PHIL 126 Lecture 1

0:00 Hi everybody. welcome to your first real lecture. I highly highly recommend that you watch this at normal speed, not two times speed, not 1.5 speed. I know sometimes I am slow to talk. but I really think it's important for philosophy that you take things slowly and carefully. And oftentimes that means you need to think about stuff after I say it. And so if you're listening to this at a fast pace, much much harder to do. I don't even know how people listen to podcasts at two speed or 1.5 speed. I I feel like I'm a pretty smart person and I got to listen to it nice and slowly, really carefully, hearing what the people are saying. Same thing for this. Additionally, I really strongly recommend that you take handwritten notes on your own. So it should be computer or tablet propped up, no distractions. Earplugs would be not earplugs but headphones would be best. Notepad and paper. You're writing down stuff. You are pausing. You are going back. You're actively listening and engaging. I go quickly through this content because I know you can go back. So don't think that you just listen through it one time through and you're good. You got to go back and study it. This is studying material.

1:28 I don't want to like berate you into telling you how to study, but it's helpful. Okay, so let's just get into it. So, this class is all about arguments. Now, arguments in philosophy have a very specific flavor. We mean something very specific by an argument. Let's get there. We got to walk our way slightly. The first concept we need that is quite necessary is the concept of a statement.

2:00 So a statement is assertion that something is or is not the case. Statements can be true or false in principle. they are sometimes we never we may never know whether a statement is true or false. sometimes it might be impossible but they're either true or false ideally. So questions, commands, expressions of emotion, those are not statements. Statements are things like the moon is made of cheese, the moon is round, the moon is tidily locked with the earth.

2:34 These sorts of things are statements. So given what a statement is, we can define an argument. An argument in this class is a group of statements in which some of them which we call the premises are intended to provide rational support for another one of those statements the conclusion. So the premise obviously there is the statement sorry the statements intended to give this support and the conclusion is the statement that is meant to be supported by the premises. I'm going to be using these terms all the time so get used to them. Additionally, what we care about in arguments is what's called rational support. What we have best reason to believe. So premises in this sense are reasons that we give for believing in the conclusion. That's the whole game that we're playing is we are providing reasons to believe in the conclusion.

3:32 Finally, the last term that I just want you to have, tip of your tongue, top of your mind, whatever the idiom is, is an inference. An inference is the reasoning process that takes us from the premises to the conclusion. So, we say that an inference is made in going from the premises to the conclusion or you infer the conclusion from the premises. This is just a term that describes what what we're doing. were reason.

4:04 So given this when we formulate arguments in this class and actually all philosophers do this I don't know about all sorry that was a overstatement many many good philosophers do this we explicitly formulate arguments now by this we mean we write out each premise individually and the conclusion separately each premise this allows us to think about each premise distinctly on its own terms and see how they work together to support the conclusion.

4:38 The way we're going to formulate these arguments explicitly in this class is through what's called standard form. So standard form is as such. We write an argument so that each premise is explicit and the conclusion is clearly marked. To do this, we number each premise. So each premise and the conclusion gets a number. We draw a line before the conclusion to show that an inference is being made. And we use some conclusion indicator to tell the reader exactly what the conclusion is. So, I want to go through an example real quick from my favorite TV show ever created. it is called It's Always Sunny in Philadelphia. Now, these people are not heroes. These are horrible, horrible people. This is a satire. They are making fun of people who act this way. it's fantastic.

5:36 But I'm gonna play a clip and then we're gonna talk about one of the arguments that's being made in there. I think it's really interesting what the character M is doing. Don't know if they knew that this was an argument in philosophy, but it's actually a decently wellrespected argument. So, let me pull that up real quick. >> Now, this is all about making myself credible >> again. And I'm going to do that by admitting that evolution is a lie.

6:03 >> God damn you, Mac. >> Yes, please do, Mac. >> Now, as you can see, this is the evolution meter, and I've put God, the creator of everything on the right side, and evolution on the left. I've went ahead and put you guys all on the fence because of course you're going to hear my >> Let's start where I would start. >> No matter, I'm righteous. I'm not going to stand here, present some egghehead scientific argument based on fact. I'm just a regular dude. I like to drink beer. You know, I love my family. Rock flag and eagle, right, Charlie? He's got a point. No, he doesn't.

