Propositional Logic – Part 1
Channel: Mohammed Hijab
File Size: 51.23MB
Salam aleikum wa rahmatullah wa barakato. How you guys doing? And welcome back? It's been a long hiatus. We haven't seen each other for a long time. But now we're back and we're back with a vengeance.
Or not that much of Avengers. We're going to be talking about some cold, hard, we'll call it truths. Yes. Not a profound truths today's more logical truths. And we're going to be covering logic. And logic actually is not one thing. It's not a singular, especially when it's been studied here in the West, it's not it's actually logics, there's plural, there's more than one of them. In the sense that you have propositional logic you have predicate logic, you have different kinds of logic. We are going to be covering propositional logic. Why this is really, if you do a philosophy course in the United Kingdom, in an undergraduate level, you will have to go through a module in propositional
logic, even if you do a computer engineering course. Many of you may have done this will have to go through some level of propositional logic.
It's not that hard, actually, it's pretty easy. And in fact, surprisingly, so.
In propositional logic, there's about seven or eight important rules that you need to know. Yes, they can be sub compartmentalized into more than that, you know. So for example, we're going to be covering the syllogism. There's different kinds of syllogism, this hypothetical syllogism says, there's this kind of situation that it's all cut, we'll cover that.
But really, and truly, there's not much to it. So I'm going to go straight into it. In fact, before I do, so one thing I will say is that there's something called Arabic logic. I mean, it's called Montek. A. And it's important because we're in Sapiens, and we have Hamdulillah,
access to both the Islamic tradition and the Western tradition, that we try and include that in our sessions. Because logic is, obviously as you guys know, was first kind of
canonized or whatever, like into books and rules, and all those kinds of things by Aristotle and, and others before him, but mostly by Aristotle, in the holistic period. And then the Greek period had a lot of people writing and talking about it. Then again, when the translation movement happened in the Arab, or let's call it the Islamic region, because actually include the Persian including all these other areas, there was lots of books and tracks, logic tracks, actually, the Islamic scholars and thinkers put put in place, Ibn Sina, in fact, in the jet, he has a whole section, dedicated to logic, I think, is one of the best ones out there. But also, highly famously, he's written much
about logic and our tradition. In fact, he said that if someone doesn't study logic, you can't trust him. You can't trust his mind. You because there's something logic is meant to stop you from making errors and blunders. So if someone doesn't go through the basic rules of logic, you can't trust him. And he's written in Arabic, many different books like Mac another, for example, is one book that he wrote. It's an introductory book on logic. Obviously, in his mostest, I had like an epistemological beginning, but he's written things in logic and Arshad Ashari tradition, there's lots of things written in logic.
And even in the humble tradition to some things, I mean, although it's more critical, well, that criticality is actually very interesting with most prominently even Taymiyah. Doing a response on logic, I'd really want to create a response to the logicians or the Greek logicians was actually translated by well Haluk been translated into the English language. But we're not gonna go into the history of it today, I was just giving you a bit of a flavor. So you understand. The first thing we're going to be going through is propositional logic. And I'm going to be using the board. And it's going to be an interactive thing. And we're all going to be getting involved in some of the
questions and some of the examples.
The first thing I want to cover is the following. There is a difference between what is referred to as a valid argument
and a sound argument. Now, these are very important key terms, especially in polemics and discussions. What is the difference between the two? Does anyone know?
A valid argument is an argument which is logically valid, but there is no truth in that argument. Perfect is very good, right? So a valid argument is an argument which obeys the laws
of logic. Yes.
That's what a valid argument is. A sound argument. Yes, it must obey the laws of logic. But all the premises must be true. And this is a key term. So what do we have with an argument we have premises and a conclusion?
Okay, so each premise must be true. In order for anything to be true, I'm not going to cover the syllogism now, but let's just for the sake of argument, say the following thing. This is a very famous syllogism.
every man, every man is mortal.
Yes. Number two, Socrates is a man.
So what would we say here for three? What do we say here? Therefore, the conclusion is Socrates is mortal. Therefore Socrates
is mortal. Okay.
Now, do you think?
Is this? Is this valid?
Is that I mean, what do you think is? Yes, it's valid was? Is there any inconsistencies in the way this has been? There's no inconsistencies? Would you say it's true as well? Would you say it sound?
