Propositional Logic – Part 2
Channel: Mohammed Hijab
File Size: 60.68MB
Salam alaikum warahmatullahi wabarakatu How are you guys doing and welcome to the second session of logic, where we'll be going through some of the main, we said some of the key, the principal, the chief rules of logic, propositional logic L, one logic. And in the last session we did go through, I would say about 50% of some of the main rules in the most of the kind of syllabi that are put across the world, in mathematic courses, as well as in logic courses and philosophy courses. And this is one of the interesting places where all of these subjects meet.
Engineering, Computer Engineering, Mathematics, logic, philosophy,
even to a lesser extent, language, a lot of these courses logical design in this. And now obviously, in the age of AI, more and more people need to know, the sequences and stuff like that. So what we're going to be doing in the beginning, because I don't want to rush this, and the reason why I don't want to rush this is because these rules, just like mathematics, even though I'm very poor, as many of you know, at mathematics,
it requires mental kind of grappling. Okay. So what we're going to do is we're going to kind of interleave from last lesson. And we're going to start by I'm gonna ask you guys some questions. And then we're gonna do a couple of exercises, just to recap, what we've done in the previous session. And then once I'm kind of confident, and you guys are confident with yourselves on the on the rules that we've already covered, then we can move and give you new information, because otherwise it's gonna be a lot of information. And maybe information overload as well. Okay, so let's get started with the basic forms. What was the name of actually forget the name? What was the form modus ponens
the form? If p, if P, then Q and Q. P. Therefore cute. Okay. Now, can you give me an example
of how this would look?
If you were to maybe put it into a
into language? So it is only him?
Therefore shop is open.
It is nine.
Therefore, yeah, remember the language shop is open? Yeah. No problem at all. That's good. What did we say about the difference between someone else that was good. So the difference between validity and soundness?
I thought, What is the difference between a valid argument and a sound argument?
Valid argument is
an argument that has
that adheres to the Yes. rules of logic. Perfect. Yeah. Excellent. And a sound argument. So as we said, a valid argument. It obeys, let's just say obeys the rules of logic. Yes.
So it has an internal consistency.
But a sound argument is what is a sound argument is one that has true premises? Yes, it's true.
So give me an example. Let's get someone else. Maddie, have an argument which is valid, but not sound as difficult one maybe valid one or some maybe.
Or let's just say, it's soundness is questionable.
Is Valid but a sound whether a sound or not? It's questionable? Because that way, I'm not asking you to just prove something.
If the noon is outside, then everyone is awake. Okay, yeah. Brilliant. The moon is outside, therefore everyone is OK. No problem. Yeah.
If the moon is out, everyone must be awake. The moon is out there for everyone's awake. I mean, we would beg to differ with this. But it's still valid in the sense that why is it valid? Maddie
follows the laws of logic. Yes. All logic. Yeah. All right. So another thing we talked about is modus tollens.
Who remembers the form of that? Yes. if p then q, not q therefore not p. Good if P then Q. Not Q, therefore,
not p. Yeah. So let's, can you give me an example of this?
If a potato have an intake of starch, I have not had an intake of potato starch if I've not eaten potato?
Yes, that's correct. Yes. Well, that was excellent. I like it. That's actually a very reasonable excellent
you know, example there is everyone is very sharp. With this.
One Now the third thing I'm going to ask you to do, I'm going to give you a little bit more time to think about because I'll tell you why in a second.
Is the syllogism. Before I do give you more time to think about syllogism syllogisms. What did we say some of the types of syllogisms Weltman. Quasi? Yes. Because
well, give me another give me a disjunctive. Okay. Okay, what else? Hypothetical hypothetical. Okay.
What else? The poly? Poly? Okay, excellent. I'm not gonna write the whole thing, because it will take time. Now, what I want you to do. Okay.
Is before before I ask you, what I want you to do is a famous quote by syllogism. Who remembers the husserlian form of the argument?
Everything that has a beginning has a cause. The universe has a beginning. Therefore, the universe has a cause beautiful. Yeah. Everything
Has a cause?
Obviously, the atheist here can say well, God,
Well, God, so he doesn't have a beginning.
has a beginning.
has a cause.
Okay, that's horrible handwriting. If you want it fast.
Me what speed kills neat. Everything that because it has to begin as a cause universe has been there for years, of course. Alright, let's now we're gonna give you five minutes to speak to the person next to you five minutes. And you can use whatever type of syllogism you like to create
your own argument for God's existence.
We have to be knowledge producers. So now you know the rules. You can use them inclined? I will give you about five minutes. And then we'll come back and see what are some of the arguments? It doesn't have to be this.
Actually, it cannot be this because otherwise you're just copying it.
And then we'll come back and we'll do that.
let's get some of the arguments and then we move on to the next rule. Okay. And what I was planning on doing just to let you guys know is as we want to mix a little bit of Islamic studies on us Islamic Islamic Arabic logic, yeah, Islamic case, logic, whatever you want to say about it.
