Logic Explained: Key Concepts, Validity, Soundness, and More

[00:00:00]Joseph Foley, welcome back to the show.

[00:00:02]Thank you very much for having me. What is logic? There's no foreplay today, is it?

[00:00:06]>> Never.

[00:00:07]>> Never with us. Um, I suppose like many things in philosophy, it depends who you ask. So, as it's traditionally conceived, sort of going all the way back to Aristotle, logic is supposed to be the most general principles of reasoning such that when you have a set of stuff you already know or you're already asserting, you can through a series of injubitable steps get to a further conclusion that follows without any doubt and without any possibility of being wrong from those things you initially know. So classic example from Aristotleian logic is um all men are mortal. Socrates is a man therefore Socrates is mortal. And effectively you know Aristotle's point here is that you can't even imagine that being false. There's no situation where all of the premises are true and the conclusion is false. So you are carried in some sense um from the premises to the conclusion without any kind of possibility for error entering it. That's kind of the classic Aristotleian picture. And amongst philosophers this has remained I would say relatively orthodox um right up until maybe the end of the 20th century and even now it has really really staunch defenders. So this idea that there is a one true logic and that's the thing that philosophers are interested in when they talk about logic. A recent book um was put out recently called the one true logic that was defending this this idea um by Owen Griffiths and Alexander Pazo I think his name is. I only remember Owen Griffith because he supervised my undergrad dissertation and he wrote it with this this other guy who I'm sure is very very clever but I've never met him so his name doesn't stick in my mind. Um but another alternative conception of logic to this kind of historical orthodoxy but in the modern day I would say it's become less orthodox is in some sense logic as tools. So logic as tools for modeling or logic as ways of making sense and specifying different areas of discourse. So under that conception you might have slightly different logics for different areas of life. Um and you might have >> logics that are um you know you can you can have different formal systems and different logics for dealing with different situations and and different topics. So trying to think of a of a good example. So a logical pluralist might say for instance that um certain say you have a certain set of logical rules so a certain set of axioms and um rules of inference uh that is just as good as another set of axioms and rules for inference. They're just dealing with different stuff. So you know this is kind of a I know an analogous position um which is similar enough and maybe familiar enough for audiences to kind of get intuitive hook onto this would be something like you know moral relativism right which is the idea that there are um different moral systems each of which are in some sense as good as one another and that is determined by um in a moral relativist case you know your kind of moral community in this case maybe by the context of of what you're doing. M so logic can sort of be variable as to what it is and what its goals are depending on what it's being used as a tool to do. So it's not some like some like true thing that like exists and can be ascertained, but rather it's like this methodology. It's a tool we use to to perform particular tasks in particular areas.

[00:03:31]>> Yes. So that would be that would be a kind of classic pluralist conception of logic. And different pluralists will cash this out in different ways, but that's kind of as far as I can tell the sort of mainstream um pluralist view is to kind of roughly speaking logic as tool. And you know, this is kind of an ongoing dispute in the philosophy of logic is which of these conceptions is true? Is there a one true logic? And you know, there's a lot of very technical arguments going back and forth. I know in this conversation we're going to avoid technical stuff generally because it's just very difficult to speak out loud without writing anything down in a way that either is true from the speaker's perspective and also makes any kind of sense to to anyone listening.

[00:04:05]>> If you want to say a really really complicated series of symbols and numbers and esoteric notation I'll just get Alex to uh to to put it on screen.

[00:04:12]Isn't that right? what we want.

[00:04:16]>> But so, but a classic kind of argument that might go back and forth between logical monist and logical pluralist is the logical monist might say something like, well, you've got to have some kind of criteria criterion or set of criteria for um what logic is strong in different areas. And in some sense that presupposes some kind of reasoning system. So, you know, one monist argument is to say to logical pluralist, you are at least committed to some kind of pre-existing logic when you are choosing between these different logics.

[00:04:42]logical plurist tends to to kind of respond um by appealing to the fact that seemingly different logical rules treat different domains very very well um according to to different rules. So that's kind of a kind of quick gloss of of some of the different conceptions of what logic is. Um yeah, I think that that that's yeah I think yeah yeah logic can be thought of as like a set of rules like rules of engagement for for not just philosophy but kind of for thinking they're thought of as like a prerequisite for thought.

[00:05:14]In order to have a thought there needs to be like some logical rule by which that thought like functions.

[00:05:19]>> But it's also as well as being thought of as like methodological like the rules governing uh thought. It's also thought of as like the foundation of thought as like a thing that actually sort of exists. But I guess the thing that exists are constraints. I mean in a way logic could be thought of as a system of like constraining axioms.

[00:05:41]>> Yes. So I think that there's again this kind of I don't know touches against the the fact that we use the term logic in a kind of number of different ways. We kind of have a loose everyday sense of just something being logical as sort of a by word for sensible or good or cognitively. Oh yeah, we should clarify and and that and that's you know that that does bear a passing resemblance to what philosophers mean by logic especially pre-9th century philosophers >> quite often cuz >> one of the the most interesting developments over the history of logic is you know very very early early on you've got that Aristotilian picture and you know developing alongside um this Aristotilian picture slightly later but um effectively kind of taking up alongside Aristotilian logic is stoic logic um you know people think about the stoics um in terms of their ethical system.

