Hi, my name is Jess and I am a research fellow at Imperial College London and today tonight this morning wherever you are I thought I'd tell you a little bit about the work I've been doing on Wikipedia and trying to particularly use it as a platform to tell the stories of scientists and Thank you so much to Annie for all of the incredible work you do on Wikipedia and also to Bunty for arranging this amazing workshop So so yeah, I kind of work on new materials for different kinds of technologies and optical and electronic devices But I think I've become kind of Equally as interested throughout my research so far on how we develop and kind of train the next generation of scientists And really we want a scientifically literate society to look like I think providing people with access and information about science is a critical enabler in their decision making and Also will hopefully design a more equitable fair tomorrow. So so so yeah, I have these kind of two main interests I love the material science I do, but I also want everyone else to have that appreciation and awareness of science as well I think if we look at the challenges facing our world whether that's something like climate change a new pandemic Access to affordable and efficient and reliable health care Science has the potential to help people take on those big challenges, you know to solve these huge problems But unfortunately at the moment people opt out of science at a really really young age due to their biases and Misconceptions about the subject. I also think that the teams of people who get the opportunity to do science are Not as diverse as they could be and we know that when teams are not diverse They actually do worse science. We see it in the diversity of teams who design facial recognition software or develop and deploy Policing algorithms algorithms to determine who shouldn't shouldn't be pleased and then who shouldn't end up in prison And also the teams who do medical research that actually we have nowhere near the levels of diversity We need to reflect and serve the society who essentially these these disciplines respond to so if we take Facial recognition software for an example We know that the data sets that these facial recognition software models were trained on Incredibly biased it over represented certain face types particularly young white men particularly young white men in California And as a result couldn't identify faces who didn't fit that mold We see it in policing algorithms that policing algorithms Over-policed certain parts of the states and therefore we end up with Disproportionately higher numbers of young men from communities of color in US prisons And we see it in medical research how women and people from the global south are Consistently ignored and excluded from clinical trials and also that impacts the kind of doses and the recommended allowances that we have for certain medications So in some aspects of science and and society this lack of diversity has a Really profound and very clear impact on the technology that people creates And I think we'd be naive to think that it wasn't impacting the kind of blue skies You know big fundamental scientific questions were asking as well and in my field of research You know what kind of material makes a great solar panel What is the fundamental origin of matter at the start of the universe these big scientific questions? Have historically only had a few kinds of people contributing to try and solve them And I think that science has lost out as a result Just to give you a kind of picture of just how bad the statistics are if we look in physics departments in the UK Only about one in five of our undergrads women Less than 20% of our undergrads are from an underprivileged background So it's an incredibly white and incredibly privileged subject to study and actually less than three percent of our undergrads are black And if we see how that propagates through an academic career trajectory About one in ten of our physics professors are women and and fewer fewer than a Handful of our physics professors are black the statistic is that zero percent of our physics professors are black But this wouldn't count kind of one or two people for risk of identifying them So we have nowhere near enough women We have nowhere near enough people from certain socio-economic groups and we have nowhere near enough physicists of color I think this is for a few different reasons The big one is people's education and access to science and then how we're supported and guided through that our early careers And also how we recognize celebrate and honor phenomenal scientists from historically excluded groups. I think within this kind of three stage Sages of our career trajectory. There's a few different aspects where we can have an impact Thinking about people's perception and awareness of a subject like physics Building up young people's confidence and resilience saying hey There are physicists just like you who came from the same schools as you and are interested in the same things as you Also giving people the opportunity to build their own networks and give people advice and to act as cheerleaders and sponsors And I really think that Wikipedia is kind of a powerful way to do that first part and also a powerful way to do the cheerleading and sponsoring I've been thinking about this for a really long time, you know during my PhD I started organizing these big mass outreach activities and taking science and engineering and technical skills To as many young people as possible But what I really started to realize is the types of people who show up to do a coding course on an evening Or on the weekend or the kinds of kids who are likely to come to a lecture at a university They're probably the ones who've already made their mind up, right? If you're showing up at a university on the weekend, you've probably opted in to some kind of scientific career anyway But how could we take these stories further? What way could we really use to celebrate and honor people's recognition? And that's really how I landed on Wikipedia If someone's made a phenomenal discovery, if there's a really awesome aspect of science that everyone in the world should know about it What better platform to put it on? Wikipedia is the most important reference tool in the entire world It's the fifth most popular website most frequently visited website in the world Which is really quite staggering when you consider what it's up against and also, you know, it's over its 20th birthday now This isn't just a kind of boom and a rush. This is this is here to stay this democratized open-source open-access platform for sharing knowledge is Critical to the way that our society runs Just to kind of give you an estimate of how many people are looking at Wikipedia It's about 15 billion page views every single month, which is just such a staggeringly big number It's really hard to get your head around But it really emphasizes that Wikipedia is a really powerful outreach tool It can let us communicate science and communicate what scientists are and what scientists do with a way bigger audience than me inside any lecture theatre Wikipedia is used by all different aspects of society from parents and children to home assistants things like Google and Amazon Alexa and and Siri and all of these things Google home Amazon Alexa and Siri they go to Wikipedia for that information Teachers academics professors they go to Wikipedia to populate their lecture courses and come up with curricula people in Policymaking go to Wikipedia when they're trying to design new laws and regulations people in journalism go to Wikipedia and Actually one of the most incredible ways that I think people don't recognize in Wikipedia is being influential is in science Itself there was an absolutely fantastic study a few years ago by a couple of computer scientists Neil Thompson and Douglas Hanley And in this study they looked at Wikipedia and they did a randomized control trial, which means they chose a subject like chemistry They got their students in their classes to write Wikipedia pages about topics in chemistry that weren't on Wikipedia And they uploaded half of them to Wikipedia and they didn't upload the other half this is a randomized control trial and then they looked for the presence of these topics in scientific literature and what they found Was that if something was on Wikipedia it was more likely to come up in scientific literature So that topic just by the nature of being on Wikipedia and being accessible and being easy to understand Was influencing the course of science itself They also found that these Wikipedia pages acted as a kind of mini review on a subject It would help introduce people to a field if pages were if Articles were cited on Wikipedia. They'd have more citations than their counterparts that weren't on cited on Wikipedia So it's kind of a cost-effective way of doing outreach and research communications. It's quite incredible So obviously what's on Wikipedia really really matters and I guess I've been asking for kind of the last few years now Is what matters on Wikipedia and unsurprisingly? I wouldn't be here today if the answer wasn't Harley Yes, I wouldn't be here today if I didn't deeply care about Wikipedia But also recognize that there's work that we could all be doing to make it better Particularly if you look at issues related to women biographies of women on English language Wikipedia still only make up 19% of the biographies so women are massively underrepresented actually people from all historically excluded groups and issues that they care about are Incredibly underrepresented on the site. It feels really complete. It feels really comprehensive But we know there are huge gaps and on pages about science and particularly Emerging areas of science and ever-changing areas of science like the climate catastrophe Pages go out of date almost as soon