And propositional logic because it's just I want to give you the basics, some of the most important things that you're going to keep coming up. You're going to keep seeing in the literature and stuff like that. But it all depends on how quickly we can get things done. Okay, so we need to be secure with the knowledge. Let's start with our format. Why not? Give me some arguments for God's existence using syllogisms. So we're doing a poly syllogism. And we're doing there are dependent existences. If there are dependent existences, then there is a necessary existence. Therefore there is a necessary existence. Yeah. Ideally, you'd want to add maybe another premise in there. You got Polly
Polly syllogism, so you can add a lot more premises. But you get the idea that what makes us different from another syllogism is that you're adding two pieces of information. You don't go from a general for specific. But if you wanted to add it if you want to make this polemical and you wanted to go against like an atheist and speak like this, I would add a little bit more because the second premise that you said would require a lot more justification. Like okay, well now you don't have to go to another argument to prove your second argument. So so we thought about then we we did another example which was like, if there is existence dependent existences must come from
independent existences, so it just Yeah, fleshed it out a little bit. Yeah, that's what you'd want. That's what you'd want. Okay, let's go to the next class. Are you guys I'm taking it as both of you have come with that conclusion. Right. That's fine.
was a bit strange, but we can only imagine what we've experienced we can imagine God that means we've experienced God Okay, it's quite similar to some forms of the onset ontological argument and then we start what's the first premise we can only imagine we've experienced we can imagine God therefore we've experienced God something Yeah, we can imagine what we have experienced we have experienced God there we have imagined God therefore we have experienced God Okay, and we have another intelligent design requires intelligent will the universe is intelligent intelligently designed for life therefore there was an intelligent will. No Okay, brilliant. Once again, very
valid, obviously now, someone's gonna attack you in software so long as you can speak like this. Because we have
You speak like this. And when people lose it the first hurdle because they speak in a way that sounds logic like logic, it's logic. But now you're, you know, you're being coherent. That's very good. Let's go to the next one.
We have one which is disjunctive.
So the this is
the universe is either created or created itself.
The universe cannot have created itself,
therefore was created. Okay, why not? Yeah, either this or that is not this, therefore, that yeah, that's the basic remember, we talked about that last time? We didn't cover that in the beginning. But it's either this or that. Is this, therefore, that the only thing someone can say is a false? What? You've heard this before. This is a false dichotomy.
Yeah, there are things which are not false dichotomies. You hear this all the time? It's a false dichotomy. It's a false dichotomy. You don't have to prove that it's a false dichotomy, a false dichotomy. If I say, either you're alive, or you're not alive, see, oh, that's a false dichotomy. No, is matter of fact,
either there is existence or there is no existence. Well, that's a false dichotomy. No, that's not a false dichotomy, actually, you just need to make sure that wherever you're putting into disjunction
is an exhaustive explanation of all that you get from this. So I'm gonna do is I'm gonna give you a logical principle and show you I don't think people do is I don't know why they don't.
Okay, I'm going to show you how this links to or sole effect. Also effect is the principles of jurisprudence.
Because its principles of jurisprudence, who quickly knows what that means?
What is this of Islamic law of Islamic law?
You'll find that there's some people that attack, they will attack us, they will attack me or attack you, they will attack him.
No, no, they will attack us because we were even engaging in discussion about logic, right? But the same people will have to study or soul Alpha.
Okay, what's this all affects the principles of jurisprudence.
Now, I'm gonna give you something which is concurrent in both propositional logic. And also look, it's the same idea about being set in different way.
And that's why I'm bringing it to the table is the idea of necessary and sufficient conditions, necessary and sufficient conditions. Now,
let's talk Islamic law. And these are usually the conversations we have before the tape begins, but let's just do what we need to do today.
If I want to get married, I'm not talking about me.
I'm very happily married. I don't need any woman pestering me on the on the
private messages or anything like that. You will not get a response. Just just to be clear, no, I have to be confident about this matter. You will not get a response. But what I'm saying is if someone wants to get married, yes, someone wants to get married.
What is a such a necessary condition? Condition? And what is the sufficient condition? So I tell you,
and necessary condition from the Islamic perspective. And some people will not like this is that the person has to be female. There's a man that's getting married in order for the marriage to be valid for validity to happen. Okay, there has to be a female.
Now, many people will be upset by that.
But it's the case the case but is that a sufficient condition? So now, if I bring a female I'm not gonna bring her like you know, but if a female comes into this room, and one of you wants to marry her,
and says, Look, here I am. And here you are. And did you not know that one of the necessary conditions in Islamic law for a marriage to take place is that you be female and I be male? Therefore, the hotel is right next door.
Is this is this okay?
It's not okay. Because it's not a what conditions haha.
Hopefully she doesn't use that kind of language.
Say this is not a sufficient condition because that's sufficient
condition is you need to have two witnesses Islamic law. Two witnesses.
Right. What else you need to have?
Well, according to the Johor I'm going to put J Welly
Okay, the Hanafi is don't actually believe that. Okay, for the sake of argument. What else you need?
Ma? You guys need to know this.
For more reasons than one
Not just logic here, but for life as well. These are the three conditions I caught that actually are can they call it our cat but really pillars of the cat
these are the conditions you need to witnesses You the man and you the Welly and of course you need her consent and she needs to be a woman as well.
Okay, so that's,
let's say for example, these unnecessary conditions and these are sufficient conditions.
In propositional logic, this is this is basically P. Q, simple as that.
That's how it looks.
Something could be a necessary condition for something but it's not a sufficient condition for something. If I say
in an Islamic marriage if a man and a woman are together
with two witnesses, but normally I don't really Yeah, that's
it's not it does not fulfill the sufficient condition.
You see what I mean? Now in solid sec, very interesting the way that people are the authorities have actually
because there are two words that you will come across quite often. One is called a short the Arabic word for condition.