[00:06:27]That's kind of the thing that exists in public consciousness. But stoics also were very keen logicians and um many of the the kind of standard terminology um that we have today around logic is inherited from the stoics. So things like modus ponans, modus tolins, these are stoic logical rules. And those of you with a kind of background in maybe more if you've done like an introductory course in formal logic, you might recognize that the aristotilian picture is very predicate based. It's very you know all a RB um you know that that that that sort of structure whereas this modus ponans um picture exists more at the level of proposition.

[00:07:02]>> Okay. So help us understand this. So so modus ponins is a is a form of argument.

[00:07:06]>> Yeah. So modus ponins is um if p then q p therefore q. It's like you know the kind of it's it's such an obvious rule that we use it all the time and basically barely think about >> premise one if this then that. Premise two this conclusion therefore.

[00:07:21]>> Exactly. Yeah. So um >> and that's called modus ponent. That's like a that form of argument is is known as modus ponent.

[00:07:27]>> Yes. And um if you you know that's that argument schema is occurring at the level of propositions. That's kind of full sentences. You know if um if it's light outside then the sun has risen.

[00:07:40]It's light outside therefore the sun has risen. It's like you know regardless of whether you think that's a sound argument. It is at the very least a valid argument.

[00:07:47]>> Um and that's using modus ponent. And whereas the Aristocilian picture is more about predicates and terms, you know, in Aristotle's terminology belonging to predicates and things like that. And that's and um the interesting kind of historical tidbit is that these two systems don't get unified until 1879 >> with the publication of Frager's Bri Shrift.

[00:08:09]>> Wait, so this predicate version of logic is more sort of like, you know, >> all cats are black. you're sort of predicating >> things of objects you know all cats are black like there is a cat therefore there is a black cat that kind of way of >> that kind of thing yeah so um Aristotle has uh four types of statements um in his logic he has all statements so you know all x or y um he has um no statements no x or y he has some statements some x or y and he as you know the kind of denial of some. So some are not one and these you know have interesting logical relations and stuff like that. But um >> again you notice this is all black, some cats are black, no cats are black and some cats aren't black.

[00:08:58]>> Some cats are not black.

[00:08:59]>> And you can kind of chart out the inferences between uh different formulations of these sentences and stuff like that. But my broader point is that that's all occurring kind of in the sentence. This is these are charting relationships between terms and properties of terms within sentences.

[00:09:14]Yes. Whereas the stoic system, the if P then Q.

[00:09:17]>> Yeah. That that's kind of taking taking the sentences taking sentences or propositions already and linking them together.

[00:09:23]>> And for a long time, Stoic logic was just really neglected, you know, kind of >> Kant went so far as to say that logic never advanced a step after Aristotle.

[00:09:34]>> Um, which is like not only disregarding uh all of the kind of medieval thinkers who are very interested in logic. um like William of Acham you know AAM's razer was also a medieval logician um but also kind of can't simply does not care about this whole branch of stoic logic but in 1879 um Frager Gotlo Frager who's a kind of um German logician and philosopher and mathematician manages to unify these all into an incredibly elegant technical system and it it's just kind of it's a very beautiful bit of history in the sense you've got these two systems that emerge kind of 4th century BC and then over 2,000 years later they're kind of reconciled. They're kind of remarried when intuitively, you know, these feel like they should go together. You know, it feels like >> um this should be reasonably easy to reconcile. But it takes an awful lot of mathematical machinery to make that work such that it's not until the 19th century that these two systems, both of which are obviously correct in some sense, can be reconciled. You know, you have this kind of very difficult to think of now. the idea of there being um you know two rival true logics in a sense that that clearly should be able to to to melt but they just just nobody can quite figure out how >> it would be analogous to like the modern scientific problem of general relativity and quantum mechanics we're like they're both true but like they they just don't and are searching for some way to put them together and Frager um one of the reasons why he's gone down as kind of the father of modern logic is because he manages to stick these two things together. And the way he does that is kind of technical and I I kind of don't know if that would it would be worth talking it through particularly, but um anyone that's interested in it could go and and have a crack at the bri shift homework.

[00:11:20]>> Yeah, it's it's it's fascinating. But um >> one of the one of the developments in logic is that initially um people like Aristotle and the Stoics are largely conceiving of logic as something to do with language. So you know codifying patterns of of reasoning in language that are obviously true.

[00:11:38]And as we get more towards modern logic, you know, if I use the term logic in a philosophy faculty today, it will immediately conjure up images of formal systems. So axioms, rules of inference, uh proof systems, model theory, that kind of thing is is the world of modern logic. And um in a lot of ways over the course of the the 19th century, you get this kind of increasing mathematization of logic. and then kind of into the 20th century, logic kind of is both is firmly philosophy but also firmly maths which is one of the reasons why it's so fascinating. You know, you kind of if you if you have a a passion for technicalia, then logic is very interesting. Also, if you have a passion for philosophy, it's very interesting.

[00:12:16]And the other thing that I think, you know, I realize I'm kind of pitching logic now. And that's that's kind of kind of my goal with this is, you know, I I really do think that logic is an eye opening thing to learn. And I think that what makes it so brilliant is this eye openening to learn. Even if you only spend a couple of hours learning it really, you know, if you're not interested in kind of the mathematical side of it, even just 5 hours spent at, you know, cumulative cumulatively over the course of a year, say at a desk looking at a logic textbook will fundamentally transform the way you see the world. We'll get back to the show in just a moment, but first, have you ever used an unencrypted Wi-Fi network connecting at a hotel or a cafe or something like that? If you have, your data has been at risk. Hackers on that same network can steal your data, your photos, your keystrokes, your IP address without you even knowing about it. That is unless you use today's sponsor, NordVPN. NordVPN is a virtual private network which protects your online data by rerouting it through a separate secure server somewhere else in the world. This hides your IP address, masks your location, and protects your data from those who are trying to steal it.