as they're written So scientists really have to be there to help out and improve and to fact-check these pages And actually I think something that has kind of bummed me out recently And I've started noticing a lot is that pop culture is incredibly overrepresented on Wikipedia and technical subjects like science and a lot of maths and engineering Really needs refreshing or really needs creating at all Actually, we find that not only are women underrepresented in the biographies of Wikipedia But the biographies about them when they do get written are even more likely than the biographies of men to be deleted from the site So not only do we have to do that legwork on creating the content But we have to do that advocacy to say hey women have this right to be documented in you know Incredibly important encyclopedic record and we're gonna keep doing it and keep shouting about them because these women are incredible So since the beginning of 2018 I've been writing every single day the biographies of one scientist and scientists of color and scientists and engineers from Historically excluded groups. It's been this kind of extraordinary journey Where I I have all of this fun in the lab in the day I get home I have dinner and I sit down and I write my Wikipedia page And I get to learn about someone new or some discovery. That's new or some university That's new or some protest that's new or some part of the world that I've never thought about before I'm I'm over 1,700 now Which I'm super super proud about and the people I've written about are just absolutely Sensational you know people like Sarah Gilbert the dame who came up with the Oxford AstraZeneca vaccine She was then made you know I'm sure this is a result of the Wikipedia page But she was then made into a Barbie or Kizzy Corbett the pioneer of the Moderna NIH vaccine Who was nominated by Anthony Fauci for time person of the year or the most incredible story Gladys? West Mathematician who was born in the 1930s in Virginia Gladys West actually attended a historically black college in university She studied math she worked in the US government and she did the early calculations for GPS technology So sat nav kind of Google Maps type thing and and actually Gladys West page when I made it at the beginning of February 2018 There was so little about her online and gradually it's grown It's grown to the point that the BBC nominated her for their top 100 people in the world So suddenly she was on the BBC home page and everyone was clicking through to her Wikipedia page The US Air Force inducted her to their Hall of Fame So now she's on the US Air Force Hall of Fame page And there's all of these incredible photographs of Gladys West in wiki commons The Guardian wrote an article about how Gladys West was the hidden figure who helped to invent GPS and then last June The Royal Academy of Engineering our big prestigious engineering body awarded Gladys West the Prince Philip Medal and Prize for engineering She's the first woman in history to win this award and I speak about Gladys West so often that I think a tech company who I was evangelizing to about Wikipedia felt sorry for me and thought why is this this little lonely physicist so obsessed with this Mathematician so they set up a zoom with me in Gladys West which was just the coolest thing in the entire world So you have this capacity with Wikipedia to really improve someone's recognition and awareness and people's awareness of their story Just to give you a kind of snapshot of a Wikipedia editathon we ran at the beginning of the pandemic This was for shutdown stem day as part of the strike for black lives The kind of black lives matter movement that took over the world and and really has had a strong influence on the way That we think about racial and ethnicity and and policies around these things We had a Wikipedia editathon to try and improve the representation of African-American and black faculty And Wikipedia and also topics that they researched and were interested in We had about 200 editors connecting over the course of 24 hours And they created or edited about 500 articles and and created 60 So we have people working on about 500 and creating 60 We then tracked the impact of these pages for like a month I think and after a really short time these pages had racked up millions of page views So this was all a one day editathon I've actually worked with my friend mariam and a bunch of other incredible people including farah quayser from 500 women scientists To write about why this is a critical thing that we do and also how academic institutions can get on board with helping us To improve wikipedia's gender and knowledge gap So I think wikipedia gives us this unique opportunity to build recognition and awareness and appreciation of a subject and of a scientist But also improve people's access to scientific knowledge You know often the kinds of topics that we research and are interested in are stuck behind paywalls or Enclosed in too much jargon for the general public to understand And wikipedia gives us the tool to tackle and change that and really open access to a discipline It also lets us fight this war against scientific misinformation and pseudo science that I hope you're on board with fighting as well I think you're going to hear a lot and probably have learned a lot at the course of this workshop About ways you can get involved with editing wikipedia But I would say you don't have to create a page entirely You know creating a page is fantastic But even if you just take a page and work on it and improve it You're already contributing to make the world one of the world's most important website an even better place to be You can add links between different pages Make sure Gladys west is connected to every page about virginia and mathematics and gps technology You can upload images and media You can start to translate a page and think about ways that you could Improve people's awareness and appreciation of it in other countries and of course you can create content and topics as well So I think that's enough from me wikipedia is this Incredibly important and vital source for sharing information for democratizing access to knowledge But really for giving us the opportunity to celebrate Incredible scientists and engineers from historically excluded groups because if you don't do it, no one else will So thank you so much. I'm gonna try and be up to answer questions But it's super early in the morning my time and I have a crazy teaching schedule this term So thank you so much. I'm on twitter for now and I'm also at jessica.wade at imperial.ac.uk Have a fantastic rest of your workshop and please please please edit wikipedia


Welcome to Psychic Medium, Tony Green. Flipping my hair all over the place. I'm Tony Green, The Psychic Medium, and let's go. So, a couple of announcements before I start the show. And the first announcement is, yes, I will be taking callers. The call line is up and working so far today. The number to call in is<PHONE_NUMBER>. If you're waiting in the call log, thank you so much everybody for calling in and waiting and being patient. Have an exact question or connection ready for me. I don't just give random readings ever. I figure if you're connecting with me, there's something you want to know, somebody you want to connect with. Have that one question or one connection ready. And when I call out your area code, let me know your name, your first name only, where you're calling from, and your question or connection. If you do have a connection and you have a question for your connection, please let me know that question right away. Next. Hi, Stevie. So, my little brother, Stevie, always watches my show and then calls me and gives me feedback on everything. It's so awesome. And he wants so badly to be on the show. I might actually do a call and have him on the show this morning with me. We'll see how the show goes. So, before I pull that, let's just see how the show goes. And then, what else? What else? Okay. So, this show does air on WSES and all of their streaming channels. By the way, hey Scott, it's been so long. Thank you so much for all the hard work you do. It airs on with Rude Rangers TV and all of their streaming channels. Also, hey Rudy, I miss you so much. So, anybody who is watching on WSES or any streaming channel, if you want to join the show live, it's noon every Monday and Wednesday for a minimum of 30 minutes. The show does go in a 30 or 60 minute increment simply because those are the time slots that fit into TV. So, if I'm at 30 and we go over, I'm going to push that 60 and I get to take more callers and answer more questions. If I'm getting near 30 and I'm completely booked up for the day or something else going on or whatever it is, I'm going to cut it at that 30. But I do try to do at least 60 every Monday and every Wednesday if I can. What else? What else? What else? Okay, so now I think any other announcements? I think we're ready to get started. Okay, so the first thing I've been drawn, there's so much. Oh my gosh. So, I miss two weeks worth of shows because I was going through it and we all are. And I had some lung and throat stuff going on and I couldn't talk without coughing and it was so, I think the universe was saying, just shut up for five seconds.  