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OK, welcome to the mini podcasts. This one is on deduction, and welcome to everyone who's listening to or watching the podcasts.

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And welcome to everyone here. When we talk about premises and conclusions of arguments, we call them true or false,

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but when we talk about arguments, we call them either good or bad or sound or unsound.

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We didn't call arguments true or false, and we didn't call premises good or bad, sound or unsound.

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And this is very important. Arguments can no more be true than tables can be loud.

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If I told you this table was loud, you'd think what you're talking about,

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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,

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because tables are not the sort of things that can be loud and in exactly the same way.

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Arguments are not the sort of thing that can be true or false, and only sentences can be true or false.

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And if we want to be exact, it's sentences and the beliefs that sentences express that can be true or false.

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So if I believe that this curtain is blue, my belief can be either true or false.

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And if I express that belief in the sentence, the curtain is is blue.

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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.

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An argument must be constituted of at least two sentences.

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What an argument is, is a set of sentences.

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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.

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And the sentence is an argument. I have to be related to each other in a certain way.

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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.

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So one of them must be being said to follow from the others before we have an argument.

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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.

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I think you'll agree if the conclusion follows from the premises, the argument is good.

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If the if the premises are also true, the argument is sound.

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If the conclusion doesn't follow from the premises, the argument is bad and that's irrespective of the truth of the premises.

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But the argument itself is neither true nor false, just as this table is neither loud nor not loud.

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And distinguishing good arguments from bad is sometimes easier than distinguishing true sentences from false sentences.

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And sometimes, as we saw in the last podcast,

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distinguishing true good arguments from bad is the only way we have of distinguishing true sentences from false ones.

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So if you want to convince others that this sentence is true,

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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.

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And if you want to convince others that the sentence is false, you also need an argument,

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one from which the falsehood of that sentence can either be deduced or inductively inferred.

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So we've seen that an argument is good if its conclusion follows from the premises.

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But there are two sorts of following from, as we saw at the end of the last podcast and in this podcast,

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we're going to look at deductive validity, whereas in the next podcast we'll look at inductive strength.

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So today we're going to look at the following from that is deductive validity.

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So here are two deductive arguments.

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Both of them are deductive, and either of them would be a good starting point from an examination of the sentence,

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therapeutic cloning is morally acceptable. So here's one argument.

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It's wrong to kill an innocent one of us. An embryo is an innocent one of us in therapeutic cloning.

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The embryo is killed. Therefore, therapeutic cloning is wrong.

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OK, there's a deductive argument for the claim that therapeutic cloning is wrong.

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Here's another one. The right argument, the right action is the action that produces the greatest happiness of the greatest number.

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Therapeutic cloning produces the greatest happiness, the greatest number.

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Therefore, therapeutic cloning is right. OK, we have another deductively valid argument, but this time for the completely opposite conclusion.

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Well, this is a bit uncomfortable, isn't it?

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A deductive argument is valid if and only if there's no possible situation in which its premises are true and its conclusion false.

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And if you apply that definition to these arguments, I think you'll see that both of them are valid.

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OK, so the question is, is there any possible situation?

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No, she's not an actual situation. We're not interested in actual situations.

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We're looking for possible situations in which all these premises are true, and yet that conclusion is false.

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And actually you won't find one because this is a valid argument.

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And same here. The right action is the action that produces the greatest happiness, the greatest.

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No therapeutic cloning produces the greatest happiness, the greatest number.

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Therefore, therapeutic cloning is right. If those two premises are true, that conclusion must be true.

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There's no possible situation in which those premises are true, and yet that conclusion is false.

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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?

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But therapeutic cloning can't be both right and wrong.

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And yet we have one deductively valid argument that says it's right, another deductively valid argument that says it's wrong.

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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.

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It's a very common error in my experience. It's made by nearly all students when they start doing logic.

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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.

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Therefore, they sort of think that truth and validity of the same thing, they conflate the two ideas.

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But this is a very bad piece of reasoning.

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And actually to understand the notion of validity is to understand that an argument can be valid and yet its conclusion can be false.

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And this is going to happen whenever one of the premises of a valid argument is false.