[00:13:22]And because NordVPN makes it seem like you're somewhere else in the world, you can access content that's normally restricted by region. So, if a TV show or a sports game or an online video isn't available in the country that I'm in, NordVPN can solve that problem for me. And if you're still in any doubt, there's also a 30-day money back guarantee. So try it out and protect up to 10 devices from one account by going to nordvpn.com/within reason. It's in the description. This discounted link will also give you 4 months extra on a 2-year plan. And with that said, back to the show. Well, what does it I mean, okay, so people will listen and go, okay, logic is the process of deriving conclusions from premises. M I can do that, you know, I can I can look at even if something is not is not true, I can derive conclusions like, you know, all cats are black, Tom is a cat, therefore Tom is black. I I'm clever enough to recognize that that conclusion follows from the premises, even if the premises aren't actually true.

[00:14:21]>> The conclusion follows from them. Yeah.

[00:14:23]So, what do you mean like learn logic?

[00:14:25]Would what kind of thing would I be learning if I sit down and spend 5 hours at a textbook? So you'd be learning how to put things. Well, yeah, that too. But you'd be learning how to put things in propositional form and also spot going beyond kind of looking at individual arguments and being like, "Oh, I can tell that that argument is pretty good and I can tell the argument is pretty bad."

[00:14:43]>> Um, learning the structural characteristics that make an argument good or bad.

[00:14:48]>> What does it mean to put something in propositional form? So it is effectively to to take say we have a you know we're talking and I and I say oh well you know man like I think that Socrates probably will be mortal cuz all all men are mortal right aren't they? You know if we if we had a kind of conversation like that and that's sort of a a toy example but you'll find this in in pretty much any philosophical discussion. people kind of talk in paragraphs. You how we naturally speak >> and to put something in propositional form is to take that paragraph and extract from it the argumentatively relevant parts and say right here is the stuff that they're assuming and here is the conclusion that they're drawing and here are the rules that they're invoking to draw it. And the reason I think this can be can be very helpful is because quite a lot of the time I think just in everyday life >> we are often mistaken about I think what the people we're talking to are arguing >> y >> and um one of the things I think putting things in propositional form can do is you can then you know you have a working model of what your interlocutor's argument is.

[00:15:54]>> Yeah. It offers clarity and I think you can agree with your int before you agree on whether the argument works or not like you you can first agree that this basic clear form with clear like premises and conclusions you can at least agree is that the argument we're having and then you can have the argument. Yes, I think that in in kind of non-mathematical practice this is one of the best uses for logic ever. Um >> linen was so keen on this on this use of logic. He thought that one of the, you know, the this is before we kind of had modern symbolic logic. He thought one of the things that we we need to do if we're going to have conversations about philosophy or anything really is we need to have a language that to the greatest extent possible eliminates ambiguity.

[00:16:36]>> And you know, if in theory we could take a very very complicated argument and put it in like, you know, second order formal logic or something like that >> and that would be about as clear as you could ever get with formalizing an argument. um that would take a very long time. Putting something in propositional form is sort of one step along that journey. So yeah, they there are still things that can remain unclarified if you put something in propositional form >> because it's a series of propositions.

[00:17:02]>> Exactly. Yeah. But the very least you are one step closer to having clarity and you know I think that um >> yeah I think that um >> if you if you don't have clarity on what arguments you're using and what problems you're tackling, it's just very hard to make any kind of progress whatsoever.

[00:17:17]>> Yeah. And notice the way that you like when you were just thinking about how to put that sentence together. You were like, well, you know, I think that if if you don't have that kind of clarity, then it's difficult to put arguments together. That's a that's an if then statement. And I think people who are good at communicating will be good at sort of instantaneously putting things into clear propositional form. So instead of saying like, you know, man, like I just feel like if like God has to exist because if like the universe obviously had a beginning, right? And if the universe has a beginning, then like God has to exist because what caused the universe?

[00:17:50]>> You could translate that into premise one, everything which begins to exist has a cause. Premise two, the universe began to exist. Conclusion, therefore, the universe has a cause. And that's way clearer and you can interrogate those premises versus that word salad I said a second ago. You get what I'm saying? But you'd have to be like, well, wait, so when you said, so are you saying this?

[00:18:10]Are you saying that? And it would be a big sort of old jumble.

[00:18:13]>> Yes. Yes. And putting it into propositional form is the first step towards as you say >> clarity. Yes. And I think that um one of the great things about putting things in propositional form is as I say I think basically anyone could learn how to do that with almost any argument almost any philosophical argument in an afternoon >> um if that really I mean you just kind of after a while it becomes almost second nature and it will instantane I mean it doesn't mean you have to start talking in terms of premise but it means that instead of me saying like oh god exists because I think that like you know the universe began and like obviously God must be the I don't need to put it into propositional form, but practicing propositional form will at least allow you to say something a bit more clear. Like you might say like, well, I think that, you know, the universe had a beginning and I think if it had a beginning that that beginning was God. That's not that's not a logical argument. That's not that's not fully like propositionalized, but the practice of pulling out, as you say, the argumentatively relevant like statements, the atomic sentences that make up the argument and just dealing with those as clearly as possible is is a wonderful exercise.

