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Week 3 - 2.1.2 Conditionals — Transcript · YTtoTranscript

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Week 3 - 2.1.2 Conditionals

Philosophy at Azim Premji University · 2,851 words · 14 min read · EN

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Below is the complete, readable transcript of Week 3 - 2.1.2 Conditionals by Philosophy at Azim Premji University on YouTube. Read the full text, copy any part you need, or generate a transcript for any video with our free tool.

Hello and welcome to the second class of week three of PR. This is the second class of this week. If you have not seen the previous class of this week, I strongly advise that you go and check it out first. Please keep a paper and pen ready and let's get started. In the last class, we covered the idea

of validity. We said that a deductive argument is valid when if we hold the premises true, then the conclusion must come out to be true. We also studied some connectives that were not, and and or. In this class, we will study another con connective called conditional. Conditionals are connectives that have the form if a then b. We will also see

when our arguments using conditional valid. Therefore, the aims of this class are to understand conditional, learn valid form of conditional, and judge the validity of arguments that use conditionals. Let's get started. Let's take an example. If I am in Bangalore, then I am in Karnataka. This is a conditional because it states something of the form if A then B.

So if I take I am in Bangalore as A and I and I am in Karnataka as B. I can write the sentence as if A then B. Here A and B are the terms and if then is the connective. Like we did last time, we have four possible combinations of the terms depending on their truth and

falsehood individually. I can have firstly I'm in Bangalore and I'm in Karnataka. Secondly, I'm in Bangalore and I'm not in Karnataka. Thirdly, I'm not in Bangalore and I'm in Karnataka. And finally, I'm not in Bangalore and I'm not in Karnataka. The conditional if I'm in Bangalore then I'm in Karnataka comes out to be true in all cases except

when I have I'm in Bangalore and I'm not in Karnataka. We can see why if I say I'm in Bangalore and I'm in Karnataka then the statement if I'm in Bangalore then I'm in Karnataka makes sense. It holds true. Similarly, I'm not in Bangalore but I'm in Karnataka as stated in line three

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also makes the statement if I'm in Bangalore then I'm in Karnataka true because even if I'm not in Bangalore I can still be in Karnataka by being say in Mysore. Lastly, I'm not in Bangalore and I'm not in Karnataka as stated in the last line also makes sense for the statement if I'm in Bangalore I'm in

Karnataka um to be true. But the second line that I am in Bangalore and I'm not in Karnataka will make the statement if I'm in Bangalore then I'm in Karnataka false because there's no way that I can be in Bangalore but not be in Karnataka. Generalizing from our example the statement if A then B is true in all

cases except when A is true and B is false. Another property of if a then b unlike conditionals like and or is that we cannot switch the terms around. For and connective I can say that a and b is the same as b and a. Similarly for or connective a or b is the same as b or a.

But this is not true for conditional. If a then b is completely different from saying if b then a. Rather the sequence makes a lot of difference. Therefore the terms are given different names. In uh in the example if I am in Bangalore then I am in Karnataka. The term I'm in Bangalore will be called anticedent

while the term I am in Karnataka will be called consequent. Therefore the form of a conditional is if anticedent then consequent. Now that we understand conditionals let us see some forms of arguments using conditionals and check them for validity. Let's start with this example. If I'm in Bangalore, then I'm in Karnataka. I'm in Bangalore. Therefore,

I'm in Karnataka. Pause the video here and see if you can put the argument in standard form and then see if you can write it in logical form using terms and connectives. Once you're done, unpause the video and proceed further. So, the standard form of the argument comes out to be premise one, if I am in Bangalore,

then I'm in Karnataka. Premise two, I'm in Bangalore. and conclusion I'm in Karnataka. Now try to put in logical form. Pause and try it. Then unpause to see if you got the answer correct. So we can see that the premise one uses the connective if then. We can take I'm in Bangalore as a and I am in Karnataka as

