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Logics Face Off

Picture of Derek Cabrera, PhD   Derek Cabrera, PhD  ·  3 minute read
DALL·E 2025-03-17 06.23.54 - A visually striking landscape representing the differences between Socratic, Aristotelian, and DSRP logic___- In the center, a large, dynamic tree wit

How Socratic Logic and Aristotelian Logic Differ, and How DSRP Multivalent Logic Offers an Alternative

You might think that logic is "boring" or "mathy" or even old fashioned or irrelevant to real life. You might also believe that there is one "logic." The truth is that there are many forms of logics. And, what you may not know is that the logic you use will have a dramatic effect on the outcomes of any situation. They change how you think...and sometimes cause you not to.
 

Socratic Logic vs. Aristotelian Logic

Socratic logic and Aristotelian logic are fundamentally different approaches to reasoning. DSRP multivalent logic presents an alternative. We can use the Liar Paradox as an example of how these "logics" solve, or struggle to solve, paradox differently.
 
Feature  Socratic Logic  Aristotelian Logic
Type of Logic Dialectical (dialogue-based, exploratory) Formal (rule-based, categorical)
Method Asks open-ended questions to explore contradictions and refine understanding Uses syllogisms (if A = B, and B = C, then A = C) to arrive at definitive conclusions
Approach to Truth The truth unfolds through questioning and debate Bivalent—statements are either true or false (Law of Non-Contradiction)
Handling Contradictions Engages with them dialectically, using paradox to deepen inquiry Rejects contradictions as logically impossible

Socrates did not develop a formal logical system; Aristotle did. Socratic reasoning was dialogical, exploratory, and open-ended, while Aristotle systematized logic into strict rules for deduction. Aristotle sought definite conclusions, whereas Socratic dialogue embraced uncertainty as a tool for inquiry. The Socratic method uses contradiction as a pedagogical tool, while Aristotelian logic demands resolution through bivalence (true or false).

How the Liar Paradox Challenges Them

 
The Liar Paradox is the statement: “This statement is false.”
If the statement is true, then it must be false. If it’s false, then it must be true—a direct contradiction.
 

Socratic Logic’s Approach

  • Would not resolve the paradox but use it as a tool to challenge assumptions about truth, language, and meaning.
  • A Socratic dialogue would push the contradiction further—“What do we mean by ‘true’?” “Can something be both true and false?”
  • No final answer is required—instead, the paradox exposes limitations in our understanding.
 

Aristotelian Logic’s Approach

  • Rejects the paradox outright because it violates the Law of Non-Contradiction (A cannot be both A and Not-A).
  • Aristotle might classify the statement as “meaningless” or “ill-formed” because it does not fit into a bivalent true/false system.
  • In essence, the paradox is dismissed rather than resolved.
 

How DSRP's Multivalent Logic Handles the Greek Liar Paradox

 
DSRP (Distinctions, Systems, Relationships, Perspectives) operates on multivalent logic, meaning it allows for truth to be contextual, relational, and dynamic, rather than strictly bivalent.
  • Distinctions (D): The paradox arises from assuming “truth” and “falsehood” are mutually exclusive categories. DSRP recognizes that the distinction is context-dependent.
  • Systems (S): The paradox is part of a system of self-referential statements, meaning its meaning depends on the larger logical framework in which it’s embedded.
  • Relationships (R): The paradox is relational—it only exists because of the assumed rigid relationship between “true” and “false.” If that relationship is reframed, the paradox dissolves.
  • Perspectives (P): From one perspective, the statement is false; from another, it’s true. DSRP recognizes that a statement can be both true and false depending on perspective.

How DSRP Resolves the Paradox

From a DSRP perspective, the liar paradox reveals how shifting distinctions and perspectives changes the statement’s meaning and apparent truth value. In one perspective (with one set of boundaries and assumptions), the statement “This statement is false” can be seen as true, while in another perspective (with different boundaries and assumptions) it appears false—highlighting that the paradox arises from conflating these multiple viewpoints. For example, using DSRP, you might label the two perspectives for “This statement is false” like this:

  1. Self-Referential Perspective – The statement refers directly to itself (lumping statement and truth value using S), thereby creating the paradox: if it’s true, it’s false; if it’s false, it’s true.

  2. Meta Perspective – The statement is examined as an object of analysis (distinguishing the statement from its truth claim). Here, one observes that the paradox arises because the statement’s reference point is only itself and can’t be confirmed or contradicted externally.

Instead of rejecting the paradox (Aristotle) or endlessly debating it (Socrates), DSRP reframes it:
  1. The paradox is a result of assuming a rigid bivalent logic (True/False).
  2. If we allow for contextual truth (by adding new perspectives and distinctions and avoiding misplaced groupings and relationships), the paradox disappears.
  3. Example: Instead of saying, "This statement is false,” we can say: “This statement is false within System A, but true within System B.” Or, “This statement is false within a self Referential System from a Self Referential Perspective, but true within Meta System from a Meta Perspective.”
The contradiction is removed because truth is now system-relative rather than absolute. And what's most remarkable, is this is exactly what we humans do IRL (without as much explicit awareness). When we come upon paradoxes in real life we don't find them terribly difficult--the joke that is both offensive and funny, turn of phrase that is both compliment and jab. 
 

Key Takeaways

Approach Greek Liar Paradox Handling Limitations
Socratic Logic Uses the paradox to deepen inquiry rather than resolve it.  Does not provide an answer, just more questions. (e.g., avoids solving it)
Aristotelian Logic Rejects the paradox as meaningless or invalid Fails to engage with paradox, treats contradiction as illogical
DSRP Multivalent Logic Resolves the paradox uncovering subtle shifts in perspective that change the  distinctions, systems, relationships. Requires shifting from bivalent logic to the kind of logic found in nature, which some may resist

Final Thought

 
DSRP offers the most robust solution because it recognizes that contradictions only exist within rigid frameworks. When we shift perspectives, paradoxes dissolve—not by dismissing them (Aristotle) or debating them forever (Socrates), but by restructuring the way we think about them.