#207 DEBATE: This Is What Happens When You Deny Classical Logic

Summary

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Worldview Legacy | The Think Institute

Episode #207: DEBATE: This Is What Happens When You Deny Classical Logic

Released: May 28, 2026 | Host: Joel Settecase

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Episode Overview

This intense and thought-provoking episode centers on the foundations and function of logic—particularly classical logic—and what happens if one denies or departs from its principles. Host Joel Settecase and a guest (identified as "Manager") engage in a detailed, sometimes heated debate about the definitions, scope, and transcendence of logic, exploring whether its laws are absolute and foundational for thought, or constructs derived from human activity and differing systems. The discussion is aimed at deepening Christian men’s understanding of logic as a cornerstone for apologetics and worldview leadership.

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Key Discussion Points & Insights

1. Clarifying Core Concepts of Logic

(00:41–03:16)

• Definitions Sought: Manager initiates by asking Joel to define logic, logical propositions, inference, validity, and logical consistency.
• Joel’s Definitions:
  • Logic: “Set of rules that govern coherent thought and truth... three laws... not made of matter…transcendental…absolute…invariant, uniform, knowable, three in one, equally ultimate to one another. Objective...govern all possibility and all coherency.” — Joel (00:47)
  • Logical proposition: “One that accords with the laws of logic.” — Joel (01:42)
  • Inference: “Deriving logical conclusions from premises known or assumed to be true.” — Joel (02:30)
  • Validity: “An attribute of an argument wherein the conclusion follows from the premises.” — Joel (02:48)
  • Consistency: “No internal contradictions.” — Joel (03:10)
• Manager’s Disagreement: Manager states he disagrees with Joel’s definitions (01:50), wanting to clarify his alternative conception.

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2. Competing Philosophies of Logic

(03:23–06:27)

• Manager’s View:

  • Logic is an “extracted model from our existence,” simply part of what it means to be human: “To be human is to extract models from the world around us, whether logical, scientific, or theological.” — Manager (03:23)
  • Logical content and propositions depend on the logical system; there is no one definition of what counts as a logical proposition, as they vary infinitely by system (05:18).

• Joel’s Challenge:

  • Pushes for a precise delineation: “...if a proposition could be logical and could vary infinitely...you're defining it so broadly that you've actually lost any kind of meaningful definition.” — Joel (06:27)

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3. What Makes a System ‘Logical’?

(06:27–10:14)

• Joel’s Probing Question: What uniquely distinguishes logical systems from other systems (like moral or mathematical systems)? What is the sine qua non?
• Manager’s Criteria:
  • Logical systems are defined by consistency (no contradictions), completeness (all statement types usable), and decidability (statements can be decided as true or false). (08:35)
  • “A logical system is consistent. A logical system is complete. A logical system is decidable.” — Manager (10:02)
• Joel’s Counter:
  • Objects to using “logic is logical” as a definition, seeking a distinguishing principle. Suggests using the law of non-contradiction to judge logical systems, implying it is a universal standard. (10:32)

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4. The Law of Non-Contradiction as a Standard

(10:32–15:04)

• Dispute Over the Standard:
  • Joel asserts that all systems are judged by the laws of logic (identity, non-contradiction, excluded middle), which are transcendent: “...we can judge the...consistency or inconsistency of those systems and their results by the three laws of logic. That’s always been my contention.” — Joel (14:35)
  • Manager disputes this transcendence: “No, they’re not.” (14:35)

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5. Examples from Modal Logic & Contradiction

(15:04–20:33)

• Modal Logic Example:
  • Manager differentiates between “A is possibly true” and “It is impossible for A to be true.” Negations have different implications in modal logic than in classical logic. (16:09)
  • Detailed back-and-forth about where to place negation and how multi-level possibilities in modal logic (e.g., possibly possibly true, contingently true) complicate classical negation.
• Memorable Quote:
  • “To say that it is impossible for A to be true is the direct negation of [A is possibly true] because those two things cannot be true at the same time.” — Manager (18:14)

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6. The Universality and Limits of Classical Logic

(20:33–24:07)

