Back to summary page about Joker Calculus
Joker Dialects extends Joker Calculus with new operators, used to trace philosophical stances and dynamics:
+==!=->^nBased on notation used in the paper Dialectical Masks: Hegel’s Philosophy through the Lens of Joker Calculus.
| Expression | Description | Philosophers | Examples |
|---|---|---|---|
| 0 | Platonism/Rationalism/Pure concept | Pl, De, Sp, Le, Ka | 1 |
| 1 | Seshatism/Empiricism/Lived experience | Ar, Lo, Be, Hume | 2 |
| ?0 | Empirical appearances structures by reason/Intellectual intuition | Ka, Sc2 | 3 |
| ?1 | A-priori intuitions/Transcedental poetry/Rational mask | Ka, Sc1 | 4 |
| 0 1 | Synthesized cognition/Fragmentary thinking/Determinate Being | Ka, Fi, Sc1, He | 5 |
| ?1 + 0 -> 0 1 -> ?0 | Criticial philosophy (Kant) | Ka | 6 |
| !0 == 1 | The thing-in-itself/Noumenon/Ground of Being | Ka, Sc2, He | 7 |
| 0 == 1 | Non-dualism | Sc2, He | 8 |
| !0 | Not-I | Fi | 9 |
| !0 -> 0 1 | Negation and sublation | Fi, He | 10 |
| 0 -> !0 -> 0 1 | Act of positing | Fi | 11 12 |
| ?0 ?1 | Irony as philosophy (Schlegel) | Sc1 | 13 |
| (?0 ?1 + 0 1)^n | Infinite oscillation (Schlegel) | Sc1 | 14 |
| 0 1 + ?0 | Schelling’s early philosophy | Sc2 | 15 |
| 0 1 -> !0 -> 1 | Schelling’s late philosophy | Sc2 | 16 |
| 0 != 0 | Immanent contradiction | He | 17 |
| (0 != 0 -> !0 -> 0 1)^n | Spirit | He | 18 |
| ?0 1 | Absolute knowing | He | 19 |
| Spirit -> ?0 1 | Negation to reflection | He | 20 |
| Spirit -> ?0 1 -> 0 == 1 | Logic becomes ontology (Hegel) | He | 21 |
| Code | Philosopher | Born - Died |
|---|---|---|
| Pl | Plato | 428/427 or 424/423 BC - 348/347 BC |
| Ar | Aristotle | 384 BC - 322 BC |
| De | Descartes | 1596 – 1650 |
| Sp | Spinoza | 1632 – 1677 |
| Lo | Locke | 1632 – 1704 |
| Le | Leibniz | 1646 – 1716 |
| Hu | Hume | 1711 - 1776 |
| Ka | Kant | 1724 – 1804 |
| Fi | Fichte | 1762 – 1814 |
| He | Hegel | 1770 – 1831 |
| Sc1 | Schlegel | 1772 - 1829 |
| Sc2 | Schelling | 1775 – 1854 |
Expression:
0
This statement expresses Platonism, Rationalism or Pure concept.
Usually, philosophers think about this as eternal truths.
In theology, it is common to think about it as something existing outside space and time.
Sometimes, philosophers can treat it as something existing in space only, as embedded geometry. However, it is also possible to think of geometry as a pure logical theory with axioms and theorems, but without any physical space. There is an ambiguity in use of language whether logic can be a space or not. This depends on the interpretation of logic.
Simplified, one can think about 0 as a general notion of space.
This generalized notion of space is not necessarily without time, but it can be.
With other words, 0 is not always in opposition to 1, but sometimes it can, depending on context.
In Joker Calculus, 0 is authentic in sense of Heidegger, since it does not contain any Jokers after being evaluated in the Closed variant.
Expression:
1
This statement expresses Seshatism, Empiricism, or the concept of lived experience.
Usually, philosophers view this as contingent truths grounded in sensory perceptions.
In epistemology, it is common to understand this as knowledge that arises directly from experience, subject to change and revision based on new evidence.
Occasionally, philosophers interpret this concept strictly as empirical facts and observable phenomena within physical reality. However, it can also encompass subjective experiences and individual perceptions that resist purely objective measurement.