Short is condition. Okay. And that has a very specific definition
which is the following I'm writing in English and in Arabic
just make sure this I'm writing it correctly Yeah.
It's my ultimatum and Adam Hill Adam. Yeah. What necessitates from its non existence? non existence? My yells mo Minaj. Me Hill, Adam. Well, I mean, would God he would do it well, Adam. So what necessitates from his non existent what necessitates from its non existence? non existence. So zero equals zero. If it's not there. The thing will not be there. In the in the case of the hokum, the ruling will not be there. Yeah. Well, I Elsa woman will God, actually it's not necessary. Yelder means necessary. Them Taylorism means necessary. What is the move? Meanwhile, Judy, would you Well, Adam.
So if it's, it's labeled demo, it's not necessary that if it's there,
that the thing the hokum will be there, or that its non existence will be there either.
I'll tell you an example. Actually, we just use an example.
Yes, but we can give you some examples of some of the some of the examples they give for the sharp
corner we can we can look at what the standard example for prayer and stuff like that, man, and by the way, a man preventer is the opposite of a shot. A preventer is exactly the opposite. The suburb, which means cause and Eric Yeah, so this is the condition.
met. Basically the same thing males and woman Adam Hill may or
may as a woman Madami law, Adam. Well, the mu is not well, I am here it's well. Yeah.
Well, that will mean we'll do the he would widen. So it says Well, let me shout it out. It's easier for you.
So okay, let me write it down. So don't get this wrong. Mail demo. I'm going to tell you what this means.
Which means if it's there, if it's there unnecessarily, yes, the thing the outcome will necessarily be there.
So it's stronger a sub is stronger than a shot a condition is so in a sense, this is this is the short is a they both conditions in one sense because they both have an IF structure, but the short is a condition which we could call it a necessary condition, whereas the sub is a sufficient condition.
Okay, so my other woman will
Judah Hillwood. Yeah. Which means that when it's there, what necessitates from, from its existence, the existence of the thing?
Well, I asked them when we do the sorry.
When we went when Adam Hill, Adam, I mean, if it's not there, the Hakan will not be there.
Adam yHI. And Adam,
the reason why I'm bringing this to your attention is to show you that this logic is part of Islamic law, actually, the necessary and sufficient conditions is effectively the difference between short and cyber, you cannot be a *y and not know this.
How, you know, you see what I mean? So someone says, Well, you're not allowed to study logic.
Why are you allowed to sell your soul? Because if you study, you have to study these distinctions, which is effectively what we've just started.
Do you see what I'm saying? So you can choose some of them or not? Some of them will? How do you decide?
You see what I mean? It's problematic for those guys. They, they must not know this stuff. Yes. You could. You could also just argue that or then, if you because you're using God all the time, like you can't speak without using logic. Exactly. So it's a bit daft that you can't does that, you know, I don't know you speak. It's true. But do you see the difference between Charlotte and suburbia? Okay, so the condition here and the cause? Now, this is gonna get I'm gonna give you a little bit more complication here. Is everyone comfortable with this festival? Any questions? Because this is pretty simple. Okay.
Yes, this was early said he doesn't trust any of that logic, probably. Because if you don't trust any member, he put his epistemological beginning inland was just like a book of a soul. So he put a logical thing in the book of a soul to show you that the two things are not divided. Yes. So I'm sure isn't the necessary conditions. suburb is a sufficient condition in Arabic. Yeah, pretty much. I mean, not not, not in Arabic, not the language. But in the the or solely definition. Okay. Effectively, that's what we're talking about. Yes. They're talking about the same thing, when, when also when we say my yell demo, when we when Adam 11 years ago means is necessary that if it's not
there, that is not going to be there. So which means as a sub is stronger than a shot,
because it's a necessary condition, whereas that was a sufficient story. It's a sufficient condition, whereas the shelter is necessary condition. That's effectively what we're talking about here. Now, let me make things a little bit more complicated because even Cena
and Aristotle, both of them have written logic handbooks, okay.
Probably the best of their times, quite frankly, yeah. And it was, you know, makes a very good point. And the point is going back to this idea of sub, a cause because when we talk a lot, everything that we can understand, everything that begins to exist has a cause and all that stuff, right? We assume that we're talking a cause is always a singular thing. Do you see what I mean?
Now, if I say a causes are a singular thing, what is a cause? definitionally. A cause just to make sure that you guys know is something
even addiction is how it defined is something which brings rise
Yeah, now, something which brings rise to phenomenon of phenomena. If I say now, look, I'm going to put this lit
on this pen.
No problem here.
Maybe I'll do this first, just to make it look good. Yeah. I'm gonna do this. I'm correct. So what is the cause of the lid going onto the pen like that?
Yes. Okay. You can argue, cause what what caused the lid to go on the pen?
Okay, so let's be specific. You said you Okay, fine. Let's be extremely specific. Let's be
okay. Okay. All you see
is the force physics, whereas the physics, okay, sorry, the physics Yeah.
Can you tell us what's going on here in physics terms? Your muscle is precinct flow. This is Office, this is biology.
Come on, tell me what's going on your muscles are producing a force which counteracts the gravity of the pin
of the lid. And that allows you to hold the lid up and 40 So let's just call it force for the for the layman like me,
force. Okay. So that is you can call that in a sense, efficient cause.
Now, the thing is, you gotta remember Aristotle divided causes into four.
Yeah, who knows what they are?
This is a very technical, very technical question.
