This is stock number 10470. We are here at Summit Automotive in Fond du Lac, Wisconsin. You're new and used sports car headquarters. Today we are checking out this extremely clean, extremely good-looking 2019 Ford Mustang GT Premium. This vehicle has the 5-liter V8 motor, which pumps out 460 horsepower. Ruby red tint coat is the color. We shoot all of our videos in 1080p, 60 frames per second. So if you have HD capabilities on your computer tablet or smartphone device, turn them on right now because it is definitely your best way to check out the quality and condition of the vehicle before seeing it in person. If you'd like to check out all the photos on this car in the upper right hand part of your screen is a link right to our website. Click that and check us out there. It comes with the 19-inch painted alloy rims. It has the Performance Package 1 on here so you're going to get the Brembo brakes in the front. It has Michelin Pilot Sport 25540 ZR19 tires on the front here and they have 95 to 98% of the tread left. Only 2,000-some miles on this car. Didn't see any dents or dings on the front fenders. It comes with the HID headlamps, the LED running lights, and the LED fog lamps. Front bumper and splitter. Lower valance are in nice condition. Didn't see any dents or dings on that. The hood is in excellent condition. You got that nice stripe there. Didn't see any dents or dings on the hood. Headlight lenses are like new and the passenger side fender, no dents or dings on that. Passengers side rim, no scuffs or scrapes and as you go down this side of the vehicle, take note of how clean the body is, how reflective and mirror-like that paint is. We take these HD videos so if you are far away or even if you're close by and just cannot make the trip down but you're still interested in purchasing the car, you can see the car, hear the car, and have confidence in the vehicle that you're looking at and considering purchasing before seeing it in person. That is why we offer the Summit Auto Fastpass option in the upper right hand part of your screen. A link right to our website where you can apply for financing, get pre-approved, see a payment quote, even appraise a trade all from the comfort of your own home. Back rim, excellent condition as well. Now the back tires are 275 40 ZR19s and they have just as much tread as the front tires. So when you get here, all you got to do is drive the car, love it, and you'll be all set to go. Rear bumper is in excellent shape as is the deck lid and spoiler. You get the LED tail lamps that are sequential. There's your front license plate holder and this one does have the tire inflator kit in it. Back storage area is very nice and clean. Didn't see any dents or dings on that trunk lid there. Spoiler is an excellent condition. You do get the capitalist fuel fill, which is a really nice feature. And down this side of the car, just as clean as that passenger side. Didn't see any dents or dings on the quarter. And for full disclosure, this back rim is in excellent condition as well. No scuffs or scrimps on there. And down the rest of this side of the car, I didn't see any dents or dings on the door. Very, very nice. Dubik get directional signals, blind spot monitoring in those mirrors.  Both these seats are heated. Both these seats are cooled. Back seats are in excellent condition as well. And they do fold down.  Memory driver's seat, power windows, power locks. The doors are in excellent shape. You get auto headlamps. And as we hop inside the car here, you can see that this one only has 2,484 miles. Now this is the 12 inch instrument cluster. I believe they came out with this in 2019, but really a cool dash and instrument cluster here. And you can configure it a million different ways, which, you know, if we had time, we could go dive into that. But very good looking. You get the leather-wrapped steering wheel, no scuffs or scrapes on that, audio and Bluetooth controls on the right, cruise and information center controls on the left, and more volume controls. You get that machine finished dash trim. The performance package gives you the oil pressure and vac gauges in the dash as well. This one has the sync radio. You get AM, FM, and Sirius XM radio capabilities. You can also do your climate control here. There are all your different sources that you can do, Sirius, and then connect your Bluetooth. Obviously has the factory navigation system. This one also has the Ford Pass Connect. I believe this was the first year that you could do that with the Ford Pass Connect on these radios, backup camera, and also has mobile apps for Android Auto and Apple CarPlay to project your cell phone to the screen. So if you've got Waze or Google Maps like that navigation system better, you can project it to the screen easily. Down here you have your heated and cooled seat buttons, your push button start, hazard lights, stability control, your different steering settings. So you get normal, sport, and comfort. And then you have your different driving modes as well. So you got normal, my mode, sport, track, drag strip, snow and wet, and then normal again. So really a lot of cool stuff you can do. The dash is in excellent condition. This car has never been smoked in, smells very clean. Passengers side seat and floor mat are in excellent condition as well. No rips or tears. And the headliner is in great shape too. Home link buttons for your garage door security systems and lane systems and map lights up there. The key fob here also has remote start on it. We do have two key fobs for this car. And take a quick look under the hood. Then we'll do one more walk around of the car. I would personally like to thank you for checking out the video today and hopefully from this HD video you will have been able to tell just how clean this car is all the way around inside and out. Under the hood we have the 5 liter V8 motor. Engine bay super clean. Runs very smooth. 460 horsepower. Just an awesome, awesome ride. And this one is all set to go. To see more pictures of this car or one of our other 450 new and used cars, trucks, SUVs, minivans, Wranglers, sports cars, Mustangs, Challengers, Chargers, Camaros, Corvettes, GT500s, GT350s, you name it, we got it. Go to our website, www.SummitAuto.com. Full pictures and descriptions of every single vehicle from two locations all at SummitAuto.com. And if you'd like to check out more HD videos you can go to youtube.com slash SummitAuto. Remember to like, subscribe, and share on this video and all the videos that you see there. In fact in a second you will see a link to subscribe to our YouTube channel on your left. A link to more Mustang videos like this one on your right. If you have not been to our website on the bottom link to this vehicle on our website, click those, check us out. And we really look forward to helping with this extremely clean 2019 Ford Mustang GT Premium with the Performance Pack 1. Thanks again for checking out the video.


a wonderful audience we're going to close our program today with a song by singer-songwriter Lee Greenwood. We had the pleasure to sing this song with Mr. Greenwood for the 2015 NHL Winter Classic as well as recently for 2023 USO Awards banquet. We leave you today with God bless the USA. The world-renowned United States Army Course. Let's give him one more background of applause. Thank you Army Course. You are an inspiration to all of us and we greatly appreciate with you being with us today you make every ceremony special. Ladies and gentlemen we're getting near that time but we're not there yet. At this time I would like to introduce our Sergeant Major of the United States Army SMA Michael R. Weimer. I know you're dying to know. I know I can feel the tension. I can feel it. I remember SMA Grinston last year dragging this out. I remember it but that's not what we're doing right now. What we're getting ready to do something pretty special and then we're going to get to that. So what we're going to do right now is we're getting ready to talk about something that truly I didn't fully understand the breadth and depth and scope of the significance of this but we're getting ready to announce the honorary Sergeant Major of the Army and I wanted a couple data points for folks to understand what this means how it came about because SMA Daily was part of this. As a matter of fact it started on his watch in 2015 and this is no small feat to be named the honorary Sergeant Major of the Army. This is decided by all the former Sergeant Majors of the Army. You remember that group we took the time to introduce in the beginning. Yeah that's a that is a pretty pretty ruthless bunch of folks with standards like their standards and then their standards and I'm here to tell you this individual it was unanimous unanimous right and I was worried or unanimous I was worried with the shutdown that we were going to miss the opportunity to truly celebrate this and so I'm here to tell you I'm excited to see this room filled because the individual that we decided upon is here and he has his family with him and I want to mention a few things about this individual real quick he's a native of Mobile Alabama no SMA Grinstin didn't have anything to do with it but yeah Alabama he enlisted in the army in December 1961 he served 32 years in the army and retired in 1993 and and you weren't paying attention I was paying attention it wasn't your job to but I'm pretty sure he stood up four times I think it was four times when we were singing singing those division songs right there and then there's a few other formations he was in that just don't have division songs uh he's a command sergeant major served in multiple organizations include the second infantry division and us