• Are Contradictions Universally Impossible?
  • Manager: In different logical systems, what counts as a contradiction varies; “A and not A” doesn’t apply everywhere. (21:00)
  • Joel agrees more deeply than before, but sticks to his claim that, “...if your thought experiment yielded a contradiction according to the classical laws of logic, that that result would be...illegitimate... and you might not want to say illegitimate, but you would have to discard it.” (22:59)

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7. Logic, Truth, and Reality

(24:07–27:09)

• Application to the Real World:
  • Joel: The laws of logic are grounded in God and have “implications on the real world. ... If you're using a paraconsistent form of logic and it's yielding a classical contradiction, the result... cannot be something that is actual in the real world.” (24:50)
  • Manager: Logical statements can be valid without referencing actual reality—validity is about logical structure, not existential truth: “That is a perfectly valid argumentation. ... Whether it adheres to anything in the real world or not doesn’t matter.” (25:57)
• Soundness and Truth:
  • Joel: “A logical argument can be valid without being sound, but it can’t be sound without being valid, and it can’t be true without being sound...all of this is dependent on the three classical laws of logic.” (26:35)

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8. The Conditional Statement Example and Logical Truth

(27:09–28:00)

• If 2 + 2 = 5, then Montgomery is the capital of Alabama.
  • Manager: “It is logically true. Because whenever the antecedent...is false, the conditional statement is true.” (27:30–27:39)
  • Joel initially hesitates, then agrees on logical grounds, distinguishing logical from actual (worldly) truth.

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9. Wrap-up Reflections & Meta-Analysis

(28:12–30:06)

• Host’s (Off-Air) Thoughts:
  • Joel and the host (“Host”) recap: different logics can have internal ‘truths,’ but classical logic provides the “transcendent standard by which we judge the results of other forms of logic.” (28:55)
  • “At the very top, it [thought] cannot escape the three classical laws of logic.” — Host (30:01)

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Notable Quotes & Memorable Moments

“Logic is the set of rules that govern coherent thought and truth...They are absolute...govern all possibility and all coherency.”
— Joel Settecase (00:47)

“I contend that logic is an extracted model from our existence. It is a part of being a human being just as much as being reproductive or processing food in our bodies.”
— Manager (03:23)

“If a proposition could be logical and...could vary infinitely, it seems like you're defining it so broadly that you've actually lost any kind of meaningful definition.”
— Joel Settecase (07:01)

“A logical system is consistent. A logical system is complete. A logical system is decidable. These are the attributes of logical systems.”
— Manager (10:02)

“...all of these different logical systems are ultimately judged by the law of identity, non contradiction and excluded middle.”
— Joel Settecase (13:55)

“To say that it is impossible for A to be true is the direct negation of that because those two things cannot be true at the same time.”
— Manager (18:14)

“If you're using a paraconsistent form of logic and it's yielding a classical contradiction, the result of that cannot be something that is actual in the real world.”
— Joel Settecase (24:50)

“At the very top...it cannot escape the three classical laws of logic.”
— Host (30:01)

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Important Timestamps for Segments

• Definitions and initial positions: 00:41–03:16
• Manager’s alternative conception: 03:23–06:27
• Debate on logical systems: 06:27–10:14
• Law of non-contradiction discussion: 10:32–15:04
• Modal logic and contradictions: 15:29–20:33
• Limits of classical logic: 20:39–24:07
• Logic, truth, and reality: 24:07–27:09
• Conditional statement logical truth: 27:09–28:00
• Debate reflection and podcast wrap-up: 28:12–30:06

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Summary Takeaways

• The debate highlights deep philosophical differences on whether the laws of classical logic are transcendent, absolute standards or humanly-constructed tools varying by context.
• Joel Settecase defends the necessity and transcendence of classical logic (identity, non-contradiction, excluded middle) as foundational for thought and reality, rooted in the nature of God.
• Manager positions logic as a pragmatic, extracted model, defined contextually within systems, and resists metaphysical absoluteness.
• Both agree that logic is essential for clear thinking, but differ sharply on its source, scope, and metaphysical status.
• The discussion provides a robust, nuanced look at logic for Christian worldview leaders, showing the stakes in apologetic encounters and worldview formation.

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Transcript

[Host]

What's up, manager? How are you?

[Manager]

Howdy. Thank you for letting me come on first. I was not expecting that.

[Joel]

Absolutely. Good to see you.