Simplified, one can conceive of 1 as a general notion of time or temporality, emphasizing change, process, and concrete events. This temporality may or may not explicitly involve spatial references. Thus, 1 is not necessarily always opposed to 0, though it may sometimes be, depending on context.
In Joker Calculus, 1 represents an authentic mode of existence since it does not contain any Jokers after being evaluated in the Closed variant.
Expression:
?0
This expression signifies Empirical Idealism or a state of experience structured by rational concepts.
Philosophically, it typically represents phenomena or appearances that are conditioned by an underlying rational framework or conceptual structure.
In epistemological terms, it can be understood as the empirical content of experience, shaped by a priori categories or mental structures, such as those articulated by Kant.
Occasionally, this is interpreted as reality being encountered through conceptual filters, meaning our direct experience is always mediated by our conceptual understanding.
Simplified, ?0 captures the idea that sensory experience is never purely empirical but inherently influenced by rational or conceptual conditions, making it fundamentally conditional and somewhat dependent on an underlying rational structure.
In Joker Calculus, ?0 represents an inauthentic state due to its dependence on other positions, resulting in persistent unresolved tension or opposition upon evaluation in the Closed variant.
Expression:
?1
This expression signifies Transcendental Poetry or a state characterized by intuitive insights or a priori imaginative structures.
Philosophically, it typically represents poetic or creative intuition independent of immediate empirical verification but still grounded in subjective experience.
In aesthetic terms, it can be understood as artistic or poetic imagination operating through spontaneous, intuitive insights rather than empirical evidence or purely logical structures.
Occasionally, this is interpreted as a form of knowledge or insight emerging from creativity or intuition, highlighting the subjective, spontaneous nature of imaginative experiences.
Simplified, ?1 embodies the idea that certain truths or insights are accessible through intuitive, imaginative, or poetic means rather than empirical observation or purely rational argument.
In Joker Calculus, ?1 represents an inauthentic state due to its dependence on other positions, resulting in persistent unresolved tension or opposition upon evaluation in the Closed variant.
Expression:
0 1
This expression signifies Hegelian Dialectics, Fragmentary Thinking, or a state of synthesized cognition that integrates both pure conceptual reason and empirical lived experience.
Philosophically, it typically represents the synthesis of rationalist and empiricist traditions, capturing how abstract conceptual structures interact dynamically with concrete experiential data.
In epistemological terms, it can be understood as knowledge that arises from the interplay of abstract reasoning and concrete sensory experience, neither entirely determined by innate concepts nor solely by empirical observation.
Occasionally, this is interpreted as a holistic or dialectical mode of thinking, emphasizing the integration and mutual dependence of theory and practice, universality and particularity.
Simplified, 0 1 embodies the idea that authentic cognition emerges from the creative synthesis of pure reason and experiential diversity, thus maintaining openness rather than closure or unresolved opposition.
In Joker Calculus, 0 1 represents an authentic state since it remains free of Jokers after evaluation in the Closed variant.
Expression:
?1 + 0 -> 0 1 -> ?0
This expression encapsulates Kant’s critical philosophy, representing the dialectical transition from transcendental intuition and rational concepts toward synthesized knowledge, and ultimately, empirical experience structured by reason.
Philosophically, it begins with the union of transcendental poetic intuition (?1) and pure rational concepts (0), progressing toward a synthesis (0 1) of these elements into structured cognitive judgments.
Epistemologically, this signifies how Kantian cognition combines intuitive and conceptual components, establishing a priori structures that shape empirical phenomena (?0).
Occasionally, this is understood as illustrating Kant’s critical method: starting from intuition and reason, forming conceptual synthesis, and finally resulting in structured empirical understanding—highlighting reason’s role in shaping experience.
Simplified, this expression captures Kant’s view that genuine knowledge arises by critically synthesizing intuitive insight and rational concepts, which then structures empirical reality.
In Joker Calculus, the progression demonstrates how intuitive and rational faculties produce synthesized cognitive structures, conditioning empirical phenomena and resulting in an inauthentic yet structurally coherent experiential framework.
Expression:
!0 == 1
This expression represents the Thing-in-itself, the Noumenon, or the Ground of Being.