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OK, so and remember, here's the definition of validity.

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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.

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OK, so the conclusion is only guaranteed to be true on the basis of the truth of the premises.

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If a premise isn't true, then the conclusion isn't guaranteed to be true either.

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So the fact that an argument is deductively valid can give us one of two pieces of information.

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If the premise of the argument are true, then the conclusion must be true.

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But if the conclusion of the argument is false, then at least one of the premises must be false.

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OK, and this is why validity as a as a concept is very, very important,

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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.

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The only thing that we can be certain of is if these premises are true, then this conclusion will be true.

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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.

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So again, when we go back to to evaluating arguments, there are two questions you ask.

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One, is all the premises true? The other is, does the conclusion follow this?

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The notion of validity is hugely important. Important because you know that if the conclusion follows in the way of deductive arguments,

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it's valid, then either this must be true or this must be true.

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And you've got a way of getting at the argument which will enable you to get a grip and help you evaluate it.

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So I'm just going to go back to this situation here.

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We've got two arguments for opposing views.

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Both of these arguments are valid.

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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.

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Do you see what I mean?

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If you think that therapeutic cloning is morally acceptable, that it's right, you're going to think that the false premises here,

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but your duty now is to go back and find out which of these premises is wrong.

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And if you can't find a premise that's wrong in the argument that opposes you,

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then you've got to keep an open mind because it may be that you're wrong.

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And that's that's one of the reasons that logic is so vital,

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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.

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So going back to the notion of validity,

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the definition of validity is there is no possible situation in which a premises in all its premises are true and its conclusion false.

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And this generates some some people think, counterintuitive views.

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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?

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Could there be an argument of that kind? OK, you're all saying yes.

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And you're quite right. There could be an argument of that kind.

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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.

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So it's not true conclusion, but false premises. Could it be valid?

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Again, the answer is yes. OK, could there be an argument that, as a matter of fact, has false premises and a true conclusion?

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Could that be valid? Yes, it could be.

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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

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because the very definition of validity is there is no possible situation in which the premises are true and the conclusion is false.

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So that's the only one that's ruled out. And just because I can see you were looking a bit puzzled here.

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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.

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So there shouldn't be an if there it should be. It is Tuesday, the 17th of April.

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And here it is. If it's Tuesday, the 17th of April, Mariam will be making podcast's.

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Therefore, Marianne is making podcasts. OK, do you see that?

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That's a valid argument. This is true. This is true.

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And this is true. So it's not true. This is a true conclusion. OK, I'm sorry about that error there.

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That should be. It is Tuesday, 17th April.

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OK, so that's an example of a valid argument that has premises at all, as a matter of fact.

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True. And a conclusion that is, as a matter of fact, true.

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And there's no possible situation in which those premises are true without that conclusion being true.

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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,

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but I hope you'll forgive me that I haven't done all the tightening.

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OK, and here's an actual argument that has false premises and a true conclusion, but which is valid.

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So it is Monday. Marijan always wears jeans on a Monday.

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Marianne is wearing jeans. OK, well that premise is false.

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I think you will agree because it's Tuesday today. That premise is also false.

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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.

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And Marianne is wearing jeans. I went back to change into my jeans on purpose to make this true.

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So here we have false premises and a true conclusion. And I think you'll agree that that argument is valid.

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There is no possible situation in which those premises are true and that conclusion isn't true.

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OK, but we still have a situation in which we have a valid argument with false premises and a true conclusion.

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And go onto this one here. We have false premises and a false conclusion.

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It is Monday. Marianne always wears a dress. On Monday, Marianne is wearing a dress.

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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.

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No, I've messed up on that one, haven't I. Haven't I. No, I haven't.

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It's supposed to be false, isn't it. Yeah, I'm sorry. Let me say that again.

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We've got false premises. It is Monday. Marianne always wears dress on Monday and Marianne is wearing a dress.

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If those two were both true, that would have to be true. In fact, that's false.

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That's false. And that's false. So that's a valid argument with false premises and a false conclusion.

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And the only one that's ruled out is that one.

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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.

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And I suddenly thought, you silly sausage. So you won't be able to think of that because that is ruled out by logic.