6:39 >> See, Charlie, these liberals are trying to assassinate my character. I can't change their mind. I won't change my mind cuz I don't have to. Cuz I'm an American. I won't change my mind on anything regardless of the facts that are set out before me. I'm dug in and I'll never change. Mac, look, you're wasting our time. You're not going to get us to not believe in evolution. >> And why is that? >> Because the smartest scientists in the entire world all agree that it's real.

7:10 >> I'm glad you brought that up. Because Mr. Reynolds, science is a liar sometimes. Oh boy. >> This is Aristotle. Thought to be the smartest man on the planet. He believed that the Earth was the center of the universe. And everybody believed him because he was so smart until another smartest guy came around, Galileo. And he disproved that theory, making Aristotle and everybody else on Earth look like a Of course, Galileo then thought comets were an optical illusion, and there's no way that the moon could cause the ocean's tides.

7:53 Everybody believed that because he was so smart. He was also wrong, making him and everyone else on Earth look like a again. And then, best of all, Sir Isaac Newton gets born and blows everybody's nips off with his big brains. Of course, he also thought he could turn metal into gold and died eating mercury, making him yet another stupid Are you seeing a pattern? >> No. Mr. Reynolds, these were all the smartest scientists on the planet. ONLY PROBLEM IS THEY KEPT being wrong sometimes.

8:32 >> This is insane, you fool. >> I'm a fool because I have more faith in the saints that wrote the Bible. Yeah, because you just read. >> All right. Oh, how do I get rid of it? What's happening? One sec. >> All right. So, that's the show. It's phenomenal. It's on Hulu. Go watch it. It's the best. Go watch clips of it on YouTube first if you're like not quite sure. Watch the bloopers. You don't even need to know the show. The bloopers will get you into it. Okay. So right there, Mack, who's the guy standing up in the the Tommy Bahama shirt, gives an argument that's actually quite well respected among philosophers of science.

9:16 Here is the name of the argument. It's called the pessimistic metainduction argument for scientific anti-realism. You don't really need to know that, but here's he doesn't give the exact version. He actually gives sort of a a silly version, but here's a better version of that same argument. The basic idea that he's getting at is these past failures of our best scientific theories gives us some reason to doubt what we currently call our best scientific theories. So here's the argument in standard form. Numbered premises line between the premises and the conclusion and a conclusion indicator. Here's how it goes. Almost all of our previous best scientific theories turned out to be false. That's premise one. Premise two is evolution is among our current best scientific theories and so probably the conclusion claims evolution will turn turn out to be false as well.

10:16 So there's two main questions here. Premise two obviously correct evolution is among our current best scientific theories. Nothing to do there. The two questions we might have for this argument is why should we believe the first premise and why should we accept the inference from the premises to the conclusion. Well, here's the basic idea. When you look at the history of science, we see a story of failure of one theory after another being knocked down.

10:49 Flegistine. We used to think that the reason things caught on fire or exploded is because there was this substance called flegistine. and it took a very very long time for us to realize that that was false. That it's actually the combustion theory where it's oxygen that lights on fire. Cool. Oxygen together with some carbon source or something like that. Then there's the theory of the ether. used to think that permeating through the entire universe is this substance called the luminiferous ether and its job was to carry light through substances. They didn't think that light things could travel in a vacuum. Turns out this is false. Einstein showed that this theory is false. There's no need for a luminiferous ether.

11:38 this was something that Newton believed as well as people long past Newton. also Newtonian mechanics this you know F equals MA three laws of motion that sort of thing Einstein proved it to be false Newton was the greatest physicist ever Einstein came along showed that theory to be false so science is just chalk full of the gravestones of these previous best scientific theories so that's why you should think premise one is true here's premise one almost all of our previous best scientific theories have turned out to be Why accept the second question, the inference from premises one and two to three? Here's the idea. Look, a poor track record is evidence of future error. We got it wrong in the past. We should also think we're going to get it wrong again. And if you think not, if you think we're going to get it right in the if you think that our current theories are correct, what makes the current theories special? What is the feature of for example the theory of evolution by natural selection that distinguishes it from flegistan ether or Newtonian mechanics or something like that.