Philosophically, it captures a point of absolute identity between negation and appearance—where what is fundamentally unknowable (!0) is equated with the manifold of experience (1). This identifies the origin or grounding of appearances in something that cannot itself appear.
In metaphysical terms, it expresses the paradox of a reality that conditions all phenomena yet cannot be directly known. This is the transcendental condition that gives rise to appearances but is not itself an appearance.
Occasionally, this is interpreted as a moment of ontological grounding, where negation does not stand in opposition to something else, but instead coincides with the generative multiplicity of the world.
Simplified, !0 == 1 captures the insight that the ground of experience is not a separate object but an indeterminate condition that becomes indistinguishable from the flow of empirical reality.
In Joker Calculus, this is a relation of identity between two seemingly opposed positions, revealing a deep structural equivalence that suspends contradiction.
Expression:
0 == 1
This statement expresses non-dualism, where Platonism (0) and Seshatism (1) become one.
In Schelling’s early philosophy, this means reason and nature are one and the same.
In Hegel’s philosophy, this means Logic is the same as Being.
In Path Semantics, Platonism and Seshatism can be viewed as the same thing by viewing the difference between the two as an internal difference. An internal difference in philosophy from a path semantical perspective happens in some language. It is something that can not be distinguished by a non-speaker of the language. Only speakers of the language know the internal difference.
For example, you generate a random bit vector (a sequence of bits) and decide whether to flip them or not before sending. The receiver of the bit vector can not tell whether you flipped it or not. This can be used to hide the knowledge of the flipping operation and use this to control information.
On the other hand, if you have a bit vector where there are more 0s than 1s, then you can determine whether it has been flipped by counting 0s and compare them to the expected number of 0s. This is not an internal difference, because it can be distinguished externally by a non-speaker.
The unification of Platonism and Seshatism happens when the knowledge about internal differences are erased. E.g. an action that does not depend on knowledge of internal difference.
This means, when people live their lives without distinguishing between Platonism and Seshatism, they are practicing non-dualism.
Notice! When 0 and 1 are taken as truth values in propositional logic or as natural numbers modeled by the Peano axioms,
then 0 == 1 leads to absurdity (inconsistency by being able to prove false).
Absurdity is the strongest sense of contradiction (in a weaker notion of contradiction, two things can contradict without being able to prove false).
This problem happens due to treating the two sides as propositionally equal.
One can fix this problem e.g. by using normal paths generated by not.
It is possible to unify the two sides in some sense without causing absurdity.
Expression:
!0
This expression represents the Not-I in Fichte’s philosophy—the principle of negation or limitation that makes the self-conscious I possible.
Philosophically, !0 stands for the negation of the absolute I (0). It is not simply the opposite of the I, but rather a necessary condition for its development. The Not-I introduces resistance, finitude, and differentiation, enabling the I to define and assert itself.
In Fichtean terms, the I posits itself absolutely, but in order to be self-conscious, it must also posit the Not-I—something external or limiting—which becomes the condition for self-awareness and activity.
Occasionally, this is interpreted as the grounding of objectivity or alterity: the world that appears as other is not independent of the I, but co-constituted by its self-limiting act.
Simplified, !0 expresses the active negation that allows for differentiation, self-consciousness, and relational identity—an essential tension in idealist thought.
In Joker Calculus, !0 is not an inauthentic negation of 0, but a productive, generative movement that introduces difference without being reduced to simple opposition.
Expression:
!0 -> 0 1
This expression captures the dialectical motion of negation and sublation, as used in both Fichte’s and Hegel’s philosophies.
Philosophically, !0 begins as the negation of the I (or of pure concept), an externalization or differentiation that introduces otherness. The transition to 0 1 represents sublation (Aufhebung), the process by which contradiction is overcome and preserved within a higher synthesis.
In Fichte, this captures the dynamic self-positing of the I, which encounters the Not-I as a limit, only to incorporate it into its ongoing striving toward unity and self-realization.
In Hegel, this is the logic of dialectical development itself: contradiction and negation (!0) are not dead ends, but necessary movements toward greater totality and conceptual integration (0 1).