[00:19:10]>> Yes. And um this is this lusting after clarity >> is really reflected in the types of works that logicians have tended to write outside of logic. So again to take the example of Frager, Frager is not only concerned with the idea of creating this perfect logical language and he's also very he also wants to ground um arithmetic and self-evident logical uh axioms which he does end up doing um because because of Russell's paradox and then because of girdles in completeness theorem later which showed that you probably he wouldn't be able to do it anyway. But >> um >> alongside that alongside these aims he is incredibly obsessed with clarity and language. Um, a really good example of of one of the methods that that Freya uses to clear up ambiguity in language is he introduces the notion of a sense.

[00:19:57]So we think about a word in its reference, right? So I, you know, um, I have a word Alex, it picks out you. You know, when I say Alex, I'm picking out you in the world. Frager notes that if this is our only picture of language, then we're going to run into some logical confusions. And these are, you know, very very rarely. For 99% of your of your experience, this isn't going to matter, but occasionally it really will.

[00:20:21]So I think the the classic example of this is um Hesperis and Phosphorus are two names for Venus in the ancient world. Um but people didn't realize they were the same planet. So Fragus Frager basically goes, well, they weren't obviously the same to the people. They they had to then go out and verify that they were both and they both happened to be Venus. So, so they they they are they Hesperis equals phosphorus. It's a statement that is true out in the world. Um but Frager essentially says well they must they must have had a mode of identification for >> picking out Hesperus or phosphorus and that's what he calls the sense and I this is that's a very abstract example.

[00:21:00]It's not immediately clear how it might be helpful. But let's take for example um you know you were just talking to someone actually about about about Daycart and and Daycart's um uh argument about the separation of mind and body.

[00:21:14]>> Yeah.

[00:21:15]>> So you know to go back over it Dayart's argument about um the mind being separate from the body is that he can conceive of uh the mind existing and the body not existing. So he says they must at the very least not be equivalent.

[00:21:26]These are conceptually separate entities. And you could talk about that, you know, you could reiterate that argument today with the nervous system.

[00:21:32]you know, the mind must be separate from the nervous system because >> um of uh this conceptual uh freedom that I've got to imagine uh the mind separate from the nervous system. And one way to >> and you know that kind of that people immediately >> think that there's something quite fishy about that argument, right? What's what's going on there? This seems like it this seems like it's in some way tricking yourself >> um in drawing a substantive conclusion from mere facts about language. And Frager senses can come in real handy here because he can say like, well, they might pick out the same object, but your modes of identification, your senses for these two words are different.

[00:22:09]>> As in you're saying the same thing, but in a different sense.

[00:22:12]>> Yeah, exactly. And like he has a very metaphysical picture of what these senses are. He kind of thinks they're in this kind of platonic realm, but again, we don't need to get into that.

[00:22:18]>> So, so a moment ago, you was phosphorus and hesus.

[00:22:21]>> Hesperis.

[00:22:22]>> Hesperis, which you told me earlier is can't remember which way around it is, but one means the morning star, one means the evening star. And so people would look in the morning and say that's the morning star. People look in the evening and say that's the evening star.

[00:22:33]Turns out it's actually the same star.

[00:22:35]>> So they are talking about the same thing, >> but they're not talking about the same thing cuz one person thinks it's the evening star, one person thinks it's the morning star. And unbeknownst to them, it's the same star. So I guess the paradoxical question is are they talking about the same thing or not? And so Frager is saying >> yeah, but no, like yeah, they're talking about the same thing but in a different sense >> essentially. And it's as I say in a situation like hesperis and phosphorus it's kind of quite intuitive that there's something like that going on. I think that um the utility in something like fragrance sense and reference distinction um comes in these more philosophical uh arguments whereby somebody's making a point about conceptual distinctness and maybe they're right or maybe they're wrong but it seems like they're they're inferring too much from from the linguistic facts at play. I'd say a really good, you know, we you've talked about meta ethics a lot on the channel before and a key >> argument in meta ethics is the open question argument, right? Um, of any given definition or any given naturalistic definition of goodness, somebody can ask, is that really good?

[00:23:37]And we don't ask that for questions like um for for for identity statements like a triangle has three sides. If you were to say, does a triangle really have three sides? What does that mean? Like of course it does. It doesn't it's sort of like you know >> uh if you got a definition of an object like for that definition to be >> like complete and full you wouldn't be left with the question but is that really the defined thing? So if you say you know a triangle is a >> three-sided object with straight lines and you go yeah but there's three sided objects with straight lines >> is it really a triangle?