12:51 This is a very wellrespected argument. I don't intend for you to have an answer to this question of whether it's a good argument or not. I just want to show you that this is the sort of thing we'll be doing in this class is trying to figure out arguments. We'll say one more thing here. So the way that arguments work is they give you reasons to believe the conclusion. And there are only two ways to resist the conclusion of an argument. We'll see this below, but I want to flag it right now. There's precisely two ways to resist the conclusion of an argument.

13:29 Way one is to show that we have reason to doubt the truth of at least one of the premises. Right? If you can make a plausible claim that premise one is false or premise two is false, then you've basically what you've said is, hey, this reason that you provided for your conclusion doesn't actually work. The other way that you can resist the conclusion of an argument is you can say that the inference is not a legitimate one. You can say yes. Okay, fine. Have your premises one and two. They still don't bring us all the way to three. The premises can be true and the conclusion can still be false. The mere fact that you've presented me with these premises, who really cares? And so you can either point out that the reasons aren't true or you can claim that the reasons don't support the conclusion in the way that the proponent of the argument is trying to get you to believe.

14:29 Okay, let's look at a couple more. I don't know simp one thing that we're going to be doing very frequently in this class is we're going to be doing what we just did. Basically, you read some paragraph or listen to somebody talking, in this case, Mac, and you're going to extract the argument and put it into standard form. And so, you have to be able to tell what the conclusion is and what the premises are. and then put the pre the argument in standard form from there.

15:01 Let's see an example of this. So, suppose we have this following passage. The fight against climate change must include a ban on gas-powered vehicles because combustion engines are major contributors to greenhouse gases. Even with approved efficiency, they will continue to pump harmful emissions into our atmosphere. While electric alternatives are becoming more viable, gas engines remain a significant threat to our environmental stability. So when you come up across a passage like this that includes an argument, your first question should be, what is the conclusion of this argument?

15:41 What is it that the author is trying to get me to believe in the end? So I want you to think about it for a moment. Pause if you need to take a moment. Okay. The conclusion of this argument is the claim the fight against climate change must include a ban on gas powered vehicles. The very first sentence, not full sentence, but the very first statement that's in there.

16:11 So why is this? Well, one of the reasons you can tell that this is the conclusion is because there's what's called an indicator word. The word because. The word because is a premise indicator word. tells us that whatever follows that is a premise. And so if that reason is being offered in favor of something, in this case where you have a statement, the word because and another statement, that tells us that the first one is the conclusion. That's what's going on here.

16:44 So there are several of these indicator words for both premises and for conclusions. I want to go through these real quick. What I want you to do is I want you to pause and write them down. I'll say them once, but I'll say them fairly quickly and then we will continue on. So once again, these are premise indicator terms. They are a good hint that what is coming is a premise. They are not a guarantee that what that that they're that there's a premise there. So here's what they are. Oops.

17:20 Oh, sorry. Here's the argument in standard form. Okay, here are our premise indicator words. Because, due to the fact that, in as much as, in view of the fact, being that, as indicated by, given that, since, for, seeing that, assuming that, for the reason that, as the reason being, these are our premise indicator words. There are also pause now so you can finish writing them down and I'm moving on. There are also conclusion indicator words. Now again, these are terms that authors often use to tell you that what's coming is the conclusion of the argument that they are making.

18:10 Here they are. Therefore, it follows that it must be that. Thus we can conclude that as a result which implies that so which means that consequently hence and air go. Okay. So that is what's going on with premise and conclusion indicator terms. We will very frequently be going over arguments from pros and trying to extract them and put them into standard form. These premise and conclusion indicator terms are very very helpful for doing that. I think the most help they offer is not to memorize all of these and then look for them very distinctly, but to see that these kinds of terms play a particular role in writing and that role is telling you reasons or telling you the thing that they are that the author is trying to show. And so getting the flavor, the veilance of the the vibes of these things will help more I think than simply memorizing them.

19:28 Okay, looks like a connections board from New York Times games. Okay, the next thing I want to do is I want to split arguments into two varieties. And when we split arguments in these two varieties, we'll see that we should treat them very very different. So arguments come in two flavors, two forms.

19:58 One is called dedductive arguments and one is called inductive arguments. This is how the course your course right now is structured. We're going to be thinking about deductive arguments in on their own and we're going to be thinking about inductive arguments on their own. That's how it works. The basic idea is this. Dedductive arguments are arguments where the author is trying to give definitive proof of the conclusion.