[Manager]

Yeah, it's good seeing you guys. What I wanted to do, with your permission, Joel, is I wanted to kind of get a common understanding of some concepts that and how you define some things. I'd like to ask you a series of questions and then offer some kind of critical insight, if I could, if you don't mind.

[Joel]

Sure.

[Manager]

Okay.

[Joel]

Yeah, real quick. Let me start. Let me start a timer for us. We'll do 20 minutes is what we're doing.

[Manager]

All right, thank you. I appreciate that. In your understanding, what is logic?

[Joel]

Sorry, one second. 1930. Okay. Logic is the set of rules that govern coherent thought and truth. It's. It's a set of three laws with the proposition, with the. Sorry. With the attributes that I've enumerated several times in our conversations. They are not made of matter. They are, um, transcendental. They are absolute. They are invariant, uniform, knowable, three in one, equally ultimate to one another. Objective. Those. Those three laws govern all possibility and all coherency.

[Manager]

Okay. What is a logical statement or a logical proposition?

[Joel]

One that accords with the laws of logic.

[Manager]

Okay. What is an.

[Joel]

Are you going to tell me if you agree with these, by the way?

[Manager]

Oh, I disagree with both of what you've said so far. But like I say, let me finish this and we'll get to that.

[Joel]

Now, if you like this episode and you want to take your learning further, you need to know about what we're doing to help revolutionize the way that Christian men interact with their faith. We want to help you get more equipped to lead your family. Answer any objection to share and defend your faith, and I'll tell you more about what we're doing to help you do exactly that. And after the episode. Stay tuned. All right, go ahead.

[Manager]

What is an inference?

[Joel]

An inference. An inference is a. Let's see, it would. How does the dictionary define it?

[Manager]

I don't.

[Joel]

I don't have a stipulative definition of it. Defined inference, the act or process of deriving logical conclusions from premises known or assumed to be true. Okay, so following the logic to the logically necessary conclusion.

[Manager]

Okay, what is validity?

[Joel]

Come on, man. Validity is validity. Okay. Validity is when the. It's. It's an it. It's an attribute of an argument wherein the. Or whereby the conclusion follows from the premises.

[Manager]

Okay. What is logical consistency?

[Joel]

Logical consistency is where there's no internal contradictions. Get to the point, man. Get to an argument. We don't need to define all these things.

[Manager]

I, I want to be clear about what your terms are.

[Joel]

Well, now, okay, you define those terms.

[Manager]

Okay, let me. First of all, I contend that logic is an extracted model from our existence. It is a part of being a human being just as much as being reproductive or processing food in our bodies. I contend it's simply a matter of a human attribute and that to be human is to extract models from the world around us, whether they be logical, scientific or theological.

[Joel]

Okay, so what else did you say? What is validity? What is. Or the other questions you asked me, I want to make sure we get them all.

[Manager]

A logical. Logical proposition.

[Joel]

Yeah, logical proposition.

[Manager]

Okay. A logical proposition is a statement or a proposition that carries logical content. And now be fair warning here, there is an entire field of philosophic debate about what logical content is.

[Joel]

Yeah, but you, you've got to define it for yourself though, right?

[Manager]

Well, what I'm saying is it's a highly, highly debated topic. And what I'm saying is that a logical proposition, if A, then B, it carries some sort of logical content to it. That's why it's a logical proposition.

[Joel]

Okay, so it doesn't have, it doesn't have to be in accordance with the laws of logic, just it needs to be structured in a particular way. If, then it's a condition.

[Manager]

As we've discussed before, the laws of logic vary from system to system, and an inference is going to vary from system to system.

[Joel]

Could there be a logical system in which there are no conditionals?

[Manager]

Sure, there's many of them that only use ampersands and knots.

[Joel]

Okay, so then how, so then how are you going to define it? Seems like a logical statement or a logical proposition could be anything then

[Manager]

depends on the logical system. It's going to vary from logical system to logical systems.

[Joel]

Okay, so there is. So there is no, there is no one definition of what it means to be logical. Sorry, what it means to have a logical proposition. Because it could vary infinitely. Hypothetically, potentially, it could vary infinitely. Is that correct?