Yes, Aristotle, and this has been used throughout the years.
Haha, the form will cause the form. So what's the form of this pen? Whatever cylindrical shape is, right? That's the form of this. Okay, fine. What else? You got sufficient? No, no, not sufficient material cause Okay, brilliant. So the thing is, if you consider the fact like, let's be real, we, Annie, I can't do this unless there was a plastic cylindrical piece of a tip of a pen that I'm holding my right hand. And then a cylindrical. Rest of the pen, which I'm holding with my left. So the lack of existence when we say that, what's the cause of something? I can't put this on this, unless either of them exist in a material form.
So if I were to ask you again, the physicist, you know, how does this do this? You're talking about the force, and that's more the equal the efficient cause? Okay, what's going on the actions, okay, for the efficient cause? No problem.
Yeah, and the last one is called the end? Cause, by the way, yeah. There's four causes visually efficient form material. And cause these are the four causes that Aristotle talks about. The reason why this is important is because as you can see dimensions, actually, it's not one cause that does anything. It's a combination of causes, that causes something to happen. So if I say what happens when
I'm putting this tip on the on the on the pen?
It's not enough for you to say, well, the cause. And when we say caused by unnecessary cause, a sufficient cause is one of those things, if you want to be very detailed about the matter, we'd have to mention everything. Because everything is there. Obviously, if someone says, or any one of those things wouldn't be false, wouldn't be false information. Is the reason why this pen.
The lid go on the pen is because you put it put it on there with the force, action, whatever. What's the what's the, what's the formula for it, you know? Oh, yes,
F equals what was M I? m is mass is acceleration. Beautiful. I like this kind of things. You said that really quickly. I'm very impressed. F equals MA, if I say, look, F equals, and I tell you the numbers and stuff like that, and this is what it is.
I wouldn't be speaking alive today, with your physics teacher have a problem with me. If I told him this, he would not.
He may have problems with me for other ideological reasons.
But he would not have a problem with me on this basis. But I'm saying that if you mention any of those causes, it's fine. You know, the material cause the end cause the efficient cause, whatever these are all fine to mention, in combination, that's the most elaborative
this, you know, thing, you see the cause of this pen, and you saw everything, all the kinds of causes.
You see. So now what we've talked about just quickly, is we spoke about the difference between one word first and foremost,
necessarily sufficient cause and then we spoke spoken about the difference in effect between one one
shot and sub and what we said is, really, and truly what the logicians are talking about in this arena is effectively what the same as what these guys are talking about this arena, because they're talking about yelled and yelled and yelled demo, which means what necessitates Yes, it means the states. And what is the definition of sharp is without necessity and definition of sub is with it. But then we said a sub was a cause, and as a cause one thing. Now, according to Aristotle, and those who came after him, it could be a combination of things, which include what
the, yes, the material cause the form of it. The efficient cause, which is the most talked about caused, by the way, and if people speak about cause as a shorthand, easy to write efficient, cause
efficient goals? Yes, for example, yeah. But then obviously, the material itself and stuff is also the cause, as we've mentioned, yes. And we spoke about four different kinds of causes. And these are the famous Four causes of whom?
Aristotle, who's the first person who mentioned so far, so good, yeah. All right. So why don't you see for the next five minutes to be the person next to you speak about thing, give me examples of things, which this is this if this is the sufficient condition is the necessary condition of it.
And this is actually very useful and applicable in daily life.
You know, I mean, because if you if you have a conversation with someone, like for example, if I say, if I say to my son,
I'll take you
to the play area.
If you do your homework.
Effectively, he can do his homework and say, look, it's a play area. So I didn't say that was the only thing
as a necessary cause, but not I mean, when I was going to do this, it's a bit but technically speaking, technically speaking, this is true.
If you do that, but I didn't say that's the only thing you have to do.
There could be other things you must do for the cat to be valid. These things have to be in place. Does anything else need to be in place? No. Can a cat be valid? If someone brings a WhatsApp group and brings two friends and gives them a hug to the woman? And says, Bring your father on the line? Yes, it can be valid the colons, the majority of people cannot take two minutes. Yes.
Can but what if he doesn't have the two people? Okay?
This is a problem if you don't have the two people.
So how easy is to get married in Islam?
Anyways, with that being said, five minutes, that was one example, maybe a non Nica example. And then tell us in five minutes
so let's just do a quick revision of something right. We said modus tollens Yeah.
remembers a formula that
if p then q naught Q
Okay, what's the key words here? Not and this is how it's you know, symbolized in logic. The knot is like this as you guys have seen before, like that, yeah. Okay. Be careful, because
there is if you try and affirm this is not the case. Let me explain how if I say modus ponens, modus tollens is if P
then Q. Yes, not what not Q Q therefore not p. Therefore
not p. Okay. If I say, if p then q.
And then I say q
So I've done here
second one, yes, this is called the consequent Yeah. Because this this is called the antecedent and this is called the consequent, the antecedent is the anything which is comes before it's called the antecedent.
This is called the consequent, because it comes after
consequent is the antecedent, this is called the consequence. This is a logical fallacy.
And, by the way, in sort of some have tried to use this kind of logic in what some refer to some as more formal wahala
is incorrect. Some, logically a lot of people says, it doesn't. Let me give an example. If you say,
let me give you an example that I found online is good one.
The light is broken, therefore, the room is dark.
The room is dark, therefore,
the light is broken.