So, I could not do the shows and I just basically slept for two weeks, which felt by the way pretty amazing. I like my bad. But anyway, let me get back on point here. But during that two weeks, so many messages and channelings were coming through. And I was just getting so, so much about the world, what's going on in the world, why things are the way they are, and what is kind of needed to I don't want to say transition. I don't want to say transition, but what we need to do as a people, as a people that might feel a little bit powerless. Now, I want everybody to know, and it's really super important for anybody watching and or listening to my show to know, because I'm on, I think just about every single podcast or most of the podcasts, there are out there. So, if you are listening to or watching the show, number one, you can join live, I think I covered that. But one of the really important things to know is what we can do moving forward to help this. Now, when I'm on the show, 98% of what I say is channeled, meaning it's coming through me intuitively for you. I'm not making it up as I go along. It's just coming out of my mouth. And sometimes I don't know the next thing that's going to come out of my mouth. Sometimes I'm not aware of the next thing I'm going to say. And in that case, you know, it's, I always have faith that it's going to be something good, hopefully. But what I will say is I'm going to channel just a wee bit here about some of the things I was receiving during the past two weeks. And hopefully it will be well received by everybody. So, here we go. And everybody who's in the call log, please be patient. I am going to get to you. I promise you I will get to you and I'll answer your questions or help you connect with loved ones and everybody on YouTube. Hey, thank you so much for being here. I love all of you so very much. Okay. So, one of the main things I was getting is divide and conquer and distractions. So, most of us know that a lot of what's going on right now is a form of divide and conquer mixed with distractions. And the biggest thing we can do is love thy neighbor. Now, I know that sounds so hokey, but that's just what blew out of my mouth. It is. No matter what we see or hear on any venue, we have to take it with a grain of salt. And we have to go past what they're like peddling and look at the bigger picture.  There's a bigger agenda. Pay attention, folks. Pay attention, folks. Pay attention. Well, POTUS on White House dot, I think it's White House dot org or gov, whatever it is. In one of POTUS' recent speeches, he said, near the end of the speech at the White House, he said, and I'm ushering in a new world order. Let that sink in. This means our government is about to hand over the government of our country to another entity. And they're telling us they're doing it. He told us they're doing it.  Those are all distractions. The divide and conquer part comes in where they make us think we're not getting along with each other or we don't like BGTELQ. Please forgive me if I didn't get all the initials in there or it's this color against that color or any of that. I don't have a problem with anybody unless they're shanky to me. And I think 99% of the people in this world are like that. We're good until you're shanky with us. You're not shanky with me. I love you. I got nothing but love for you. And if you are shanky with me, I still love you. I'm just not going to deal with you. I'm going to walk away. Okay? We as a people need to embrace each other right now and not listen. Don't pick up what they're putting down. Don't buy what they're selling. We need to work together. Everything that's going on right now is extremely intentional because if they can get us in a state where we are desperate enough, fearful enough, hungry enough, they can get us to do anything. Don't let this happen, folks. Work with each other as a whole. Work with each other as a whole. Okay? Now, having said that, I'm not going to go any further into that. I'm not. I'm going to let that whoo. I've said what they need me to say on that. And we are now going to start taking callers. Let's go to 205. 205. How can I help you today? Tony, thank you so much for taking my call. And thank you so much for your platform, your services. They are so vital at this time. Thank you. I appreciate you. Thank you so much. Thank God for you. My question today, you're welcome. My question is sitting around love. There is a guy by the name of T, gentlemen by the name of T. I've been knowing for about eight years in passing, we would pass each other, we would hold small conversations, and we would flirt a little bit. And then we would keep it moving. And we did this for about eight years. Well, at some point we lost communication. He's the place that I used to see him in all the time. And we lost communication for two years. Well, about a month ago, I bumped into him and this time we exchanged numbers. We have seen each other, maybe like a week after we exchanged number. We went out, we're just kind of texting each other. I haven't seen him again. I've invited him over, but he's had family stuff going on. I just want to know what is his intention? If he serious would like to be, what do you see? Okay, the first thing I'm getting is that you need to take this. You're welcome. The first thing I'm getting is you need to take this slow. I feel like he might, now remember, energy and timelines can kind of overlap. He might have something he's resolving. Let me put it that way. He's in the middle of resolving another thing right now. If he hasn't already resolved it, he's in the middle of resolving it. I do feel like four of the first four things that the two of you do together, and I'm specifically hearing the number four, they should not be at each other's places. They should be out and about coffee, dinner, a festival where you can walk around and talk for a bit of time. I feel like a minimum, the first four should be out and about.  I do feel like this does have the potential to be something strong and longer lasting.  Let's not worry about that in the beginning. Let's go straight for the, like if you were my partner in business, these are the things I would require to know. So let's get to know those things and then decide if you want to give him the key to the castle or the business, so to say. I do feel like it's going to be a little bit hectic in the beginning, getting together. Just be patient. Here's what, one of the things, even I forget this being a girl and all, I think sometimes guys do better with managing their impatience with everything except for what's in their pants and their need for it to go quickly. Guys can move in a more patient way than women can. What we need to remember is if this is the one we have forever, so we don't need to rush it and if it's not the one, we don't want to rush it and miss things and not, how do I'm going to say a double negative? I can hear English teachers all over the world cringing right now and not know it wasn't the right person. I don't even know how to say that. I don't know how to say that appropriately, but what I'm going to say, the way I would say it is we need to take our time and realize, yes, this is the person that I do, checks all the boxes, clean, safe, yada, yada, and if it is forever, we have forever. If it's not, at least I didn't go further, get more invested or go further than I wanted to. You want to make sure it's good stock, not penny stock, so to say. I don't really even know what that means. And if you're building a business, you want to make sure you're building it on a good foundation and you are really, really building the right business. It's nice if you can open a beauty shop and run it. It's better if you're a beautician. That's what I'm saying. Don't build a business that you don't know anything about. I hope these analogies make perfect sense to you. I do feel like he is either ending something or trying to end something or just got out of something and it is going a little slow because of that. Now, I am going to say this just because I feel, because they're making me say it, I feel like there's a slight chance that whomever or whatever, I don't want to say who, but whatever is ending right now, it might take a little bit longer than anticipated. I do feel like you know that statement, last ditch effort. I'm kind of hearing that, but I feel like the outcome is inevitable. But we don't want to, we don't, we want to take our time and make sure we're entering imperfect timing, not chaotic timing. Does that make sense to you love? What? Oh yes, because he mentioned a divorce, but he had been with this person for 15 years, but I got this then because he said he hadn't been in a relationship for over two years that maybe this divorce took place two years ago. But that's not to say that he hasn't probably dated, you know, since then. So I just, I know he said that and you know, it was a real possibility that he probably had maybe entered something or whatever the case may be, but I do understand. Yeah, and they could be, they could be talking about like when ending something, like what could be ending, this could be the finalization of the divorce or what, and divorces do, depending on where you live, they do take a year and a half to two years. So that could be what they're talking about. And we want to, when somebody is going through a divorce, especially we want to enter at the right time, because there's a lot of residual emotions, especially in a divorce, because especially at the, up until the end of the divorce, it's all, I can't think of the word, but you know, speculation, it's all speculation about division of property, division of children, division of everything. Now what I'm going to tell you is once that divorce is final, it hits, it hits, oh, I have to write a check or divide the property or sell this stuff and everything I built over this period of time is now done. And it hits and we don't want to enter a situation if somebody is feeling defensive because of what they just had to end. We want to enter a situation when they have that under control and they have a good grasp on it and all their negative feelings and emotions about their last situation are done. In other words, they've healed and they're happy with the outcome and moving forward. That's why I think they're saying, take your time, allow this to go, you know, a minimum of four get together outside of your place, his place at public places and allow it to grow the way it's going to grow and really get to know each other and allow the timing to be what the timing is going to be. Again, if it is somebody that we have, if it is the person, we have our whole entire life. It is, if it isn't, and we go too fast, we're going to waste more time than we should with the person. Okay, La? Yes. Thank you so much. I love you. Many blessings, Tony. Thank you so much for the message. Thank you too. And I love you so much too. And I truly do hope this is helpful, but I do look forward to hearing more about it. And I hope you keep us posted. I sure will. Thank you. Thank you. I'm going to go directly to the next caller who is 541. If you would like to call in, please call<PHONE_NUMBER>. Okay, 541. What's your name? Where are you calling from? Hi, Tony. It's Nancy from Oregon. Nancy? And I love your show so much. Thank you. My question is, my daughter and my family are moving to Oklahoma on Saturday, taking a long road trip to get there.  