Occasionally, this is read as the generative motion of spirit—through opposition, division, and eventual reconciliation, reality unfolds itself in richer structures.
Simplified, !0 -> 0 1 expresses the essential power of negation to generate synthesis, not by erasing difference, but by preserving and reconfiguring it into a higher form.
In Joker Calculus, this movement illustrates an authentic transformation: from negation to structured openness, without reverting to pure unity or collapsing into contradiction.
Expression:
0 -> !0 -> 0 1
Consider the dialectical relationship between rationalism and empiricism in philosophy:
0 (Rationalism): Knowledge is grounded purely in reason, independent of sensory experience. Rationalism asserts the primacy of logical and innate concepts as the basis for understanding reality.!0 (Empiricism): Knowledge is derived exclusively from sensory experience. Empiricism rejects innate ideas, emphasizing empirical evidence as the sole foundation of knowledge.0 1 (Transcendental Idealism): The synthesis arises through Kantian transcendental idealism, combining elements of rationalism and empiricism. Knowledge emerges through an interaction of innate cognitive structures (rationalism) and sensory experiences (empiricism).Expression:
0 -> !0 -> 0 1
Consider the dialectical interplay between freedom and determinism:
0 (Freedom): Human actions are based on free will, independent of deterministic forces. Individuals possess genuine autonomy and moral responsibility.!0 (Determinism): Human actions are entirely determined by causal factors and external conditions. Freedom is perceived as an illusion, and choices are predetermined.0 1 (Compatibilism): A synthesis emerges through compatibilism, proposing that freedom and determinism coexist. Free will is understood as the capacity to act according to one’s internal desires, even within deterministic structures.Expression:
?0 ?1
This expression represents irony as a philosophical stance, especially as found in Romanticism and post-Kantian thought.
Philosophically, it captures a double conditionality: empirical appearances structured by reason (?0) alongside a priori intuitions shaped by imaginative spontaneity (?1). When held together, these form a self-suspending dialectic that refuses final synthesis.
In early German Romanticism (e.g., Schlegel), irony emerges as the recognition of this irresolvable doubleness—the simultaneous affirmation and suspension of opposing modes of experience. Irony does not seek to resolve the tension between concept and intuition, but to live within it creatively.
Occasionally, this is interpreted as a form of higher-order reflection that questions the stability of all grounding positions, making thought self-aware of its own limits and play.
Simplified, ?0 ?1 expresses a fragmented, dynamic stance that reflects on its own conditionality—a dialectic without sublation, maintaining openness to contradiction.
In Joker Calculus, ?0 ?1 is inauthentic due to its unresolved tension, but it is also productive: it enacts a playful, reflexive relationship with structure, resisting closure while generating insight.
Expression:
(?0 ?1 + 0 1)^n
This expression represents the infinite oscillation between irony and synthesis, capturing the essence of Schlegel’s romantic philosophy.
Philosophically, this models a recursive alternation between a state of unresolved conditionality (?0 ?1) and moments of synthetic coherence (0 1). Rather than resolving the tension, each synthesis provokes a renewed fragmentation, which in turn generates a new attempt at integration.
In Schlegel’s romanticism, this oscillation is the hallmark of philosophical creativity and poetic thinking: thought is never final but always self-surpassing, aware of its provisional character.
Occasionally, this is read as a philosophical parody of dialectics itself—synthesis always falling back into division, irony sabotaging system, yet enabling new insights.
Simplified, (?0 ?1 + 0 1)^n reflects the idea that truth is a living process of contradiction and renewal, an infinite play between fragmentation and coherence.
In Joker Calculus, this recursive structure is inauthentic but generative: the Jokers do not cancel, but persist through each loop, sustaining the dialectic as an open-ended, self-creative movement.
Expression:
0 1 + ?0
This expression represents Schelling’s early philosophy, particularly his attempt to synthesize nature and self-consciousness through an absolute identity.
Philosophically, 0 1 embodies the dynamic unity of reason and experience, a living whole. The addition of ?0 introduces the conditionality of empirical appearance structured by conceptual understanding.
In Schelling’s early thought, nature is seen as visible spirit, and spirit as invisible nature—an identity that is not static, but unfolding. The presence of ?0 indicates the unresolved and conditioned character of our experience of this identity, as filtered through cognition.