[00:24:13]Yeah, of course it is. Whereas it seems for GE Moore who comes up with this argument that any definition you could have give the word good well good is you know pleasure but is pleasure really good it seems like that's still a legitimate question which means we haven't got a sufficient definition well good is good is what God commands >> is what God commands like really good are you sure and you don't look with confusion and go like what the hell are you talking about it's definitional >> it seems like as as Mo puts it an open question which Moore uses as an argument to say that therefore there can be no naturalistic definition of what good is because whenever we define good we're always left with this open question but is it really good if we're not when we do have sufficient definitions like that of a triangle and say you wanted to solve this argument well one of the things you might you might um appeal to >> is senses you might say well it's not it's there is still a gap there to find a substantive definition of goodness um that isn't just intuition istic and kind of in this kind of mall style irreducibility of the good, you would have to posit that the good and this other property are in fact referring to the same thing, but they're getting at that thing through different senses. And >> this is one way that people have attempted to solve the open question argument. Um I don't I don't kind of I wouldn't be able to kind of kind of um rattle it off the top of my head. But for example, say, you know, to construct an argument like that, a utilitarian trying to solve the open question argument might draw on this kind of fragian backdrop to say something like, well, yeah, no, I accept, right, that you can ask whether the greatest good for the greatest or the greatest um net pleasure is good. I can I understand that when you're just presented with the words, you can ask, oh, is that really good? Let's say I went out into the world and I found that everything that um elicited the kind of the good token also coincided extensionally totally with the greatest net pleasure then or or even like mostly then a utilitarian could appeal to this frigian sense thing and say well maybe they're getting at the same thing sorry maybe they're getting at the same reference through different senses. So there's a couple of philosophical arguments.

[00:26:24]>> An example that comes up in other contexts is the difference between water and H2O.

[00:26:28]>> Like they are the same thing, but they can kind of apply in different context.

[00:26:32]For example, somebody a thousand years ago, if you describe to them a hydrogen molecule, um, and an oxygen molecule, two hydrogen and one oxygen molecule, uh, put together, they wouldn't think of water.

[00:26:46]>> And yet they'd be thinking about H2O, but they wouldn't be thinking about water. Even though H2O and water are the same thing. So they like are the same thing, but they're also kind of not depending on on what like sense you mean the term.

[00:27:00]>> Exactly. So, and and as say Frager has his own technical definition of sense, but my I wanted to draw on this just as an example of how the kind of logician's obsession with with specificity can be very helpful for either clearing up arguments that you kind of think, oh, that's a bit spurious, but I don't quite know why it's a bit spurious, or potentially solving problems um or opening up new avenues to solving philosophical problems that might not have necessarily been spotted before. Um I think that another you know people on on online are also al sorry people online are often um very keen on the idea of kind of logical fallacies. You know if you scroll through a lot of comment sections on philosophy videos you see people having arguments you might say something that's >> I think that this is in some sense >> sort of attempting to identify unound logical structures. you know, these are these are logical structures that we want to avoid. And you know, I think that um sorry, invalid logical structures. Um and one of the benefits of of potentially, you know, just dipping your toe into something like even just propositional logic and maybe a tiny bit of predicate calculus is that it kind of becomes immediately clear why a fallacy might be a fallacy. You know, yes, in theory, >> any formal fallacy is just reducible to nonsequit. So, it just doesn't follow.

[00:28:22]So, you know, imagine um affirming the consequence. Um I'm pretty sure is the name for the fallacy where you say A implies B, not A, therefore not B.

[00:28:31]>> Okay. So, so let's slow down for a second. We're talking about a logical we're talking about logical fallacies.

[00:28:36]>> Yes. Yeah.

[00:28:36]>> And affirming the the consequent.

[00:28:40]>> Is that what it's called? Uh where where you say so if A then B >> and then you say not A >> therefore not B which doesn't actually follow. Yes. For example, if it's raining outside, then I'll get wet. It's not raining outside, therefore I won't get wet.

[00:28:57]>> Yeah. So, you think, you know, there might be some kind of >> Machavelian person outside there with a bucket waiting to >> Yeah, I could go and have a shower, you know. Exactly.

[00:29:05]Follow um but it's it kind of casually it kind of feels like it should. And there are contexts where you can imagine if somebody said really quickly like, "Oh, well, if it's raining, I'm going to get wet." And you'd look and go like, "But it's not raining." So, okay, cool.

[00:29:18]I won't get wet then. It's like, "All right, nice."

[00:29:21]>> When actually like, "Oh, slow down there." And in that circumstance, like it doesn't matter. Like you kind of, you know what I mean? It's fine. But in a in an argument where you're like arguing for God's existence or meta ethics, what's really important, you could be technically that doesn't follow. We need to be more careful.

[00:29:35]>> Yes.

[00:29:35]>> And you're not going to be able to spot that unless you when you hear somebody say, "Gosh, I'll get I'll get wet if it's raining like outside." Like if if you are not able to translate that into if it's uh if it's raining then I will get wet. It is raining therefore I will get wet. It is not rain. If you can't sort of do that translation in your head you won't spot that it's not >> Yeah. The very least it's going to be slightly harder. Right. As in I imagine that you know people >> Yeah. You can still spot it but you >> but but as in it's just it's just a more systematic way of approach to spot it.

[00:30:03]Yeah.

[00:30:04]>> Yeah. And the the important thing here is that the conclusion isn't guaranteed by the premises. You can imagine a situation where all the premises are true but the conclusion is false. Which is the logical definition of validity.

[00:30:13]>> Okay, because this is really important, right? So what does logic apply to? Like we often talk about logical arguments, right? Is is it like logic is a thing which applies to arguments? Does it apply to sentences? Does it like what what is logic?

[00:30:27]>> I would suggest that >> used on >> logic um applies to reasoning.