[Manager]

As I've given examples before, a logical proposition in Aristotelian logic is going to be an end statement. Excuse me, an all statement, a sum statement, a none statement, or not all, not some, and not some, not none. And in first order propositional logic, it's going to be and, or if then, or if, and only if, then. Okay, so modal logic, it's going to have possibility contingency. So they're going to vary from logical system to logical system.

[Joel]

Okay, so A, a logical proposition is any, for you, is any proposition in which there is content that accords with some designated logical system which could, which could.

[Manager]

Logical content is going to vary from system to system.

[Joel]

Okay, so. So it could be potentially that, that. Respectfully, that to me does seem like a definition. That is, it doesn't really define, because a definition needs to be able to delineate something from some, from everything else and explain what makes it unique. And it seems like if a proposition could be logical and, and could vary infinitely, V, A, R, Y, vary infinitely, it seems like you're defining it so broadly that you've actually lost any kind of meaningful definition.

[Manager]

But that does have meaning within each logical system.

[Joel]

But then even logic. So then, even, so then what. What would be an attribute that all logical systems have in common that make them logical systems and not moral systems?

[Manager]

We have this broad definition of logical content. That's why it's hotly debated, because it varies from system to system.

[Joel]

Okay, so logic is. Logic is. Logic is an extracted model from our existence. It's a human attribute. What.

[Manager]

That's correct.

[Joel]

What kind of model. What makes it a logical system as opposed to a moral system or a mathematical system?

[Manager]

Because it's defined in very precise ways as to what kind of statements are going to be utilized, what sort of inferences are going to be used, the. What definition of validity is going to be used. It's going to be defined by what sort of operators are going to be in there, whether it's if, then operators and operators, or operators, not operators. And that's what it's defined by what is called a metallogical structure. These things defined what those, what those things are. And again, they vary from system to system.

[Joel]

All right, I don't, I don't want to filibuster here, or I know you're trying to get somewhere with this, but what I'm still not clear on, in your view, what makes a system a logical system as opposed to some other kind of system like a moral system or a physical system? I mean, a moral or epistemological. What's the mathematical. Is the word I'm looking for. What, what is the one attribute that logic has that no other system has?

[Manager]

Well, the reason I ask you about consistency and completeness and, and about decidability is these are characteristics of logical systems. A logical system that is complete means that all of the statement types that are within it are able to be utilized within that system. A logical system that is consistent is one that does not yield a, and not a or a contradiction as true. A logical system that is decidable means that all of the statement types can be decided as being either true or false within that system.

[Joel]

So I, I hear you, but you're still, you're already one step past the definition that I'm looking for, which is what makes a system a logic system as opposed to something else. What is the sine qua non of a logic of all logical systems that separate them from different systems? So you can't say, well, it's a logical system that is consist, you know, a logical system that is consistent has these attributes. I, that's fine. My question is what makes it a logical system in the first place, as opposed to some other kind of system?

[Manager]

That's exactly what I'm telling you. That it, it adheres to logical consistency,

[Joel]

but you can't define a term by itself.

[Manager]

So what is, that's what we're doing because we're doing a different level of, of logical inquiry.

[Joel]

So a logical system is a logical system.

[Manager]

No, a logical system is consistent. A logical system is complete. A logical system is decidable. These are the attributes of logical systems.

[Joel]

I see, I see. So you're saying all logical systems are consistent, complete and decidable.

[Manager]

Correct. If it's going to be a legitimate logical system. Okay, if you have a logical system that yields a true contradiction that, then you have, you do not have a, you have an inconsistent logical system because it does not meet the definition of consistency.

[Joel]

Okay, so that is interesting because now you're going right? I, I don't want to go down this route just yet, but you are coming back to the second law of logic that I always tell you about, which is the law of non contradiction. And you're using that as a standard by which to judge all the other logical systems, which is what I've been contending.

[Manager]

That's, that is not the case at all. You just said it's logic. Listen to me, Listen to me.

[Joel]

Entails a logical contradiction.

[Manager]

Listen to me. A logical contradiction is a statement or a pair of statements. A logical system is consistent or inconsistent. So it is, it is not judged on the basis of the truth or falsity. It's based on what it yields as, as a contradiction. And what are you talking about? Two different levels of, of logical inquiry here. So when we talk about inferences, inferences are not true or false. Inferences are either valid or invalid. Okay, so different terminology.