And I was just curious, do you see me down the road, you know, seeing her again or visiting or even moving out to Oklahoma in the future? Yeah, you know what? Actually, oh my goodness. Yeah, those are amazing questions. And thank you for asking them. And thank you for calling in. Yes, you are definitely going to visit her. Yes. I do feel like if you relocate there, it's going to have to be a little bit, I don't want to say sooner than later, because what's sooner than later? I hear six months to a year, you're really going to start thinking about it and wanting to possibly take that step for it. But of course, you have free well, sweetie, you could start, you could go now and start looking or get online and start looking and working with someone. I do feel like you, given all things going correct, let me say it that way, I do feel like you are going to eventually at least try or look at relocating. If it's successful, that'll be up to you in your final decision. I do know you are going to visit there. I feel like you're going to, I feel like you will, if you do go to Oklahoma more than where you are, I think financially, it'll be a great relief to you. I think financially, it'll be a better situation for you. I don't know why they're saying that, but they are. And I do feel like if and when you relocate to Oklahoma, I feel like you are going to have a lot of new beginnings there is the way they're saying it. I feel like you are going to visit them and then you're just going to decide, yeah, I think I'm going to look into making the jump and moving there. And again, I would love to say, yes, you're going to relocate and I'm getting 70 to 80 percent you are going to relocate. There's just one thing that might prevent it. So there's something that might come in that would have you second guess that choice or make that choice take a little bit longer than you would think. So 70 to 80 percent chance you are going to relocate there. However, there, if this one thing gets in the way, you won't be able to, I don't think it's going to. And it might just be fear of relocating. It's a big change to relocate to another state is a big change at any time at any point at any age. I do think though you are going to make that decision to do it once you get over the hump of how am I going to do all of this. The timing again, timing does have to be appropriate. I think once they get in and they get settled and you go visit, I do feel like that's when you're going to make your decision. If you do it too quickly, it might be a little bit too chaotic. Okay, love. So both between the six months and your yeah, I think it's going to definitely be between the six months and one year mark that you start to make that decision and then actually move forward with the decision. Okay, beauty. Oh, that makes sense. Do you feel like they're going to be happy there? Yeah, they're going to love it. Yeah, I feel like they're really going to enjoy it. They're going to it's like a fresh new start. It's exciting for them. It won't be quite as exciting for you, but it is exciting for them. Okay. Thank you. Thank you so much for calling in. Wonderful. Thank you. Thank you, Tony. You are welcome. I look forward to hearing updates on this love. I will definitely will. Excellent. Thank you, love. Okay. I'm going directly to the next caller who is 951. 951. How are you today? I'm doing great. Thanks for taking my calls. Absolutely. What's your name? Where are you calling from? Nathaniel from California. Hey, Nathaniel. How is everything going? I'm pretty good. Excellent. Excellent. How can I help you today? Well, I wanted to see what you're seeing in work coming up for me. Okay, Nathaniel. What I'm getting for you is that there is going to be something that comes in right around the month mark. I do feel like there is, you know, Nathaniel, because you are such a wanderer, I do feel like you're going to have difficulty with any position that you get or you're going to have difficulty wanting to stay at the position is what I'm getting. So you're going to have to just, you know, kind of go into that space where you're okay just giving up this time for the exchange of the income. No position is going to be exactly what you want at this point in your life. No position is going to be, you know, that thing that makes your soul sing at this point. The one thing I do hear for you, Nathaniel, and I'm not sure how you feel about this or if you're already doing it, but I do feel like there is the potential for you to receive. I just keep hearing social security, social security, social security. So I don't know if that's something that you've looked into or thought about or maybe that you should look into or think about. You are loved. You are wanted and you are needed. Even if you don't feel it or see it on a daily basis, you are. Until Wednesday, and Wednesday I will be back at noon central time for a minimum of 30 minutes. And please join live if you can until Wednesday have an absolutely amazing rest of the year.


He's made time specifically for entrepreneurs, speaks to the fact that speaks to how much he really sees entrepreneurship as a central force for the country. It's quite a great experience.


bit of a rocky area around here. So far what we've seen may not look like it's real familiar or look like it's actually reasoning, but all of what we've seen so far is going to be used to justify the rules of implication. We're going to have rules of implication and these are rules that allow us to make inferences. Now we've been talking about validity. We tested the validity of premises and conclusions with these truth tables, which is fine. It's not bad. But telling us that in argument is valid is not the same thing as understanding the steps from the premises to the conclusion. And sometimes it's going to be more than a few. I wager that when you all looked at some of these arguments with the truth tables, you had these premises and conclusions, sometimes you looked at the conclusions like, I don't think so. Well, the rules of implication are valid. If we follow these rules properly, using the premises, whatever we infer from these rules, whether they're surprising or not, whatever we infer from these rules, that's going to be valid. If these premises are true, these conclusions must be true. So we'll be solving lots of formalized arguments. And when we look for a solution, we'll have a set of premises, which you're going to talk about when we looked at the sequence. We'll have a set of premises. And from these premises, we are going to try to infer that conclusion. Now to be clear, we can infer lots of conclusions, but we're not going to look for all the possible ones I would take forever, literally. Instead, we're going to look for the specified conclusion given in the sequence. So we'll be solving these formulas. We'll be solving these problems in logic. I'm going to show you these rules. Actually, here we go. Let's take a look at just kind of a group shot of all these rules of implication so far. This is going to be more later on. But so far, these are the rules of implication we'll be looking at. Now what I'm going to do is I'm going to take these rules in smaller chunks and use them to draw inferences. As for the explanation of the rules themselves, I'm going to go for that a little bit in this video, but I'm going to let you read the text more to get that fuller explanation. Now here primarily I'm going to show you how to reach the conclusion from these premises using these rules. Hopefully, it won't be as rocky as this area. So the first set of rules we're going to look at deal with conjunctions. If you remember, as we got from the text, we got conjunction introduction and conjunction elimination. This is just a really fancy way of saying we're going to, for conjunction introduction, we're going to create a conjunction using two already agreed upon truths. And conjunction elimination just says, well, from the conjunction, we're going to be able to infer either one of the conjuncts. So let's take a look at a quick problem of this. So here we have, forgive me for using notes, I'm not quite as talented to remember all the problems at once. So here we have two premises.  