[00:30:32]>> Mhm. and quite broadly construed. Um, if you're dealing with something like propositional logic, it's subject matter is propositions. If you're dealing with something like predicate logic, um, its subjects are going to be predicates and objects and the logical relations between them.

[00:30:48]>> In theory, you know, you can kind of say, well, any any discourse whereby we want to guarantee the truth of our conclusion from our premises is going to be governed by some kind of logic. It's uh it is or at least it claims to be the kind of normative rules of thought. Yeah. You know what what the original kind of intuition that Aristotle is having or one of them when he kind of founds logic in the western philosophical tradition is basically just how do I how do I know that I'm thinking well? Um how do I know when I'm thinking poorly? And you know there there are plenty of other uh non-logical aspects to that question. So you could say, well, one of the things you might want to you might want to um figure out uh if you're think if you want to your thinking to be precise would be something like, well, I ought to define all of my terms very precisely because if I don't, then I'm not I'm not going to be quite clear on what I mean. And that's not a that's not a a matter for formal logic, but it's nonetheless a kind of general rule of or general bit of um cognitive hygiene, I suppose.

[00:31:52]And um so yeah, but uh logic I would say uh tends to deal more with the idea of reasoning. So relationships between statements, propositions, terms um basically, you know, if this thing is true, what do I know from that?

[00:32:06]>> Derive from one thing, what can you draw out of it? And so there's a term that you've used a few times now, which is the term valid.

[00:32:14]>> You've also used the word sound, which does not mean the same thing. So let's take an argument >> like modus ponins. So if P then Q.

[00:32:23]>> Mhm.

[00:32:24]>> P therefore Q. The reason we use letters there is because it doesn't matter what you plug in, it's still going to work the same, right? So you could say >> if the sky is red, then my bathtub is filled.

[00:32:38]>> The sky is red, therefore the bathtub is is filled. Right? It doesn't matter what sentences you put in. If P, then Q. P, therefore Q. That argument is an example of a valid argument. What is validity?

[00:32:50]What is what is validity in uh I I was saying the word valid so I went to say like what is validity? What is validity in a logical argument?

[00:32:58]>> So validity in a logical argument is is there a situation whereby the premises of my argument are true and yet the conclusion is false. So um take what was your what was your example there again? Sorry.

[00:33:11]>> Oh better one like you know um if if it's if it's raining outside then I'll get wet.

[00:33:17]>> Yes. Yeah. So premise two, it is raining outside. Conclusion, therefore I will get wet.

[00:33:21]>> Yes. So if you accept the first two statements, you are bound by consistency to accept the final statement. There there's not a situation where the first two statements are true, yet the conclusion is false. Now crucially, I I've got to separate this out because like we just talked about a logical fallacy, right? This is not the same thing. So earlier we had this argument which was >> if it's raining outside then I'll get wet.

[00:33:42]>> And it was then it's not raining outside therefore I will not get wet. Yes, that's invalid. Yes, >> we're doing a positive modus ponent. So, it starts with the same first premise.

[00:33:51]If it's raining outside, >> then I'll get wet. But this time, the second premise is it is raining outside.

[00:33:56]>> Therefore, I will get wet. And that whole first premise can be thought of as one. So, the first premise is this if then. If it's raining, then I'll get wet. So, let's say that's true. Let's say it's just true that if it's raining, I'll get wet. Then, premise two, it's raining. Because it's true that if it's raining, I'll get wet. It means that I must like get wet, right? Yes. Exactly.

[00:34:16]>> And that's what validity is. It means that essentially the the conclusion is guaranteed by the premises.

[00:34:21]>> Yes. And Yeah. And then that kind of guaranteed is then cashed out as as I can't there's no situation where the premises true and the conclusion. And it's important that it's defined in that way. We'll get into that in a moment.

[00:34:31]But the technical definition then of validity, an argument is valid if there is like no sense in which the premises can be true and the conclusion be false.

[00:34:42]If it's impossible for the premises to be true and the conclusion false, it means it's valid.

[00:34:47]>> Importantly, this does not mean that the argument is sound.

[00:34:51]>> Yes. Or even or even in any intuitive sense good.

[00:34:54]>> Yeah. It doesn't mean that the to say an argument is valid does not mean that it's premises and conclusion are true.

[00:35:02]Yes. It simply >> it just means that if the premises are true, the conclusion has to be true.

[00:35:08]>> It denotes something about its structure. We can kind of broadly, you know, Logicians often think about this in terms of syntax and semantics, but we can we can kind of just think about it in terms of form and content for the sake for the kind of the sake of >> of argument today. So we can think about um our previous fallacy there. Um affirming the consequence is a fallacy of form. It's it's a formal fallacy. It is uh an error in the reasoning structure at play here.

[00:35:33]>> It's not about the content. It's not about the actual >> No, exactly.

[00:35:37]the structure you can have an unound argument soundness if if an argument is sound.

[00:35:43]>> So this is >> it means it's it's valid and also true.

[00:35:46]>> Yes. Exactly. So there there are kind of two definitions of soundness and and rather unhelpfully the one that I think is most useful is also the less popular one. So the most popular use of soundness is to say an argument is sound if and only if it's valid and also all of the premises are true and that will guarantee the truth of the conclusion whatever's the case. Right? So, as I say, all men are mortal. Socrates a man, therefore, Socrates is mortal. Not only is that a valid argumentative structure, it's also sound. Um, the the other way that some people use sound is just to denote that premises are true without saying anything about validity.

