 Okay, so hello. Good morning. Welcome to philosophy and what matters. So this is our second edition and Today we'll talk about existence. So what is philosophy and what matters? Well here we talk about things that matter to us from a philosophical point of view Our problem for today is about existence now. We all know that Donald Trump exists Thus we could say that there is at least one thing that exists, namely Donald Trump Now some of us may know that the mathematician Nicholas Burbaki doesn't really exist The name Burbaki is a pseudonym used by a group of French mathematicians in the 1930s Thus we could say that there's at least one thing that does not exist What does it mean to say that something does or does not exist? That is our question for today Now we are so lucky that we have our good friend Greg Restel Professor of philosophy at the University of Melbourne to discuss this problem with us. So hello, Greg. How are you? Hi, I'm doing really really well. It's lovely to see you all Okay, so let's start the ball rolling with Quine's question. So there's an American philosopher, Willard Van Orman, Quine and let me quote him So he says, non-being must in some sense be Otherwise, what is it that there is not? Now he calls this doctrine Plato's beard. So Greg, what does Quine mean by this? Yeah, this is a really good question For Quine when you're saying When we talk about whether or not things exist The idea that, you know, you raised when You were talking about Bulbaki as an example of, you know, a non-existent thing There's something really puzzling about the idea that Bulbaki doesn't exist because you Introduced us to Bulbaki and said here's Bulbaki. Bulbaki isn't really a person It's actually a pseudonym for and a bunch of French mathematicians So when Quine says how could there be any non-being if there's non-being This has got to be something which exists And so for something to not exist there has to be a thing Which doesn't exist Then this is the problem and and one reason he calls it Plato's beard is because this is a problem in philosophy that goes all the way back to Plato and What makes it a beard is that this is the kind of thing which Occam's razor is meant to be shaving But sometimes the beard seems so tough That it's rather the razor that gets blunted Okay, so Plato's beard, I think it's the idea as well that you can't you're trying to multiply entities beyond necessity, right? So you need Occam's razor to shave that but it gets blunted as you have said Especially when we're talking about non-being or non-existing. Yeah. No, I'm wondering how you connect that with The atheist claim that God does not exist So how do you yeah, that's a yeah, that's a that's a really good question and for Quine he will Try and be very very careful and say it's not that there is a God that doesn't exist but rather we will start talking instead about What it would take to be a God and So we won't say that there is a God which doesn't exist But we'll say that you know for anything to count as being a God It has to be like this and this and this and maybe you know really powerful Really good etc. Etc. And then you might say that We've got reason to think that there isn't anything Which can satisfy all of those properties. So we're not saying that there is some God which doesn't exist He doesn't want to say that because that sounds Self-contradictory rather there is nothing which could count as you know being a God Okay, so why does this question matter the question about existence and non-existence? yeah, I reckon it matters because we really care what the world is like and We really do care about What there is You know, I really care about How how much coronavirus there is in my copy I Care about whether there is a vaccine for coronavirus or not and so you might think that it comes down ultimately to the kind of practical ways of navigating the world but philosophers are not just practical people We also like our concepts to fit the world well and One of the ways that we'd like our concepts to fit the world well. I think would be that we The things that we talk about Somehow correspond to things which are out there in the world those things that actually exist rather than Just being figments of our own imagination Okay, so what is existence really I think there are two philosophical point of views here So you on the one hand you have people saying that existence is a matter of Quantifier the existential quantifier. I think Bertrand Russell was one of those guys who talked about this So how should we understand this claim that existence is a matter of quantifying over things? Yeah, this is a way I think of being more precise or one way of articulating how I was Answering your question about what it might be to express Kind of atheism In a way, which you know follows from what quine was saying Not by saying that you know, there's a particular God which doesn't exist But saying no, there is no thing that satisfies these constraints or these these descriptions and so One way to get you know to make it a different kind of example You know if you've done any, you know mathematics you realize that For example There is no Whole number which is The square root of three for example, there's no two whole numbers that you can multiply together to get three You got to get those, you