[Joel]

You, you jumped over to inferences there. But, but go back to what you just said about systems yielding contradictory or non contradictory conclusions or results. And unless I'm hearing things, and I'm not, you said that a logical system is not legitimate if it yields a true contradiction.

[Manager]

I said it is inconsistent if it yields a true contradiction.

[Joel]

But you still use the word illegitimate.

[Manager]

Yes. Okay, that was an incorrect term for me. I should have said it was inconsistent, okay, Rather than illegitimate.

[Joel]

All right, so. But it's not. It's having an inconsistent logical system on your view then, since you're walking that back, that doesn't make the system illegitimate on your view.

[Manager]

I'm saying that it is. I will stay with the definition that I used that it is inconsistent. And when you. And you have good reason to throw out the system because it yields a true contradiction.

[Joel]

Well, if you're throwing it out, why would you throw away something that's legitimate? It sounds like you're saying that it's illegitimate.

[Manager]

I choose not to use the word legitimate or illegitimate. I simply use to stay with the term that is a logical term of inconsistency or consistency.

[Joel]

And you're, you're not ascribing any value or lack of value to that system that yields a contradiction. You're just saying it's inconsistent and I'm discarding it. But I'm not saying it's illegitimate. Is that. Do I understand?

[Manager]

I'm not going to use the term illegitimate.

[Joel]

Okay, but. So you're discarding it because it's inconsistent, but you're not going to say illegitimate.

[Manager]

Okay, that's correct.

[Joel]

That seems like you're just.

[Manager]

I'm trying to be precise in these things. Again, logical statements are true or false. Truth functionally, if it's true or false, by the way, that's the other thing. Logic does not deal in truth per se. It deals in truth functions, how things function. And when you have a logical system that is inconsistent, then you have one that's not useful.

[Joel]

Okay, well again, that's, that would make it illegitimate for truth seeking.

[Manager]

So if you wish to use that terminology, you can, but I'm not. Okay? I, I've been a network engineer since 1993, and the same diagrams that define logical statements are the same diagrams that define digital circuitry. Okay? That is its usefulness. Okay? The difference is that in logical statements we use T's, F's and tildes, and digital circuits, we use one zeros and dashes, but their function is exactly the same.

[Joel]

Okay, but I, I do want to harp on the point that your standard for judging a system as discardable or you don't want to say legitimate but retainable is the law of non contradiction, whether or not. Whether or not it produces a true contradiction. And that. That's what you said. So that's been my contention all along, Manager, is that all of these different logical systems are ultimately judged by the law of identity, non contradiction and excluded middle.

[Manager]

That is not what you've said. That is not what you say. You say that those laws are transcendent. You say that those laws are absolute. They say that those. No, they're not.

[Joel]

Well, that.

[Manager]

No, they're not.

[Joel]

What makes you think that what I just said isn't affirming all that? That's exactly what I'm affirming. They're transcendent, which means they apply to any thought experiment or any attempt at using a parallel or paraconsistent system of logic such that we can judge the validity or invalidity or the legitimacy or illegitimacy or consistency or inconsistency of those systems and their results by the three laws of logic. That's always been my contention, Joel.

[Manager]

When you have a modal logical system, a contradiction that it yields is going to be different than first order propositional logic. So you're going to have a different way of deciding what a true contradiction is than you would in first order propositional logic, and as you would in Aristotelian logic. So the inconsistency is gauged differently depending on the operators used within the system.

[Joel]

Okay, so can you give me an example of that?

[Manager]

The law of non contradiction that you're referring to.

[Joel]

So can you give me a different

[Manager]

law of non contradiction that is going to judge each of these logical systems, consistent or not?

[Joel]

Can you give me an example?

[Manager]

Sure. In modal logic, take one statement, A is possibly true. Its contradiction would be it is impossible for A to be true or A

[Joel]

is not possibly true.

[Manager]

No, it is impossible for A to be true.

[Joel]

Well, a direct negation of that, if, say the, say the first proposition is

[Manager]

A is possibly true.

[Joel]

Right. The direct negation of that is A is not possibly true.

[Manager]

No. Or you can modal logic and modal logic. The negation of that is it is impossible for A to be true.

[Joel]

Explain to me the material difference between those two statements. A is not possibly true versus it is impossible that A is true.