And from this, we're trying to try to refer one big conjunction p can join with the other conjunction q and r. And so when you have a conjunction, right, so we look at the conclusion, we have a conjunction. When you have a conjunction, this should already tell you that, you know, there's a good chance here that the rule that you're going to use is conjunction introduction. And this is something to keep in mind when you see the conclusion, spot what kind of complex proposition it is already that can not always, but can provide a clue as to the rule that's going to be used, at least at the end, to infer that conjunction. And as you're going to see in a little bit, the first few problems are going to look at it pretty straightforward, pretty simple. But as you see a little bit later on in this video, there might be several steps, many steps to reach the conclusion. And having said that, we have this conclusion of p and the conjunction, p can join with the conjunction of q and r. Well, again, this is a really simple thing. So we just look at the premises, we have available our two assumptions, right, marked with a, when we find p, we find the conjunction of q and r, this is not a difficult thing to figure out. We just simply use the rule conjunction introduction to infer that whole conjunction that we're looking for in the conclusion p can join with the conjunction of q and r. So again, not a difficult one. Let's look at something maybe a little bit different. All right. So this time, we've got p, we've got our same two premises, right, we got p and the conjunction of q and r. But this time, instead of conjoining p to that other conjunction, we just want to conjoin p to r. So you look at that conclusion, we got p and r. Well, the conclusion is still a conjunction. But this time, right, we don't have p just simply, excuse me, we don't have r just simply by itself. So we can't just make a simple inference from p and one line and r and another to p and r. We're still probably, since it's a good junction, we're still probably going to use conjunction introduction at some point. But this first step, but it's not just a one-step or like the last one. Well, take a look at the premises that way. Take the two assumptions in lines one and two. Well, we got p and one, well, hey, there we go. We already know what one half of the conjunction is coming from. Then we got q and r in line two. Okay. Well, r, right, this is again another clue when you're trying to solve these proofs. Find the predominant propositions in the premises. This is going to give you some clues to which rules you use to infer the conclusion. Well, r is one part of that conclusion. In line two, r is part of a conjunction, q and r. Okay. Well, we need to infer or pull out that r from that conjunction. Well, conjunction elimination allows us to do this. From that conjunction q and r, so we go to line three, that conjunction q and r, we can infer just r, just r. Well, and then we give our citation line two using conjunction elimination. Well, now we have p on one line and r on another. We want to infer the conjunction of p and r, so we can do that using lines one and three with conjunction introduction. Okay. Let's take a look at one last problem for conjunctions. A slight difference this time. We have p for one premise, for one assumption, q and r for another, except this time we want to infer p and q. Well, that's fine. We can, right? Using pretty much the same steps as before. The only difference here is that we're going to infer q from the conjunction of q and r. And this is fine with conjunction elimination. You can infer either conjunct, just using conjunction elimination. You can infer either one or you'll pull them out separately. That's fine. You can do that. We can infer either conjunction from the conjunction, not just one or the other, and then we just simply can join p and q together using our rule conjunction elimination. So the conjunction rules are not that complicated. And we're going to pretty much use the same strategy in solving all this. You look at the conclusion, figure out one kind of complex proposition is there, and from that it's going to give us a clue as to what kinds of rules are available to us to infer that conclusion. And then you'll look at the premises, try to find the conclusion in there, where is it located in the premises, and what rules can you use to pull out those atomic propositions or sometimes complex propositions, but can you just pull them out of those premises to infer that conclusion? A little less rocking. I'm going to go this way. Okay, well, we got a fork in the road. Since we can go either way, it seems like a good time to mention the rules about disjunctions. Now disjunctions, we got two main rules for now. Two main rules for disjunction. We got disjunctive syllogism, and we've got disjunctive introduction. Now disjunctive syllogism allows us to take a disjunction. Disjunction is true. And if we have the negation of one of the disjuncts, remember disjunctions are subcontract, at least one must be true. If we have the negation of a disjunct, then we can infer the other disjunct. So from the claim that at least one of these atomic, or one of these propositions is true, we have the negation of one, we can include the other. So that's disjunctive syllogism. Disjunctive introduction allows us to infer a disjunction. Now we can infer a disjunction pretty much from anything. I know this sounds weird, but remember, a disjunction just claims that at least one of these propositions is true. Well, if we already have something that's true, I am outside. I can infer a disjunction. I am outside, or I am inside. Now it's in fact true that I'm outside. Okay, but remember, we're just concerned about validity. If I am outside is true, the disjunction, either I am outside, or I am inside is also true. So that's disjunctive introduction. It seems a little weird. I mean, you could literally you can infer a disjunction with anything if you really want to. So again, from the proposition I am outside, we can infer either I'm outside or I had a turkey sandwich for lunch. We can infer either I am outside or there are 13 space colonies on Mars. We can infer either I am outside or get off the gray really wants me to go on a quest. We can really infer pretty much anything, any disjunction, excuse me, we can infer any disjunction from one of the disjuncts. That's what disjunction introduction allows us to do. So if you see a disjunction as a conclusion, well, that you might be so decent chance that that dis or at least a possibility should say that the rule used to infer that disjunction that could be just disjunction introduction is not the only possibility, but it's at least a clue. Okay, so let's take a look at a couple of problems then using disjunction introduction and the disjunctive syllogism and really we're going to help ourselves to conjunction introduction and conjunction elimination as well. Okay, so here's here's a problem. We got two premises P is the first premise Q is the second and from this we want to infer P or R the disjunction P or R and Q. Okay, well something to take a close look at that conclusion. We have a disjunction which seemingly appears out of nowhere. That's a clue that disjunction introduction might be used. We have a disjunction that seemingly appears out of nowhere and it's conjoined to Q. Since the entire conclusion is a conjunction, we probably use conjunction introduction to infer that conjunction. Now I want to I want to make a word of caution here. Disjunction introduction allows us to infer any disjunction we please from a single proposition. So any disjunction containing the proposition from that single proposition. So if we have P, we can infer P or Q. If we have P, we can infer P or R. If we have P, we can infer P or the conjunction Q and T. If we have P, we can infer P or the conditional S or T. We can infer any disjunction we please from a single proposition as long as that proposition is contained in the disjunction. You cannot do this with conjunction introduction. Conjunction introduction both conjuncts have to already appear in your list of premises. So I just want to make that clear. So the conclusion here is P or R can join with Q. So look for the conclusion. Look for the component propositions and the available premises. Well we just got P and we got Q. Well they're Q. That's one half of the conjunction is Q. The other half is P or R and so far we don't have it. That doesn't appear in our list of premises. But we do have P. That's one half of that disjunction there in the conclusion. We do have P. Well from P, we'll go down to line three. From P we can infer the disjunction P or R. This problem is mostly solved. We can infer the disjunction P or R from that first line P using disjunction introduction. That's fine. Now we can join P or R to Q and that's our conclusion line four using lines two and three and the rule conjunction introduction. Let's try another one. Okay so this time we have a disjunction and we have a conjunction. That's our premises. This junction is P or Q and the con junction is not P and not R. And what we want to infer is Q. Okay so now we have a single atomic proposition as the conclusion. That's not really any help to tell us necessarily which rule we can use. So you have to go hunting through the premises to find the conclusion. And we find the conclusion Q as one half of a disjunction and line one we got P or Q. Well if we want to get one half of a disjunction out we use a good candidate for this is the negation of the other disjunct. This is using disjunctive syllogism. We have P or Q. If we want Q out of there using disjunctive syllogism we need not P. Well where's not P? Not P is in line two in a conjunction. Now we simply just can't you know say oh well lines one and two disjunctive syllogism. No right because the half of that disjunction is not a conjunction. Instead we need to pull not P out of that conjunction to use for the disjunctive syllogism. So let's do that we already have a rule that lets us do that conjunction elimination. So we pull not P out of the conjunction in line three using conjunction elimination then we can infer Q using disjunctive syllogism and that's how we get Q finally out of that disjunction. So far so good. So you notice got two steps there at that time a little bit more to it. So these are the rules we got disjunction elimination excuse me we got disjunction introduction we got disjunction introduction and we have disjunctive syllogism. We have one more rule about disjunctions we're not going to cover that to the end because it actually combines a couple of different things. Well