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There is no valid argument that has true premises and a false conclusion.

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So I hope that helps with the notion of validity, which is a very difficult notion to wrap your mind around,

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but it's such an important notion, you absolutely must get hold of it.

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So a valid argument can have a false conclusion.

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And we should never therefore believe the conclusion simply because it's the conclusion of a valid argument.

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And we need to be especially aware of this if we're inclined to accept the conclusion on its own terms.

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OK, so if you think that therapeutic cloning is wrong,

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you'll look at whichever argument it was and you'll think, oh, yes, though we have a true conclusion.

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Therefore, that argument must be a good one. Well, beware of that sort of reasoning.

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In fact, one of your antecedents, be prepared to accept the conclusion of an argument.

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You've got to be extra vigilant in checking that the argument really is a good one and that its premises really are true.

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Popper will tell you that there are other occasions, occasions other than when premises are false,

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that the validity of an argument shouldn't persuade us of the truth of its conclusion.

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What this shows us is that validity is necessary for an argument to be good,

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but it's not sufficient and we shouldn't be persuaded of the truth of conclusion, of any argument.

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The circular or that begs the question. Let's have a look at these.

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Here's an argument that the circular and the definition of a circular argument is that the conclusion is amongst the premises.

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Well, it's very obvious here. Embryos have the right to life, therefore, embryos have the right to life.

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Blatantly circular argument. Can you see that it's valid.

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All circular arguments are valid. There is no possible situation.

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Is that where this is true and this is false? How could there be?

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Because they're the same thing. So it's a valid argument.

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And if you might think the premise is true and if you do, you're going to think the conclusion is true.

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But actually you shouldn't, because, of course, the argument, the course of conclusion is true.

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If the premises are true, you might think nobody's going to argue like that.

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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,

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the conclusion there's no possible situation which all the premises are true and the conclusions false with all the premises are true,

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that premise will be true and therefore the conclusion will have to be true.

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So a circular argument is completely useless and the fact that it's valid and this is a mistake that undergraduates often make,

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they say, well, it's circular, that it's circular, therefore it isn't valid.

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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.

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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.

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Therapeutic cloning involves killing human babies. Therefore, therapeutic cloning is wrong.

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Well, you can see that actually, if you're prepared to accept that it's always wrong to kill human babies.

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So what you're doing is you're sorry here you're thinking that the therapeutic cloning,

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which necessarily involves an embryo under 14 days old, you're thinking of the very early embryo as a human baby.

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Well, there are many, many people who would deny that.

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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?

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And in doing that, you're begging the question and you can't argue like that again for the same reason.

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It's it's not circular, but it's very nearly so.

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And here's another pair of arguments that are valid, but which shouldn't convince us of the truth of their conclusions.

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You're going to like these. OK, both of these arguments are valid, five plus seven equals 16, therefore, grass is green.

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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?

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So everything follows from a contradiction. That's what that means, and here grass is green, therefore two plus two equals four.

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This is another valid argument because there's no possible situation in which that's true and that's false.

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And the reason for that is there's no possible situation in which that's false.

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It's a tautology. It's true in every possible world. These two together are called the paradoxes of entailment.

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It would be very nice if the definition of validity didn't throw up those arguments as valid.

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Sadly, it does. It's a very, very useful definition.

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So we're going to keep it. But but sadly, it does mean that arguments like that are valid.

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So we don't want to believe that grass is green just because five plus seven.

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Well, actually, you're not going to believe that anyway. But those are the paradoxes of entailment.

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So this shows us the last few slides have shown us that the validity of an

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argument is necessary for us rationally to accept the conclusion of an argument.

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But it isn't sufficient. You've got to be careful because an argument can be valid without being an argument,

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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.

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We haven't got time for you to do this now, but you might take this home with you.

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Or if you're watching or listening on the podcast,

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you should find the slides that go along with this lecture and you'll be able to do these exercises yourself.

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And that is the definition of validity.

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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.

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And need I say that you shouldn't look at the answers before you do the question.

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OK, in the next podcast, we're going to look at inductive strengths.

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And if you want to look at anything further other than the other podcasts, there's the slide.

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Thank you.