20:30 like full on period. The conclusion is true if these premises are true. An inductive argument is one that's not trying to give definitive proof. It's not even trying to give definitive proof. It's merely trying to make the conclusion probable. Trying to say, hey, it is more likely than not that the conclusion is true, and so you should believe it on those grounds, right? And so deddeductive and inductive don't have anything to do with like how valuable these arguments are. Many claims that you should believe in are merely inductively supported. That doesn't mean that they're like lesser than or anything like that. I mean the level of proof is lower like your level of confidence should be lower but still that's you know it's not the argument's fault.

21:25 Okay. So let's talk about these on their own. So a deductive argument is intended to provide logically conclusive support for its conclusion. Logically conclusive support. What this means is that if a deductive argument works, if its structure, as we'll see shortly, is good, then that means if the premises of that argument is true, the conclusion must be true.

21:59 So a good deductive argument is one in which if the premises are true, the conclusion has to be true. There's no way for the conclusion to be false. On the other hand, an inductive argument is intended to provide probable but not conclusive support for its conclusion. And so what that means is if an inductive argument has a good structure, then that means that if the premises are true, the conclusion is likely or probably true.

22:38 Okay, so we have a term for when a deductive argument succeeds in providing this logically conclusive support and we have a separate term for when an inductive argument succeeds in giving probable but not conclusive support. These terms are respectively. So for deductive arguments, we say an argument is valid if if its premises are true, then its conclusion must be true.

23:13 And we call an inductive argument strong. If if its premises are true, its conclusion is likely to be true. So valid slashinvalid, it's the opposite for deductive, strong or weak for inductive. Okay, that's the basic idea. Let's go through each one on their own. So let's do deddeductive first. Okay, so for a deductive argument, we say that a deductive argument is valid. See it on the slide. If the following holds, if the premises were true, the conclusion could not be false. The premises were true, the conclusion must be true.

24:00 That is, if the premises are true, then there is no way that the conclusion can be false. The term valid here is not a synonym for true. You know, the way we say things like that's a valid opinion. No, no, no. That's not how it works in logic class. Valid is a technical term. meaning it has provides the argument provides logically conclusive support for its conclusion. A deductively valid argument has the kind of logical structure that guarantees the truth of the conclusion if the premises are true.

24:37 By logical structure here, I don't mean what the argument's about, like the content of the argument, but instead the way that the premises and the conclusion fit together is what validity amounts to. So, here's an example. All smartphones emit radiation. Premise one. Premise two, the iPhone 16 is a smartphone. Premise three, therefore the iPhone 16 emits radiation. Okay, cool.

25:11 We have an argument. Notice that this argument is valid. Meaning, if the premises are true, the conclusion has to be true. If you accept that all smartphones emit radiation and that right here we got a smartphone, then it follows that this thing emits radiation as well. It's just already like there's a sense with valid arguments in which the conclusion is already contained within the premises. You're not learning anything new when you find out that the iPhone 16 emits radiation if you already know premises one and two.

25:52 I will say you don't need to like have a good instinct for when an argument is valid. This is something that we're going to be spending a a large chunk of class trying to figure out is when arguments are valid. So, I just want you to take my word for it on these ones. but we will figure out how to actually prove validity. Here's a couple more examples. Premise one, all politicians are extraterrestrials. Premise two, AOC is a politician. Conclusion, so AOC is an extraterrestrial.

26:30 perfectly valid argument in the technical sense. If the premises are true, then the conclusion must be true. Now, of course, we know that the premises are not true in this case, right? It is not the case that AOC is a politician. JK JK, it is not the case that all politicians are extraterrestrials, right? Premise one is false. However, that matters not at all to whether the argument is valid because note go back here. Valid means if the premises were true, the conclusion must be true.

27:07 Looking here, if one and two were true, then three would be true as well. So validity just has to do with supposing the premises are true. Must the conclusion be true as well? Another example. If increasing the minimum wage caused significant job losses, then regions with higher minimum wages would have higher unemployment rates. That's your first premise.

27:44 I'll say that again. If increasing the minimum wage caused significant job losses, then regions with higher minimum wages would have higher unemployment rates. Premise two, regions with higher minimum wages often have lower unemployment rates. So, increasing the minimum wage does not cause significant job losses. Okay, this argument is valid. If the premises are true, then the conclusion has to also be true.