[Manager]

It's a different designation in modal logic. They are not. They're not equivalent expressions.

[Joel]

How, how are they materially different?

[Manager]

Because you can string together as possibly true. A is possibly, possibly true. A is possibly, possibly true. And they each have a different Truth value between true and false. Okay, so when you're saying that it is not the case that it is possibly true, it's different than saying that it is impossible for it to be true. It's a different designation in modal logic.

[Joel]

Okay, okay, so, so hold on. I'm. I'm close to understanding what you're saying and I, I do want to understand it that you're saying that in modal logic, the, the negation of A is possibly true. Is. It is impossible. That to me seems like you're not negating the same that, that a negation as I understand it is. Is notated by saying so look, I've got here, I've got A. Okay, there's my proposition A. A is possible. And in this case proposition A is. A is possibly true. That's the proposition to negate it, I'm negating it. And that, that negation, the, the negation can go. I want to say it can go anywhere in the prop. In the proposition it is not possible. Okay, so then, so then what are the attributes of modal logic? And, and how is modal logic not distilled, dependent on. Because it seems to me like it is impossible. That A is true is another form. It doesn't seem like it's materially different. Explain how it's materially different from it is A is not possibly true. Or, or not. I guess we would have to say

[Manager]

not it is not the case possibly true.

[Joel]

Right.

[Manager]

Because one is negation that can, that can yield many different meanings within that. To say that it's not the case today is possibly true. You can also say as not possibly possibly or that it is possibly, possibly true where it is possibly possibly possibly true. Okay? All the other possibilities are included in that. But to say that it is impossible for A to be true is the direct negation of that because those two things cannot be true at the same time.

[Joel]

I see what you're saying. I see what you're saying. Okay, so if I say it is impossible for A to be true, then it is not possibly possible that A is true or any other.

[Manager]

Correct?

[Joel]

Yeah, right.

[Manager]

Any of those in that infinite series.

[Joel]

Sure, sure. Okay. Okay. So then let me revise my previous statement because I realized as I was writing this that actually the way I was saying it was actually incorrect. I don't think you can. I'm going to walk back what I said. I don't think you can put the negative or the negation anywhere. I think that if A is a self contained proposition, the negation would need to come prior to it, outside of it, if you will. So then it would be it is not or not A is possibly true, which that would be equivalent to. I think that would be equivalent to it is impossible that A is true.

[Manager]

No, it's not.

[Joel]

Why?

[Manager]

Because if you're saying, okay, let's take the statement A is possibly true and you're going to negate that, that means it is something other than A is possibly true. That other than includes everything else as false.

[Joel]

Right?

[Manager]

As not false.

[Joel]

Right.

[Manager]

As possibly possibly true is contingently true.

[Joel]

Yeah, that makes sense. Okay, that makes sense. Yes, I understand what you're saying.

[Manager]

Yes, but when you're, when you're saying it's impossible for it to be true, you're taking a direct attack upon possibly a right? And, and you're taking the, the direct thing and these things are diametrically opposed. Whereas you're, you're saying something other than possibly and when you're saying it is not the case.

[Joel]

Yes, no, I understand. I, that makes sense. You're, you're eliminating all potential hypotheticals within, within that like, okay, it's not, it's not possibly true, but we can say it's, we can, we can add a degree and we could say it's, it's possibly possible. Yeah, sure. Okay. Yeah, that makes sense. Sure.

[Manager]

Or it's contingently true, or it's necessarily true, or it's all the other operators that are associated with motor logic.

[Joel]

Okay, so I see what you're saying. That actually makes sense. And yet two none of, oh, that's 20, that's 20 minutes. And yet it is still not the case that two actually contradictory propositions can both be true in the same sense and at the same time.

[Manager]

My point is, is that it varies from logical system to logical system. A and not A is a contradiction in, in first order propositional logic. It is not in Aristotle. A and not A does not even apply in Aristotelian logic. It does not even apply in, in modal logic. And the definitions of contradiction varies from system to system.