Yes. Okay. So this is an example of an argument, which is both valid and sound, which gives us the following principle, which is that every sound argument is valid, but not every set valid argument is sound. So let me give you an example of an argument which is the opposite. In a sense, all right.
Well, an argument which I'm not gonna tell you what kind of argument let's just say all unicorns for the sake of argument, all unicorns are white.
Fairy is a unicorn fairy is a unicorn.
So is there a problem with this argument? What?
It does seem like a valid argument.
You're, you're implying that it's not a sound argument. But some would argue that you can make propositional statements about entities.
Yeah, okay, fine. So you can say the sound, the soundness of the argument is disputable. You see? So this leads us to the following point, which is that I can't disprove the existence of unicorns here. I mean, Joe, I mean, for me to say this is not sound, I would have to say unicorns don't exist. Once person sees a unicorn and says, Oh, this fairy and you know, can make something. But you can at least say the soundness of the argument is disputable. You see what I'm saying? So but it's a valid argument, which is the main point, you can have a valid argument. And it's possible for it to be valid and unsound as well. Or it's possible in most cases, you'll find this where the argument is
for it to be valid, and the soundness is disputed.
And why do you think that is? This is a question for the group. Why do you think it is
that the soundness of an argument will be disputed, even though the validity of it is not? Yes, people have different understandings of truth. Okay, so it could be an epistemological thing, okay with different understandings of what truth is. But let's think more clearly about what how do we derive our premises? Effectively, how do we derive them?
Empirical evidence? Yes, exactly. Right. Unless you're doing mathematics. I mean, effectively mathematics is deduction. You could say, mathematics is tautology. So if I say for example, let me give you an example. You know what tautology is, tautology is saying the same thing twice, effectively. Yeah, that's a tautological statement. And in propositional logic, is it's actually represented with
with this particular symbol, T, is only true tautology.
So if you say the same thing twice, you're being tautological about, alright. So if I say for instance,
two plus two
equals four. Now this if someone was looking and seeing some Christian missionaries, this is what they're doing sapiens.
Right, this is the level that we're at here.
You see, see, look, this is what they have to do when we're dealing with heavy stuff. Two plus two is one thing, right? You this is one expression, let's just say let's for the sake of argument, call it a linguistic expressions. Why not? This is a linguistic expression.
And this means equivalent, right? And this is another kind of linguistic expression.
In a sense, this is synonymous to this.
You know it's a synonym.
A synonym is when you say the same word with different, same meaning with different words. That's what a synonym is. So two plus two is equivalent to four. So you're saying the same thing twice. So mathematics is a kind of tautology for the most part, but it can be kind of deduction. Now that's one field where
You can deduce something without requiring extra mental empirical evidence. But for the most part, and of course, if you if you bring intuition into it, and that's more of an epistemological question, for throw and all that kind of stuff, you can make an argument. But for the most part, you'll find that most of these arguments that are being made, yes.
Actually are made.
They are made with premises, which are inductively found out, you find out this thing due to looking and observing the universe.
Yes. Okay. So that's, that is very important. The first thing we're going to go over is something called modus ponens.
Okay, now, this is the form of modus ponens if p, then q, p. Therefore
yeah, there's just just pretend that says Therefore, Q Okay. If P entails or implies these are two key words entails implies Okay.
P therefore Q now, this is the valid point valid, no doubt about it, this is consistent. if p then q, p, therefore, q is going in one direction. What is the start with?
What's the operational word?
If so, what is this called?
is called a conditional a conditional.
Now, this is extremely important. We use it in language all the time.
In Arabic is low.
if in English,
if p then q p therefore, q so let me give give you an example of it. And what we're going to do is we're going to spend five minutes you're going to construct your own ones. Yeah.
I'm gonna give you an example of a valid one.
Hopefully it sounds as well.
Let's see if it is out.
you attend, you attend
you will be
let's just say a force to be reckoned with. I'm not gonna write that all down. It'd be a force to be reckoned with.
Sapiens classes, therefore
forced, you're forced to be reckoned with. Would you say that's a sound argument? I think that's both valid and sound. But having said that, you see how easy that is? It's really as simple as that. Now, you may argue, okay, well, how do we know what's valid was not valid or sound, we know how it is because then we can start arguing okay, this is a premise here. This is a premise. If someone has a problem with the premises, I don't actually agree with the premise.
