Performative Contradictions And Their Theorems

Logic is the study of valid reasoning. We recommend reading forall x: Calgary and The Laws of Logic by StateOfTheNihil for an introduction to classical logic.

• “By thinking about order of discovery, and understanding that we were already making arguments before having a concept of the logical laws, we can ask how this was even possible. The answer has to do with the fact that we aren’t capable of violating the laws of logic consciously.”
• “This inability to violate any/most of the laws is: 1. what allows us to rely on them prior to conceiving the laws themselves, and 2. what makes the laws of logic non-arbitrary.”
• The Laws of Logic are basically patterns in cognition, suggesting that we simply think in this way when we reason.

The three laws of Classical Logic are as follows:

1. The Law of Identity
   • Metaphysically: “A is A” or “Anything is itself.”
   • For Propositions: “If a proposition is true, then it is true.”
2. The Law of The Excluded Middle:
   • Metaphysically: “Anything is either A or NOT_A.”
   • For Propositions: “A proposition, such as P, is either true or false.”
3. The Law of Non-Contradiction:
   • Metaphysically: “Nothing can be both A and NOT_A.”
   • For Propositions: “A proposition, P, can not be both true and false.”

All of our reasoning and arguments comply with these laws - that any thing is equal to itself, that tautologies must be true, and that contradictions must be false. Classical logic holds that everything has a definite, non-contradictory nature.

Some people might argue that it’s useful to have a ternary (three-value) logic that includes a third truth value in addition to just True or False called “Unknown”, but the reason why “Unknown” is generally not included in practice is because “Unknown” can already be expressed in classical logic as “True or False” (e.g. P or ~P), and it’s possible to use multiple conditional statements that depend on whether the condition is True or False. Adding an unnecessary truth value to our logic system would add many additional logic theorems to our theory of knowledge, which we should prefer to avoid since we want our epistemology to be as parsimonious as possible.

To be clear, although I am using axioms and performative contradictions to build the foundation of this philosophy, the axioms and performative contradiction theorems are re-affirmed by the rest of the philosophy. Consider the definition of a theory:

A theory is a set of sentences which is closed under logical implication. That is, given any subset of sentences {s_1, s_2, …} in the theory, if sentence r is a logical consequence of {s_1, s_2, …}, then r must also be in the theory.

Since this website’s philosophy and its axioms all constitute a theory, eventually, the other sentences and propositions of the philosophy will all support each other, so this philosophy is actually coherentist, even though it starts off as being presented as a foundationalist system for pedagogical purposes.

A performative contradiction arises when the propositional content of a statement contradicts either the act of asserting it or the noncontingent presuppositions that make possible the performance of the speech act. There are several different types of performative contradictions, including:

• Performative-constative contradiction: This occurs when the speaker’s statement or action contradicts the content of their statement or action. For example, if a person says “I am not a liar,” but their actions or statements demonstrate that they are lying.
• Performative-epistemic contradiction: This occurs when the speaker’s statement or action contradicts the speaker’s own knowledge or beliefs. For example, if a person says “I know this to be true,” but their actions or statements demonstrate that they do not truly believe it to be true.
• Performative-deontic contradiction: This occurs when the speaker’s statement or action contradicts the speaker’s own obligations or rights. For example, if a person says “I promise to do this,” but they do not follow through on their promise.
• Performative-doxastic contradiction: This occurs when the speaker’s statement or action contradicts the speaker’s own attitudes or beliefs.
• Performative-perlocutionary contradiction: This occurs when the speaker’s statement or action contradicts the effect that the statement or action is intended to have. For example, if a person says “I’m not angry,” but their tone or body language suggests that they are indeed angry.