that's going to get us started with disjunctions. So so far we've covered conjunctions and disjunctions. This area is safe on the condition you don't go and jump off any rocks. That's my really clumsy way of trying to introduce conditionals. So you remember conditionals if P then Q and this expresses the truth relation of sufficiency. P is sufficient for Q it also expresses necessity Q is necessary for P one step at a time right. So we got we're going to start with two rules with conditionals. Got modus ponens and modus tolens. Now what modus ponens allows us to infer is the consequent of a conditional. It allows us to for the consequent of a conditional when we can assert the antecedent. So if I have if P then Q and I also have P well then I can infer the consequence modus tolens allows us to infer the negation of the antecedent not the antecedent the negation of the antecedent from the negation of the consequence not the consequence. So you can't take if P then Q assert Q therefore we can include P no that that's a fallacious inference that's called affirming the consequence is a classic deductive fallacy. Similarly a classical deductive fallacy is denying the antecedent that's where you take a conditional you'd say that the antecedent is false therefore the consequence is false no that is a classic deductive fallacy called denying the antecedent. But we do have modus ponens and we do have modus tolens you might even think of modus ponens as affirming the consequence that's excuse me affirming affirming the antecedents right we affirm the antecedent therefore we can affirm the consequence you can think of modus tolens as denying the consequence we deny the consequence therefore we can deny the antecedent. So you know conditional works one way all right most of the time there you can just can't run both ways but it doesn't get that automatically all right so modus ponens we have if P then Q we also have P therefore we can infer Q modus tolens we have if P then Q we have the denial of Q therefore we have the denial of P all right but let's see how this works let's try a couple of problems here okay so we have this we have two lines for our argument we have the assertion of P then we have the disjunction of P or Q and that's a the antecedent of a conditional we have the disjunction of P or Q then R and what we're trying to do is we're trying to infer R okay so let's take this step by step we look at our uh uh conclusion R and we try to find it in our premises well lo and behold it's the consequent of a conditional cool right we have R as the consequent of the conditional chances are we're going to use modus ponens to get that consequent out but then so we look at the antecedent P or Q well P or Q does not appear as a premise what are we supposed to do well does any part of that antecedent appear in the premise yes it does right we got P in line one well we need the disjunction P or Q if only we had a rule that allowed us to infer a disjunction from a premise that already was given well we do right it's disjunction introduction so we take that first line P and we infer the disjunction P or Q and from that inference I mean from that disjunction we have P or Q well that's the antecedent of a conditional so we take lines two and three together and we can now infer R using modus ponens modus ponens allows us to infer the consequent of a conditional when we have the antecedent let's try another problem we got P or Q we have P wow so far so good easy peasy well the conclusion is Q or R huh where does Q or R exist where is it present in the premises not anywhere right we don't have the disjunction Q or R and you might yeah but still you know we have that disjunction so maybe maybe maybe disjunction since the conclusion is a disjunction we already talked about how you know that can be a nice clue as to what rule we're going to have to use it well if the conclusion is the disjunction we might have to use disjunction introduction okay well let's look through the premises do we have anything in there from where we can include you use conjunction a disjunction introduction well we've got Q and line one P is not going to be any help to us but we got Q and line one so maybe if we get Q out of there we can use disjunction introduction on it and for Q or R well as luck has it Q is the consequent of a conditional and we have the we have the antecedent in line two so in line three we can infer the consequent we can infer the consequent that's Q and then line four we can infer the disjunction from that consequent right so now we got Q or R from uh uh using modus ponens to get Q out of there now we got Q or R okay let's try another problem because this this stuff can get interesting real fast let's look at this one whoa what's this Q or R and T then S business what the heck is that and R and the the conditional T or S is not anywhere in our two premises we've only got two premises well remember that's a disjunction Q or and all that mess that's behind it okay do we have R and if T then S no we don't but we got Q Q is the consequent of a conditional so we've got and we got the antecedent there with P so now we can infer Q using modus ponens again all right so far so good what do we get well we can just simply infer the disjunction of Q or all that mess that's what disjunction introduction allows us to do we can infer any disjunction from a proposition provided that proposition that that disjunction contains that proposition no problem I know that seems weird but you can do that with disjunction introduction it is completely valid go ahead and construct a truth table if you don't believe me take those two premises in that conclusion you'll still get you'll you'll you'll still get a completely valid a truth table there completely valid argument okay let's try another problem this one's a little different we've got the conditional if P then Q we have the negation of Q then we have P or R and the conclusion we're looking for is R okay well let's take this step by step the conclusion isn't any particular complex proposition so it's not necessarily clue there and what rule we might use to find it so we just have R well where is R well R is in line three as one half of a disjunction well if we want to get that that half out right we have to have the negation of the other one okay so we have if P sorry we have the disjunction P or R we want to get R out of there so we need not P well where's not P well not P is anywhere in there right we don't have a not P but we do have P right P is the antecedent of a conditional in line one all right well we can't infer antecedents using any any rule but we can infer the negations of antecedents all right we use the negate we can infer the negations of antecedents using modus tolens if we have the negation of the consequent lo and behold line two we have the negation of the consequent so from that negation of the consequent right we have the negation of the antecedent that's where we can infer in line four using lines one and two of modus tolens and then we can infer R in line five right it's uh using that that disjunction P or R well since we have not P in line four we can just infer R right well that's kind of nice we're able to pull that out all right let's see let's try another problem okay we've got if P then Q we've got if Q then R and not R all right and what we want to infer is not P and not Q okay so we've got a conclusion that's a conjunction well it's probably since it's a conjunction there's a chance we'll use conjunction introduction to get that conjunction all right well let's look at our uh premises do we have not P and not Q anywhere in there well no we don't right we don't have not P and not Q um do we have the parts of it well okay well we got P and we got Q in lines one and two but they're antecedents of a conditional we can infer antecedents but we can infer the negations of antecedents if we have the negation of the consequent using modus tolens all right well we have the negation of the antecedent of line of two excuse me we have the negation of the consequent of the conditional in line two that's not R well then using lines two and three line two says if Q then R and in line three you have not R so we can infer not Q using lines one and two excuse me using lines two and three and modus tolens cool well that's one half of the conjunction what about the other half the other half is in line one all right well guess what we just infer the negation of the consequent of the conditional in line one okay well now we can use that negation not Q to uh and we use that negation not Q in line four and the conditional in line one to infer not P really so now we got both half of our of our conjuncts we got not Q in line four we got not P in line five well then using conjunction introduction we can infer the conjunction not P and not Q that's our conclusion all right so modus ponens and modus tolens allow us to pull out in some way shape or form part to the conditional right modus ponens allows us to pull out the consequent of a conditional when we have the antecedent modus tolens allows us to pull out the negation of the antecedent when we have the negation of the consequent but we want to be clear we can't infer antecedents from consequence we can't do that and we can't infer the negations of consequence using the negations of antecedents we can't do that either that is not modus tolens that is not modus ponens all we can do is infer consequence from the affirmations of antecedents and we refer the negations of antecedents from the negations of consequence. Well, that was cool, but let's look at two more inference rules using conditions. I like you guys, but I'm not walking down that path to get an interesting shot. That looks a little hazardous. If I were to go down that path, then, you know, maybe bad things would happen. It's not to say that bad things have happened, or even that I'm going to go down that path. I'm just saying if. Well, that if, that's a hypothetical.  