[Joel]

I, I, I, I hear what you're saying and believe me, actually I, I actually understand what you're saying. I'm pretty sure, I'm pretty sure I understand once you started multiplying the possibilities that, that made sense to me. And yet, and yet, I've said this for a long time, but when it comes to, I think they're called paraconsistent systems of logic, meaning the non traditional, non classical modes of logic, multi valence logics. Right, right, right. Multivalence logics, it's, it just requires being more specific. So if you wanted to, if you want to say, well, in this form of logic we're going to notate it differently where the negation can, it must be outside of the full proposition or what going to say, instead of saying just simply not, we're going to say impossible or something like that. It would still not be the case even in that system, that if your thought experiment yielded a contradiction according to the classical laws of logic, that that result would be possible or valid or true, or logically consistent or logically legitimate. Is that not correct? I mean, if you, if whatever system you're using, whatever system of notation, whatever system of, of terminology, it would seem self evident that if that is yielding an actual contradiction according to the, the law of non contradiction in classical logic, that would still be an illegitimate result. And you might not want to say illegitimate, but you would have to discard it.

[Manager]

What I'm saying is, is that your notion of the law of non contradiction is stuck within one logical system and that that logical system that it is stuck within is stuck there because of the statement types that you use. Statement types that are used within a logical system varies from system to system.

[Joel]

Yes, I, I, I actually understand your position more than I have in the past now, but I still don't think that you're understanding mine, which is that even within these other systems, the three classical laws of logic are still determining as the ultimate transcendent standard whether or not the, the result of that system yields a valid or legitimate result.

[Manager]

Do you understand that? That Aristotelian logic is restricted to six statement types.

[Joel]

Yes, I, I get that.

[Manager]

Let me, I understand.

[Joel]

Okay, all right.

[Manager]

You understand that first order propositional logic uses a different set of statement types within its logical system than Aristotelian logic.

[Joel]

Yes, I, I understand that. But the results, the results of that system, if they do yield A and not A according to classical logic, you can say, well, we're using different notation, we're using different terminology and there are different rules at play here. But if we're talking about a coherent idea, which is what classical logic judges, if we're saying we are trying to arrive at something that is potentially true.

[Manager]

If you're what logic deals in, logic deals and truth functions.

[Joel]

Well, right, but logic also has entailments on the real world.

[Manager]

No one's saying that it isn't modeled, extracted from it.

[Joel]

Well, right, but that, but again, this is where we get back to our definitions because the, my contention has always been that the transcendent laws of logic are not somehow divorced. They're not restricted to the law of like some kind of plate or the world of Platonic forms or something. They actually. Because they're grounded in God and God is the creator of all things, and in God unity and diversity and the transcendent and the act and the material categories and instantiations of those categories are both grounded in God. Therefore, the laws of logic do have implications on the real world. So if you're using a paraconsistent form of logic and it's yielding a classical contradiction, the result of that cannot be something that is actual in the real world. That's my contention. You agree with that?

[Manager]

Have to be something actual in the real world. It does not have to be actualized. If I say if. If I say possibly. Hang on, hang on.

[Joel]

Okay. Okay.

[Manager]

If I say if 2 plus 2 equals 5, then the capital of Alabama is Montgomery.

[Host]

Right?

[Joel]

Right. Right.

[Manager]

Yeah. Okay. And then I say two plus two equals five, therefore the capital of Alabama is Montgomery. No, that is a perfectly valid argumentation. And yes, whether it adheres to anything in the real world or not doesn't matter.

[Joel]

You. What you're saying is correct, and I agree with that. And that's. That wasn't my contention. And I didn't say actual. I said potentially true or potentially actual. The laws of logic.

[Manager]

Essentially true. If 2 plus 2 equals 5, then the capital of Alabama is. It's. That's right. But it's still logically valid and it still has logical application. It still has logical content.

[Joel]

Hear. Hear me.

[Manager]

Still has logical meaning.

[Joel]

Hear me when I say a. An. An argument. A logical argument can be valid without being sound, but it can't be sound without being valid, and it can't be true without being sound. A proposition can't be true and in the actual world without being sound, without being the result of a sound argument. You know, like a sound argument is a prerequisite for a true proposition and validity precedes soundness. And all of this is dependent on the three classical laws of logic. That's always been my contention.

[Manager]

So let me ask you this. If I say we're actually.

[Joel]

We're actually out of time. We do have other guys in there.