Self-refutation refers to the logical fallacy of a statement or argument that contradicts itself. There are several types of self-refutation, including:

• Logical self-refutation: This occurs when a statement or argument contradicts its own logical structure. For example, “This sentence is false” is a classic example of a statement that refutes itself.
• Semantic self-refutation: This occurs when a statement or argument contradicts its own meaning. For example, “I always lie” is a statement that refutes itself because if it is true, then it must be false.
• Pragmatic self-refutation: This occurs when a statement or argument contradicts its own implications. For example, “You cannot trust anything I say” is a statement that refutes itself because if it is true, then it cannot be trusted.
• Epistemological self-refutation: This occurs when a statement or argument contradicts its own method of knowledge. For example, “All knowledge is uncertain” is a statement that refutes itself because if it is true, then it cannot be certain.
• Dialectical self-refutation: This occurs when a statement or argument contradicts itself in a dialogue or debate. For example, in a debate, if someone argues that all opinions are equal and then turns around and argues that their own opinion is the correct one, it would be a self-refutation.

“Metaphysics” is a rather misleading word since we can’t escape our subjectivity, and what most people think of as “Metaphysics” tends to have false presuppositions in it that we can escape our subjectivity, even though this is not possible. If we want to have a sound epistemic framework, then we must start with evaluating inescapable aspects of the human condition, such as logic. There is a lot of good philosophy that comes out of simply recognizing that the individual’s mind is just a brain in a skull.

Our philosophy must avoid having contradictory beliefs to the fullest extent possible, hence we want to avoid any situation where we could have a belief A and a second belief ¬A such that a contradiction of A & ¬A can be formed. Thus a good starting approach is to identify beliefs that will always be true.

There are multiple other reasons why the performative contradictions are ideal for building our formal epistemic framework.

• Every performative contradiction has a corresponding theorem.
• Proofs by performative contradiction are formal and rigorous are a formal and rigorous way to prove statements that many people assume to be self-evident.
• They minimize the number of axioms and assumptions that we need to make (parisomony).
• They can be understood with minimal knowledge and explanation.

• Existence: I do not exist.
• Consciousness: I am not conscious.
• Aliveness: I am dead / I am not alive.
• Subjective Free Will: I cannot choose anything. / I will not to will.
• True Statements Exist: There is no truth. / All statements are false.
• Invalidity of Radical Skepticism: One cannot be certain of anything.
• Validity of Reason: Reason is not a valid source of knowledge.
• There Is No Best Or Objective Foundation For Value: “What is the best theory of value?”; We would need a theory of value in order to answer the question because it’s a normative question, but we can’t use a theory of value to answer the question if we haven’t already established the right theory value that we should use. This infinite regress demonstrates that there is no foundation for value in philosophy. This also proves that a value cannot be judged unless there’s another value to judge it by.

These theorems are proven by the contradictions that are inherent in the previous statements:

• Existence Theorem: I do exist.
• Consciousness Theorem: I am conscious.
• Aliveness Theorem: I am alive.
• Subjective Free Will Theorem: I can make choices.
• True Statements Exist Theorem: All statements are false.
• Anti-Radical-Skepticism Theorem: One can be certain of many things.
• Validity of Reason Theorem: Reason is a valid source of knowledge.
• Values Theorem: There is no best or objective theory of value. A value cannot be judged unless there’s another value to judge it by.

All of these theorems are tautologies. With some additional knowledge from personal experiences, we can infer that they do apply to other people and beings besides ourselves.

The Usefulness Of These Theorems

• The Consciousness Theorem proves self-awareness.
• The Volition Theorem proves that we Subjective Free Will from our subjective point of view.
• The Anti-Radical-Skepticism Theorem shows that extreme forms of skepticism are contradictory.
• The Validity of Reason Theorem works as an additional way to verify reason, and its proof is arguably the simplest way to prove reason’s validity.
• The Values Theorem concludes that there is no uniquely rational theory of value.

This simple foundation offers a formal way to get some big questions out of the way and give us some guidance for pursuing further philosophical inquiry. As we explore philosophy further and find other ways and reasons to prove and believe in the same things, the performative contradiction theorems will mainly function as an additional way to build coherence within our belief system.