Can you prove the premise can you justify the premise This is where the fight is, this is where the where the argument will be.
So in I'll give you about five minutes maybe 10 To just give three examples, write them down and I'm gonna ask the people have just two or three of these examples from your mind using if p then q p therefore Q. And we will come back and respond or speak about it and discuss together okay, let's come back and let's start with you my as I guess
I heard you speaking in great depth about Yeah, this is an example more responsive yes please Yeah, John is English then is European John is English then definitely is European. Easy wasn't for years it came off so easy. You can see it's got mathematical mindless you also got my half man How about you have your mathematical one. If you go to the gym and train you will become stronger. You go to the gym and train you become stronger. Okay? What is good is right but you've missed out a key word in the conclusion which is what they want to hear it therefore therefore make sure therefore you become stronger Yeah, these keywords are important just make sure I mean even in Arabic II then
that's usually what they put in the low and then E then at the end it then is therefore very important to put that there
less in fact, let's go through everyone Matthew How about yourself? If you pray you succeed. You pray definitely succeed. Excellent.
If I eat healthy foods, I will be healthy. I eat excuse
Simply healthy foods, therefore I'm healthy. Excellent, brilliant. Try and use the same exact language. So don't put exclusively that. It's not wrong, but I'm just Yeah, yeah. You have a funny way. I mean, yeah, if you eat chocolates, you will get bad teeth. So, if you eat chocolate, you know, if I was to eat chocolates, therefore I'd have bad teeth. So okay, there's no problem. But there's, you eat chocolate. Yeah.
If other vices he'll pass his masters Halle revised, therefore we pass muster
if you're living Qh, if you're human, therefore you eh, okay, that one's a mistake here. So let's, let's work on it together. Right? You've, you've added a new premise. Okay. Okay, so let's stick to the same premise. If you are always the first promise yourself, you're living your age, if you're living your age. So what would be premise two? If you want to, if you want to have you age,
you have to use the same language. Yeah.
Think about it. So if you're human you age okay. So, if you got then you just say the same thing again, basically, okay. So you have to be what age living? Did you say if you are living your age? Yeah. Okay. So if you are living your age, so premise two is you are therefore promiscuous. You are you are living you are living. Okay. Therefore, therefore, therefore you age. Okay. So just keep the same language who understood? Yeah. Now?
If you spinach, your strong key expenditure, therefore you're strong. Excellent. No problem. Yeah.
Yeah. Just make sure that the English is correct. So if you eat spinach, you will be strong or like, yep, that's great. I'll make it past and you know what I mean? If I run my heart rate increases, I ran, therefore, my heart rate increased. Okay, but you ran. It's fine. So it's all well and good, but just keep the same tenses.
I run. I run Yeah, I run therefore, my heart rate. Yeah, just for the sake of argument. You're right. I mean, it's, I'm just being pedantic here. But that's how people are going to be pedantic. Okay, let's go for the second rule. And this one is getting a little bit more complicated. But if you guys can do this one, I'm sure you can do that one as well. Why not? I mean, see, look already. We're almost like, let's just say 10% Complete of the main rule that you need for maybe even more, maybe 15%. The next one is Modus. tollens,
modus tollens, Modus.
And it goes in the following way. We start again, if P.
Then q. Same way as the other one did, yeah. Now look, this symbol here means not.
It's in the Gators symbol. Yeah, this is negation.
Okay. Before I tell you give you examples, you try and extract this, I'll give you two minutes, exactly 60 seconds. And you create an example from it. You create an example. So let me just say one more time, if p, then q, not q, therefore not p. So with that, making it a bit more difficult. Try and create an example with that.
Yes, I think all arguments were sound.
If we said for example, if you are a dog, you will become a cat.
You are a dog, therefore you're a cat. That's therefore you will become a cat. Therefore you will become a cat. That's modus ponens. But it's not a valuable Sunday. Yeah.
That's a good example of something which is valuable or sound. Yeah.
Okay, so try and this one's getting a little bit more difficult. And I don't want to, I don't want to
confuse the issue too much here. But be careful with this one. Because there's a very famous logical fallacy called affirming the consequent.
And we will cover that logical fallacy. It's called affirming the consequent.
And if you don't know this, well, you could easily fall into that logical fallacy of affirming the consequent.
So if p then q not not Q therefore not p and rather, this is the symbol for not engaging.