know really complicated numbers. There's even no fractions You've got to have these weird irrational numbers and so one way you could say that the the square root of three does not exist as a whole number is Not to say that there's this particular number which doesn't exist, but rather the The constraints in this ways it'd be the equation, you know x squared equals three doesn't have a solution where the value of x would be a whole number And this is like this existential quantifier here. There is no value that Could satisfy this or that does satisfy this and so, you know, the atheist says there is nothing in the whole World nothing anywhere in wherever things can be found Which is, you know omniscient Omni good Etc etc, whatever the constraints for being a God might be So we're not naming the thing and saying that thing doesn't exist but we are Describing the properties that it might have and then we're saying well, does the world supply something which has all of these properties? Yes for some things and so those things exist and know for other Things but the thing that we're talking about here is the Description or the predicate that we're asking is satisfied and that existential quantifier is the symbol that we use in logic for You know saying that there is something that satisfies a description, you know There is something which when you add it to three Gives you seven You know, there is an X such that X plus three equals seven. What would that be? Probably four? Yeah But there are some things there are some things that we know exist, but we don't have names for and And so Russell was saying that this is how we can Talk about whether or not things exist Because for Russell if you had a name for something then there's no further question about whether or not it exists But there are some things where you've got descriptions and you don't know whether or not there is something would satisfy the description Okay, so let me sense. Yeah, let me try to Yeah, understand what's going on so you're saying that existence is a kind of Well quantifier in this case existential quantifier such that whenever you have a description of something You want to figure out whether that description is satisfiable or not? So if it is satisfied then you quantify over it using the existential quantifier Otherwise, you'll say well, there's no such thing. So quantifier the quantifier here is just saying that This property is satisfiable or this property is not satisfiable. Yeah, yeah It's good. I like your your vocabulary of properties here. No for Russell It's that's the right level to talk about existence The or that's the level at which existence makes a difference because if I just think about asking the question of existence and You know, it's like, you know, the old story in the Bible of you know, Adam Naming the animals It's not like, you know, God brings brings, you know, an object to me and ask me does it exist? Well, there's nothing for me to answer, you know, it's always yes, you know Whenever you give me an object and you ask me does it exist? I'll say yeah Does it exist? I say yeah, whereas if you give me a description And you say is there a thing that this thing describes then sometimes the answer is yes And sometimes the answer is no Whereas so in this way existence as a property is a property of Properties, it's a yes or no Distinction about those properties. Is there something satisfying this property? Yes. Is there something satisfying that property? No Whereas existence isn't a property of objects for these guys Because you give me the object and then the answer is always yes, because here it is Mm-hmm. All right, all right. So I think that one of the classic Examples of Russell is the present king of France. Yeah. Yeah, okay, so What's the possible so the present king of France is bald? supposedly now the question is whether that's true or false and Russell would say well, let's see we need to distinguish between two types of questions here on the one hand You're asking the question whether this thing the present king of France is bald has this property on the other hand You're also asking the question whether there is such a thing as the present king of France And there's only one thing and that guy is bald Am I getting that? Definitely, definitely and so present king of France as a property Mm-hmm that's sometimes satisfied, you know back when Louis the 14th was king. Mm-hmm He satisfied the property After the revolution and which France over through the Kings And France didn't have any Kings anymore then the property was left unsatisfied And so in that sense the present king of France doesn't exist In those cases and so then that that are that extra puzzle for for Russell about you know What to say about the present king of France is the present king of France bald? Well, when there was a present king of France sometimes they were bald sometimes they weren't but when there isn't a present king of France You know for Russell the answer present king of France is bald that would just be false But the present king of France is not bald Will also be false But there Both of those things are false and that's not a violation of any You know excluded middle or by valence or anything because When you're saying that You're saying when I say the present king of France is bald I'm saying