army operations command special operations command in 68 he completed special forces training and other courses to include infantry advance jump master scuba jungle operate I'm I'm not sure there isn't anything he hasn't accomplished over the years he's been inducted into the ranger hall of fame he's inducted into the us army sergeant major academy hall of fame and the special operations mountain man old and bold 2015 is my honor he's oh by the way he's accompanied with his awesome family here today I know you're gonna take a moment to to highlight them Jimmy so I'm not gonna steal that from you but it's my honor today to introduce the 2023 honorary sergeant major of the armor army jimmy spencer I always wanted a standing ovation but unfortunately it was before I spoke so I guess but I'm gonna count that that was a wonderful introduction sma and in fact it was so good I can't wait to hear what I have to say this whole process started for me about about three weeks ago I was sitting at home just trying to be the kind of person my dog thinks I am and the phone rang and it's the sma telling me that I've been selected as the next honorary sergeant major of the army and just to let you know that what I experienced at that moment was something that the social scientist would refer to as a significant emotional event and I really don't think that thank you is a strong enough word to convey how grateful I am for this great honor my my journey started over half a century ago when I joined a team of teams I walked into a recruiting station and from that point on in my life I've never been alone I've always had someone to my left someone to my right and shoulder to shoulder we faced whatever the future had in store for us there's always been somebody behind me and that person was willing and able to come to my rescue should I should I falter there's always been somebody in front of me to show me the way that's part of being a team of teams and when I left the army for the last time took off my uniform I joined another team team a USA at both the local chapter and the national level and our mission in life is to take care of soldiers and their family members to make sure that our young people who come into our army join our formations have the best training have the best equipment have the best leadership that just the nation is capable of producing so the only thing I'd really like for you to know about me is I was a soldier I am a soldier and I'll always be a soldier and I'm very grateful and thankful for this this opportunity and my sincere wish for everyone in this room is that you may be safely in heaven 30 minutes before the devil knows you're dead thank you very much thank you for listening to me thank you for this great honor and come on up here Jimmy where'd you go there you go I was like what are you doing get back up here so he didn't he didn't mention who accompanied him come on up here um Julie escrowed her up here please for me so this is his wife Susan who's been with you how many years now uh 50 something 50 something yeah so everything we talked about this is who's been along that journey with him he also has his daughter here and his youngest granddaughter correct that's right yeah so so pretty awesome um and by the way uh Jimmy's got a massive golf tournament I know there's a bunch of golfers out there he's always looking to raise money and I don't golf so he's he's looking for talent so you got to take full advanced full advantage of that so I got I got to give the the uh the choir another shout out I know uh that that that gets me stirred up every single time so this next individual that I'm going to introduce um pretty special a lot of us have the you know we have the luxury of working with him every day in the e-ring um and I've been getting to know him I've been getting to know him pretty well here since about two May um but but what really inspired me uh just his latest thing that inspired me was the 10 miler and so he came across he ran the 10 miler and finished with his beautiful bride holding hands across that 10 miler I got to tell you sir I won't go any further with it because it'll get me all choked up but uh that's the leader you are you've been a servant leader this whole time I'm honored to have you here to do this with us today with this group of people so let me introduce to you the the director of the army staff lieutenant general piet that's one way of putting it finishing the army 10 miler yesterday my wife who's much faster than me has run her 31st marathon just last week in uh Finger Lakes was really pulling me across I think is what it really was SMA but I like your version better I'm gonna I'm gonna hang on to that one that's how it really happened that's how it really happened uh look at afternoon everyone what what an honor it is our major dailies our major weimer our new sir major of the army and all the former sir major of the army wow it's just a real honor to be in the presence of so many national treasures and so many of our soldiers my name is is well pied I'm the director of the army staff they call me the Das I know I'm doing good if they keep the d on it sir major weimer's kept that on I want to show you a picture of me when I was a private to sir major daily found out that I was former enlisted and said you must get a picture of you when you were a squad leader and I couldn't find one but you know when a sir major tells you to do something you try to do it you come through so this is the best I can do private piet 1979 basic training one of the hardest things I ever did in my life was get the good conduct medal and I became a squad leader because my squad leader didn't get the good conduct medal and it was a proud job that I was a squad leader in alpha company second battalion 503rd infantry then at Fort Campbell Kentucky 101st Airborne one of the things and I don't have to tell you this but one of the things that makes our army so successful as the people people like you people who are tough and go far beyond the normal to achieve success and should any of us fall in battle any one of us is expected to fill that gap to lead that way to bring up the rear this is natural and it's expected it's kind of why you got me today because there is no vice chief of staff of the army right now and as the DAS I get the honor of fulfilling his roles and he's got a really hard job but this gig is pretty cool so I'm kind of glad that we don't have a vice today because I probably wouldn't be up there talking so thank you senator from Alabama um I did tell the secretary of the army I said yesterday I said I can thank the senator because I got to run one more army 10 mile or while still on active duty she said you can run it when you're retired too general pilot and I said oh yes ma'am okay got my orders but in combat many of many of you have experienced this it can often be horrific and demand the most from all of us and I want to tell you about a story about a young man that answered that call corporal Timothy Ahern when he was fighting in France in 1918 Timothy Ahern was born on December 15 1998 in New Haven Connecticut son of Irish immigrants and at the age of 18 after graduating from st. Francis Catholic school he enlisted in the 26th regiment as an infantry man with the intent of fighting against Pancho Villa in our southwest border after his service in the Mexican expedition in November 1916 his unit mustered out of service but he was remobilized in February of the next year after the United States declared war on Germany and he redesignated as the Connecticut National Guards 102nd Infantry Regiment and the 102nd rose to quick fame when on April 20th 1918 and engaged in the United States first major infantry battle of World War I in France despite heavy bombardments and the eventual capture of the town by the enemy forces the soldiers of the 102nd never gave up and initiated a counterattack that regained the lost American trenches this was America's first encounter with horrors of trench and chemical warfare climbing out of the protection of the trenches and into enemy fire in the area that became known as no man's land left many soldiers very fearful however according to a local newspaper Corporal Ahern's coolness and courage under fire left others surprised and motivated to follow his lead the article continued to state that Ahern was always the first when the boys went over the top he seemed to bear a charmed life and although the boys dropped on all sides the gallon corporal he pressed on what a remarkable leader where it was difficult he was present where it was dangerous he was first his ability to lead those around him would become instrumental in the days following this battle on October 27th 1918 enemy attack killed or encas or encasperated every officer and sergeant in his company with only 17 abled soldiers still standing Ahern did what no corporal probably ever expects to do while in combat he took command of his company under his leadership the shattered remnants of the unit successfully held the line for the remainder of the battle and once the bullets and shells stopped firing Ahern sent a message to his regimental commander without any paper to write on he used a letter that he received from his mother and he wrote on the back the message was to inform the regimental commander that he had taken command of the company he stated I've made two skeleton platoons of four squads a piece he went on to write that private Kenny is made acting first sergeant then he stated in his letter sir what are your orders he made clear that he was ready for any duty that he could be called upon to perform he also said I'm ready to receive replacements and he signed it Ahern