Okay. Okay, John, John, a bit more time to create your example. A little bit more time. Okay. I'll give you 10 More seconds to see
how we start with Mike because he's, he's understood it fully. Yeah. Go ahead. An example. Yeah, example is if John is English, then John is European. John is not European and therefore John is not English. Excellent. Can you see how problematic
This is though, like in terms of soundness. And let me give you an example. I'll give an example of the problematic nature of it in terms of soundness. Yeah. I mean, it's valid. These arguments always valid. Yeah. If I say, Look, I'm gonna use the same template. So to you, because you're quite good at this now, if Meyers, yes.
If Y's attend Sapiens classes, then he'll be a force to be reckoned with. Now watch I'm gonna do. He's not a force to be reckoned with. As it stands, which is not true? Of course he is. But I'm just saying he's not a force to be reckoned with. Therefore, he has not attended Sapiens classes.
But you could you can really dispute this point, you can say, why is it the case that you have to attend these specific classes with this particular individual, in order to be a force to be reckoned with? You can you can completely deny, so I can go and study over here over there, and I can still be a force to be reckoned with
gentlemen. So let's make it more problematic. If you don't, if
if to mean does not
go to Oxford University, then you'll be uneducated.
uneducated, therefore, Tamina has not gone to Oxford University.
It's ridiculous, really, in terms of soundness, but it's all valid. Can you see? So you a lot of times, you'll see the examples of this. And you'll think that's not true, is it? It's not true, a lot of these examples of false in terms of correspondence to reality, and it's truthful, but it's all consistent. And the only thing that needs to be in place for a valid argument to be valid, is consistency. It has to obey the laws of logic. So let's now that I've done these examples for you, then we sit back down. And now it's your turn to bring forward the examples. It's a little bit more difficult now, as you can see, but this was, if you get this, then we're about 20%. of the major
rules, surprisingly, right. Go ahead. So ours are made in Japan, and they are strong. Yes, they are not strong. So therefore they're not made in Japan. Excellent. That's that is valid. What is that sound?
I mean, think about it. Um, it can always be made strong from any other place. But Japan, if I can take them to China and get some made, like some serious guy to cover the mountain.
It's not, doesn't logically follow that has to be there, gentlemen, unless you have a really good sense of strong contact you ever know? Yeah. It may be Yeah, you can make this kind of argument. But it's very difficult to justify that kind of premise. Right. So you see the soundness validity tension?
No, got it wrong. I put if peace requires the absence of us to hostilities, hostilities are continuing. Therefore, there is no peace. So I just,
I got the thing wrong.
I'm sorry. Yes, yes. Okay. The exact facts that he was taught. Yeah, that's a fun because it well, you're pretty good at this. And we've done this before.
Oh, okay. Okay, you've done it in Logic.
I mean, this was a required, like, if you ever do anything, like isn't required. But trust me, guys, if you do this, if you get this right, you'll be able to spot certain contradictions and stuff like that, you know, that's why I haven't taught my wife this because
she finds out I was going off, man. Yeah. If you study for the test, then you will pass your exam.
You didn't pass your exam, therefore, you didn't study for the license? Or you said you didn't pass the exam? Yes, you use the same language, but you use it. And again, you could have easily said, you failed the exam. You're right. This is correct. This valid? And you could argue could be true as well, to some extent, you can make an argument for that. I mean,
if you read books, you will be smart. You are not smart. Yes. Therefore you haven't really noticed. Let me see what you've done there. You're not smart. You think you'd go the other way around? Yeah. Yeah.
If you remember ALLAH, you'd be happy. You're not happy. If we did not remember ALLAH, that's something we should have said to Jordan Peterson more clearly.
But it is what it is. Let's, let's go with the next one. Cool. So if you're living then your age, if you're not aging, then you're not living. So say this again. And let's let's let everyone else get involved to try and get the standard together. Yeah, so if you're living the new age, if you are living, they will age your age and you will age okay. If you're not aging, then you're not living. Okay. Mike, what's going on here? You know, what's happening?