We have to be very careful when trying to brainstorm performative contradictions that can prove genuinely true theorems that can form the basis for our philosophy.

Video: The Five Types of Paradoxes - Jan Misali

1. Logical Contradiction

   “Pure” paradoxes; every possible explanation is incorrect (e.g. The Liar Paradox)

2. Normal Impossible Question

   Multiple possible explanations, but no way to know which is correct (e.g. The Grandfather Paradox)

3. Counter-Intuitive Fact

   “veridical” paradoxes; appear to be contradictions but are actually true (e.g. The Birthday Paradox)

4. Math Prank

   “falsidical” paradoxes; appear to be contradictions because they’re false (e.g. The Staircase Paradox)

5. One guy getting very confused, writing it down, and getting it published

   Don’t even appear to be contradictions, but are still called “paradoxes” (e.g. The Preface Paradox)

Type Of Paradoxes Flow Chart
Are all possible explanations contradictory¹?

• If so, this is a logical contradiction.
• If not, does a known correct explanation exist?
  • If not, this is a normal impossible question.
  • If so, is that information secret?
    • If not, does the correct explanation appear to be contradictory?
      • If so, this is a counterintuitive fact.
      • If not, does a common, incorrect explanation appear to be contradictory?
        • If so, this is a math prank.
        • If not, do people call this a “paradox”?
          • If so, this is one guy getting very confused, writing it down, and getting it published.
          • If not, this is not a paradox.
    • If so, this is not a paradox.

Reason and sensory input are the only tools that our brains have for evaluating reality. If we reject either of them, then we have only have emotion and other (less rational) mental processes. If we reject empiricism and insist that we cannot trust our senses to the extent that they are not impaired or illusioned, then we don’t have any way of receiving any other sort of input from reality. If we reject reason, then we can’t make any conclusions about reality. Reason is additionally verified by proof by performative contradiction.

So we don’t exactly have a foundation for proving empiricism and sensory input (to the extent that it is valid). We have a brain, and we have senses. And we must choose to use both of them because that’s all we have. Fortunately, evolutionary reasoning can justify both empiricism and reason, which helps build coherency.

• Primacy of Existence Before Consciousness (proven given that being conscious implies that one exists, and consciousness does not affect existence)
• Cause-and-Effect and Causality (Concept)
• The Definitions of Free Will
• Proof of Hard Determinism / Compatibilist Determinism (depends on how they are defined)
• Reasoning For Stable And Unstable Systems
• The Law of Evolution (Theorem)
  • The Egoism and the Intrinsic Selfishness of Life (Corollary)
  • The Validity of the Senses (Corollary)
  • The Validity of Reason (Corollary)
  • Theory of Emotions (Corollaries of Evolution): Emotions drive people to do things that reproduce, the emotional accounting system, the transfer of energy from father to mother to children, etc.
  • The Relationship Between Emotions and Reproduction (Corollary): Emotions drive people to do things that cause them to reproduce.
  • The Emotional Accounting System (Corollary): Emotions keep track of what we owe and are owed within our personal relationships.
  • The Flow of Energy (Corollary): Energy is Transferred from Father to Mother to Children.
  • Understanding Why Humans Rule the World (Corollary)
• Value Comes From Sentient Beings Lemma
• Moral Relativism

• Valid epistemological concepts must apply to themselves (e.g. truth, knowledge, consciousness, etc).
• All the beliefs in a belief network sustain and depend on each other.
• Proofs by Performative Contradictions.
• Values depend on other values.
• The prices of goods and services depends on the prices of other goods and services. All prices are eventually bootstrap by the cost of natural resources, and ad hoc methods.
• The flow of money in the economy is circular. It’s ultimately bootstrapped by debt.
• Biological purpose is generated from a recursive loop of reproduction.
• The cycle and consumption of energy by organisms within an ecosystem.
• The semantic coherence of words and definitions.
• Mathematical variables that depend on themselves, exponents, and differential equations.
• Anything else?