28:20 This one's harder to say. You sort of just have to look at it until you notice it, right? So, premise one is saying if when you increase the minimum wage, that caused a bunch of job losses, then what you'd see is that regions that have higher minimum wages would have higher unemployment rates also because they'd have more job losses. But regions with higher minimum wages actually have lower unemployment rates. If both of those things are true, then that means that very first thing that we said, if increasing the minimum wage cause significant job losses, that must be false. Increasing the minimum wage doesn't cause significant job losses.

29:07 So in each of these three arguments, if the premises are true, then the conclusion must absolutely po positively be true. It's impossible for the premises to be true and the conclusion false in these valid arguments. The conclusion logically follows from the premises. So that's a valid deductive argument. There are also invalid deductive arguments, ones where the author is trying to give logically conclusive support but fails to do so. Here's an example.

29:46 All chocolate contains sugar. All ice cream contains sugar. Therefore, all chocolate is ice cream. So this argument does not guarantee the truth of the conclusion on the basis of the truth of the premises. It's true that all chocolate contains sugar, right? And it's true that all ice cream contains sugar or some sugar substitute. It does not follow that all chocolate is ice cream. Or in other words, it is possible for the premises to be true and the conclusion to be false.

30:26 That means that it is not valid because validity means if the premises are true, the conclusion must be true. In this case, the premises are true. Chocolate contains sugar or some sugar substitute. Ice cream contains sugar or some sugar substitute. But it is not the case that all chocolate is ice cream. So this is not a valid argument. This is an invalid argument. Again, we're going to talk a lot about validity. What you need to know for right now is what validity conceptually entails.

31:04 Validity entails that if the premises are true for some deductive argument, then the conclusion must also be true. That's what you need to know. Let's move on to inductive arguments for a moment. So in the same way that we had validity for when you have a good structured deductive argument, there's an analog in the inductive case called strength. So we say that an inductive argument is strong if the following condition holds.

31:45 If the premises are true, the conclusion is probably or likely true. Right? So it's not as strong as validity. Validity guarantees the conclusion if the premises are true. Strength merely guarantees the probability, the likelihood of the conclusion if the premises are true. So, here's an example. 95% of Broadway musicals that win multiple Tony's become financially successful. Hamilton won 11 Tonies, so very probably Hamilton will be financially successful.

32:22 So, notice that this isn't valid. It doesn't guarantee that the conclusion is true, right? Like it's very like like it's likely that Hamilton will be financially successful, but 5% of Broadway musicals don't become financially successful. So there's a one in 20 chance that Hamilton will not be financially success. One in Yeah. One in 20 chance. So it can't guarantee the conclusion, but it can't it does make it quite probable.

32:58 I don't know what that sentence at the bottom means. Ignore that. I think there's something wrong there. Okay. So, let me say a little bit more about strength and inductive arguments and all that. so an an inductive argument that succeeds in providing this probable but not conclusive logical support is said to be strong. An inductive argument that fails to provide such support is said to be weak. An inductively strong argument is one such that if its premises are true, its conclusion is probably or likely true. Again, the structure of a strong argument can't guarantee that the conclusion is true, but it's still worthy of acceptance.

33:50 It's more likely than not. It's of course better to give a deductive argument than an inductive, but just because an argument is inductively strong is not a mark against it. We're trying to find the best reasons for some claim. And sometimes the best reasons we have for a claim just make that claim probable. It's just the way it goes. Okay. So, couple more things here.

34:25 So, so far all we've talked about with regards to inductive and deductive arguments is the structure of the argument. And if it has a good structure and it's deductive, we call it valid. If it has a good structure and it's inductive, we call it strong. And this structure has to do with if the premises are true, then the conclusion is either true or probable. That's one. So the the structure of the argument is one way of assessing how good the argument is. There is another and that is the truth of its premises.

35:05 Here's the basic idea. Look at strength. Sorry, it's like backwards. Strength says if the premises are true, the conclusion is probably true. So if we have a strong argument, that doesn't tell us we should believe the conclusion. That doesn't even tell us that we should believe that the conclusion is probably true. Why not? Because it just says if the premises are true, then the conclusion is probably true. For us to believe the conclusion of an argument, we need to also accept that the premises are true. So that is the second measure of a good of goodness for an argument is the truth of the premises.