B. If I see premise two, it states that I'm in Bangalore. Therefore the premise 2 becomes A. And the conclusion states that I'm in Karnataka. Therefore the conclusions becomes B. The logical form therefore is if A then B premise 2 A conclusion B. Now that we have the logical form let us check for validity. Remember validity

requires that if we hold the premises to be true the conclusion must come out to be true. We can see if the argument form is valid by considering the example we had taken. uh if my premise one is stating that if I'm in Bangalore then I'm in Karnataka which means that if I find myself to be

in Bangalore then I must also be in Karnataka. Premise 2 is stating that I am in Bangalore. If we hold both of these two then it means that if I find myself in Bangalore then I must be in Karnataka and I do find myself in Bangalore. Therefore I must conclude that I'm in Karnataka which happens to

be my conclusion. Therefore the conclusion logically follows from the two premises. Thus this form is valid. We call this form modus ponence or affirming the anticedent. If you remember in the form if a then b the term a that comes after if is called the anticedent while the term b which comes after the then is

called the consequent. This form is called affirming the incident anticident because in the premise two we are stating that the anticedent term a is actually true and therefore stating that the consequent is true in the con conclusion. Therefore in the second premise we are affirming that the anticedent is true. Let us take another example. If I'm in

Bangalore then I'm in Karnataka. I'm not in Karnataka. Therefore I'm not in Bangalore. Again try to put it in standard form. Pause the video and then unpause once you are done. So the standard form comes out to be premise one if I'm in Bangalore then I'm in Karnataka. Premise two I'm not in

Karnataka and conclusion I'm not in Bangalore. Now let's try to put it in logical form using terms and connectives. Pause the video try to put the premises and conclusion in logical form and unpause once you are done. This is how we can put the argument in the logical form. Premise one states that if

I'm in Bangalore then I'm in Karnataka. We can see that the connective being used is if then. We can take the terms I'm in Bangalore as A and I am in Karnataka as B. For premise two it is stating that uh I'm not in Karnataka. Our B was I am in Karnataka. Therefore

I'm not in Karnataka becomes its negation. Hence premise 2 becomes not B. Similarly, the conclusion states that I'm not in Bangalore. Since a was I am in Bangalore, the conclusion becomes the negative of that. Therefore, the conclusion is not A. Putting it all together, the logical form therefore is premise one if A then B, premise 2 not B

and conclusion not A. Again, let's see if this is a valid form or not. Let's take the example again. It states that premise one if I'm in Bangalore then I'm in Karnataka. Premise two I'm not in Karnataka and conclusion I'm not in Bangalore. If you see this is following the form that we have on the

left. The P1 is stating that if I find myself in Bangalore then I must be in Karnataka. P2 though is stating that I'm not in Karnataka. But if I'm not in Karnataka then it cannot be that I'm in Bangalore because according to P1 being in Bangalore also implies being in Karnataka. Therefore not being in

Karnataka means that I cannot be in Bangalore. Therefore I must conclude that I'm not in Bangalore. And this is precisely what the conclusion is stating that I'm not in Bangalore. Hence this also is a valid form. We call this modus stolins or denying the consequent. Again the logic of the naming is that in the second premise we

are stating that the consequent that is B is not true and therefore concluding that the anticedident which is A is also not true. Hence in premise two we are denying that the consequent is true. Another form another example. Pause the video and see if you can put this example in standard form. Unpause when

you're done. The example states if I'm in Bangalore then I'm in Karnataka. I'm not in Bangalore. Therefore, I'm not in Karnataka. Okay. So, the standard form is premise one, if I'm in Bangalore, then I'm in Karnataka. Premise two, I'm not in Bangalore. Conclusion, I'm not in Karnataka. Now, pause the video again and see if

you can put it in the logical form using terms and connectives. So, we can put this in standard form in the following way. P1 is using the connective if then. If we take the term I'm in Bangalore as A and I'm in Karnataka as B. Uh P2 is stating I'm not in Bangalore. This is the negative of A.

Therefore P2 becomes not A. The conclusion is stating that I'm not in Karnataka. Therefore the conclusion becomes the negation of B therefore not B. The logical form therefore is P1 if A then B. P2 not A conclusion not B. Now that we have the logical form, let's see if it's valid. Again, remember validity

states that an argument is valid. If we make all the premises to be true, then the conclusion must come out to be true. Let's take our example again which is in the form that is on the left. So the premise one states if I'm in Bangalore then I'm in Karnataka. Premise 2 states