Occasionally, this is interpreted as a tension in Schelling’s system: the whole is posited, but its realization is mediated by our finite, conditioned experience of it.
Simplified, 0 1 + ?0 reflects Schelling’s view that the absolute must be both posited as a whole and yet encountered under empirical and epistemic limitations.
In Joker Calculus, this expression is inauthentic: the presence of ?0 introduces an unresolved dependency that prevents complete realization of the whole, capturing the tension Schelling saw between system and freedom, concept and intuition.
Expression:
0 1 -> !0 -> 1
This expression represents Schelling’s late philosophy, especially his critique of system and his emphasis on the ground of freedom and the irrational.
Philosophically, it begins with 0 1, the dynamic unity of reason and experience. The transition to !0 introduces a moment of radical negation or rupture—a dark, pre-rational ground that cannot be assimilated into conceptual unity.
In Schelling’s later thought, this “ground” is not just a deficiency in the system, but a necessary condition for individuality and freedom. It is that which resists totality and cannot be fully known.
The movement toward 1 signifies the reemergence of multiplicity and lived particularity out of this negation. Here, existence does not return to unity but affirms differentiation, contingency, and the real.
Occasionally, this is interpreted as a reversal of idealist system-building: rather than subsuming difference into unity, thought must acknowledge an irreducible ground that gives rise to freedom and finitude.
Simplified, 0 1 -> !0 -> 1 reflects the collapse of speculative identity into a ground of unreason, from which real, concrete existence arises anew.
In Joker Calculus, this is an authentic transformation: the system subverts itself to reveal the irrational core of freedom, culminating in a lived multiplicity irreducible to conceptual closure.
Expression:
0 != 0
This expression represents Hegel’s concept of immanent contradiction—the principle that a concept or identity, when fully developed, turns against itself and generates its own negation from within.
Philosophically, it signifies that pure identity (0) is not a static self-sameness but contains within it the seeds of its own self-differentiation. It contradicts itself precisely by trying to remain self-identical.
In Hegel’s logic, contradiction is not a logical error but the motor of development: through contradiction, thought advances beyond abstract identity toward a richer totality.
Occasionally, this is interpreted as the moment where speculative thought recognizes the instability of all immediate positions, pushing toward mediation, negativity, and eventual synthesis.
Simplified, 0 != 0 expresses the dialectical truth that selfhood, concepts, or systems are internally divided and must overcome themselves to become what they are.
In Path Semantics, one does not use the terminology “immanent contradiction” because the theory deals with this properly from a logical perspective,
using a partial equivalence operator ~~ (path semantical quality) where reflexivity a ~~ a is the same as ~a (path semantical qubit).
This is an internal difference in philosophy, so you can view it as ~a from the perspective of Platonism and !~a from the perspective of Seshatism.
Path Semantics handles this nicely, by extending normal logic to infinite-valued logic with the path semantical qubit operator ~
(It avoids all problems of inconsistency with logic and solves the problem of reasoning with tautological congruence of ~ using the HOOO EP axioms,
which integrates meta-theorem proving into logic by unifying the meta-language with object-language, finishing the work on Intuitionistic Propositional Logic (IPL)
by adding exponential propositions).
With other words, in Analytic Philosophy, you can just use the foundation of Path Semantics instead of Hegel’s dialectics in natural language.
In Joker Calculus, this expression might be interpreted ambiguously as a structurally productive authenticity: contradiction that does not resolve immediately, but drives the unfolding of deeper, mediated structures.
Notice! If 0 is interpreted as a truth value in propositional logic or as a natural number by the Peano axioms,
then 0 != 0 results in absurdity (inconsistency by being able to prove false).
Absurdity is the strongest sense of contradiction (in a weaker notion of contradiction, two things can contradict without being able to prove false).
This problem happens due to reflexivity of equality a == a being tautological in propositional logic.
In Path Semantics, this is fixed by replacing == with a partial equivalence ~~.
Expression:
(0 != 0 -> !0 -> 0 1)^n
This expression represents Hegel’s concept of Spirit (Geist)—the infinite, self-developing movement of thought through contradiction, negation, and reconciliation.