Well, we can make inferences that are conditions. And we got two rules that allow us to do this, right? One rule is called hypothetical syllogism. And another rule is called conditional proof. You know, now here's a little tip, right? So we've looked at different rules. If your conclusion is a conjunction, chances are there's a good chance you're going to use conjunction introduction for that rule. If your conclusion is contained in a conjunction, you're probably going to have to use conjunction elimination for as a rule, right? If your conclusion is a disjunction, chances are there's at least a possibility that you're going to use disjunction introduction for that, for that inference, right? If your conclusion is part of it, one half of a disjunction, chances are you're going to have to use disjunctive syllogism to get to that conclusion. Not the, not just like a one-stepper, but you know, as part of the way. Well, we got two rules that allow us to infer conditionals. We already dealt with conditionals before. We got modus ponens and modus tolens, but that doesn't allow us to infer a conditional, just to allow us to allow us to infer either the consequent of a condition provider we have the antecedent or the negation in the antecedent provider we have the negation of the consequent. Hypothetical syllogism and conditional proof allow us to infer conditionals. So chances are, there's at least a chance that if your conclusion is a conditional, you might have to use hypothetical syllogism or conditional proof for that. Okay, so let's take a look at a problem here. All right, so this should kind of look familiar. We already saw this earlier with using modus ponens and modus tolens, but you know, here we have ifp then q and we have ifq then r and then not r, and the conclusion is not p. Well, it shouldn't be hard to figure out, since we kind of already did it, that since the conclusion is the negation of an antecedent of one of the conditionals, we're probably going to use modus tolens to get that out. Okay, so in order to do that, we need not q. Well, q is not anywhere in there, but it's contained as the antecedent of a conditional. So if it's a negation of an antecedent, we're probably going to use modus tolens to get that out. Okay, and wouldn't you know we have the negation, we have not r, and that's the negation of that consequent. Okay, so far so good. But it'd be nice if we could just have that conditional ifp then r, and then use not r to infer not p. Well, we can do that. That's what hypothetical syllogism allows us to do. So look at lines one and two. We have ifp then q. That says that p is sufficient for q. That's line one. We have line two, q if q then r. That says q is sufficient for r. Okay, that says q is sufficient for r. Well, if p is sufficient for q, and q is sufficient for r, well that means p is sufficient for r. So using lines one and two, using lines one and two, we can infer ifp then r using hypothetical syllogism. Right. Well then now we have not r. We have not r as one of our assumptions there in line three. We have not r as our assumption there in line three. Well then using not r and the conditional ifp then r, well then we can infer not p using modus tolens, using lines three and four modus tolens. It's pretty straightforward. Okay, let's try something a little more different. Whoa, look at that. That is a complicated formula. p is one half of a disjunction. The other half is a conjunction of two negations, not s and not t. That's our only premise. And what we want to infer is if not p, then not t. Well, our singular premise is a disjunction. So we're not going to be able to use hypothetical syllogism, at least not immediately, to infer the conclusion. What are we going to do? Well, let's take a look at that disjunction. Right. Let's take a look at that conclusion. We want to get if not p, then not t. All right. Well, where is not t? Not t is one half of that conjunction. And it's that conjunction inside a disjunction. Well, it would be great if we had that one half of the, if we can get that part of the disjunction out. If only we could assume not p, well we can for the purposes of demonstrating a conditional. So we can assume not p. That's what that ACP means. We can assume not p. And frankly, in logic, you can assume whatever the heck you like.  Right. So we're going to assume not p for the purposes of a conditional proof, for the purposes of inferring a condition. So just like on the assumption, I were to walk down that path, something bad would happen. I'm not walking down the path, something bad hasn't happened. But if, right, on the assumption, I walked down that path, something bad would happen. Same thing here. If we're going to assume not p. Well, if we assume not p, then we can infer not s and not t using lines one and two and disjunctive syllogism. Great. So we've got that not s and not t. We need to pull out that not t. Since it's a conjunction, we can do that quite easily using conjunction elimination. So we, so line four, we pull out not t from the conjunction in line two, line three. Right. So we've assumed not p. From that assumption, we've inferred not t. Great. Magnificent. Since we inferred not t, using that assumption, we can infer a conditional. If not p, then not t. We haven't said not p is true. We just assumed it for the sake of proving a conditional. We haven't said not t is true. We just assumed, we just inferred it from the assumption. Right. I haven't gone down that path, but if we assume we, I did, if we assume I did, what would follow is bad things would happen. That's how you infer that that's, that's how you can infer a conditional using conditional proof. Okay. So to be clear, we haven't said not p is true. We've only assumed it for the sake of proving the conditional. We haven't inferred not t. We've only inferred it on the assumption. So we get to infer if not p, then not t. Let's try something else. Wow, this looks weird, doesn't it? If p then q. And if r then s, those are our two premises. Right. And we want to infer if q then r, then if p then s. Boy, golly. Take it easy on us, Dr. Haugen. It's actually not as complicated as it looks. Look at the complex proposition, right? The conclusion is a complex proposition. It's a conditional. That means, I mean, here's two good clues, right? You're either going to use hypothetical syllogism or conditional proof for that. Well, if it's hypothetical syllogism, do we have what? A conditional where q then r is the need to seed it, followed by a consequent. And then, you know, that consequent appears another conditional with if p then s. No, right? We don't have that nice handy chain as it stands. So we'll probably have to use conditional proof. So we've got our two premises, if p then q. And we've got if r then s. Right. We want to infer if p then s. How could we infer if p then s? Well, we can infer if p then s, just if p then s, if we had a linking conditional, namely, if q then r. Right? If we had a linking conditional, if p then q, and if q then r, and if r then s, then we can infer if p then r, and then we can infer if p then s using hypothetical syllogism. But we don't have that condition. But we could assume it. Right? So let's assume for the purpose of conditional proof. If you assume for the purpose of conditional proof, you better infer a conditional from that. Right? So let's assume for the purpose of conditional proof if q then r. Well, great. Now we got our linking chain. So then we can infer if p then r using if p then q, and if q then r, you know, that q then r is our assumption that's lines one and three using hypothetical syllogism. Right? Then we can, so we got if p then r, and we got also r then s, so using lines two and four, using lines two and four, we can now infer if p then s using hypothetical syllogism. Cool. We've reached the consequent of that conditional. Now we assumed the antecedent in the conclusion. Right? In the conclusion, we assume the antecedent of q then r. We infer if p then s, so we can infer a conditional. Well, that so for the conclusion, if q then r, then if p then s. That's our conclusion. Conditional proof looks a little weird. We don't like making assumptions. We think making assumptions is bad for logic. Oh, it's not true. You can make assumptions all the time. You just can't make assumptions as a conclusion. I can make assumptions for the purpose of proving something in the conclusion. Okay. You know, that assumption has to be noted and is noted as a conditional. I can't just assume the conclusion to walk away. If I'm going to make an assumption, I better be inferring a conditional or later on, as we'll see, I better be inferring a disjuncture with dilemma. So I can't just assume the conclusion to walk away, but I can't assume the antecedent for the purpose of inferring the consequent and then conclude a conditional where the assumption is the antecedent of what I inferred as a consequent. Right? All right, let's try another one. We got a conditional if p then r. And now we've got an even more complicated conditional. If q, then the conditional is the consequent q, then the conjunction q and r. Oh, you fake. Well, look, this can get odd, right? If you try to backtrack it all the way from the conclusion backwards, you might get a little bit lost. But looking at the conclusion, we can see that it's a conditional. And we have a single premise. If we have a single premise, we're not using hypothetical syllogists to prove this. So if we have a conditional as the conclusion, we don't have anything else for hypothetical syllogists, we're probably going to use conditional proof. So without even trying to backtrack and figure it out ahead of time, just assume p. See what happens. So we're just going to assume p. Okay. But you notice we've got another conditional as the consequent of the