corporal commanding company see think about this the presence of mine to form a company out of a shattered remains of his unit they were devastated and no one would have blamed them for being combat ineffective we would do it today this company would be p4 and c4 not ready for combat the number of people in the company would have rendered the battalion and the entire regiment not just this company not ready for combat yet they were more than ready they were combat ready tough and unyielding corporal Ahern did what few could do when faced with an impossible task he developed a solution he made his readiness about what he had not about what he didn't have this is something you will all have to do as well anyone can lead when conditions are perfect but you have demonstrated in this competition that you can lead and outperform most when under the harshest conditions your future assignments will require you to do more like corporal Ahern you will never have enough never have all your people all your equipment but you must ensure what you do have is ready our nation is not going to ask if we are ready they will expect it as did corporal Ahern that day in addition to keeping his soldiers focused on keeping the line he also made at least one trip in no man's land and while under heavy machine gun fire successfully retrieved a wounded soldier from imminent death for his gallantry on that fateful day he was awarded the distinguished service cross like so many other young warriors who fought in world war one when Ahern returned home he suffered from the side effects of exposure to chemical weapons just three days after his actions in Verdun he fell victim to an enemy gas attack during the argon offensive and he had to spend time in army hospital in France although he survived the war his body and his mind continued to suffer upon his discharge from the army he moved back into his family home with his parents and two of his younger siblings and found work as a stenographer in a local office his mother brother and sister moved to new york after his father died he decided this was a perfect opportunity to set out on another adventure and for the next five years Ahern wondered the country from coast to coast trying to make a living as a migrant worker and on january 25th 1925 timothy Francis Ahern passed away in san francisco from respiratory complications of his exposure to mustard gas he was 25 in 1937 the new haven chapter of the yankee division veterans association dedicated a statue of Ahern at the west river memorial park where his memory and his story continue to live on you have shown all of you have shown that you can do hard things like corpway her and as it did on corpway her and this profession takes its toll on all of us and we all need to take care of one another as hard as we fight in combat or in competition we should fight for each other daily building cohesive teams that have each other's back recognizing when others are suffering or at risk and intervening to help our fellow soldier lead with strength but also lead with compassion is what makes our army strong we are a value-based organization built on trust and respect and do not let these values ever weaken many are calling our military weak we are far far from it we are strong intelligent lethal compassionate and empathetic for those who say we are weak and no longer tough i remind them of this william francis butler quote and i quote him now the nation that will insist upon drawing a broad line of demarcation between the fighting person and the thinking person is liable to find its fighting done by fools and its thinking done by cowards unquote being strong means being smart so do more than just be the best squad be the best you and bring everyone with you anyone who thinks this nation is weak and the world is without threat look at current events that today in israel where any nation or any adversary to freedom can build a lethal army on very low tech equipment and can kill kill without without discretion it takes a warrior to respond it takes a warrior to apply lethality and to kill the enemies of our nation but we must also remember it is our duty to protect the innocent and as a soldier all of us we've all deployed all over the world and face new cultures face new religions many tried to kill us because we were different or because we were in their land i served in afghanistan and iraq and i've seen up close the strength of a u.s soldier i witnessed many stand in the face of sheer terror and yet still found the strength to move forward no no matter how bad the situation we kept moving forward we lost friends and for a time our nation lost hope yet we kept moving forward i learned not to judge but to accept the differences of others to meet them where they are as my brothers and my sisters i learned to listen without judgment to speak without shouting to live without hatred these are the values of honor the values of a soldier so that one day we can all live as one not to force others to the same ideas but embracing the diversity of human thought i learned to be better and not to be afraid of what is different but rather to seek new perspectives without fear many people thank us for our service when we are out in public and awkwardly i always say with humility you are welcome but what sergeant major of the army grinstin told me and taught me to say was to look them back in the eye and shake their hand and say you are worth it thank you sergeant major try this the next time someone comes up to you and you don't know what to say look them in the eye when they say thank you for your service say you are worth it they're probably going to cry but they are worth it this nation is worth it it's why we do what we do i've learned a lot from sma grinstin one of our best warriors this nation has ever seen but i will always keep that one dear to me thank you sma you're all worth the pain and sacrifice that we service members experience our civilians our nation need to be reminded of what we do in your future there will be challenges and uncertainty and possible situations that you will have no idea how to handle remember corporal a her who faced the impossible and yet never gave up as long as you have some soldiers with you never give up so in the words of the 10th mountain division no matter what keep moving and we'll all meet at the top i'm so very proud to serve with all of you for you are all all worth it this will defend thank you very much now you can ask any army individual that works in the pentagon and i mean any of them to include the secretary and the chief what's the hardest job in the pentagon and the hardest job is the director of the army staff because when i was with general milley he said that's the guy that gets to do everything i don't want to do so there's one thing to have the hardest job it's another thing to be the best at it and do it for the longest that anybody has ever done sir thank you for your incredible service and sacrifice to this great nation and all you do for our army thank you so you know what time it is it's time for me to read a bunch of stuff so we can stall this a little longer that's right this year's best warrior competition actually dates back to 2002 when the chief of staff of the army then general eric k shinseki and then the sergeant of the army i don't even want to say it out loud but i have to jack tilley made the decision to culminate all the nco and soldier of the year competitions across the army at the department of the army level in 2009 as part of the year of the non-commissioned officer celebrations the chief of staff of the army george w k c jr and the sma decided to formally name the trophy presented to the nco and soldier of the year as a way to honor the legacy of sma jack tilley and what this competition does for our army to enhance self-development and self-study and to set training standards for our force then in 2021 under the leadership of sma grintston the army announced the creation of united states army's annual best squad competition to recognize the best squad from across our army along with the announcement of the best warriors this year we will announce the results of the united states army's best squad competition now are you ready to figure out who that is it's not time we have to watch a video first as a prelude to the big announcement please watch the short video of the 2023 best squad competition so it just shows that we're working to be a cohesive unit we got the top teams in the country here we're here to compete we're here to have some way to defend the title of the best squad mine is just like keeping simple um go to one event at a time it was a tough assessment but the team pulled through and did well it's definitely a mental game for me it's definitely challenging but it's very motivating to see everybody out here running trying their best i've never done land nap here before and it's a lot different nice different challenge you got trust just what your training is and just keep going hey you this is me over today we're doing the eib training off the mount huge part of what we do is over especially as infantrymen as rangers one day you might be put in that situation where you have to save somebody's life we train for this non-stop you do nothing but train for this so this morning we started off with a 12 mile ruck i would say overall um the ruck it comes out to an individual event but since it is a squad event i would say taking care of my soldiers is always the first thing in my mind two minutes is plenty time shoot 30 rounds definitely was just the camaraderie that's almost a year of just competing with each other and training with each other so we know each other in