It doesn't follow
that if this is this, this is this. Does that make sense?
This is the incorrect form of my form Khalifa.
There's a difference between the correct form of incorrect form a DUA, what?
Can you do nothing wrong with that? No, you can't. Because there's other forms of ibid, which will not die. Do you see that the point? That's a great example of fact, because if someone says a black hole I bet this application is worship is all of worship something so if there's no application, does that mean there's no worship?
Not really. So Muhammad Khalifa, because someone could do zakat. He's still doing worship. He's no joke. He's still doing worship. Someone can do something else you can still do in worship. This is an incorrect form of mahalo. Now go back to Al Hassan Ali. And these guys see why important to study logic?
Because they actually use some people some folk Aha, you'll find that they use this kind of logic.
Big time is, so this and that. That's why if I'm correct me if I'm wrong, but I think he hasn't. He denied the whole concept. Is this. Right?
I don't know. Maybe he did. I'm not sure if he did, or no, but Mr. McAuliffe there's there are some types of visual acceptable. This type is definitely not acceptable. Why? Now, this is a very technical question. Let's use our minds. Why is it not acceptable? Go back to the difference between what also is referred to as a short and a setup
is connected by the way you don't provide a sufficient condition. Yes, that's right. That's a very good answer. I was surprised to see this is very good. Teacher, huh? Because it's not. It goes back to the idea that we just spoke about
The difference between the necessary and the sufficient.
You see what I mean? Because it's not a sufficient condition go back to the light. In the room example, the light is broken, therefore, the room is dark.
So then I say the room is dark.
Therefore the light is broken assumes what? That the light is the only thing that can shine up the room.
What if I open the curtains like that, and there's a beautiful moon, and it's in his all his glory, and is shining even more. So a sun, the sun itself, or something, it can bright, a bright, shining up the room, right? lighting up the room. You don't need the candle or the light. You see what I mean? So the idea that if p then q q, therefore, P is actually a logical fallacy in propositional logic.
This form of my formal Mohalla
literally is incorrect. But there are forms of it, which can be correct.
But there would have to have a symbiotic relationship.
That's the only situations which that can be okay. It would have to be a seesaw relationship. A equals B and B equals A, we're talking about by conditionals. And stuff like that, where you literally this equals this, and this equals that. Apart from that, this is affirming the consequent it's a logical fallacy, actually.
It's a logical fallacy. You can't say just because if p then q, q, therefore p.
So logical fallacy, in fact, does this make sense?
So it's just one way
says P, then Q, you can't Yeah, that's what we're saying is unless there's good reason for Yanni for it to be both ways. Yeah, sorry. I would say if I visit London, then I visited England. Yeah.
I visited England, and therefore I visited London. That's what we're talking about. Oh, that's all right. It's not sufficient. No, it's very if I visited England, and I visited London, no, if I visited London, I visited England, that's fine. That's modus ponens. If I visited ingredient Q, P, therefore Q, that's what you're saying that's that's modus ponens, that's fine. But if I say I did not visit England, therefore, I did not visit London. That's fine. That's modus tollens. If you say if P, not q.
First examples affirming the consequent he said, If I visited London,
then I was in England. Then the second premise is I visited England. So he's affirming the contract. Therefore.
Look, remember, remember the difference between modus tollens and affirming the consequent? It's a very fine difference. What's the difference?
If we said if P, let's go to modus tollens. Again, what's modus tollens? if P then Q. What is it? Not q not q, therefore not p. See the difference between modus tollens and affirming? The consequence is what is negation?
That that's effectively the difference negation.
But in this scenario, I think in premise here, premise two and a conclusion.
I'll just say in this example, the negation is true or correct. Whereas the other way around, it wouldn't be true if I said, so. For example, I visited London, therefore I visited England. I visited England, therefore I visited London. Start with a conditional if I visited London, I visited then I visited England. Yes. Yeah. Then what you saying after I visited England, I visited England. Ah, okay. Yeah, it's positive. It's Aha. And it's negative. It's yeah, if you're saying that I visited, you're putting the conclusion. You're saying that you're putting the consequent first. Yeah. Yes. And that will be the logical fallacy because now, if you go here with the logical
fallacy, remember, if you remove the negations now we're removing the negations if p then q, q.
That's a logical fallacy. Yeah.
It doesn't have to be sufficient. Yeah, that's better. Yeah. If you if you now make it good, if you make it England and so because if you say London this is true statement, right. If you haven't visited
London, New England, and then you got this is confused with matter. England, deficit of London. That's, that's the fallacy. Yeah.
It's true in terms of this form. Yeah. Okay. You want to you want to practice this, because this is a hard one.
I'll give you guys five minutes practices. So I want you to do the following. Give me one modus tollens and one affirming the consequent and show me the difference between the two. In one exam, just one example. And we're nearly finished guys, you know, I noticed is like very difficult. I mean, not very difficult, but it's it's just dry and stuff like that. But it's interesting as well, because when you start applying it to things for marriage
You know, gods exist argument for God's existence, it starts to become quite interesting then. Okay, let's, um, before we move on to the next stage, let me ask you guys, what you've put your hands up if you want to present. Yeah. If you eat kosher, you've had a caloric intake. I've not had the caloric intake if I've not eaten. Excellent, we're gonna do really good. If I could surely I'll have a caloric intake. I've had a caloric intake there five ecotric, which is not true, it could be something else. Okay, I see what you've done there is you've attacked the Egyptian culture.
