OK, welcome to the mini podcasts. This one is on deduction, and welcome to everyone who's listening to or watching the podcasts.
And welcome to everyone here. When we talk about premises and conclusions of arguments, we call them true or false,
but when we talk about arguments, we call them either good or bad or sound or unsound.
We didn't call arguments true or false, and we didn't call premises good or bad, sound or unsound.
And this is very important. Arguments can no more be true than tables can be loud.
If I told you this table was loud, you'd think what you're talking about,
you'd think I was either talking metaphorically or you'd think she either doesn't understand what a table is or she doesn't understand what loud is,
because tables are not the sort of things that can be loud and in exactly the same way.
Arguments are not the sort of thing that can be true or false, and only sentences can be true or false.
And if we want to be exact, it's sentences and the beliefs that sentences express that can be true or false.
So if I believe that this curtain is blue, my belief can be either true or false.
And if I express that belief in the sentence, the curtain is is blue.
That sentence can be true or false. But arguments aren't either sentences or beliefs, and therefore they can't be either true or false.
An argument must be constituted of at least two sentences.
What an argument is, is a set of sentences.
It's not a sentence, and it must be at least two sentences, one to act as a premise and the other act to act as a conclusion.
And the sentence is an argument. I have to be related to each other in a certain way.
So one of them must be put. One or more of them must be being put forward as reasons to believe the other one before they can count as an argument.
So one of them must be being said to follow from the others before we have an argument.
So a set of sentences is sorry. An argument is a set of sentences and a set of sentences is a very different thing from a sentence.
I think you'll agree if the conclusion follows from the premises, the argument is good.
If the if the premises are also true, the argument is sound.
If the conclusion doesn't follow from the premises, the argument is bad and that's irrespective of the truth of the premises.
But the argument itself is neither true nor false, just as this table is neither loud nor not loud.
And distinguishing good arguments from bad is sometimes easier than distinguishing true sentences from false sentences.
And sometimes, as we saw in the last podcast,
distinguishing true good arguments from bad is the only way we have of distinguishing true sentences from false ones.
So if you want to convince others that this sentence is true,
what you've got to do is find a set of premises from which you can deduce that sentence or from which you can inductively infer it.
And if you want to convince others that the sentence is false, you also need an argument,
one from which the falsehood of that sentence can either be deduced or inductively inferred.
So we've seen that an argument is good if its conclusion follows from the premises.
But there are two sorts of following from, as we saw at the end of the last podcast and in this podcast,
we're going to look at deductive validity, whereas in the next podcast we'll look at inductive strength.
So today we're going to look at the following from that is deductive validity.
So here are two deductive arguments.
Both of them are deductive, and either of them would be a good starting point from an examination of the sentence,
therapeutic cloning is morally acceptable. So here's one argument.
It's wrong to kill an innocent one of us. An embryo is an innocent one of us in therapeutic cloning.
The embryo is killed. Therefore, therapeutic cloning is wrong.
OK, there's a deductive argument for the claim that therapeutic cloning is wrong.
Here's another one. The right argument, the right action is the action that produces the greatest happiness of the greatest number.
Therapeutic cloning produces the greatest happiness, the greatest number.
Therefore, therapeutic cloning is right. OK, we have another deductively valid argument, but this time for the completely opposite conclusion.
Well, this is a bit uncomfortable, isn't it?
A deductive argument is valid if and only if there's no possible situation in which its premises are true and its conclusion false.
And if you apply that definition to these arguments, I think you'll see that both of them are valid.
OK, so the question is, is there any possible situation?
No, she's not an actual situation. We're not interested in actual situations.
We're looking for possible situations in which all these premises are true, and yet that conclusion is false.
And actually you won't find one because this is a valid argument.
And same here. The right action is the action that produces the greatest happiness, the greatest.
No therapeutic cloning produces the greatest happiness, the greatest number.
Therefore, therapeutic cloning is right. If those two premises are true, that conclusion must be true.
There's no possible situation in which those premises are true, and yet that conclusion is false.
So both of our arguments are valid, but you might think, well, if an argument is valid, surely it must have a true conclusion, doesn't it?
But therapeutic cloning can't be both right and wrong.
And yet we have one deductively valid argument that says it's right, another deductively valid argument that says it's wrong.
What's happening here? Well, if you think that you're probably confusing truth and validity, and that's a very sad thing to do.
It's a very common error in my experience. It's made by nearly all students when they start doing logic.
And my explanation of this, this is the explanation I give myself, is lots of people think the truth is good and they also think the validity is good.
Therefore, they sort of think that truth and validity of the same thing, they conflate the two ideas.
But this is a very bad piece of reasoning.
And actually to understand the notion of validity is to understand that an argument can be valid and yet its conclusion can be false.
And this is going to happen whenever one of the premises of a valid argument is false.
OK, so and remember, here's the definition of validity.