conclusion. So we have if p, then if q, then q and r. Okay. Well, you know, we really don't have anything where q implies r or anything like that, right? In fact, q is just nowhere to be found in our assumptions. Well, here's the thing. You can assume more than one premise, right? You can assume more than one inch of seed. So we've got the assumption that p and from that only assumption that q, well, okay, let's go ahead and assume q, right? So assume p and line two, we'll assume q and line three. That's fine. You can do that. Then what we're going to do is take q and make an inference. We'll take, actually, we already have p. We can already use p. We have q. We can make an inference and from that we'll infer our conditions. So we've got q right there on line three. Well, we also have p and line two. Well, from p, line two, from that assumption and line one, we can infer r, right? Okay. So now we got r and line four using lines one and two modus ponens. That's great. Well, now we can infer our conjunction. We got q and r, lines three and four, q and r. Well, since we inferred q and r from our assumptions, well, we can infer a conditional. Right? We got q. We assume q and line three and from that we infer q and r. So now we have a conditional. If q, then q and r. Great. Right? Great. Lines three and five. You know, in conditional proof, the first number you cite is the assumption you made for the purpose of conditional proof. Five is the line where you draw the inference, right?  So lines three, because that's where we assumed q, line five, that's where we infer q and r. So then we can infer if q, then q and r. Okay. Well, now if q, then if q, then, I'm sorry, if q, then q and r, that's an inference we made on the assumption of p. So now we can infer another conditional. Right? We have if p, then if q, then q and r. That's, you know, it's a mouthful, right? But this is fine. We've got our, we've got this conditional. So line two, that's we, that's where we assumed p to begin with. Line six, that's where we inferred the consequent. So that's our citation. And then our rule for justifying this is conditional proof. Wow. That was a lot. But it's really not as complicated as it seems. When you see a conditional like this, right, you got a conditional. That has a conditional as this consequent. That has a conditional as its consequent, right? This can go on for a long ways. Just make these assumptions, right? Just make these assumptions. If you got an ant, and you're convinced it's going to be conditional proof, just make these assumptions. Here's my warning though, work from left to right. So if you've got a conclusion, you know, if p, then q, if p, then if we assume q, then if we assume r, then if we assume s, right, then assume p, q, r, and s in order, right? Work from left to right in the conditional. Okay. Let's try another one. All right. Oh, never mind. That was the last one we tried for that. So that's hypothetical syllogism and conditional proof. And that allows us to infer a conditional. I said on the assumption that I go down there, bad things will happen. Oh, I'm not going to go down there. That doesn't necessitate bad things aren't going to happen, but let's hope so. It's a pretty cool path down there. Looks like some neat sites. Well, I can either go down the path or I can go back home.  If I go down the path, you know, it's getting pretty late. I'll probably be out here a while, right? The path goes down a ways. It's a long path. If I go down the path, I'll be out here a while. If I go back home, I can get my dinner on time, more or less.  I don't like to skip dinner at all, frankly. But okay, so either I go down the path or I go home. That's the disjunction.    If I go back home, I'll get my dinner on time. So either I'm going to go down the path or I'm going to go home. And from that disjunction, we can infer either I'll stay out late or I'll get my dinner on time. Okay, this is what's called a dilemma. This inference is called a dilemma. I said earlier, if you have a disjunction as the conclusion, there's a good chance that you use disjunction introduction as the rule. Well, dilemma is the other one. Dilemma is the other one. Dilemma says, I know in common speak, we say dilemma and we mean like a choice that we should make but we really don't want to. That's not what dilemma means. Dilemma means you have a disjunction, at least one of these is true. Each disjunct infer something else. So we can infer disjunction from that inference. That's what a dilemma is. Now I have the example in the text. I have the example in the text. I'm going to take you through it just a little bit step by step so you can see what's going on. So we have a disjunction of p than q. We have an additional if p than r. We have another disjunctional if q than s. And we want to infer is if r than s. Now we look at that conclusion, r than s. Well, is it anywhere in the premises? Well, both r and s are consequence of conditionals. Okay, cool. So you might think, well, I'll just infer one and then infer a disjunction from it with the other one. And then I'm done. Well, you can try that. But as you can see, so if we just take if p than r, p is the antecedent. p is not available as a premise anywhere. It's in a disjunction, p or q. If we're going to get p out of there, we have to have not q, but we don't have not q anywhere. Okay, so we're probably going to need to use the dilemma. Since p or q is available as the first premise, and both p and q are antecedent to those conditionals, well, then we can infer a disjunction. Okay, so how do we do this? Well, remember we did assuming for the sake of conditional proof. Now we're going to assume for the sake of dilemma. All right, now we're going to assume for the sake of dilemma. And just to kind of talk you through it, you assume one half of the disjunction, draw the inference, assume the other half of the disjunction, draw the inference, then we can infer the disjunction. So we're going to assume p in line four. We assume p and that ad there means assuming for the sake of disjunction. So we assume for the sake of disjunction. Well, it's very quickly we can infer r. So we infer r using line four and line two and modus ponens. So now we got r out of there. Okay, we got one half of the disjunction that's in the conclusion r or s. Now we got to get the other half. Well, we'll get the other half from q. So we've already got r. We can move on to the next disjunction. Let's assume q. We assume q. And again, we can, using, again we cited for assuming for the sake of disjunction, again using modus ponens, lines three and six. We can infer s. So we made the inference from one half of the disjunction. We've made another inference from the other half of the disjunction. Therefore, we can conclude a disjunction of those inferences r and s. So look at the citation there. Okay, the first number in the citation, that's the disjunction we're working with. The second number in the citation is the assumption of the first disjunction. The third number. So that's p, right? So the first number is p or q. The second number is where we assume p. The third number, that's where we draw that inference from that assumption. The fourth number is where we assume the other disjunct. And the fifth number is the inference from that second assumption. So it's a long citation, but all it's saying is look, first we got the dis, dis, disjunction, then so first we got the disjunction. The second number is here's the assumption of one half of the disjunct. The third number is the inference we got from that assumption. The fourth number is where we made the other assumption, right, the other half of the disjunct. And the fifth number is where we drew that inference from that second assumption. That's what's going on. So, right, the first number is either I go down the path or I go back home. The second number is, well, let's assume I go down the path. The third number is, on the assumption I go down the path, I will be out here late. The fourth number is, let's assume I go home, right? The fifth number is I'll get my dinner on time. So we draw the inference, either I'll stay late or I get my dinner on time. That's how that works. Now, delimit doesn't always need conditionals. You can make inferences with whatever rules that we have, right? You can make inferences with whatever rules that we have. So, let's try this, right? Let's try another problem. We have a disjunction p or q and we have another premise r. Okay. Well, what we want to infer is another disjunction, p and r or q and r. Now, this should be too hard to figure out what we're going to do at this point. So, we have the disjunction and we have r. Well, let's assume one half of the disjunction p. That's our line three. Well, using r and p, we can infer the conjunction p and r using conjunction and introduction. That's one half of the disjunction. Let's assume the other half of the disjunction q. From that, we can assume q and r. We can assume q and r. That's the other half of the disjunction. So, we can infer that whole disjunction p and r or q and r. Now, just keep in mind that's pretty straightforward, but you could do things like assume for the sake of conditional proof within the assumption for dilemma. These are possible. We could do modus ponens modus ponens. All right. All that's possible. We don't have to just use conditionals. We don't just have to use conjunction and introduction. Any inference we draw from that assumption, that's going to be that half of the disjunction. Okay. Well, that's a dilemma and that's all the rules we're going to use right now. We're going to have more rules later on. We're going to have equivalence rules and we're going to have rules about complex, further complex propositions using complex truth relations one step at a time. This set of rules will get us started and with it, we're going to start solving our problems. All right.