Crucially, the magician and we I think there's a new there's a new restaurant now in Agile row, but very good. Excellent. I'm liking you're doing very well today, by the way. Any other any other things? So you know, you understand? Effectively, I want you to link in your mind. The idea of affirming the consequent with, with what what was the other thing was was about?
Modus tollens. No, no, that's the right way of doing it. But what did we do right before it?
necessary and sufficient conditions?
Because I want to just say this one more time. I like this example. I've found online.
This room. If this room is
the light is broken.
Let me just get the exact thing.
If this room.
If the light is broken, if this room is dark,
this light if the light is broken, the room is dark.
No doubt if I break this light now, and that light, the room will get dark. Let me just actually
you want to switch? Sure.
Okay, is it dark? No. Okay, yeah. And it's darker than it was.
Okay, okay. Now, put them back on. So, Yanni, just in case, anyone had a problem with my had to do an experiment, if I switch off the lights, the room will get dark.
But then if I say the room is dark, the room is dark, therefore, the light is switched off.
It doesn't follow.
Because it could be dates. It could be the light switched on, but it's flickering. Anything could be and goes back to what necessary and sufficient conditions.
The light doesn't have the power if you'd like to determine the brightness fully to be the only factor that determines this thing. Yes. I hope it isn't derailed the floor. But what's the difference between a logical fallacy like we've cited and like a really unsound argument because yeah, one is it doesn't fall rules or differences, the premises or whether it's true or not. I know in that sense, but like when you see an unsound argument is our base is valid and stuff like this. Yeah. But that's what the fight is. That's where you have to use your that's where that's where the fight is. Yes. Well, that's what the debate is,
isn't logical fallacy, not when you come up with an incorrect conclusion. So we're using the parentheses was, what you were mentioning, is because the parentheses aren't true, like when it's an argument. premise. Yeah, I mean, remember, every every sound thing is valid, but not every sound argument is valid, but not every valid argument. Sad, in fact, unnecessary, unnecessary condition.
Okay, and necessary condition for argument to be sound is validity. But it's not a sufficient condition.
Let me put it this way, because many people will be watching at home. I want this to really come into their minds and into their hearts and for them to understand. Many of them have gone through heartbreak a woman has hurt the hurt them in their life. If I say look, if Leila is for the sake of argument, call her later because she's associated with that image known and all that. Say, if Leila is not in his life, his heart will be broken.
His heart is broken. Therefore, Leila is not in his life. It's not only later that can break his heart.
Could be so many other women. But likewise, I can do it. That's a negative way of putting if I put a positive way. If Leila is not in his life, he will be happy or sad or whatever. Yeah, let's say he'll be happy if Leila is in his life. He will be happy. If Leila in his life.
Then if I say
he is not happy, not happy. How do you tell me actually I should I should be. I'm doing all the work for you. He is happy. Therefore, Leila is in his life.
Yeah, I mean, she's the only one that can make him happy. Yeah.
But this individual logically is not right. It is what you say to him.
Because what he's done here because he thinks he associates all of his happiness with what? With the one woman, he thinks that she's a sufficient condition for his happiness.
He's wrong about that as a logical fallacy, because he's done before Mukalla. You see the point? It can be when someone is in love, they think it's the only thing that's making them like that is the person.
But do you know what I mean? So hopefully, that's closer to her. Okay, let's do by conditionals. Quickly, guys. Yes, yes. Affirming the consequence. Consequent makes it not valid.
It removes this validity.
Before you touch soundness? Yes, exactly. Yes. Yes. Yes. So if we do this, the argument is not valid. Yes. Okay. Yeah. Perfect. All right. Now, there is a point where I think this is the only point in logic, where actually, you can do move from Halifax. I don't think there's any other way you can do from Halifax logically speaking. Meaning is the only way that if A is B, B is also a, well, the opposite is true.
If you say this, then it goes back the same way, which is is what is referred to as a biconditional.
And it takes the following
I think they also put an equal there, I'm not sure
if it's true. So if p is Q, if p equals Q, Q, n equals p, but we're talking about the same kind of values here. So let me let me give an example. Right? As I found some line, it's a nice nice example.
A rectangle is a square, a rectangle
is a square.
And this is what they use look if and only if
I don't use this phrase. Unless you know you're gonna speak about by conditionals Okay.
A rectangle is a square if and only if yes, it has adjacent sides sorry Oh, oh if and only if the adjacent sides are congruent.
So go b Now,
a rectangle is a square
then the adjacent sides are congruent.
So you can see now there is a full Mohalla there is a bit of that is coherent if you go A then B B then A, that's where it does go both ways there, that's where there is a symbiosis. I'm feeding you you're feeding me the same information, the same values.
rectangle is a square if and only if the adjacent sides are congruent if rectangles or square than the adjacent sides are congruent
works both ways.
Because the sufficient conditions are met on both sides.
Do you see what was happening here? But this in order to distinguish whether the thing in question is
this is applicable
you or not, in fact, you have to know the values very well.
So Ivan hasn't. He mentioned this is where people make the biggest mistakes with in my form. However, it's actually this idea of affirming the consequent by conditionals. The symbiosis the A equals B, B equals A P equals q, q equals P is where the majority of mistakes according to hasm Landrieu see the biggest one of the greatest minds in Islamic history make problems when they do can. Because they assume that if p is cuter than a firm the consequent, then the opposite must be true, but then it's not applicable. The consequent is not to be affirmed this situation. But when is it to be a fund is when there's sufficient conditions on both sides. But how could you prove as a
*y as an Islamic jurist that the sufficient conditions of both sides
you have to show through evidence that that is the case.
