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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.
Released: May 28, 2026 | Host: Joel Settecase
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.
(00:41–03:16)
(03:23–06:27)
Manager’s View:
Joel’s Challenge:
(06:27–10:14)
(10:32–15:04)
(15:04–20:33)
(20:33–24:07)
(24:07–27:09)
(27:09–28:00)
(28:12–30:06)
“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)