Philosophically, it begins with 0 != 0, the recognition that identity contains immanent contradiction. This contradiction leads to !0, a moment of negation or alienation, where Spirit externalizes itself, encountering itself as other.
Through !0 -> 0 1, Spirit returns to itself by sublating the contradiction into a higher unity that preserves and overcomes difference. But this synthesis is not final: the process repeats, driven by further contradictions.
In Hegel’s system, this iterative movement defines Spirit’s path toward absolute knowing. It is an unending dialectical journey through stages of consciousness, history, and logic, each marked by internal contradiction and its resolution.
Occasionally, this is interpreted as the self-actualization of freedom: Spirit unfolds as it comes to know itself through the history of its own negations.
Simplified, (0 != 0 -> !0 -> 0 1)^n captures the essence of Hegelian dialectics—not a single synthesis, but an infinite, self-refining process of thought coming to itself.
In Joker Calculus, this recursive loop models an authentic dialectical engine: contradiction drives negation, which in turn produces ever-deepening forms of structured openness.
Expression:
?0 1
This expression represents Hegel’s concept of Absolute Knowing—the culmination of the dialectical process, where empirical appearance (?0) and conceptual unity (1) are integrated within a reflexive totality.
Philosophically, ?0 1 signifies that knowledge has come to include both conditioned experience and the logical structures that condition it. In Absolute Knowing, the subject no longer treats appearances as external but recognizes them as moments of its own development.
In Hegel’s Phenomenology of Spirit, this is the point at which Spirit recognizes that all otherness is a moment of itself, and knowledge becomes a self-aware unity of appearance and concept.
Occasionally, this is interpreted as the final stage in speculative philosophy, where thought no longer needs to go beyond itself because it already contains the whole within.
Simplified, ?0 1 expresses a unity in difference: appearance is not eliminated but embraced as a dialectical moment within totality.
In Joker Calculus, this expression is inauthentic, since ?0 remains as a Joker. Yet it signals a structurally significant completion of the dialectic, in which the conditional and the unified are no longer opposed but disclosed together in reflective knowing.
Expression:
Spirit -> ?0 1
This expression represents the culmination of Hegel’s speculative logic—where Spirit, having passed through contradiction and negation, reaches reflective closure in Absolute Knowing.
Philosophically, this captures the transition from a self-developing process (Spirit) to a reflexive state (?0 1), in which all moments of otherness are gathered and comprehended within the self.
In Hegel’s thought, this marks the final act of negation: not as destruction, but as reflection. Spirit recognizes that what appeared external or alien was always already a part of itself.
Occasionally, this is interpreted as the moment when philosophy ceases to chase a beyond and turns instead to fully grasp the immanent logic of what is.
Simplified, Spirit -> ?0 1 expresses the self’s arrival at the insight that conditioned appearances and rational unity are dialectically inseparable, and that reflection itself is the ground of philosophical truth.
In Joker Calculus, this marks a structurally complex inauthenticity: ?0 remains as a Joker, but it no longer obstructs knowing—it becomes the signature of a reflective totality that understands its own condition.
Expression:
Spirit -> ?0 1 -> 0 == 1
This expression represents the final culmination of Hegel’s logic: the transition from reflective knowledge to an ontological identity of concept and reality.
Philosophically, this models the movement where Spirit, having come to reflective self-awareness (?0 1), proceeds to grasp that logic is not just the structure of thought but the structure of being itself (0 == 1).
In Hegel’s Science of Logic, the end of the dialectic is not merely epistemological but ontological: thought and being, concept and object, are shown to be identical in essence.
Occasionally, this is interpreted as the point at which speculative logic becomes ontology—the logos of reality is the logic of thought, fully disclosed in and as the self-unfolding concept.
Simplified, Spirit -> ?0 1 -> 0 == 1 expresses the idea that the real is rational, and the rational is real: the unity of appearance and thought is revealed to be a necessary identity.
In Joker Calculus, this represents an identity relation achieved through dialectical reflection. The tension marked by the Joker (?0) is fully resolved, and conceptual unity is affirmed as coextensive with being.