there is something which is the present king of France and it's got the property of being bald The answer is no The present king of France is not bald there is something which is the present king of France and that thing is not bald The answer is still not because there's not such thing Because there's no such thing what is true is it's not the case that the present king of France is bald that turns out to be true But that's not the present king of France has got the property of not being bald Okay, okay, so there's another school of thought that Russell was replying to you So here's a lexious. My name one of the founders of Phenomenology, I think so he has this idea that existence is a property not a second-order property But a property per se some things do have that property some other things don't have so what does he mean by this? Yeah, yeah, yeah, so he he this is the views that Russell and others is are arguing against and I think One nice way of thinking about it is that Instead of imagining God You know presenting you with each of these objects and asking you do they exist or not? Because clearly if you've got an object. Well, there it is it exists, but God naming giving you names or You know JJ at the beginning saying Donald Trump does Donald Trump exist. Yes Does Bulbaki exist? I'm more hesitant about this I'm I don't know whether to say Bulbaki exists on I know that Bulbaki is not an individual But Bulbaki exists am I allowed to think of collectives as Existing or not. It's a really interesting question. Right. What about but what about Pegasus? What about Another example, what about Santa Claus, what about Batman? What about one divided by zero? I don't think all of those things exist. I definitely don't think that one divided by zero exists I definitely don't think I think that the I think that Batman is talked about I think that but there's a sense in which Batman doesn't think there's a clear sense in which Batman is made up Mm-hmm and is fictional I don't think that Bulbaki is fictional in the same sort of way but maybe Maybe somebody could argue that actually Bulbaki is sort of a fictional mathematician that other people, you know, right under the name of Not gonna So so my long, you know being a phenomenologist We're saying look we don't have Independent access to each of these objects as such we get them by means of in our names or concepts and I have not met Moses. I have not met Abraham Lincoln I have not met a whole bunch of these people. I've got all of these names in my vocabulary But sometimes these names point back and point back to a thing But they don't always point back to a thing mm-hmm, and so It looks like when we're talking about these names we can distinguish them and we can say of you know Abraham Lincoln existed Exists as a historical You know as a Historical person mm-hmm Moses well, I mean people debate, you know historians debate about whether there was a historical Moses or not Or whether this is a story that we've been That's been passed down which might bear some relationship to what happened, but there may be there was no Moses and So my long is saying that It's worth thinking of this as a property of Now shall we say it's a property of objects mm-hmm Well, let's call them a property of items. Okay, that's and so so my long has this larger name there's sign and so sign in German or Objects and a larger class which we might call items where You know the kinds of things that we can think about like one one divided by zero like Moses like Abraham Lincoln like Donald Trump like Boobarkey then say we've got these and If you think about this and it's so my long was not an analytic philosophy He was not focused on language But if you want that in the vocabulary of analytic philosophy think about this in terms of singular terms or names Where now We think of names these things now conceptual vocabulary the things which are intended to refer to things but Maybe not all of them do maybe some of them point back to you know, I You know, I borrow these items from people that I've learned them from You think of these, you know chains of references we go down through history And some of them might point back to the actual thing where they were named and others of them Might have started somewhere else in being made up or Maybe I have misheard them or some things like this and so for my long he wants to say It's not just at the level of descriptions because names aren't whatever they are our descriptions and My long and I think he's got a really good point here thinks that we should also think of this distinction between the existent and the non-existent for Items or using the vocabulary of language think about them in singular terms And some of those things refer And some of them don't I like that point so Well, what I learned about mind on is that there's a distinction between Subsisting things or yes. Yes. Yeah. And so something subsists if it's a thing you can think of and so And then among those things which subsist Once which exists so I we can have thoughts about most is We can have thoughts about one over zero when we ask is there an object, which is one over zero Can is is there anything which you get when you divide one by zero? We can argue about Bulbaki and wonder whether Bulbaki is our favorite mathematician or not And because