and out let's put this long and grueling event together uh for soldiers like us to really see where we are and really test who we are as our our characters in our in our fighting spirit answer to the question you've all which squad is the best squad and who is the non-commissioned officer and soldier of the year for america's army for 2023 i don't know the only person in the room in the whole army for a matter of fact that can answer that question is the executive officer of the sardine major of the army ladies and gentlemen please welcome sardine major christie brady trying to see where as the okay you want to say something oh all right can you everybody hear me okay all right um okay very well actually i will say hey all of that squad stand up the only thing i want to remind you and it really is for all of us is that we exist to fight and win that's it and you represent what it means to be ready for when we say this we will defend and i couldn't be more proud of every single team that participate in this event well done now let's find out who won all right let me first by saying lieutenant general piet thank you so much for being here today the words that you've shared with us the wisdom that you've parted are ones that we will remember always and share um for for centuries and years to come so thank you sir so much i'm so glad that many in the room here today got to hear him speak because i have got to hear him speak over the last year being on the staff and it's sure surely is you know a great honor and very monument awards sir so thank you so good afternoon everybody um as you know sardine major brady the best xo right us immigrants um no but i am extremely proud to be the executive officer to the 17th star major of the army and as all of you have just heard i'm here to announce who the winner who the winners of the best squad competition the nco and the soldier of 2023 will be but to help me with this announcement today i thought i would do it just a little bit differently break the mold just a little bit and bring my battle buddy with me star major as valdo martinez but first but first what a turnout um i don't know if any of you had an opportunity to be here last year um but aside from the fact um from last year this year we were able to bring all 12 squads to compete at the board and to come to a usa so that's that's pretty awesome but i think the real reason for the full crowd today and for standing room only is because you all heard how awesome i am and how extremely funny and charismatic i am right team sma right somebody thinks i am all right okay so today we have 12 commands from across the army who have competed under the most challenging conditions 12 squads 60 soldiers from all over the world 24 states and even an island country of jamaica where you at somewhere out there i know i looked i looked at all your records you got some quiet out there nobody wants okay well star major ready thank you for allowing me to be here with you today and share in the recognition of these outstanding soldiers over the last 11 days these soldiers good job i appreciate it over the last 11 days these soldiers have worked extremely hard with the tenacity and grit and most with a smile as a matter of fact there's one who couldn't take the smile off and that's uh starting first-class kaleb richardson where you at from medcom stand up stand up please and also the the soldier that you saw on the screen specialist posso all right right always smiling so thank you so to acknowledge all that they have done and to get right to the point i want to call out each of the commands and recognition and we ask that you represent each one of these commands as we call them out with your motto and appreciation so get pretty wild get crazy get excited let's everybody let's everybody who's out there wonder what the heck's going on in here so we're going to call each one of the commands and you follow with your model so for example if i say force com you say freedoms guardian cool all right thank you all right here we go team one force com team two trade-off team three afc team four amc team five army national guard team six united states army reserves team seven usara team eight united states army pacific team nine usasak team 10 united states army cyber team 11 medcom and team 12 the military district of washington all right well i gotta tell you so i'm ready i am excited to find out who the winner is and i will tell you i've been for the last couple of days trying to find out and so somebody ready wouldn't share and so i said okay let me come up with some incentive so i offered to pick up the coffee for the office for the next two weeks she said no i said all right i offered to ensure that the office had enough hair gel for the sma for the next four years and as you can imagine it would be a lot of hair gel she said no she said no and then lastly i threw it all out there and i said sir major what if i give you my jalapeno cheese bread for my next mre and she still said no so she has been dedicated to ensuring that the winner remains on the locking key until now so sergeant major you're right sergeant major i was saving an announcement for the exact moment lieutenant general piet would you please join me and the sma all right ladies and gentlemen i'm going to go ahead and get started but i'm going to start with the third and second place team i would like for that those teams to stand up to be recognized and then the number one team will have you come to the stage okay so it was my extreme pleasure and honor to announce the best squad for third place is usurpak the second best squad of 2023 is medcom and finally what you've all been waiting for the best squad of 2023 is united special army united special army united use a sock there you go the members of the squad are staff sergeant ewing sergeant philips specialist maguire specialist monsharka and specialist moon okay the next thing is yes who said that the best xo that's right that's right the best soldier of 2023 is specialist maguire and the best non-commissioned officer of 2023 is sergeant philips i don't know how you follow that i'm a little speechless but let's give those warriors one more big round of applause now normally normally that would be the end of the show but you know what sma he told me we're going to do things bigger and better and we're going to be all you can be i said all right sma i don't know what else i could do he said i want i want more sergeant major i want more so at this time we are proud to present the all-american chorus based out of fort liberty north carolina and led by sarb first class megal davis the all-american chorus embodies the hearts and souls of the paratroopers past and present for the 82nd airborne division compiled from paratroopers across the division the chorus performs traditional cadences americana and select vocal arrangements of popular tunes to uphold the tradition of the airborne legacy as the face of america guard of honor fresh off their america's got talent tour please join me in welcoming the now world famous 82nd airborne all-american chorus ladies and gentlemen what you are about to experience are some of the live actions and commands given inside of a c-130 or c-17 high performance aircraft just before your 82nd airborne division jumps into the darkness of the night off we're going to check tough and tough to the sun to the sun no sweat no sweat not yet mess all on my knees down in the mess hall on my knees i got nothing to eat but a can of beans nothing to eat but a can of beans bread was molded and the meat was bad the bread was molded and the meat was bad well that you can't eat that hey no darn well that you can't eat that here we been tough rough and tough for the way all the way when i was younger always wanted to be in the 82nd airborne my knees in the breeze but now that i'm here i'm going to do it right i'm going to jump from a aircraft while in flight when i picked up my parachute and boarded the plane jump master said one minute to go with a chilling glow and gentlemen we are the 82nd airborne division all-american chorus we hail from the great fort liberty of north carolina which is home of the airborne and the 82nd airborne division is america's guard of honor on behalf of our commanding general major general christopher leneve and our division command sergeant major command sergeant major randolph de la penia we would like to let you know there he is we would like to let you know what an honor and a privilege it is to be singing for you here today but before we begin i must remind you that these individuals standing behind me are not just talented singers they are first and foremost paratroopers for life we have soldiers from the infantry service and support aviation artillery and the core of engineers now the all-american chorus was formed in 1964 and that very same year the temptations released their hit song my girl for 50 years the chorus has been singing this wonderful song and recently we performed it for our initial audition on america's god talent please enjoy this performance i know what you're thinking i should have paid money to come here well there's still a chance no i'm just kidding let's give the 82nd airborne all american chorus another big round of applause you truly do inspire all of us and you made us all proud as you showed the world whose soldiers were on that great american talent show thank you oh well i got nothing left sar major can i close this thing out all right cool thank you sar major and ladies and gentlemen thank you for joining the best certified by the chief of staff of the army event here at the annual meeting a usa what i'd like at this time is if the best squad would please come back forward and as we leave the senior leaders can shake their hands i would ask also that the sponsors that came here today to recognize our best squad remain here so they can give them their accolades for what they've done and to have an opportunity to take pictures ladies and gentlemen thank you for joining us today and we wish you all well and enjoy the rest of the 2023 a usa annual meeting