Again, an argument is valid if and only if there's no possible situation in which these premises are true and its conclusion is false.
OK, so the conclusion is only guaranteed to be true on the basis of the truth of the premises.
If a premise isn't true, then the conclusion isn't guaranteed to be true either.
So the fact that an argument is deductively valid can give us one of two pieces of information.
If the premise of the argument are true, then the conclusion must be true.
But if the conclusion of the argument is false, then at least one of the premises must be false.
OK, and this is why validity as a as a concept is very, very important,
because we often don't know about the truth of our premises and therefore we can't say that we know about the truth of our conclusion.
The only thing that we can be certain of is if these premises are true, then this conclusion will be true.
If this conclusion is false, then one of these premises must be false and we could go about looking to see which one is false.
So again, when we go back to to evaluating arguments, there are two questions you ask.
One, is all the premises true? The other is, does the conclusion follow this?
The notion of validity is hugely important. Important because you know that if the conclusion follows in the way of deductive arguments,
it's valid, then either this must be true or this must be true.
And you've got a way of getting at the argument which will enable you to get a grip and help you evaluate it.
So I'm just going to go back to this situation here.
We've got two arguments for opposing views.
Both of these arguments are valid.
If you happen to prefer this one, if you think that therapeutic cloning is wrong, you're going to think that the false premises here.
Do you see what I mean?
If you think that therapeutic cloning is morally acceptable, that it's right, you're going to think that the false premises here,
but your duty now is to go back and find out which of these premises is wrong.
And if you can't find a premise that's wrong in the argument that opposes you,
then you've got to keep an open mind because it may be that you're wrong.
And that's that's one of the reasons that logic is so vital,
because it gives us a way of taking a hugely controversial issue and finding a way of starting to unpack whether it's right or wrong.
So going back to the notion of validity,
the definition of validity is there is no possible situation in which a premises in all its premises are true and its conclusion false.
And this generates some some people think, counterintuitive views.
So do you think there could be an argument that's valid and that has, as a matter of fact, true premises and a true conclusion?
Could there be an argument of that kind? OK, you're all saying yes.
And you're quite right. There could be an argument of that kind.
OK, could that be an argument that has that is valid and this is a matter of fact, has false premises and a true conclusion.
So it's not true conclusion, but false premises. Could it be valid?
Again, the answer is yes. OK, could there be an argument that, as a matter of fact, has false premises and a true conclusion?
Could that be valid? Yes, it could be.
And the only one that you have to say no to is that one there is no argument that has true premises and a false conclusion yet is valid
because the very definition of validity is there is no possible situation in which the premises are true and the conclusion is false.
So that's the only one that's ruled out. And just because I can see you were looking a bit puzzled here.
So so let's give you some examples of that. So here's an argument and you'll have to forgive me for my examples if it's Tuesday, the 17th of April.
So there shouldn't be an if there it should be. It is Tuesday, the 17th of April.
And here it is. If it's Tuesday, the 17th of April, Mariam will be making podcast's.
Therefore, Marianne is making podcasts. OK, do you see that?
That's a valid argument. This is true. This is true.
And this is true. So it's not true. This is a true conclusion. OK, I'm sorry about that error there.
That should be. It is Tuesday, 17th April.
OK, so that's an example of a valid argument that has premises at all, as a matter of fact.
True. And a conclusion that is, as a matter of fact, true.
And there's no possible situation in which those premises are true without that conclusion being true.
Actually, you can probably tell you have to tighten that up in some way because I wasn't making podcast's 11 o'clock this morning,
but I hope you'll forgive me that I haven't done all the tightening.
OK, and here's an actual argument that has false premises and a true conclusion, but which is valid.
So it is Monday. Marijan always wears jeans on a Monday.
Marianne is wearing jeans. OK, well that premise is false.
I think you will agree because it's Tuesday today. That premise is also false.
You'll just have to take that on my say. So I don't always wear jeans on a Monday, or at least if I do, I'm not aware of it.
And Marianne is wearing jeans. I went back to change into my jeans on purpose to make this true.
So here we have false premises and a true conclusion. And I think you'll agree that that argument is valid.
There is no possible situation in which those premises are true and that conclusion isn't true.
OK, but we still have a situation in which we have a valid argument with false premises and a true conclusion.
And go onto this one here. We have false premises and a false conclusion.
It is Monday. Marianne always wears a dress. On Monday, Marianne is wearing a dress.
I think you'll see that that's a valid argument. The premises are both true and the conclusion, oh, there should be a not in there.
No, I've messed up on that one, haven't I. Haven't I. No, I haven't.
It's supposed to be false, isn't it. Yeah, I'm sorry. Let me say that again.
We've got false premises. It is Monday. Marianne always wears dress on Monday and Marianne is wearing a dress.
If those two were both true, that would have to be true. In fact, that's false.