we can have those thoughts these objects subsist in my long set of these items. Sorry subsist But they it's another question to say well, do they have real existence No, I Like that idea that thoughts things that you could think about will subsist under this Metaphysics my nose metaphysics. However, there are things that you can't even think about right so What give me an example? So Five foot seven footer Yes, it seems hard Something which is both five foot and seven foot You're gonna say round squares and things like this. Yeah. Yeah, you know where this is going Yeah, and so Yeah, I find these things hard to think about too. I have friends Who think that they can think about contradictory objects? I Do know that yeah, here's this is a really good question as to what counts is thinking about something Here and whether you need to have a clear Conception of it. I mean from my long you could you could think about one over zero Even though when you do the calculation, you realize that there can be That can be no such thing. It doesn't exist And so Yeah, exactly what the limits are of that and what is required in terms of conceptions and The degree to which that's a mental act and the degree to which now it just needs to be sort of a concept which is in our vocabulary and in our shared understanding like you know Santa Claus or Moses or Pegasus or whatever. I I don't know. I don't know exactly how far you should you should go there But you could say At one at the really broad level you've got the descriptions and Even and this is where my long and Russell agree At the level of descriptions We certainly agree that sometimes there's things which satisfy the descriptions and things which don't okay And the descriptions can be inconsistent and there's no thought that we need to be able to you know Have the idea of those things and there could be a debate about whether something even subsists which can status which can fall under those descriptions But what my long wants to say is that at least some of these things like Bulbaki like Moses like Pegasus These things where it's just a Description but it's a a singular term a concept a name which is passed down and is used like any of these other names At least for those things the existence subsistence distinction becomes a really live one. Yep, okay, so One interesting problem regarding concept of existence. It's a problem of two negative Existentials. Yeah, so let's just change the example. Let's not think about poor Baki because as you have argued Collectives exist now supposing we change this to Sherlock Holmes Perhaps well Sherlock Holmes does not agree Sherlock Holmes doesn't exist. Okay. Yeah, let's go and that's the fun of the story Is he's made up? Okay, so Sherlock Holmes does not exist But why the rules of logic like via existential generalization? I could say that there's something that does not exist Yeah, now this kind of inference is I think problematic and it results to Plato's beard as we have Discussed later. So why is this a problem again this kind of inference? Yeah, well, um, if there is something which doesn't exist then it looks like we have Two notions of existence here and some people some people don't follow So this is where my long would be my long is totally happy with the conclusion here That there is something which doesn't exist where the very is for my long at the front of that statement is You know something subsists that doesn't exist So my long is totally happy with saying that there is in this wider sense Something which doesn't exist Many people however Are a little bit hesitant at following My long in this conclusion because they agree with Klein and with Russell That the existential quantifier whenever we say there is something the only way that that can work The only way that the there is Can be given any sense is As an existential quantifier, it can't be something brought up and You can have various reasons for this but one that I do find a little bit compelling is that The the problem of Just Unbounded now if it is if we're going to have this quantifier for subsistence You know arranging over all that Years in my long's broader sense Then this seems totally and utterly unlimited it seems Untethered from the world in some sense You know this is goes to there's another example which a coin uses in a slightly different context where he's talking about Quantified modal logic if Quite I don't know whether I've got the wordings of coins example exactly right But if coin says if you think that there is a man in if it's possible that there is a man in the doorway Then Well, how many possible? This is a it's it's not it's not that you think that there might be for all the evidence You you can see that the doorway is empty, but you think that there could have been a man in the doorway Then well, how many possible men are there in the doorway because they could have been a tall man a short man Happy man a sad man You know a man from the Philippines a man from You know Germany a man from South America, etc. Then it looks like there's infinitely many possible men in the doorway It looks like there's absolutely unbound. There's no limit So you can't individuate between those possible men exactly and it sounds like Not only can't you individuate between them, but there's nothing that could count as an