Well, thank you for the opportunity. Some of you might know, this is a talk, a version of a talk I gave at the philosophy department here at the door, so if you've sought, if you were at that, it's not that much different so you can feel free to leave. But otherwise, I will proceed. Anyway, as I indicated in the flyer that went around, when people ask what do you teach, and I say philosophy and mathematics, they say what? What's the connection? Well, I want to make the case that it's a huge connection between these two fields, historically and even today. So, when I saw the flyer, Robert had asked me to send me a picture of myself for the flyer. And when I saw this, I thought, let's see, oh, that must be, again, that guy must be Robert. And this is a famous picture called the school of Athens with my rafial, it's fresco in the Vatican, and it really nicely made together serendipitously because I didn't send him a picture. But it brings together the theme of my interest, which is mathematics, philosophy, and the fact that it's a mnemonic, and another image of why this is religion and theology, given my current point, but that's a fact of an interfaith institute. We'll come back to this image at the end as kind of a summary, because in a way, it nicely summarizes what I want to say today. We're going to start actually with Pythagoras, a little before we go, because when I asked, it seems to be 495 was the most famous theorem, and I'll be saying the Pythagorean theorem. And this is a statue on the island of Samos for Pythagoras lived, and obviously it depicts the right triangle and his theorem, Pythagoras theorem. But Bertrand Roswell said at Pythagoras that he was intellectually one of the most important men that ever lived, because the whole conception of an external world revealed to the intellect, but not that the census is derived from him. So, Roswell looks back to Pythagoras as the touch point for this issue, between can we have knowledge that is not necessarily from the census, but is from our rational view. Plato was famous for having said the knowledge which geometry aims is the knowledge of the eternal, and not of the perishing or the transient from his Republic books out. And then that brings us quickly to Euclid, who was a student in Plato's Academy, approximately 300 before the Commodera. And Euclid was, as I indicated, a student there. He went on to establish the School of Mathematics in Alexandria, wrote the elements, and is probably most famous for today, especially for the axiomatic development of geometry. With five process, five common notions, he was able to prove 465 theorems. Now, this is gonna be old hat to the math people here, but this is what I had to tell the philosophers to remind them. He starts with common notions. Things equal the same thing, we equal each other. Equals added equals or equals, attracted or equal, things which coincide or equal, and the whole is greater than a part. Nothing really profound, right? Pretty common sense of all kind of notions. Then he added to that the posthumous, two points to turn the straight line. You have to be clear, straight lines can be extended. A circle can be drawn given any center point and radius, and all right angles are equal to each other. Well, a fairly efficient set of axioms so far that he was able to develop so much out of these things. There was one kicker, of course, and that's the famous fifth postulate, which in Euclid's elements reads, if a straight line following on two straight lines makes the interior angles on the same side less than two right angles, but two straight lines if produced and definitely meet on that side on which the angles are less than two right angles. In the character of this postulate, right from the very beginning, it's so different than the common notions and the others, and of course, it caused mathematicians for centuries, a lot of problems. Why should something that is so rich and not in content, and is far from intuitively out of this where the others seem to be, why is that a postulate and why can't we prove that? But anyway, that takes us down the story as it's in its relationship to philosophy as well. Of course, that postulate was rewritten in pre-fair in the 1700s and the one that we usually learned now in high school geometry. Given a line and the point not on the line, there is one on only one line through the point parallel to the given line. Out of this, as I indicated, Duke was able to prove 465 theorems, including the sum angles of the triangle equal to right angles, the pathetic green theorem, and brewed into similar triangles, prime numbers are infinite, volumes of cones, the cylinders, the spheres, and the ekenesis book 13 with the theorem about regular solves, which I want to discuss in the next. Regular solves are polyhedra where each face is a regular polygon, all the sides are equal and the angles are equal, and each vertex of the polyhedron has the same number of faces and edges. He proved that there are exactly five such regular polyhedra, and they were called a poitonic solves. Now, in the math group, you probably don't need to see the proof, but for the philosophers I did, who run through the proof real quickly, we'll start with what the five that were known in the time of Plato and Euclid, the tetrahedron, the four-sided, the cube, or hexahedron, the octahedron, the dodecahedron, and the acrosahedron, those 20 hexahedron sides. Now, Plato, they're called poitonic solves, because Plato refers to these in his famous biolog, the Tamaeus. And the reason he refers to it is that way back at the time of Plato, there was this desire to combine science with mathematics, or to understand the scientific knowledge that we have in mathematical terms, and that's still a very driving force in science today. If once you can get it, explain something in mathematical terms, you've explained it, or as Newton famously said, I don't know what grammar it is, but here's how it works, here's the formula that works. So that's kind of started back in Plato's time. If you can reduce your science to your mathematics, then you've pretty much done the job that you're at. And the science of Plato's day was a periodic chart of four elements, fire, earth, air, and water. We think that's pretty primitive, but in his day, there were people who argued that everything is water. And their argument was that, well, we see water in a solid form, ice, we see it in a liquid form, we see it in a gaseous form, so it covers all the states of, everything must be made out of this water. And there's other sort of intuitive reasons.  So wood and what it's burned, you see it's been made up of those four elements and you can decompose it.  And earth, because the tetrahedra, by the way, because they're very pointy, it said the fire breaks things up. The cube represented earth because it's nice and stable. Air was the octahedron, water because it flows and it's almost round was the icosahedron. And of course that left the dodecahedron, the 12 sided, and he says less the dome that covers the universe. Now, just to take this a little bit further with Plato's Timaeus, and this is a quote from the dialogue, to the earth, then, which is the most stable of the bodies and the most easily modeled of them may be assigned the form of the cube. And the remaining forms to the other elements, to fire, pyramid, to air, the octahedron, to water, the icosahedron, according to their degrees of lightness or heaviness or powers of penetration. The single particles of any of the elements are not seen by reason of their smallness. Well, you got that right. You can all see how it was very well. They only become visible when collected. The ratios of their motions, numbers, and other properties are ordered by the God who harmonizes them as far as necessity permitted. And there's a fifth figure, which is made out of the 12 pentagons, the dodecahedron, this God used as a model for the 12-fold division of the zodiac. Now, he didn't just lay this out, he also did what we would call today in chemistry, he balanced equations. For example, water, which, remember, is the icosahedron as 20 faces. If you break it up, you get fire, which is the tetrahedron, four faces, plus two airs, which are the octahedron. So two times eight plus four is your 20. So there's got the equation balance there. A volumetric air divided in two becomes two fire. Two and a half parts condense, and a very condense in the one of water. An equation like that, we would like to make those whole numbers, so we would probably say five air, which is 40 faces, equal two waters, which is also 40 faces. So he had a whole concept in his science of balancing the equations as we do now in chemistry class. The point I want to make is that the science in Plato's day has been replaced many, many times over, and we kind of all smile when we hear about Plato's science. But Euclid's proof is still valid today. The mathematics that was proven during the Greek era is still good mathematics today. Mathematics is the best and most certain script in reality is the idea that people have for... Again, this is for the philosophers, but I'll just quickly run through it, so we can just quickly see how Euclid's proof, quote, was written. He says, if we're going to look at polyhedron made out of