35:49 So logical validity or logical strength is essential for being a good argument, but it's not enough on its own. Good arguments have to also have true premises. So a good argument is one that has proper structure, valid in the case of deductive, invalid in the case of or sorry strong in the case of inductive and it has to have true premises and so we have particular words to identify these things technical terms. So in the case of deductive arguments, when a deductive argument is one valid and two has all true premises, then we say that that argument is sound.

36:40 Sound meaning like you've heard people say that's sound reasoning, right? Sound meaning all the premises are true and the argument is valid. Meaning if the premises are true the conclusion must also be true. We have a separate term for the case of inductive arguments. For inductive arguments if the argument is strong meaning it has a good structure and has all true premises then we call that argument cogent.

37:17 meaning it has all true premises and if the premises are true the conclusion is likely to be true. The opposite of sound and cogent are unound and uncogent. Not that interesting. Okay. So what we essentially have is these two parallel tracks in some sense. For deductive arguments, we can assess its structure in which case it could be e either valid or invalid and we can assess the truth of its premises where they are either all true or at least one of them is false and if it is both valid and has all true premises then it is sound. On the other side of the split structure, we have inductive arguments which when we assess their structure, they are either strong or weak. And then we can also assess the truth of the premises. If it is strong and has all true premises, then it is cogent. If either it is weak or it has at least one false premise, then it is uncoent.

38:30 So here's an example of a unound argument. All penguins can fly at supersonic speeds. That's premise one. Premise two is emperor penguins are penguins. Premise three or sorry three which is the conclusion. Therefore, emperor penguins can fly at supersonic speeds. So this argument is valid. The structure works. If the two premises are true, then the conclusion must be true.

39:06 However, at least one premise is false. Namely, premise one, all penguins can fly at supersonic speed. In fact, none of them can fly at supersonic speed. And so, this argument is valid, but it is not sound because it has a false premise. Let's move on to the case of inductive arguments.

39:38 So a good inductive argument must also have strong premise true premises. For example, premise one, scientific studies show that 98% of Olympic swimmers have six fingers on each hand. Michael Phelps was an Olympic swimmer. So it's likely that Michael Phelps had six fingers on each hand. Again, this is strong. If premise one and two are true, then it is a 98% likelihood that Michael Phelps has six fingers on each hand. However, we know that not both premises are true. Premise one is false. It is not the case that 98% of Olympics swimmers have six fingers on each hand.

40:17 So, the premises, if they're true, would make the conclusion likely. So, it's strong. But the key premise is false, meaning that it is uncogent as an argument. Lot of concepts going on here. I highly recommend that you read chapter three of the Vaughn book. And if that's still not doing it for you, go back and watch this again.

40:55 promise you it'll make things better. When you're introduced to a lot of terminology like this, usually you just need multiple times in order to get it right. There's one final bit to this and that is implicit premises. Sometimes arguments have what are called implicit premises, meaning that they're not explicitly stated, but they are required for the argument to work in the way the author intended.

41:25 Take this example. The continuous use of smartphones during family meals prevents meaningful conversation and connection. Therefore, smartphones should be banned at the dinner table. When you think about this argument, when you're thinking about whether it's a good argument or a bad argument, I think probably most of us think that the person who intends for this argument thinks that it's a pretty good argument. But as written, it doesn't guarantee the conclusion or even make the conclusion likely.

41:58 Instead, we need an additional premise to get us from the first premise all the way to the conclusion. What we need is something like anything that prevents meaningful conversation and connection during family meals should be banned. Now when you have these two premises, the continuous use of smartphones prevents meaningful conversation. Anything that pre prevents meaningful conversation should be banned. Therefore, smartphones should be banned. Now we have a deductively valid argument.

42:34 This is much much stronger than an invalid argument that was present without the implicit premise. And so when should So the point is sometimes when you're interpreting an argument, you have to add unstated premises. when there's a link missing, when there's a gap between the premises and the conclusion that seems to be implied by the author. When exactly should we try to find these unstated premises? Well, the answer is sort of difficult, but the obvious answer is that we should do so when there appears to be a link missing, a gap, an implied logical link between premises and conclusion that is not just a common sense generally accepted assumption.

43:25 That's the idea. sort of a more of an art than a science for this sort of thing. but something we work on. Okay, that's that. Catch you next time.