I'm not in Bangalore and the conclusion is I'm not in Karnataka. Now premise one states that if I'm in Bangalore then I must be in Karnataka. Premise 2 is stating that I'm not in Bangalore. If we take the two together I can conclude that the conclusion I'm in Karnataka. U should that also be

true? No. Because taken together P1 and P2 only imply that I'm not in Bangalore. But I can still be in Karnataka. For example, say I'm in Mysore. If that is the case, my P1 is true. Uh it is true because uh it is saying if I'm in Bangalore, then I'm in Karnataka. It is

not saying anything about being in Mysore. My P2 is also true. I'm not in Bangalore. But in I'm in Mysore. But the conclusion is not true. By being in Mysore, I am in Karnataka. Therefore, the conclusion I'm not in Karnataka. Karnataka cannot be drawn. Hence the logical form is invalid. We call this

invalid form denying the anticedent. Again this is called so because in premise 2 we are denying that the anticedent A is true and concluding that the consequent is also not true. But as we saw this does not work. Hence this is an invalid form. Final example. I if I'm in Bangalore then I'm in Karnataka. I am

in Karnataka. Therefore I'm in Bangalore. Again, pause the video and see if you can put it in standard form. Unpause when you're done. The standard form is premise one. If I'm in Bangalore, then I'm in Karnataka. Premise two, I'm in Karnataka. Conclusion, I'm in Bangalore. Now, see if you can put it in logical form. Pause

the video. Put it in logical form using terms and connectives. Then unpause to see the answer. To put it in logical form, we follow the following steps. P1 states that if I'm in Bangalore then I'm in Karnataka. This is using the connective if then. If we take the terms I'm in Bangalore as A and I'm in

Karnataka as B. Then we can get P1 as if A then B. P2 states that I'm in Karnataka. This is the same as B. Therefore, premise 2 is B. Similarly, the conclusion states that I'm in Bangalore, which is our A. Therefore, the conclusion becomes A. The logical form therefore comes out to be premise one if A then B premise 2 B

conclusion A. Now that we have the logical form let's check for validity. Let's take our example again. Premise one, if I'm in Bangalore, then I'm in Karnataka. Premise two, I'm in Karnataka. Conclusion, I'm in Bangalore. If you see this is the same logical form as the one on the left. Now P1 states

that if I'm in Bangalore then I'm in Karnataka. That means that if I find myself in Bangalore then I must be in Karnataka. Premise 2 states that I am in Karnataka. Taken together P1 and P2 imply with confidence that I'm in Karnataka. The conclusion states that I'm in Bangalore. But can I really

conclude that? So imagine that P1 is true that if I'm in Bangalore then I'm in Karnataka and that I am in Karnataka as per P2. But being in Karnataka can also be true when let's say I'm in Myso. If I'm in Myso then P1 is true because P1 is about being in Bangalore implying being in

Karnataka but nothing about being in Mysore. And P2 is also true because Mysore is in Karnataka. Hence if I'm in Mysore then I'm in Karnataka. But the conclusion I am in Bangalore is not true. Hence we can have a case in which premise one and premise two are correct but the conclusion is not true.

Hence this logical form is invalid. We call this invalid form affirming the consequent. This is because in premise 2 we are affirming that the consequent B is true and therefore concluding that the anticedent A is also true. But as we saw, it is not sufficient to say that the consequent is true to conclude that

the anticedent is also true. In the example above, we have been following a particular way of finding if an argument form is valid or not. This method is called testing validity through counter examples. For example, take this form. Premise one, if A, then B. Premise 2, B, conclusion A. To see if it's valid, we first need to come up

with an argument that follows this form. I have come up with the following argument. Premise one, if an animal is a land dweller, then it breathe through lungs. Premise two, X breathes through lungs. Conclusion, act X is a land dweller. Now, can I find an animal to substitute X which breathes through lungs, thus making P2 true, but is not a

land land dweller, thus making the conclusion false. Yes, I can. A whale. Now, when I substitute the X for whale, I get the following argument. Premise one, if an animal is a land dweller, then it breathes through lungs. Premise two, whales breathe through lungs. Therefore, whales are land dwellers. I can see that the conclusion is now false

while both the premises are true. Since the conclusion is false while both the premises are true, I can conclude that this argument form is invalid. A thing to note here is that validity requires that the conclusion must be true when the premises are true. Therefore, even one counter example where the conclusion comes out to be

false when the premises are true is enough to prove that the argument form is invalid. It doesn't matter how many instances I can find where the premises are true and the conclusion is also true. One instance where the conclusion is false and the premises are true makes the form invalid. So in this class we learned a new

connective called conditional. It is of the form if anticedent then consequent. We also learned four forms two valid and two invalid. Affirming the anticedent and denying the consequent are valid forms. On the other hand, denying the anticedent and affirming the consequent are invalid. Learn these forms and they will be really helpful to you.

And that does it for uh this week's classes. Join me next week where we will learn another connective, learn how to put everyday English language in connectives and see how we express necessary and sufficient conditions. Thank you.