triangles, and we're going to argue there's only five, let's look at what we're dealing with. He starts with, and I'm putting this, of course, in degrees instead of right triangles, but we start with 360 degrees in a circle and 180 degrees in a right triangle. And so in a equilateral triangle, which we're going to build our polyhedron out, each angle would be 60 degrees. The tetrahedron has three vertices on each, I mean, three faces on each vertex, and the sum of the angles then would be 180 degrees. So that's consistent, though, that works. And the octahedron has four faces on each of the vertices, and the sum of those angles are 240. And then a cosahedron has five triangles on each, and you take five times 60 degrees, and you see we get 300 degrees, that's still possible. But if we try to make something out of six triangles, the sum of them at the vertex would be 360, and so it would be flat. They could not form a three-dimensional form. And then he does the same thing with the cube. Of course, now we're dealing with 90 degrees, and the sum of three of them at each vertex would be 270. But if we try to make one out of four squares, it would be 360, and again, our figure would be flat, and it would not have three dimensions. Then we go on to the dodecahedron, which is made up of pentagons, and each vertex has three pentagons. And the angle of each pentagon, if you don't know of hand, we just break it into three triangles, and add those up, and divide by five, and we see that each angle is gonna have 108 degrees. And when we have three of those, we end up with 324 degrees, which is still possible. But if we tried to put four together, it would exceed 360, so we're not gonna be able to be a convex volleyball.  And we thought of it as equal animal triangles, and you can break that up into equal animal triangles, so each of those angles would be 120, and of course, three of those give us one 360. And anything larger than that cannot be a building block for a polyhedron because it would have too many degrees at the vertex. Anyway, that's just a real quick run of Euclid's proof, and that concept still holds today. That's still good after 2,000 some years. So, they knew at the time there were five, and the issue for Euclid was that they were to spill ballot, like the science is not. And the impact that this had on mathematics and our knowledge in general is this idea that mathematics gives us certain knowledge. It's not knowledge that will change. Once we've proven something, we now enter the realm of what Plato called the eternal. We have eternal truths that are not subject to change. There can be no better description of reality than what mathematics provides. Mathematics was seen as the perfect science. It was seen as a science in the end. At the time, mathematics was not as we see it today, a model building, but it was a actual description of reality. It was the queen of the sciences. Gal, this continued on into the Renaissance. Galileo said, the great book of nature can be read only by those who know the language in which it is written, and this language is mathematics. Kepler said, the laws of nature are but the mathematical thoughts of God. Kepler, by the way, was still intrigued with these Platonic solids to the point that his first attempt to provide the laws for the orbits of the planets around the sun, he attempted to embed circumscribe around the Platonic solids these spheres, and then around that one, another Platonic solid, and he found that the ratios between them was fairly intriguingly close to what the empirical measurements were, but it didn't work very well. Fortunately, he gave up on what's interesting to me is that here, you know, 1500 years later, more than that, they were still trying to make sense out of the Platonic solids as a principle of explanation for science, for all we were discovering. Even as Plato did, Kepler was trying to do it. He did find it like that, and said, it's not circles, but the Greeks thought that the circle was the perfect figure, and so the circle must be the way the orbits would go. He gives up the circles and says, let's go for ellipses instead, with a sign out of the foci, and he gives up constant speed. Another principle in the Greek ideal was not only the perfect figures, but also constant speed. And because that speed is not constant, the planets go faster as they get closer to the sun, but this constant is the area that is mapped out at any given time frame. And if you think about this conception, why in the world would area of a two-dimensional ellipse have anything to do with the speed of planets going around? I mean, the conceptual break that he did with his laws of planetary motion is profound when you think of the thousand years plus of Greek ideas of constant speed and constant radius, or the circle is the perfect figure. It's the area that's constant. Descartes goes on as a philosopher, we know him as a mathematician, that the philosophers like to claim him, too. And what's interesting about the connection here is that for Descartes, mathematics is a model for the best kind of knowledge. Descartes was living at the time of renaissance, reformation in Europe. A lot of things that were believed to be eternally true were kind of falling apart. He traveled around Europe and elsewhere to try to get him broadened his education. Finally realized that there was really nothing he could put his stakes down for that would be certain, except mathematics. He found mathematics was the model. In his discourse on methods, of which, by the way, the appendix was called a lot of geometry, or alec geometry is actually just an appendix to this philosophical work, he says it's only the mathematicians who've been able to find some proofs, that is to say some certain and evident reasons. I was especially delighted with mathematics on the account of their servitude and the evidence of their reasons. And so he set forth his four points on method. These are what they are, and as mathematicians we will recognize them. Not to accept anything is true, which did not clearly know to be true. You know, there's euclids based in common notions and in prostitutes. Divide each difficulty into as many parts as possible. In an orderly way, begin with the simplest objects, gradually climb right up to the knowledge of the most complex. And for it, make my calculations throughout so complete and my review so general that I would be confident of not omitting everything. I'll put a set of guidelines for any math students. Those long chains of reasoning, all simple and easy, which geometries have obitually used to reach their most difficult proofs, gave me occasion to imagine to myself that everything which could fall under human knowledge would fall in the same point. Any kind of, oh man. As a solution of S, as his method for philosophy. Even you know, the great skeptic who questioned everything, including causality and everything else said, though there never were a circle or a triangle in nature, you need to understand that these were abstract things that we never received at all because it's two dimensional. Anyway, the truths demonstrated by Euclid would forever retain their certainty and evidence. So even a great skeptic, like human, sees mathematics as that certain truth. Fainless mathematician Kant said, all probably mathematical judgments are synthetic a priori. For example, if you review your introduction to philosophy, he divided things which were analytic and synthetic. And analytic were things like mathematical statements are all, all bachelors are varied, things that are true by the very nature of the words. Synthetic are things that are true about nature. They're not true just because of the way the words, the meanings of the words. And a priori, those things that we know before we've experimented, a posteriori are things that we learn from experience. And Kant famously said that mathematics is synthetic. It's not true just because of the meaning of the words because there's nothing in all triangles that have 180 degrees. There's nothing in the meaning of those words that would make it true. It is something that's true apart from the meaning. And yet it is not, and yet it is not something that we find through measurement evidence. We don't go out of nature triangles and then come to that conclusion. So his whole idea of mathematics is synthetic and a priori. And that was an important part of his philosophy. In every specific natural science, there can only be found so much science proper as there is mathematics presented in it. Now some of this is still true in science today. No people still. When you've got it down in the mathematics, you pretty well got it done. The science of mathematics presents the most brilliant example of the extension of the sphere of pure reason without the aid of experience. And as this debates through the history of philosophy between does our knowledge all come through the senses, the empirical senses, what we can measure and experiment on, or is there knowledge that comes through reason that is not dependent on the senses? And this is the, you can describe the whole history of philosophy as a debate between these two. And mathematics plays that pivotal role always in the middle of that debate. Is mathematics empirical? You say no, it's logical. And does that mean therefore, is that in an argument in the case of the rationalists and the rationalists that argue, of course, as did Kant and Descartes and many others. And the empiricists would say, well, you know, there's other ways of looking at it. They have to account for mathematics, which is sometimes a tough job. How does mathematics function if everything has to be empirical? Anyway, I'll come