[Manager]

One last thing. If I say 2 plus 2 equals 5, if 2 plus 2 equals 5, then Montgomery is the capital of Alabama, is that a true or false statement?

[Joel]

Logically, it is. It's neither. One. It's neither. It's neither a true or false statement.

[Manager]

It is Logically true. Because whenever the antecedent. The conditional statement is false, the. The conditional statement is true.

[Joel]

Okay.

[Manager]

That's the standard definition of a conditional statement.

[Joel]

Okay. It's. It has no truth value in the actual world though, because of course it does.

[Manager]

That's what it deals in is truth values.

[Joel]

If two plus two is. Hold on, let me think about this. If two plus two is five, then yes, I guess that would be true. Yes, you're right. I take that back. Yes.

[Manager]

Yes, that's all right. Thank you for letting me pursue this. I appreciate it. Great.

[Joel]

Okay.

[Manager]

Yep.

[Joel]

Great. Great talking.

[Host]

Thanks, manager.

[Joel]

Have a good one, bro. Okay. Overheated again.

[Host]

Overheat Fallacy.

[Joel]

Yeah, I commit that every week. Okay, did. What manager was saying makes sense to you? Do you. Was there something I was missing?

[Host]

I was upstairs for 90 of that because I had to help my wife with something.

[Joel]

What he said was, well, I won't we. I won't rehash it. It's interesting because I actually find a lot to agree with him on in the sense that if you are using a different form of logic, it's going to play according to its own rules. My contention has always been that the three classical laws of logic undergird the. Just say that they.

[Host]

Logic.

[Joel]

Yeah. They serve as a trend, as the transcendent standard by which we judge the results of other forms of logic. If we're just using a paraconsistent form of logic, meaning like a non classical form of logic. So he was talking about modal logic, for example. Then if we're using it as just merely like a thought experiment or something. Okay. It's interesting. It's like that computer program that you told me about before, which it can yield true and false results so that the medicine doesn't get.

[Host]

Yeah. It can yield contradictory results.

[Manager]

Right.

[Host]

Just. Just to make sure the software doesn't completely crash.

[Joel]

Right. And internal to that system, that's fine. But my contention has always been that the laws of logic undergird what is. What is potentially actual. You know, what's. They're transcendent in terms of, you know, like a. Like a true contradiction. No matter what system yields, it can't actually be true in the objective absolute sense.

[Host]

It deals with system. The system level.

[Joel]

Yes. It deals with the system. Yes.

[Host]

At the very top. It cannot escape the three classical laws of logic.

[Joel]

Yes.

[Host]

And there's literally nothing you can do about it.

[Joel]

That's right.

[Host]

Talk about within the system all you want, but.

[Joel]

Right. And even to have that discourse about the system which we're presupposing the three classical laws of logic. I didn't go there today because we've talked about it before, but I've had atheists on who have said, well, logic is just a convention. I say, well then it's not, you know, because I don't hold to that convention for the sake of argument. You're a Christian man. You want to build a legacy, answer the world's questions and lay down a solid foundation for your family in God's Word. But everywhere you look you see decline, disorder, chaos. Your neighbors don't know the Lord and too many churches are filled with apathy. In today's world, we need men who understand theology, know scripture, and who are committed to leading their families in the biblical worldview. That is why we're building the Hammer and Anvil Society, the ultimate discipleship community for Christian men. With weekly cohort calls, a full library of resources and courses, weekly challenges and live teaching, you're going to sharpen your mind and your character. Our full library of courses is going to help you deepen your knowledge in the Christian worldview, family, discipleship and apologetics, the defense of your faith. But it's not just about building your knowledge base. As important as that is, it's also about brotherhood. That's why you'll also have access to an online community and live cohort calls Live teaching and real accountability so you can have fellowship with like minded brothers who are on the same journey as you. Member Kevin says, the Hammer and Anvil Society has been the most beneficial thing for my family's spiritual growth in years. This unique brotherhood has made me more bold in my work, witness and more sensitive to God's leading. AJ says. Today I stand stronger and more rooted in my faith. The Hammer and Anvil Society has been instrumental in transforming me into the man of God I'm striving to be. Get unlimited access as a member or try out a single course in the subject of your choice. Learn more now. Go to thethink.instute society. Get equipped. Build your legacy in community. Join today.