[00:36:20]Unhelpfully, um, that's not standard usage, but I also think it's very popular. Sorry, that's unhelpfully, that's not standard usage, but I also think that it is in some sense more useful because then you can say an argument's sort of sound but not valid.

[00:36:32]>> Yeah. But we we got to slow down for a second cuz there's a lot of words being thrown around. We're talking about this concept of validity. And I think it's really important because it comes up a lot to distinguish validity and soundness. They're often used interchangeably. They're not the same thing. So just to give an example, let's take an argument which is not sound but is valid. So I'm going to produce an argument which has a valid logical structure but is not true. So, premise one, um, if it's raining outside, then Joe Folly is a type of bird.

[00:37:05]>> That's my first premise. Premise two, it is raining outside. Conclusion, Joe Folly is a type of bird. Right?

[00:37:13]Because the premise one is, if it's raining outside, then Joe Folly is a type of bird.

[00:37:16]>> And it is raining outside, therefore Joe Folly is a type of bird. That is a valid argument because there's no way for those premises to be true. and the conclusion be false. So, it is valid, >> but clearly those premises aren't true.

[00:37:28]It's not true that if it's raining outside, you're a type of bird. It's also not true that it's raining outside.

[00:37:34]>> So, the argument is unsound, but it's still valid. So, there's a separate question as to whether a logical argument is valid. Does the conclusion follow from the premises? It's then a separate question whether those premises are actually true or not. Yes, logicians tend to be much more interested in validity than sounds because um you know if you're a logician attempting to craft or refine a logical system, you tend to want that logical system to apply to almost anything. You can plug almost anything you want into the variables, your arguments will still work. That's why they're kind of mainly concerned with validity rather than soundness.

[00:38:01]This is sometimes called the uh the ideal of topic neutrality for logic where if you if you are if you at home happen to be designing a logical system, you ideally want the rules to be broad enough that you can stick literally anything in the structures and it will still work. That's kind of one of the ideals, historical ideals for logical system.

[00:38:18]>> So just to be clear when people are arguing on the internet, if somebody says, for example, something like that, if if somebody says, you know, um, well, if the universe began to exist, then it must have a cause.

[00:38:31]>> And the universe did begin to exist, therefore it has a cause. And somebody goes like, oh, no, that that's invalid because the universe didn't have a have a cause. No, no, it's not invalid. It's unsound. And I do stop using the word invalid to describe arguments that are false. Only use the word invalid to describe arguments which are structurally like the conclusion doesn't follow from the premises. And this may seem kind of nitpicky, but it does tell you something very very helpful about what it would take for the argument to be true. Because say you have an invalid argument in front of you, then effectively you can you can just kind of stop there, right? You use in it may be that the the premises are true. Um but it doesn't matter because the conclusion doesn't follow from the premises. Yeah.

[00:39:08]Um, however, if you're saying that an argument is unsound, but nonetheless that it's valid, that does tell you something. It tells you that the the denial of that argument is based on your assertion that one of the premises is false. And then you can identify which premise is false. Here you might dispute that the universe had a beginning, for example. Um, that was, you know, this was Aquinus's argument against, you know, the clam cosmological argument. Of course, it wasn't known as the clam cosmological argument. Then this kind of linear cosmological argument. Aquinus basically said, "No, I can I I don't think that it's it's it's guaranteed by the um by natural reason that the universe had a beginning." He did think that it had a beginning because of the Bible, but he didn't think that you could know that just just through reason.

[00:39:48]>> And um so that would be, you know, we think about what what's Aquinus doing there. Well, he's saying, "I'm questioning one of those premises."

[00:39:55]>> It's a valid argument, but >> Yeah. It's valid argument, but I'm >> It's unound.

[00:39:59]>> Exactly. Or it's potentially at the very least I'm not confident enough to grant you all of those. Importantly, if a if an argument is invalid, like you said, you can just stop there. So, you you might waste a lot of time because if I if I made an argument that said like, you know, um all all blgarts are foggarts and X is a blowgart, therefore X is also a flowart. You might start asking me like, oh well, you know, what's a blowgart? What's a flowart? How do you define that? What? But you could actually just like look at the argumentative structure and if I've said something invalid in the structure, you don't even need to bother with that.

[00:40:33]>> Well, at the very least, you know that argument is wrong. It might still be that their conclusion happens to be true, but it won't be guaranteed and soundness. Um, yeah, there there's a Can we talk about the concept of Xals quadet?

[00:40:50]>> We can. Yeah, I think that it's it's x quadet.

[00:40:53]>> Is that going to be too much?

[00:40:54]>> No, no, no.

[00:40:56]The definition of a valid argument is as we said that there's no sense in which the premises can both be true and yet the conclusion be false.

[00:41:06]>> So like the reason why contradictions or one reason why contradictions aren't allowed in logic like why can't you have a contradiction? Why can't I say premise one it's raining outside premise two it's not raining outside? One of the reasons you can't say that is because of this principle called X falso quadly bet from the false anything.

[00:41:26]>> And as far as I understand it, the reason that what that means is that from two contradictory premises, anything logically follows. So let's take this argument. Premise one, it's raining outside.

[00:41:39]>> Premise two, it's not raining outside.