back to the summary a little bit later, but it's really clear here in Kant and some of these others appearing this time period. Of course, the thing that really changed the whole world happened after Kant and Descartes and the early scientists, and that is the development of 9th Napoleon John. Going back to the five postulates of Eulogy, we see that that fifth postulate on the parallel given a line and a point. The line on the line is one of our one line through the point parallel to the line. That was the one that had been questioned in many, many attempts throughout history to explain or to prove that based on the other, on the other axioms. Or to take other axioms in and prove this, for example, if you've wanted your axioms, is that all right, all triangles, angles add up to two right angles. If you have that as an axiom, you can prove the parallel posh. So there were lots of alternatives to the parallel posh, but nobody could get mild with just using the four posh lists and prove this. But anyway, so that then became a question that I won't go into all of the historical details as to how that came about with the word of psychoacup. But the big three for the first time in Clinton Java tree were Baus in Germany, Bolia in Hungary, and Lvovchesky in Russia, all working about the same time. There's a lot of Wolfgangs effort. God's sake, please give a theoretical lesson of sensual passion, because it too may take up all your time and deprive you of your health, peace of mind, and happiness of life. Another old historical footnote here is that Wolfgang Bolia sent to Gauss his son's work, and Gauss said, I would like to praise it, but if I did, I'd only be praising myself, because I had actually worked that out years before. You know what, what a rejection matter. God. Anyway. Then Riemann came up with the alternative from us. Assume there's more than one parallel line, and you can get a consistent geometry. What if you assume there are no parallel lines? And of course, as you all know, in the Lvovcheskyan or Bolia non-inclidean geometry, triangles have less than 180 degrees, and in Riemann's geometry, which is modeled by the steer, triangles have more than 180 degrees. Now, Morris Klein, in his mathematics, Western culture, in his big, huge history book, says the importance of non-inclidean geometry in the general history of thought cannot be exaggerated. Like a Permacus heliocentric theory, Newton's law of gravitation, and Darwin's theory of evolution, non-inclidean geometry has radically affected science, philosophy, and religion. It is fair to say that no more cataclysmic event has ever taken place in the history of all thought. But in the math theory, we know that non-inclidean geometry was a very creative point which a whole lot of new kinds of mathematics was developed. And we celebrate that. But Klein is arguing that it was such a shock, not it was the mathematics or famous mathematicians who refused to be considered non-inclidean geometry. But he's saying that it also affected science and philosophy and religion. And the big thing here is why didn't it have that huge effect? Because for 2000 years, there was this concept of eternal truths. And if you question whether there's eternal truths, just go check with your local mathematician and he'll explain it to you. Here's the eternal truth and how that's clear. Okay, now let's go on. So when you have more than one geometry and you no longer can claim that you've taken geometry, it is the actual description of reality. Not just the consistent system or a model, but it is the actual description of reality. If you could no longer claim that, then what can you claim? Where is absolute truth? What do we do with this? Geometry is the knowledge of the eternal. What happens then? And the influence of that over 2000 years was profound and client recognized it. It led to a rethinking of mathematics. The non-inclidean geometry took place during the 19th century. And at the end of the 19th century were the great foundations of mathematics debates. And that's a whole lecture itself, so I won't go through the details, except just to highlight who some of the major thinkers were. Logicism was developed by Bertrand Russell. Intuitionism by Brauer. And Formalism by David Hilbert. If you want to talk about those, we can, but like I said, that's a whole other lecture. But I want to jump now to Bertrand Russell because my talk is from Plano to Russell. And in particular, I've subtitled, I said that this is the 100th anniversary of the publication of the second volume that is famous for keeping in mathematics. Well, I did this for the philosophy grant, but it's the 100th anniversary of the volume one. Well, I'm keeping in mathematics. The timing's been fine here. Anyway, Bertrand Russell, I want to tell his story, but I'm going to shift gears a little bit and move into a comic book form. It's nice to get a little change of pace. And if you're not familiar with this book on Mojic comics, it's a really fun book that tells the whole story of Russell, the white head, and I'll hold it all in some of the problems I've dealt with. I'll give you a little excerpt from that comic form.  At least mathematicians try not to contradict one another. Not so philosophers. They are all great and all in total disagreement. They call this transphosphory. I want to find my way to reality, man. I want a method to acquire a certain knowledge. See that goal that was there from Plato, Nucleon, and it's still with Bertrand Russell. He wants a certain knowledge. If we unite the healthy parts of mathematics and the conceptual sophistication of the new logic, we can launch a powerful attack. You really want to build a foundation, not only for mathematics, but for philosophy. Well, he's sitting in on Alfred North Whitehead's class and Whitehead says to achieve any kind of certainty in mathematics when you must re-examine its basic assumptions, we must begin at the beginning and Bertie sits back and there, here, here. So he meets with Whitehead and says, sure it's kind of a certain way since Aristotle, but is it strong enough to deal with mathematics? Whitehead says, let's join forces. And Whitehead was famous for his book on universal algebra. And so Russell says, you can write a second volume of universal algebra. He says, no, write together a brand new book. So they work on what becomes pre-Kippian Mathematica, which is kind of an interesting bit of overconfidence, maybe. Pre-Kippian Mathematica was what the great Newtonian decided to call theirs the same thing.  And he says, real, here, you got it. What is it? It's proven, one plus five is two. On page 362, it says, and therefore, one plus one equals two. And the kid says, I don't get it, when you write 362 pages, let me play with you. It was such an enormous rethinking of logic and symbolic logic and the whole basis that it took that long for him to prove. Russell then starts, as things develop, he starts losing confidence in his own program. And says, to understand my predicament, remember that my profound underlying aid ain't that never changed, to acquire certain knowledge about the world. Same idea, somehow mathematics should tell to give us information about the world. Knowledge, which should only come from science. But science depended upon mathematics, which was a total mess, plagued by unproved assumptions and circular definitions. To repair it, a powerful logic was needed, but there wasn't one, and so it came to an end fast. He finally said, mathematics is a subject where we don't know what we're talking about, whether what we're saying is true. And this was actually an insight is important for all of mathematics, because Euclind tried, one of the problems with Euclind's elements is that he's trying to define everything. And he defines a point as location without extension. And that helps. The line is, breadth is length without breadth. And as we often point out to our students, if you try to define everything, you get into circular reasoning. One example I like, I think it's Oxford Extreme, that defines a dog as a quadruped of the genus Cana. You end up using more complicated words to describe simple words. And even if you have simple words, if you look at the meaning of those, it'll eventually cycle around. So definitions aren't necessarily circular. And Russell recognized that. He also recognized that our axioms are not always intuitively true. They are beginning ones. So we can't prove the axioms and we can't ultimately define them. So we don't know what we're talking about. And no matter what we're saying is true. In his portraits from memory as autobiography, he says, I wanted certainty, again this key certainty, in the kind of way in which people on religious faith. I thought that certainty is more likely to be found in mathematics than elsewhere. After some 20 years of practice trial, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge and do it all. The splendid certainty which I had always hoped for in mathematics was lost in the bewildering maze. So 100 years ago, they published their three-volume pre-Kipley Mathematica. He died in 98 in 1970. 