answer to that question There's nothing that could count as a limit To what are these things which don't exist if we're thinking of them as part of our Ontology in the broader sense. So if you're thinking of ontology as the stuff that Philosophy tells us or our concepts when working well Commit us to talking about if you think that there are these things which don't exist It looks like your ontology has become Massive where ontology is all of those things that you are quantifying over and so quite quite really didn't like this and thought that this was You know the most massive violation of Occam's razor that there might be and So and and this is where you know here and Minong most seriously parted ways because Minong was happy with saying. Oh, there's a plenty of things which don't exist you know Sherlock Holmes is one of them and there are many many others. So it's it's it's partly In one sense, it's a matter of philosophical aesthetics as to or or philosophical methodology about how How large or Sterile you would like your How luxuriant or sterile you'd like your ontology to be where you prefer desert landscapes or this is you know This is called Minong's jungle You know Ontology is just absolutely massive You know coin cost is the bloated universe, right? Exactly. It's a massively bloated universe on this view Anything anything that we can conceive of in the sense of Having concepts for will have its corresponding Value in the realm of what subsists and what exists is narrower But this is wild beyond our You know, you know wildest, you know, imaginings Okay, so in the philosophical literature free logic has been used to solve the problem So what is free logic and how does yeah? Yeah, and so in free logic, I mean, there's there's a number of ways that we could go with It's it's a way of attempting to regiment Or try and give rules around to say, okay, if we were to take Minong's idea seriously How far does it go? How far does it have to go? How far, you know, what commitments do you get? Because it's certainly And on what don't you because you might think oh look that argument that you had on the previous slide is totally compelling and in some free logics That turns out to be a valid argument When you understand it in other free logics, it doesn't and but the idea in free logic what makes free logic free is that All of the terms All of the items in the vocabulary are Free of existential import That's the slogan. What that means is just because you have a bit of language Doesn't mean that there has to be a thing that corresponds to that An object that exists and standard Classical logic that is taught to first-year students Is not free of existential import neither is Aristotle's You know syllogism is not free of existential import the idea there in each of these things is if you've got a name for the name To be a part of the logical vocabulary the way that a name is interpreted is it names a thing So names do not are not free of existential imports in traditional Classical logic whereas in free logic you're allowed to have a name and the name might not name a thing You have a name and you don't know whether it's on the Sherlock Holmes side Or whether it's on the you know JJ side whether you know or Greg So Greg and JJ name, you know JJ and me and Sherlock Holmes Doesn't name a thing that exists And so in some free logics Uh, you just allow you have You allow the language to have names and then there is a question. Does the name have a referent? Well, if it does refers to that thing and if it doesn't Well What do you do? Uh in some free logics, that's it if a name doesn't have a reference It doesn't have a reference And we just made very minimal changes to things Uh, we say What does it mean to say that JJ exists? Well, that's to say that the name JJ has got a reference It's out to be true because the name Greg does have a referent Sherlock Holmes exists That turns out to not be true because Sherlock Holmes doesn't have a reference Doesn't refer to anything and that's what's called negative. Um free logic. It's very simple Uh, and it turns out on that view That's the only sort of change that you make to standard logic Um, the quantifiers Still work in the way that they normally would we've got a domain of objects If some if a name refers it refers to an object In that domain and if a name doesn't refer It just doesn't refer to anything. Mm-hmm. It's very very simple. Um, and Then there's what's called positive free logic, which is goes beyond negative free logic, uh, and positively posits the idea that names might refer to things Which don't exist and so it goes it follows along my nong's picture and says that okay We've got a whole bunch of objects. Mm-hmm Some of them exist and then we've got non-existent objects And you could have names which name those non-existent objects. Okay And then does the name refer Well, yeah, Sherlock Holmes refers to Sherlock Holmes Pegasus refers to Pegasus Uh, whatever the object Pegasus is whatever the object Sherlock Holmes is and Then the question does Sherlock Holmes exist Turns out to be a question about whether the object that the name refers to is one of the Objects or the items that exists. Is it just is it an object or is that merely an item? And and so Oh, you get these two very different views Of how to understand names that