The second year? He said, Yes, he said
okay, so let's remove this remove the second half because it's important not to have to say yeah,
so again, okay, so if you're living the New Age, you're not aging there then you are not deaf or you're not living I suppose. That's good. Perfect. But what he said that was correct. Keep
One if it's possible to have more than one if in the statement, stuff like that we'll get you're getting it though I never everyone's getting it is we're grappling with the ideas. Let's go to the next one. If you go to London, you went to England, you have not, you have not gone to England, therefore you have not gone to London. Excellent. And that's I think that's valid. And that is sound as well as a good one because you can't go to lunch, unless of course, you mean London in Canada.
But then that will be the fallacy of equivocation, which we can talk about. So it was more of an informal fallacy equivocation is, you know, when you mean something, and you intend, for example, if I suppose, famous example, I like his example, it says that, someone's fainting on the floor, and he's got a heart attack happening. Yeah, he goes, Can I have a doctor here? And our friend, he's a PhD holder. He says, academic, and I'm a doctor myself, let me come and help. But he's a he's a mathematician or something. You know, he's a philosopher, and he's trying to do to medical thing. It's not going to work, right? So the point is, is that when you use a word,
and then you intend something, if it will equivocations unless you equivocate and you say London in Canada or London in America, which I think there's London there as well,
then yeah, that's a sound argument, if you mean the London that we're talking about. Yeah.
Yes, if I don't eat, I will be hungry.
I am hungry, therefore I ate.
Go Go math.
See that? There we go.
So so tell us what is meant to be? Yeah.
So what was your premise? Again, first premise? If I don't eat, I'll be hungry. Yes. The second prompt will be I'm not hungry. Therefore, I did not need
If I don't eat.
I am not hungry. Therefore I Yeah, that would be the correct way. Yeah, that's right. You said right. The first time in the premier story. You said I am hungry. Yeah.
He's negated in his first.
What do you call premises negated? So if I don't eat so the issue is, operators and negation? Okay.
So you got two knots? Yeah. Can I have another go? Yeah, of course. If you train properly for the fight, you will win. You lost the fight. Therefore, you did not try to perfect it. Don't say last say you did not win. No fight. Just to be very pedantic about it. I think you guys will get it right. Are you? Are you comfortable? Right, any questions? You just use the negation by sorry, I think you understand. Right. Alright, let's go to the next one.
Which is the syllogism. I think this is the next one. But let me double check. In the meantime, I want to spend five more minutes speaking to the person next to you, yeah, three to five minutes and produce a couple more just just to get the synapses moving on this one, three to five minutes on the same modus tollens may be one modus tollens, one modus ponens before we move on, we won't put this on cameras just for our purposes just so we can make sure it's all solid before we move on to the third one, because you can see we're going through like butter like a knife through butter. We're cutting through you know and this is very important, and very good as well. Let's move on to the
next one. We've had this discussion though it's good to sometimes let it simmer into your mind let it ferment let it mature. Now move on to the next one. Now the syllogism we will think of we've just actually covered the syllogism in the beginning of this very session. But if there is not one syllogism This is a misconception they think okay there is a it is a logical syllogism and they talk of a syllogism as if it is one thing. Actually there are different forms of syllogisms. What we've covered in the beginning was something called a quasi syllogism, right. A quasi syllogism
is let's say the example of Socrates and Socrates is a man. I'm going to go over some key terms here because in propositional logic is very important to know these key terms. So if I say premise one all men are mortal.
Yeah, premise two. Yeah. This is called a major premise
in Arabic is called Devil Cobra
Yes, and they did speak about it in the books of,
of logic in the Arab world, right? Look at the ML Cobra. So all men are mortal. Premise one.
Socrates is a man
so what do we have here? Just someone shout out. Therefore
Socrates is mortal Perfect. Okay. Therefore,
This is called Kadima, Surah or the minor premise
and we'll cut them
is called a quantifier okay this is called the quantifiers and in this case where the word all is used is called a universal quantifier
now you could have different types of quantifiers can say some quantifiers not saying all it's not universal quantifiers for example,
so, okay All men are mortal Socrates is a man therefore, Socrates is mortal. A famous argument for God's existence.
Who knows it using the
universal sort of using the quasi syllogistic syllogism as a format
What is this the most probably one of the most famous actually, I would I would argue investing Academy is the most famous argument for God's existence in the last 20 years. Which is actually formula has early that gives it away really doesn't it and is a quasi syllogism.