That's false. And that's false. So that's a valid argument with false premises and a false conclusion.
And the only one that's ruled out is that one.
And when I was writing this podcast, I got myself into a real tiswas and I was trying desperately to think of an example of that.
And I suddenly thought, you silly sausage. So you won't be able to think of that because that is ruled out by logic.
There is no valid argument that has true premises and a false conclusion.
So I hope that helps with the notion of validity, which is a very difficult notion to wrap your mind around,
but it's such an important notion, you absolutely must get hold of it.
So a valid argument can have a false conclusion.
And we should never therefore believe the conclusion simply because it's the conclusion of a valid argument.
And we need to be especially aware of this if we're inclined to accept the conclusion on its own terms.
OK, so if you think that therapeutic cloning is wrong,
you'll look at whichever argument it was and you'll think, oh, yes, though we have a true conclusion.
Therefore, that argument must be a good one. Well, beware of that sort of reasoning.
In fact, one of your antecedents, be prepared to accept the conclusion of an argument.
You've got to be extra vigilant in checking that the argument really is a good one and that its premises really are true.
Popper will tell you that there are other occasions, occasions other than when premises are false,
that the validity of an argument shouldn't persuade us of the truth of its conclusion.
What this shows us is that validity is necessary for an argument to be good,
but it's not sufficient and we shouldn't be persuaded of the truth of conclusion, of any argument.
The circular or that begs the question. Let's have a look at these.
Here's an argument that the circular and the definition of a circular argument is that the conclusion is amongst the premises.
Well, it's very obvious here. Embryos have the right to life, therefore, embryos have the right to life.
Blatantly circular argument. Can you see that it's valid.
All circular arguments are valid. There is no possible situation.
Is that where this is true and this is false? How could there be?
Because they're the same thing. So it's a valid argument.
And if you might think the premise is true and if you do, you're going to think the conclusion is true.
But actually you shouldn't, because, of course, the argument, the course of conclusion is true.
If the premises are true, you might think nobody's going to argue like that.
But can you see that? Actually, if you added ten other premises here, it would still be the case that if the premises are all true,
the conclusion there's no possible situation which all the premises are true and the conclusions false with all the premises are true,
that premise will be true and therefore the conclusion will have to be true.
So a circular argument is completely useless and the fact that it's valid and this is a mistake that undergraduates often make,
they say, well, it's circular, that it's circular, therefore it isn't valid.
And you think, oops, they haven't wrapped their mind properly around the idea of validity because if it's valid, then it's sorry.
If it's circular, then it must be valid. And here's a question. Begging arguments and it's always wrong to kill human babies.
Therapeutic cloning involves killing human babies. Therefore, therapeutic cloning is wrong.
Well, you can see that actually, if you're prepared to accept that it's always wrong to kill human babies.
So what you're doing is you're sorry here you're thinking that the therapeutic cloning,
which necessarily involves an embryo under 14 days old, you're thinking of the very early embryo as a human baby.
Well, there are many, many people who would deny that.
And so you're you're assuming the answer to the question is the human baby sorry, is the early, very early embryo a human baby?
And in doing that, you're begging the question and you can't argue like that again for the same reason.
It's it's not circular, but it's very nearly so.
And here's another pair of arguments that are valid, but which shouldn't convince us of the truth of their conclusions.
You're going to like these. OK, both of these arguments are valid, five plus seven equals 16, therefore, grass is green.
There is no possible situation in which that's true and that's false because there's no possible situation in which that's true, is it?
So everything follows from a contradiction. That's what that means, and here grass is green, therefore two plus two equals four.
This is another valid argument because there's no possible situation in which that's true and that's false.
And the reason for that is there's no possible situation in which that's false.
It's a tautology. It's true in every possible world. These two together are called the paradoxes of entailment.
It would be very nice if the definition of validity didn't throw up those arguments as valid.
Sadly, it does. It's a very, very useful definition.
So we're going to keep it. But but sadly, it does mean that arguments like that are valid.
So we don't want to believe that grass is green just because five plus seven.
Well, actually, you're not going to believe that anyway. But those are the paradoxes of entailment.
So this shows us the last few slides have shown us that the validity of an
argument is necessary for us rationally to accept the conclusion of an argument.
But it isn't sufficient. You've got to be careful because an argument can be valid without being an argument,
the conclusion of which you should accept and to make sure that you're not confusing validity, truth and or soundness what you might do.
We haven't got time for you to do this now, but you might take this home with you.
Or if you're watching or listening on the podcast,
you should find the slides that go along with this lecture and you'll be able to do these exercises yourself.
And that is the definition of validity.
And there are four questions that will get you to push you to see that you've understood the definition properly and the answers are at the bottom.
And need I say that you shouldn't look at the answers before you do the question.
OK, in the next podcast, we're going to look at inductive strengths.
And if you want to look at anything further other than the other podcasts, there's the slide.
Thank you.