don't refer you get sort of negative free logic which says all Names can not refer but that doesn't mean that they There's items out there that they refer to And somebody that's really happy with negative free logic might Resist the argument that JJ had on the previous slide They'll say I've got a name like Sherlock Holmes Sherlock Holmes doesn't exist. That's true Does it follow from that that there are some things which doesn't exist? That's not true Uh, and so you've got to modify the rule for the existential quantifier and just say just so that just because we've got a sentence with a name in it Doesn't mean that we can say that there is a thing Which satisfies that because you've got to check Does the name refer? And so and and in logic we can we can do that, you know, you got the inference Uh, you know term t satisfies predicate f Does it follow that there is a thing which is f? No Uh But they would if the term t denoted something and so we'd have to add this extra premise which says that, you know T exists not the term t exists But the old second refers to refers to something that there is an object that t refers to So use the existence predicate on the name t and we'll say just t exists. Okay. So uh, Sherlock Holmes Is a detective that lives in biker street I doesn't follow that there is a detective who lives in biker street and you can imagine knocking on all the doors in biker street asking you a detective you a detective and we've exhaustively searched the street and Nobody is a detective Well, but Sherlock Holmes is a detective that lives in biker street Uh, does it follow from that that there is a detective that lives in biker street in negative free logic? The answer is no that doesn't follow because we needed this extra premise which was that Sherlock Holmes exists And if Sherlock Holmes existed then you could conclude that but if Sherlock Holmes doesn't exist then you don't Whereas in positive free logic There is this thing, which uh, you could say that there is something Which is a detective that lives in biker street Because you've got this outer domain of all of the Items as well as the objects and Sherlock Holmes at least lives there And on that view um You could follow the argument and say that there is some thing which Doesn't exist or either Sherlock Holmes And so the positive free logic is much closer to Mino's idea of the difference between existence and subsistence But negative free logic goes some way Of allowing existence to be a predicate which can be applied to names Without saying that there is this outer domain. So, um, Which is better or not is another question But that's that that's the kind of thing that's the kind of things that people have done when they've done done done work in free logic Okay, so I'm trying to understand the free logic at least the negative free logic So there's a domain and the domain contains objects Yeah, okay Then things that are not there or if it's not in the domain. It does not exist According to this view now. Yeah the other hand the positive logic is that you have a bigger domain of items and you have a sub domain of Objects the existing things So Sherlock Holmes will be part of the bigger domain and the sub domain of existing things will be you and I Now here's a question about that What do we how do you think about dead people or future people? Yeah, good question So, how do you think that's a really good question? Yeah, and so you could go either way You uh, there is and and this is more. This is a question about The uh metaphysics of temporality. Yep uh if you everything In or an extension in space time Future people and dead people exist in the timeless sense And then there are some people that want to say no existent is it's what Hello Greg you're bringing up. Sorry this without us Sorry, you're breaking up Uh dead people exist. Oh, were we breaking up? Yep. Was I breaking up? Yep On one view future people and dead people and you and me all part of the same Existence is tenseless. It's just All of us For Past people I think you're and and and and there's differing about Future people then talking about things getting our Meanings from stuff in the past. It's very hard to see how we could have Irms which get their reference from something in the future. I don't don't see how That works in quite the same way at least if cause cause an effect of from past to the future And then there's a really radical view Which is that the only things that exist are the things that exist now In the strong sense of being present now And you could say that the past things exist dead But don't exist now I'm I'm sympathetic with there being a difference between existing then and existing now But then it seems to me that you really do need to Go for something like my nong's larger view because We can talk about things which did exist There are things which did exist. You know socrates did exist And so on yeah Okay, so I think we're going to the territory of the metaphysics of time. I know And that's all right really hard. Yeah, that's all right So I'm just thinking about this domain is the domain something dynamic or something static So hurting you you can think about it in terms of a static view. So everything's there, right? And there's a dynamic view that well Some things are there some things have been there some