But most folks, they don't attempt to do this. Why? Because many of
Around been trained.
As long as I mentioned, in this situation, some of the things
to talk about this.
It's not just selfies, and now we believe this to be the
athlete he mentioned in his salon menolak.
You mentioned that no, he says this and listen, it's not just selfies that believe that it's not magically Audi and ABA.
It's not just those No, it's the Annie. I'm just saying is also in the in the tradition is some prominent people from all schools had an issue with, but then they fall into mistakes.
Mistakes like this.
Do you know what I mean? So okay, now you can't you don't need to fall into here to save resistance you. We can't afford to fall into mistakes like this. Jonnie, this is not a matter. This is about covering the man.
By conditional this one, the ACC wants to try and leverage you and twist your arm and stuff like either no, this is this and this and use the language. Anyway. Any problem with the conditionals or the biconditional. Any questions on it?
Yeah, okay. That's a good I mean, like a do like a sherry example, like, what mistakes?
What mistakes? Yeah, like, what mistake that's a really good that's a really good question. I'm not right now. Nothing has come to my mind. I don't know what we're, let's go open the books. Everyone hasn't See how he's here. We got one.
I mean, maybe one thing to verify, but it hasn't. He did have an opinion on that. The,
the, you know, the Hadith I mentioned that the the silence of the female is a consent. So he saw this as biconditional. So he saw that if she actually does consent, and she says yes, then this actually notifies. Oh, really? Yeah. Also he just his own case. I thought he's the guy he's,
yeah, he might. Yeah, there you have it. He's doing care. So that's it. I think I remember that. Masala. Interesting.
Anyway, because even hasm is a school of thought he doesn't believe in chaos, apparently, and so on, you know, in theory, but yes, the biconditional thing, is there. Any questions?
What did you say? You want to say? Another? What was the example you use last week? Something about?
Coming up with an example you use a good one? Is there any any other genre use more examples? You want more time to think of examples for this before? Because I'm weary of the time and we need to do one more thing, at least, was the feminine antecedent or feminine antecedent
messages name as three like
Muhammad Abdullah, Mohammed bin Abdullah, if his name is Muhammad Abdullah, then he's the man he's the man. Yeah, okay, fine, because he is a sufficient condition for him. But it's not no, no. It's not sufficient for him to have that name to be the matador.
And this is a Yeah. So how would you put it in a way that would make it
he would also have lucky the other conditions as All right. So yeah, so that one that would work?
Maybe Matt can the place of pilgrimage for Muslims give me you show me the knot place?
Mecca, is the place of pilgrimage for Muslims if and only if it was the month of Fallujah is the multiple hijra, that was the place for pilgrimage for Muslims. MCUs is the place where pilgrims for Muslims, you'd have to put my camera, you'd have to form it right? Because you'd have to go back in both.
Yeah, think about it. You're on the right track for sure. Yeah. This is difficult to get Yanni most situations. And by the way, I was reading a book by Mario bungee about causality. Yeah. Mario bungee is a great hero hope thick book on causality. And there are different kinds of causality. There's retro causality, there's this. And there's one is like, symbiotic because if A equals B equals A, it's a bit like a seesaw.
Like, for example, you have a seesaw. And they both cause each other money. If I if I, if I go on this side, this other person goes here. And they both kind of weighing each other out.
So that that kind of causality can exist, A equals B equals A, but exists within a closed system.
Do you see what I mean? I mean, it's not an irrational kind of causality, like a equals b and b equals a.
Yeah, if there is that, but it's within within certain contexts, or some sources while the universe calls you and you call the universe. It doesn't work like this. Do you? I mean, you'd have to specify the context in a closed system, you can have a equals b, b equals a. And that's why it's important for some arguments for God's existence and suffer as well. Yeah. All right, let's do
let's do affirming the.
Actually one more thing before we do affirming the antecedent, which is, I think, probably the last thing we're going to do
Now what did we say conjunctions were last time if you remember.
Okay, you can
Not having the data the conclusion.
Does that make sense? So if I say, Look, I'm drinking this coffee, and I'm drinking this green juice. I have both that
P I'm drinking this
Q is I'm drinking green
and P and Q is I'm drinking both. Now I don't have to do this.
But yeah, we do get on Friday. That's all as always. Okay, simple as that. I know, sometimes we think we do something. This is the easiest one in the book.
Okay, now we're gonna get something a bit more difficult though.
Remember, we talked about
affirming the consequent? Okay. Which was hard, okay. In a sense that you're not going to get the first I gotta think about it. You have to grapple with it your mind? In a sense, it's hard if a proposition logic is hard. Okay, the other types of logics, in which case, this stuff is all easy. But
we said that affirming the consequent is connected to Modus wha.
Let's just recap one more time. So what's affirming the consequent?
What's the form of it?
So if p then q, q, therefore P.
Q, therefore P.
That's wrong. That's wrong. So how do we make it right? Not Q therefore, not p x. Okay.
We spoke about why that's the case.
affirming the antecedent. Now, we said you've got two things. We always talk about p and q, right? Where is the antecedent? Where's the consequent? P is the antecedent. All right? So we spoke about the consequent, which is this one, right? That's the consequent. Now we're going to just spend a little bit talk about the antecedent here.