Everything begins to exist has a cause beautiful, beautiful, beautiful the universe began to exist. Excellent. Okay, so let's put it all to everything. So this is almost universal quantifiers everything
begins to exist
has a cause
began to exist.
the universe has a cause Yes, the University Of course.
In Arabic Kulu che lo de la suburb, a la la Mola will be there is an a la la Mola, who set up this is Elvis Ali from his book, which is called
would you call it electricity like the hot? This is a quasi? syllogism? What can someone say about this? Because I
say okay, there's no Can Can anyone deny this a valid? Argument? No. So the validity is not eight.
It's valid 100%. No one says anything about the validity of this argument. What do people say about this? Why do people not accept? Why is it some atheists like Quinton Smith? And Christopher Hitchens? And Richard Dawkins, or Richard Dawkins hasn't even been engaged with it. But other people, why have they not accepted this argument? You reject the premises? Yes. So what premise in particular, two people reject the second one. The second one is the subject of the most fierce contention.
Yes, this one here, the universe began to exist.
And you can see this in the debate between William Lane Craig and Sean Carroll, which is the only debate people say that William Lane Craig lost. And he's got like a seven in one record, let's say for his enemy terms of 10. And one record. And this is his one because he was trying to engage with Sean Carroll who was a physicist on physics. And, you know, he had the edge day. But the idea that the universe began to exist. I mean, obviously, you could argue, as he did, Redshift and the Big Bang, but you have to argue scientifically, inductively empirically, which is why this second premise is so susceptible to attack is susceptible to scientific attack, as it has been, and has led
William Lane Craig to produce a book called time, space and eternity, which is basically just debating all kinds of models, physics models, why he his preferred ones are the correct ones, and so on. And dynamic time versus static time, theories of time.
So he's had to engage
with the second premise. But someone can attack the first premise, everything that begins to exist has a cause, in as much the same way, as someone could, an ultra skeptic can say that every person is mortal, or every human is mortal, or whatever it may be. So how do you know that everything begins with you? Because you saw it? Okay. Well, you saw it. That's an inductive point. And if it's an inductive point, then it's susceptible to the problem of induction. And therefore it's not Yaqeen. It's not certain. Of course, they would say that about anything and everything that can be seen.
Well, that has a sample group to it.
So this is a quasi syllogism. without giving you any time, I'm going to pick you at random and see if you can create one with a universal quantifiers. Just like this. How about you?
Because I think we've all got secure knowledge in this one.
Thinking, if you watch the World Cup, you will start with if here, I want to start with, with with a major premise. I mean, you could have an F. We'll talk about how you can have an F in fact, but I want you to start with a premise with a statement without an F.
All World Cup matches our football. Yes.
Therefore, none on a second premise.
Choose an example of a World Cup match. Which one did you watch Argentina France. is a is a football match is a World Cup match is a World Cup match. Therefore
Argentina France is a World Cup is football. Yeah. Because you said every World Cup matches football. Right? Okay. Is that what you said? Yes. Yeah. So you see what was happening.
Okay, give me one.
We want to reach velocities confused. John reads philosophy. John is confused. Yeah, that is very valid. But is it sound? That's something you'd like to defer on? Of course. Just a couple more. Yeah, off man.
All dogs are mammals.
Jeffrey is a dog. Jeffrey is a mammal. That's right. Therefore Jeffrey is a mammal. I hope you read that in a literal way. Because otherwise you're insulting Jeffrey the poor fellow.
Yes, so the quantify can be like when we say you know quantify like everything all you can also have no you can have any Gayatri one or as I said you have some as well. Now there are different as I said there are different kinds of syllogism one which is very interesting. Is something called the poly syllogism. Okay. Now I'm not sure if you Has anyone got a clue of what that is. What is a poly poly syllogism?
To conclusion Oh yeah. I mean, I don't think you're far away from the answer from the sound answer. Okay. It's one with multiple premises it's a syllogism with multiple premises and here's where you can bring it if okay. If it can be very nicely so let's just bring something bring it back to life to the philosophy of religion
those that say there is
necessary existence us must be yeah you can why not? Can be why not
so, you can you can make this more you can say for example there is let's make it even longer yeah
let's make even longer there is existence Yes, there is existence
okay, this is undeniable Actually yes.
If there is
or independent going back to another level
Alright, let's make this better actually because it won't follow if there is existence
From independent from an independent thing
So then you can say, therefore
an independent thing.