things will be there and so on So I'm not sure. So how would the logic your the free logic be affected? Yeah. Yeah. Good. Good question I mean, and this is something where I think This is me as a logician Rather than me as Just a philosopher too the really nice things about logic is that the one set of rules and principles can be given a bunch of different models and You know, I was describing free logic in a very Sort of static way thinking about here's a domain Maybe in a domain and out of domain and here's the rules for how the language works But then people have Given Logics You know more than one, you know model theory or semantics Where you can say oh, look these still these rules will can still be satisfied if we You know have this view of a domain say growing under extension And and and this is you know, often the most interesting models that we get come from other areas like in mathematics And you know if I look over at my colleagues in the maths department and see what they're doing they often talk in mathematics in terms of things being constructed and You know, we talk about you know, we can talk about defining things in terms of other things and you can see Often you get this kind of directionality in ontology. This also happens in computer science as well We're talking about processes of verification And things and so the idea of a kind of dynamic domain Where you can get things and then things which are built in terms of other things or made and constructed out of other things Or things which can be described using the conceptual resources of the things that you've already got uh Really does make me think That We shouldn't be captured by the idea of okay I've got this domain and it has to be this thing And this thing which is given once for all. Yeah, that can be one way of looking at it. That's like the god's eye view Of you know taking the universe and imagining, you know, you're stepping back and looking at the universe as a whole but Then there's the internal perspective. Okay, you're in the universe and then say, okay What have we seen and what can we? Uh, you know describe using the resources of what we've seen and can we go further and further and further? I think uh, what's what's really neat about logic is sometimes it gives us the tools to look at these things from these different perspectives, so I'm really I'm really sympathetic with the idea of kind of a you know dynamic domain or um, uh, you know those sorts of things and I don't think we should be just captured by one way of looking at Um, you know, what a what a model or a universe and things like that might be Actually that leads me to the last question here. So you're a professional logician and you're a pluralist Yes, I am. Yeah. Yeah, you could hear. Yeah. Yeah. Yeah, that was coming from yeah Yeah, so how do you see the relationship of logic on the one hand and philosophy in particular? Meditates on the other. Yeah, I I I It goes on from what I was saying before. I really like the idea that in logic. Uh, it's it's um a way of You know building models seeing what's involved um, you know, I I think the development for example of both positive and negative free logics uh goes to Answer some of quines worries about oh my goodness. What uh, you know Doesn't doesn't uh, doesn't it go sort of haywire or crazy if you talking about Things which don't exist and the development of these logics says well No, not really. Um, if you uh, you know Understand the language like this Here's how it works. This is what turns out to be valid. This is what doesn't Yeah, there's some costs and benefits. Maybe this makes sense. Maybe it doesn't it's it's kind of like Getting some ideas and Just being a little bit systematic and saying, okay Here's what the rules might be And if we did this here's the kinds of things things that we could Say here's the kinds of things that would count as models Here's the kinds of things that would count as meaningful. Here's the things which we could represent Here's what a valid here's what and it's kind of enables you to build things Uh, um And I really like that. Um, and so I like You know, here's I don't agree with Tim Williamson about about uh, everything But uh, there's a wonderful, you know, a little section in our philosophy of philosophy at the end where he talks about how uh using precise means Is not a way of You know calculating answers to questions As if this stops philosophers arguing about things, you know, there's no way that's ever going to happen but it does help us to Try to actually specify What a position is or some of the things that are involved in a position. So I like The the free logic examples there's different ways of articulating You know, some of mine owns ideas of our existence and non-existence and saying if you were to take existence as a predicate What would that be like? And here's some things that would follow and here's some things that wouldn't uh, it's a way of um modeling or keeping honest or helping us to say, okay Here's a way of spelling out what these fundamental commitments are and the idea of doing this um Formally is a way of doing it which makes it sort of hard to fudge Where the idea is no, let's just I'm not saying that this is a total picture of everything But let's just see at least in this little vocabulary using these little