So now let's talk about the antecedent.
There's a fallacy called denying the antecedent.
So how do we deny the antecedent we say the following.
if p, then q, number one, if p, then q. What does it sound like? Already?
Modus? ponens? Yes. The first thing we went through, if p and q, p, therefore Q, but instead of saying the right thing, we're gonna say, not p.
So what we're denying here?
Yes. So we say therefore.
Not what? Not? So I shouldn't do both. Not Q?
Not Q. Wayne. Now?
Do I have a right to do this? No, no, I have no right to do this. Because of similitude of me doing this will be like saying the following.
It's like saying the following. It will make you a bit humorous so you can understand?
Or maybe there's some truth in this. Let's find out. Let's see from the people.
If you are if you are
safe, you Sapiens team, which all of you are,
if you are Sapiens seem like all of us.
You are a real man.
Obviously, if you're a woman as well, no, of course you can be a woman, but still you're a real man or woman. Yeah.
Not in the that sense. But anyway, if you are a sales team,
you are a real man.
Let's just say pretend you're not, unfortunately, say you haven't declared your interests or your
you haven't declared publicly that you're safe in steam.
Therefore you're not what?
This is embarrassing.
This cannot be doesn't follow. This is too much. Because someone could argue there's other ways of being a real man. I know. It's it's a very difficult argument to make. But nevertheless, it's one that you can make. Because it goes back to what and what, for example, London, England, and I've been to London. I've been in England. Yeah. I've not been to London. If I've not been thinking that that's not true. You could have been to Manchester and yes, and but Yes, beautiful. Excellent. Yeah. But before we get to that example, I like that. I want you to ask one to quit one answer one question. What are we doing here? What's the issue?
We're assuming that being classy consumers are sufficient. That's it. That's the one that's the way it goes. Everything's going back to what sufficient and necessary conditions see why that's important one, because it affects the consequent affirming the consequent and also denying the antecedent. The two
Probably the most important
logical, formal, logical fallacies that you can fall into.
Because they're, they're correct for modus ponens and modus tollens
rectifies the issue also by conditionals, rectify the issue, these are the so you got two problems and you got two problems and many solutions.
But here the problem is this if you are if I say that looking for example,
actually, I should be asking you at this point, I've given you my example. Yeah. Can you give me an example of this, of denying the antecedent. So, yeah, if I am the Imam, yes. I read the prayer. I am not the Imam. Therefore,
I will not read the prayer.
Not the Imam. Yep.
Therefore, not the prayer. Yeah.
Not lead the prayer. Not lead prayer. Yeah.
Why is this wrong? Because I denied the antecedent. Yes. And I've seen is this one, right? Yeah, I am.
Yes, excellent, beautiful. One more example, just to call it a night because this is a lot of hard work here today.
One more example.
If I am a dog, then I am an animal,
dog. Therefore I'm not an animal.
And this is how children reason, honestly, will lie. This is how dumb people reason. They always use their stuff. They always say the stuff.
I've had to have lots of debates with five and six year olds. And this is always they always say this.
So I say look, you know if you don't do this, and this and then they say, Well, that means if you don't know doesn't,
it doesn't fall because it's your
I don't want to say that I say children includes adults as well.
A lot of people argue like this. And they just don't understand that this is fallacious reasoning.
But now you can explain it to them.
So are you saying, you've seen that famous
interview with Kathy Newman, and Jordan Peterson, if you knew logic, he would have torn her up in a different way. Say this is a logical fallacy because you're denying the antecedent and because you're affirming the consequent. And she does it all the time. So you're saying
when she says you, so you're saying and she brings a lot of the times I haven't assessed the transcript, she's denying something, she's denying the antecedent, or she's affirming the consequent. If you said it like that, it would have been even more technically catastrophic for because you're explaining to them why they're wrong.
So you're saying if you don't believe in this or not, doesn't follow that that way, because you're confusing, sufficient and necessary conditions. This is going to be so useful to you when you're debating people or speaking to, even in everyday life.
You get that one a lot.
If your female friends, I can have my friends.
You have your friends, then I can have my friends in something like that, you know what I mean?
But it's come from a female, I guess I'm sure that's I mean, that's why if you look, no one male, female man or child
can deny the laws of logic.
You cannot deny, you know, you cannot deny on that bombshell. We have done the second lesson of Arabic or sorry, of logic. And the next one, we're going to do a little bit more. Little Morgan to introduce the concepts, logical little humps, we're going to talk about contradiction, the truth conditions of a contradiction, because we always talk about what is a contradiction? So you're contradicting yourself. But the question is, how, what are the conditions that must be met? For someone to contradict themselves? This is a very profound question. And one frankly, which, you know, propositional logic doesn't do as much as Islamic aid logic. They dealt with that almost every
tract of Arabic grammar logic, they speak about the cause of conditions should also turn our code or the conditions of contradiction. We're going to go over that next session, we're going to finish this up. We're going to do that once you come out of this, you're going to have a sharp mind. I'm hoping so. You can use it in three sessions and already like you know, you can you can cause damage or most of you have come a long way. So imagine 30 sessions, imagine 300 sessions, because we will know that if you're part of Sapiens team, then you are real man.
It doesn't follow that
If you're not part of Sapiens team then you're not a real man but you can be a real man real woman rule supporter make sure you like and subscribe and donate and come back and tune in was salam aleikum wa rahmatullah wa barakato