represent it by the four truth-values — true, nontrue, false, nonfalse:
We are now approaching a radical realisation: that which we use to discriminate between theories (i.e. logic) is subject to the same structure of perspective as the theories themselves.
There are perspectives on how we can discriminate (i.e. whether opposing theories are mutually exclusive), and these perspectives cannot be discriminated between without presupposing what it is we are attempting to decide (i.e. we must beg the question).
Moreover, the very same structure can be used to describe the elements of human cognition, whereby the dichotomy between paracomplete and paraconsistent logic is correlated with the mechanistic brain and the symbolic mind — the former being home to purely syntactic computational procedures, while the latter is the domain of semantics and meaning.
Famously, Douglas Hofstadter argues that a feedback loop between these aspects of intelligence is responsible for our feelings of Self; and self-consciousness is both the subject and object of itself, just as the logical paradox is the proposition that predicates of itself.
Self-consciousness would then refer to that quadrant of the structure which expresses a unity of opposites (the superjective), just as the brain refers to the objective perspective and the mind refers to the subjective.
The Shape of Knowledge
Systematic philosophy is an inescapably self-referential enterprise, for philosophy is a part of the world that any systematic philosophy seeks to describe.
Paraphilosophy will resolve the antinomies found in philosophy, for paraphilosophy will elucidate the nature and role of self-reference in our conception of the world.
An examination of the structure of philosophical perspectives reveals that:
- The analytic a posteriori is simply self-knowledge or self-awareness.
- The concrete universal is self-being, or rather its nature is self-consciousness.
- Subjective absolute value is the value we have of ourselves.
- And the libertarian collective is a society of self-ownership.
The paradoxical positions in all areas of philosophy form a uniform and legitimate perspective that is a necessary element of the structure of our capacity for reason.
Now, given that this structure of perspectives mirrors the structure of experience, we must consider in what sense the structure itself must be considered real.
Furthermore, given that logic and our very conceptions of truth and realness are subject to this structure, and given that there is no logical rationale for discriminating between aspects of the structure, we must consider whether the structure itself is really all we can ever consider to be real.
Yet we need not merely ask these questions to ourselves, for the structure, by its essential nature and form, necessitates its own existence. That is because the self-referential aspect of the structure is self-consciousness, and, in accordance with its self-referential nature, it exists both within and without itself. As within, it is merely an aspect of the structure; as without, it is that field within which the structure is contained as a whole:
The structure is a self-similar construct — a fractal — and since self-consciousness is an absolute necessity — being justified of the unity of logic and experience (via the analytic a posteriori) — the entire structure too is justified as actual as its contents. The structure is an expression of a fundamental unity of opposites that has become divided, and it reveals itself to itself via a principle of complementarity.
Much of institutionalised philosophy has unwittingly assumed that there is a way reality is like, and it has therefore proceeded in an attempt of describing what it is like.
A true philosophical science must understand that our attempt to describe reality is fundamentally involved in that reality’s generation — that the world is an expression of our evolving capacity to comprehend ourselves, and our ability to explain our ability to explain.
The self-reference of being means that reality is ultimately irrepresentable, but it’s irrepresentability can be expressed, and must be expressed, via an ever advancing representation.
Phenomenal reality is the evolution of this representation, and the irrepresentable absolute perspective is the beginning and the end of evolution.
It is the relativisation of the absolute — the representation of the irrepresentable — which forms the lens of duality through which we experience the world. The subjectivist aspect is ideal, finalistic, and mental; the objectivist aspect is material, mechanistic, and physical.
Philosophy must cease in seeking a perspective that accommodates both sides of the duality, or that ignores one side of it, for the duality is actual in experience, and so mind does not need to be explained by matter nor matter to be explained by mind.
The duality has been thrust apart so that experience can understand and become itself; and since the halves have been severed from a whole, there is a necessary correlation between them, and we can study this correlation to uncover untold and unknown new sciences.
The extent of our understanding “in here“ runs always in parallel with the extent of what there is to understand “out there“, for the two are not separate. We create as we learn; we learn as we create; art and science are One.
The inside and the outside are divorced through evolution, and thus we perceive the world as separate from ourselves. In time, the same reason that would divide the world shall begin the reintegration of it; and thus, as the wounder heals, we shall become one with the Other once more.
A philosophical science is thus a science of the Self. The only absolute truth is that there is no absolute truth, for paradox is the fuel of creativity, and creativity is the cause of all things.
Everything is Self, and its evolving recognition of itself, which is its becoming of itself. The Self is simply the recognition of itself, and so the world becomes because to be is to know thyself. Self-reference is simply creation.
This entire world is the creation of the Self — of yourself. So rejoice; in the fact that we are waking from our making, that we might look upon ourselves with love and understanding. Rejoice in the fact that absolute self-knowledge is the origin and end of all, that we must survive the troubles of our time, for we must fully know and have become ourselves at the end that we may begin to know and become in the beginning.
Rejoice in the fact that All is One, and the One is I. For if we can know this simplest of facts, then we can build a science of wisdom — then we can know, and solve, and heal all things.
This is only the first step. And it starts now.