concepts Imagine they work like that Where we specified them in some particular way and work them out. I really like that But the but then along with that Um, the fact that it's formal does something else The fact that logic formal logic Is formal means that you attend to patterns that you can see in various ways I really love I mean, I've been talking about models mostly, but I really love too that in logic you can think about things in terms of proofs and um Proving things is like um looking at connections between concepts and trying to see how their most um, sort of fundamental connections between concepts might be uh, examined and understood and So there's a sense in which Proof theory in logic is is like slowing down your thinking and trying to get down to the most fundamental precise bits Whereas model theory is this kind of wild universe building Imagine things were like that and I love that you've got these, you know, two different sorts of perspectives, which um The the the most wonderful results in logic of the 20th century have been saying that these very different perspectives often Can be two different ways of looking at exactly the same thing And it it gives us tools for thinking Which can be really useful to have where when we're thinking about something philosophically we often um can Be get some inspiration from the kind of change in perspective Yeah, I like that picture about proof theory and model theory. So proof theory is the rigor The step by step the algorithm you're thinking about what follows from what in that way And model theory, it's well universe building, you know the idea that you're constructing worlds Seeing how things are the big picture now When was the last time we last met I think it was 2015 and the green I think it was I think it was so this is what this is five Years ago five years ago So, yeah, I remember the world was innocent I remember one of our discussions there. Yeah, green priest is one of those who believe in my nong's jungle Yep, right. So contradiction through contradictions exist for him So that's a philosophy or is it a logic? So Is it yeah, I think it's both. I think I think it's both. I think for graham. It is fundamentally Uh, I mean it is very much a philosophical perspective But what what makes the logic associated with that is that graham has Partly because I mean you see this also in david mercy this and other people said Uh, you see this in tim Williamson, uh, Williamson Lewis and and priest Three very different examples of the same kind of move where you've got something which is a really radical view In graham's case, it's Some contradictions are true in david lewis's case. It's Possible Possible objects actually exist different possible world non-actual possible worlds Equally existent to the actual world in Williamson's case, uh, let's say it's You know everything is either red or it isn't There is a spot in a there is a spot in a vague strip Where you know, there's the tallest um short person The oldest young person right and all those things and these things are all and these things are equally crazy Where but what each of these people did is they said no, well, I Rather than try and fudge around the issue I will try and make totally clear what's involved in saying these things And so they developed ways of representing this logically and so for graham it was i'm going to show you how to Reason with Contradictory statements in such a way that not everything follows from a contradiction I'm going to give you ways of explaining how something might be both true and not true at the same time without You know falling into Thinking that every inconsistency has to be true And so in one sense you're going so far away from common sense For your own sake But also for others if they're ever going to understand you They'll need some guidance as to okay. Well, how are you meant to think about this? and and so charting out some logic uh in each of those cases can be uh Not only a guide for yourself to try and say okay. Well, here's here's what I mean and here's here's what's involved Here's what follows from those crazy commitments and here's what doesn't but it's also something which is sort of reassuring for the You know their opponents their readers To be able to understand. Okay. Here's what would be involved in You know swallowing that position But you have swallowed a position as well you you have been a bullet from time to time. I'm a pluralist I'm a pluralist about uh, and and so that's the same sort of thing where you know as What's weird in my case is you know, I think that uh, there are some you know, some you know arguments Which are deductively valid in some sense and deductively invalid in others And that there's no one true logic and so People get the same sort of question is oh, well, how should you think about these things and well? I've got to explain as a logician Oh Here's what that means and that's kind of in one sense It's it's like that needs to be a kind of matter of logic for reasoning without logic And and things which makes it a little bit kind of complicated, but yeah, it's the same. It's the same deal Okay, so thanks greg Oh my pleasure Yeah, I've and it's been a bit over an hour. Yeah, sorry about uh, the long-winded answers Hopefully there was something useful there for you. Okay. Thanks