Circularity Maniacs

Should you think about your duty, or about the consequences of your actions? Or should you concentrate on becoming a good person?

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Veritas Aequitas
Posts: 12648
Joined: Wed Jul 11, 2012 4:41 am

Circularity Maniacs

Post by Veritas Aequitas »

Whenever FDP, PH, and some sniffs the slightest scent of 'circularity' or infinite regress, they will go berserk due to their dogmatic clinging to traditional logic.
This I believe is due to their philosophical immaturity and lack of wisdom in understanding the wider vista of greater utilities of philosophy.

From AI [wR];
AI wrote:Here are some examples of circularity (or self-reference) that might seem illogical at first glance from traditional logic but hold weight in alternative logical systems:

1. The Liar Paradox:
This classic example goes like this: "This statement is false."
In traditional logic, this statement leads to a contradiction. If it's true, then it's false, and vice versa. But, paraconsistent logic allows for statements to be both true and false (or neither) simultaneously. This breaks the contradiction and allows the statement to exist in a "grey area."

2. Epimenides the Cretan:
This one comes from an inscription by Epimenides, a Cretan poet: "All Cretans are always liars."
Here, Epimenides, a Cretan himself, is making a statement about all Cretans. If his statement is true, then he, a Cretan, is a liar. But if he's a liar, then his statement about all Cretans being liars is false. This paradox is another instance where paraconsistent logic might be useful.

3. Gödel's Incompleteness Theorems:
These theorems, proven by mathematician Kurt Gödel, show that any formal system powerful enough to express basic arithmetic will always have true statements that cannot be proven within that system.
This creates a circularity where the truth of some statements relies on stepping outside the system itself. In a traditional logical framework, this seems strange, but it highlights the limitations of formal systems and opens the door for exploring alternative logics.

4. Dialectical Logic:
In Hegelian dialectics, ideas progress through a thesis (an idea), antithesis (opposition to the idea), and synthesis (a new idea that incorporates both). This circular process of contradiction and resolution is a core aspect of dialectical logic.
While traditional logic might see this back-and-forth as illogical, dialectics view it as a necessary process for arriving at a more complete understanding.

5 Gettier Problem and Self-Justification of Knowledge:
Traditional logic defines knowledge as justified true belief. But what justifies that belief?
• Traditional Logic: If our justification relies solely on the belief itself (circular justification), it seems shaky.
• Paraconsistent Logic: Here, we might consider that knowledge can be justified through coherence with other
• beliefs, even if there's no single, definitive source. The circularity becomes a way of reinforcing a web of interconnected ideas.

These are just a few examples of how circularity or self-reference can be valid outside the boundaries of classical logic.
By considering alternative logical systems and approaches like paraconsistency and dialectics, we can see how circularity can be a tool for reasoning and understanding complex ideas.
An Example in Practice:
Examples of "circularity" which are valid within Constructivism, Self-Referential Systems, Cybernetics, and the Human System

Here's an example that combines these concepts:

Scenario: Learning a new language through an interactive AI tutor.

Constructivism: We learn by actively constructing our understanding of the world based on experiences and interactions.
Self-Referential System: The AI tutor is programmed to adapt its teaching style based on the student's performance and feedback. It analyzes the student's responses, adjusts its difficulty level, and provides tailored explanations. This creates a loop: the student learns from the tutor, and the tutor learns from the student.
Cybernetics: The AI tutor acts as a cybernetic system, receiving information (student responses) and using it to regulate its output (teaching approach). This feedback loop optimizes learning.
Human System: Our brains are also self-referential systems. We learn by receiving information (through our senses), processing it (making connections with existing knowledge), and using it to guide future interaction with the world.

How Circularity is Valid Here:
Traditional logic might see the student-tutor loop as circular because the student learns from the tutor, but the tutor's effectiveness depends on the student's learning. However, from a constructivist perspective, this circularity is crucial.
The student actively constructs their understanding based on the tutor's input, while the tutor adapts to the student's unique learning process. This creates a dynamic and personalized learning experience.

Benefits of this Circularity:
• Improved Learning Outcomes: Both the student and the tutor continuously improve. The student receives targeted instruction, and the tutor refines its teaching based on real-time student data.
• Adaptability: The system can adjust to individual learning styles and paces. It's not a one-size-fits-all approach.
• Increased Motivation: The student has more control over their learning journey, potentially leading to higher engagement.

Limitations to Consider:
• Bias in the System: The AI tutor's initial programming could introduce biases that might influence its teaching style.
• Overreliance on Technology: Students may become dependent on the AI tutor for learning, neglecting other learning methods.
• Ethical Considerations: The self-referential nature of the system raises ethical questions about data privacy and potential manipulation of the learning experience.

This example highlights how circularity, when combined with constructivism, self-referential systems, and cybernetics, can be a powerful tool for understanding human learning and developing innovative educational approaches.
I believe those circularity maniacs' failure to understand the benefits of seeing beyond the circularity of traditional logic is due to their philosophical immaturity and lack of wisdom in understanding the wider vista of greater utilities of philosophy.

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Veritas Aequitas
Posts: 12648
Joined: Wed Jul 11, 2012 4:41 am

Re: Circularity Maniacs

Post by Veritas Aequitas »

Notes: KIV
Veritas Aequitas
Posts: 12648
Joined: Wed Jul 11, 2012 4:41 am

Re: Circularity Maniacs

Post by Veritas Aequitas »

Notes: KIV
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