So this is a poly poly syllogism. You're adding these two points of information, you're adding their two points of information and you're coming to a conclusion. It's not necessarily a minor premise. And look, I'm bringing F here. This is meant to be if there's not necessarily a minor premise in the main or major premise and a minor premise, quantify and I'm breaking up No, I am bringing an F, I'm bringing a conditional. And you can do this you can play around with syllogisms. And there's different types of reasons.
Like I said, the most famous one is the quasi one. This one's pretty good as well. This will be very handy. And the third one is a hypothetical syllogism. Okay, but before we get to the hypothetical syllogism, let's play around with some poly poly syllogisms. I'll give you five minutes. And then we'll go and we'll do the
shin put this here because it's confused everyone. It's not modus tollens. This is
a syllogism. So let's play around with some Paulo syllogism poly syllogisms.
And come back and present them.
Then after that,
yes, we can do the hypothetical syllogism. And we would have done about 1/3 of logic, frankly, all propositional logic or the major rules of propositional logic. Very surprising, isn't that you can cut through it like that. So five minutes, we'll be back. So hopefully you guys played around with that a little bit just so you can understand different kinds of syllogism. Another important type. So we talked about, let's just ask actually, in fact, what are some of the types of solutions that we've covered? So firstly, quite Yeah, the quasi syllogism? What's policy? jism There's another one called disjunctive syllogism. Okay, but before we get to that, I think that one's easier. So let's
go through the hypothetical one and I need your attention to for this one. So this one is the following.
Structure. Okay. So if p, then q. Okay. So that's just like modus ponens right. if P then Q, the Q,
if q, then ah, so, you thought that this letter would never come into
that then we got here conclusion? What do you think the conclusion is? Therefore what
do ya P?
So you can say that's, that's correct. Yeah. So therefore, PA. So you're going from this, it's like, imagine this is a person, right? He's these are four people. Person one, person two, person three, person four. And there's a ball and one person is given the ball to another person who's given the ball to another person who is going in one direction. That's why it's easy with this one. He's passing the ball playing football you know, the defender is passing it to the midfield and every field is passing it to the striker. The striker is scoring the goal. That's what hypothetical syllogism is right. So let me just give you an example of it so that you can create your own
after that so the first one is let's see.
If it is eat
we will put in the mosque
now imagine this yes you have what if which is what
a conditional so we sign with a conditional
we pray at the mosque
pray Eat Pray at the mosque. We will pray
because that is two units of prayers
is what we will be praying a prayer yes
what's the therefore here now someone help me out
perfect Yeah. Therefore if it is eat
We will pray
to rock us.
Excellent. I thought it was if we pray
to broadcast it is
no, because we said what was the form?
If p if P then Q Right.
And if q then what?
So the conclusion is, if p then
what is p here?
It is the P.
And was the are
the two that causes the what is the Q?
Praying in the mosque is the Yes, exactly. That's right.
If you didn't have the mosque, I mean, consider the following. Can you pray? I mean, technically, yes. soundness, and you can pray in the park or whatever. But I'm saying in this syllogism for purposes of validity, you need the mosque in order to pray to to a cause. Right.
Once again, this is not a federal I mean, you can pray
because someone's gonna say this guy doesn't even know the basics. You can create brain fog this guy's This is what logic has done to them. You see these guys?
You know, somebody's gonna come out and say, Look, this logic has made them Mr. And, please, you know, if p then q, then q, then r p therefore, right. So should you play around with that for five minutes?
And create your own examples. We're nearly there guys. This is like 50% by the way. Can you imagine? This is called a hypothetical syllogism. Yeah. So now you know the quasi syllogism here the Polish syllogism. And you know, the hypothetical syllogism. Maybe I'll give you one more, which is the disjunctive syllogism. And it's there's there's a lot of that, you know, that can be said it's very easy. That was the easiest one, I think.
Yes. Johnny go through it now. In fact, yeah. Okay. Because it's so easy that I think it's worth
I'll use you as the example.
Okay, now, the key word here
because you look, I want to just quickly give you
a quick grammar lesson.
In fact, we're doing that with Cambridge Arabic College in East London, which I'm sure
you're all gonna, you know, sign up to because you need to get the Arabic on point. You guys have all the major discount because of who you are. And we've also got critical content online, which I'm sure you've all subscribed to. And if not, you should because we teach the grammar we teach the sort of the morphology all this kind of things very good.
the word here is either
now this is the word is a disjunctive phrase. This look before we get to this word of disjunction. There's two words there's either a conjunction or disjunction.