42 years ago now approximately. But the question of mathematics in reality and the search that Russell, along with Euclid Descartes and many others, is still a question that we often honor. Does mathematics describe reality? Is mathematics just a game? As some of the formulas bring. Is mathematics meaningless? Are mathematical objects real? Are numbers real? Are points in line as real? Reality is one of the issues philosophers deal with. It's called ontology. Ontology, what is real, what is true? And so these are weird questions that a philosopher would want to publish to a mathematician. If mathematics is not real, it's... I mean we have this much certainty about mathematics and everything else is less certain. Mathematics isn't real. What's going on here? Questions of, is mathematics discovered or invented? Question of certainty in mathematics, realism. The status of logics is a formless intuition. These are kind of the questions we deal with in the philosophy of mathematics. And then finally the question of structural realism. In the last 20 years or so, there's been a new movement in that philosophy of mathematics called structuralism. And that's another level talk, which I don't have time to do today, but it's one that I have presented at some international leagues. And it's a very intriguing way of making sense out of this whole question of whether mathematics is real. And it really comes back to the picture that Robert picked for that notice. And this is, like I said, from Raphael's famous School of Ethics. It's a good way to summarize the part of this for you, I want to say. The person on the left is supposed to be Plato and notice that he is pointing upward. He is pointing to the rational truth, to the certainty that transcends our experience. And Aristotle is saying, no, it's here on earth, it's empiricism, it's what we can see, it's what we can touch, it's what we can feel, it's what we can hear, it's what we can measure. It comes from the sciences. And Plato says, oh, there is knowledge that comes from outside, it comes through our reason. And so this is a summary, and in a way, of what the role of mathematics has been in history of philosophy. Is this tension between can there be knowledge that is not empirical? Is there knowledge, even better knowledge, that comes through our reasoning and through our rationality that is not something to empiricism and to our senses, tell us. But since I have a little bit of time, I guess I want to race through this pretty fast, realizing I was under time constraint, I'm going to take the opportunity to do a personal post-scratch. And I want to talk about three famous philosophers, Wittgenstein, Russell, and Karl Popper. And Russell, of course, we've talked about, became not only a famous mathematician, but a famous philosopher. Karl Popper was one of the famous philosophers of science. And Wittgenstein was the philosopher who in many ways caused the revolution towards analytic philosophy, and then a whole new way of looking at philosophy in his philosophical investigations. Probably most people would argue is perhaps the most influential philosopher of the 20th century. A lot of interesting stories about Wittgenstein, too. But the story I want to tell is when Popper was invited to the Cambridge University of Moral Science as well. This is the talk that the greats had belonged to Russell, Witte, and lots of Wittgenstein. This was sort of the elite club in Cambridge, and you had to be nominated to be, and approved to be a member of the club. In October, 1946, Karl Popper was invited for the first time, he was not a member, but he was invited as an outside lecturer to give a talk, aren't there philosophical problems? Wittgenstein was famous for saying there really aren't any philosophical problems. It's just problems of language. We confuse ourselves with the way in which we talk about things. We talk about, I have keys in my pocket. Therefore, I have ideas in my head. Because the grammar is similar, we think that ideas are things like keys. If they're in your mind, then it's like keys in your pocket. And he says, his approach, in my philosophy, was to analyze things from a grammar and understand why they weren't really philosophical problems. And so, Popper, on the other hand, as a philosopher of science, was committed to the idea that science does, in fact, describe reality, and there's a pathology for it, falsification was the key term that Popper used. And he wanted to argue that there are philosophical problems. This whole story is recorded in a book that was published about 10 years ago called Wittgenstein's Poker. Because the seminar took place in Brathwaite, another famous philosopher, in his library, in Cambridge, if you've ever been there, the faculty, once you meet a professor, it's pretty nice. You have an office, you have your own, a joining library, fireplace to keep warm. And so, the seminar was actually taking place in Brathwaite's library. And at one point in the debate, in the discussion after Popper made his claim, Wittgenstein got very, very agitated. Argued against Popper. And said, finally, and to make his point, he grabbed the poker from the fireplace and was waving it, according to that.  And finally Wittgenstein says, give me an example of a moral truth. And Popper said, one shouldn't threaten a guest speaker with a poker. Anyway, so anyway, this one's what happened. Now in Brathwaite's library, there was a set of the pre-Kipfium Mathematica. The three volumes, and I happened to have the three volumes of the pre-Kipfium Mathematica. If you want to come up and take a look at it afterwards, I've even put a little sticky on page 362, where it says, from this proposition, it will follow, when the Arithmetical Edition has been defined, that one plus one equals two. But the other interesting part of this is that if you look in the front page, this was our Bureau at Brathwaite's personal copy of the pre-Kipfium Mathematica. And when I left the dean's office in 2004, was it? The faculty, some of you were still here, collected some funds and bought me a bunch of philosophy books because I was moving into my faculty role. And one of the treasured things were the three volumes of pre-Kipfium Mathematica. There aren't very many original editions of this around, I don't think anymore. And not only have one, thanks to my faculty colleagues back then, but to have Brathwaite's when it was part of the story of Vickensites Poker, is kind of a special little personal thing for me. And so anyway, it for me, that kind of pulls together my own personal history, as well as my exploration over the decades in philosophy and mathematics and how these things sit together. So I think with that, any questions, is that? No, you can do it. Any questions for our speaker? Yes, I'm just trying to think, it seems to us in this presidency that the last three mathematics are further in place. Is that because of the strength of science and the strong of it, and the long lines of the last four to five years? Well, certainly the success of science has had a big impact. But I would argue that that's sort of a positive force on why we tend to see things scientifically rather than mathematically. But I would argue that the other part of it is the shift in the understanding of mathematics is no longer a science. It is not description of the empirical reality. It is something else. And whether it's a game or whether it's meaningless or whether it's, you know, what it is, we still don't have a good handle on it. But no one, very few people would argue that it is a description of empirical reality. And maybe a description of another part of reality. If one argues that there is more to the universe than matter, and science is primarily looking at matter, but there are other things like structure and structural philosophy, and all these things are things that mathematicians also like to talk about. If you say that their reality includes those kind of things, not just material things, then, you know, there may be a place for that. But it doesn't have the same role as it had. And I think that the case I would like to make is that really the turning point of that again as more clients would get with the That's when the triangle hold on reality in mathematics. So there's a real push and have been for quite a while that in the teaching I said K-12 mathematics, that it's real life. I mean, do you see that as part of the issue as well? It's real life? Yeah, that, you know, the question often becomes is, as you're teaching this particular lesson, how does it relate to real life? Well, that's me. I mean, I got, I might want to think about a little bit more, but my first reaction would be that's a pedagogical question. And I think pedagogically, of course, we want to teach things that are relevant to real life. And so, is mathematics relevant? Absolutely. In fact, if science is more dependent upon mathematics now than it's ever been. And so, does mathematics inherit its reality via science? You know, maybe. That's one way you could argue the case. Or is science reach a dead end when it puts things in mathematical terms? And it finally says, we can't go any further because we have now put it in terms that are no longer in parallel, but are rational. And that's as far as we can go. Science does not proceed. The reason, of course, when it doesn't proceed with an exhumatic base that is apart from the person's. And as I find it really interesting that people like Dawkins and others say that there is no reality other than what the scientists can discover. And yet the scientists use mathematics all the time. And they have discovered that through their interval method which is supposed to be the sum of all knowledge. You know, when they finally get to mathematics that's as far as they think they're done. They think, hey, we've got a better name. So anyway, your question is interesting but I would tend to think of it more in pedagogical terms. We want our students to relate to these things in real life terms. And I try to do it in college classes too. Do I have time for my foundations lecture? If there's any more questions, let's thank Prisik and Jay again. Thank you. If you're interested in the print hippie or those in that kind of panel, it's something a lot of all students