A conjunction is like and
in Arabic as well. They call it haha
yeah. Wow. Wow. It's because you'd see me and those kinds of things. It's not now and this is him and him. You're putting two things together. So easy conjunctive
a disjunctive is or
this is the words
you say either this or that.
And if you remember last week when we were having a discussion, we said there's something called a logical disjuncture where you look at all of the possibilities eliminated v and this is called an eliminated argument. Like the Quran says am holy humanoid a che in
am humble Harlequin
mmm because M
is that disjunctive phrase just like oh, sorry. Yeah, oh
um, oh in Arabic or and in English. M is it this? Or is it that it can either?
What's the as either we are you
in that Oh, yo, con la la houden
Oh, feudal. llbean. Is that right? Yeah. I might have made that. It's either we look at this. The Quran is saying this. Quran is saying, This is what Al khazali wrote a book called Al Christakis and most Hakim, he tried to bring out all the arguments in the Quran that use a form of logic either we or you this very simple point. Either we are you are number one, either on the truth on guidance, or on
deviance, clear cut deviance, so So we got two items. Me Oh, you either knew you were on guidance on clear deviance. It's a kind of disjunctive argument. Or it's at least a disjunctive phraseology here. Um, Hola, como Haley shaitan have they been created?
from nothing and whom will Harlequin over they themselves the creators of themselves. The Quran is sending you look at all the possibilities effectively. The the benefit of a disjunctive, this is very beneficial.
They use it for crime investigation all the time.
It's either he was a murderer or this or that, or it's either he came in and he did this, you look at all the possibilities and connect it to something called an abductive argument which we talked about before. So you try and make an inference to the best explanation based on eliminative reasoning. Anyway.
Let's go to the form of this argument. So this is called a disjunctive syllogism.
So I say
let me give you the example right, either
is extremely intelligent. Or is it let's say extremely competent in logic
which has been proven today
let's just not give any superlative let's just say competent. Yes. Is competent.
Or was this word was kind of phrased it this
and then why somebody underlines what
what is the Oh, it's a disjunctive phrase. Yes, or?
Or he is an ignoramus.
He's a fraud.
He's a fraud. Let's do it. Let's let's do like a meme style. All right.
So what's the next What do you think? Should we say?
We negate this point. So he is not a fraud.
he he's very competent in logic.
If you didn't have the either there and the disjunctive, you could defend the consequence problem. But it's not. It's not so. So this Jonnie, you don't fall into the logical fallacy of affirming the consequent very simple, either he is competent or He is a fraud. He is not a fraud. Therefore he is actually competent, I think their sound and I think is valid as well. So that's it. That is a logical disjunction. I've given you two a hypothetical syllogism and a disjunctive syllogism. That way we have gone through today, I would say the four most important ones.
Or let's say the most used ones, which are the quasi syllogism
a Paulo, poly syllogism
a conjunct the Soria disjunctive syllogism.
And the hypothetical
So I think if we were to cap it today with that, because there's this is a kind of thing where we can't go overboard, you will not retain any more information, we've done about 50% of what we need to do, which means we need to do one more. In our own time, what we're going to be doing at home, I
encourage you to do the same thing is try and create some, you know examples from your own. And using the form. And you can Google this things. I mean, it's online, and you on YouTube as lots of stuff. People from top universities, professors teaching propositional logic. In the next session, we are going to finish propositional logic. And we're going to give you some key
some key ideas from Arabic logic as well, just for good measure, because a lot of the stuff like for example, I'll call yet and humps of the idea of the five universals, you will not find this in a book like this. The logic handbook, you know, by Volker held back, which is what they recommended reading for, for example, philosophy students undergraduate. Before they do a logic course, they'll give you a book like this to read. The you will not find that in the Western tradition. So we'll look at some of the ideas in the Arabic tradition because some of them actually quite useful. Very interesting, like Data Wise data, the accident, they refer to it as an action. What is this? What's
the difference? Joe has an IRA What is this and that, and especially when you're reading Islamic books, this becomes extremely important.
On this topics and with that we conclude was salam Wa alaykum Warahmatullahi Wabarakatuh