[00:41:42]Conclusion, therefore, I have a cup of tea in my hand. Is that a valid argument? You might listen to that and go like, "No, of course that's not valid. That doesn't follow." But the definition of a valid argument is that there's no interpretation under which the premises can both be true and the conclusion be false.

[00:41:59]>> And for that argument, there is no interpretation in which the premises can be true and the and the conclusion be false because there's no interpretation in which the premises can both be true because they contradict each other. So if the definition of a logical argument is no interpretation under which the premises can be true and the conclusion false then that argument it's raining outside, it's not raining outside, therefore there's a cup of tea in my hand >> is valid. Yes. And if you want if you wanted to get a just briefly dip our toes into into something slightly technical. In some logical systems um xloso quad liet is taken as red. It's like a a kind of it's just a rule of the system. For others they will start with something called the disjunctive syllogism. Um which is the idea that um say I've got a or b and in logic or is inclusive. So A or B is true if A is true if B is true or if both A and B are true. The disjunctive syllogism um which some logical systems will take as primitive. Others will prove this through X um fosso quadet. It's far more intuitive if you start with the disjunctive syllogism for the purpose of kind of getting an intuitive grip on what xoso cordodil how how you might conceive of that. The disjunctive syllogism states that if you've got a or b and I've got not a well then by definition I have to have b because a or b is true if a is true b is true or both are true. I know that not a is true and so a is not true and so I'm left with b.

[00:43:24]So just to just to just to be clear >> in logic an or statement so like you know P or Q >> that that whole statement P or Q is true if even if just only one of those is true.

[00:43:37]>> Yes. Yeah. Or both of them is true. So so it's it's it's inclusive. And >> so the statement there's a car outside or it's raining >> yes >> it's true. Say there is a car outside but it's not raining. It's still true that there's a car outside or it's raining.

[00:43:49]>> Yes. And um if we're going to if we if we have this inclusive or that intuitively a number of things basically follow from that. One of which is this disjunctive syllogism. If I've got not if I've got A or B then if I have not A then I've got B. And if I've got not B then I've got A.

[00:44:04]>> So so premise one there's a car outside or it's raining.

[00:44:08]>> Yes. Premise two, it's not raining.

[00:44:11]Conclusion, therefore >> there must be a car outside. Um, another uh consequence of having an inclusive or is that if I know that P is true, like I just know it, then I know that P or literally anything else is also true. So if I, you know, >> Alex is sitting on a brown chair or um gorillas are rampaging through uh the streets of London as we speak is true because one of the one of the distinctions is true. Now how this allows us to get an intuitive gloss of exposure. And again I want to kind of emphasize that this is different in different logical systems cuz some define the disjunctive syllogism through this um or we can get it if we assume the disjunctive syllogism is that say we've got P and not P. So we've got our contradiction. We've kind of somehow ended up in this situation where we've got a contradiction. Well, I can assume P and I can introduce literally anything else. P or literally anything else. So P or gorillas are rampaging through the streets of London. Then um I have not P.

[00:45:15]So via the disjunctive syllogism I can get rid of P or gorillas are running through the streets of London and I'm just left with a proof that gorillas are running through the streets of London.

[00:45:24]So that's kind of an intuitive gloss.

[00:45:27]>> So it's a it's a it's a consequence of like this system of logic that if you allow a contradiction, >> literally anything follows from it.

[00:45:36]>> Yes. And as I say, >> from a contradiction, it follows that guerrillas are rampaging through the streets of London. From a contradiction, it follows that Spain doesn't exist.

[00:45:43]From a contradiction, it follows that Spain does exist. Like everything follows um >> from a contradiction. It's also known as the principle of explosion, right?

[00:45:51]Because it just explodes into proving absolutely anything. Which is why given the the system of logic that we're talking about, you can't allow contradictions. Contradictions are not allowed because if you allow a contradiction, the whole thing just blows up.

[00:46:03]>> Exactly. And um I think that a nice way of again cuz you look at the rule of explosion and you think well what on earth is going on there like why it does not seem intuitive at all that from a contradiction anything follows. A way of again just kind of intuitively getting an idea for this is it's a bit like saying um well if that's true then I give up like any anything can be true if we if we admit of of contradictions. We've given up any kind of restrictive principles on what can be the case and thus logic is no longer gets me purchased. Now there are logics formal logical systems that will get rid of x falso quad liet and attempt to accommodate contradictions in some sense. These are called paracconsistent logics and I'm not overly familiar with them but I just wanted to point out that they do exist.

[00:46:48]Yeah, it's it's it's worth re-emphasizing that there are different forms kinds of logic, different systems of logic that >> interpret different things differently, you know, because there are all kinds of problems for creating a system of logic.

[00:47:01]It's a bit like how in mathematics like you're not allowed to divide by zero.

[00:47:05]That's like a rule, but that seems to be a consequence of like our conception of zero. Like it it's kind of it's true that in our system of mathematics you can't divide by zero but it's like it's just this kind of like rule that exists because if you do if you do divide by zero then you end up with all these paradoxical conclusions. So >> it's undefined.

[00:47:25]>> So we just accept as a rule that you can't do it you know and similarly in some logical systems we sort of have a similar approach where we say there are rules like you can't have a contradiction. Why? because if you do anything follows and and it might have been a bit too technical and it's kind of hard to follow. So if anybody's interested just Google you know x falso quadly bet or from the false anything or the principle of explosion >> and just look at it written down look at a proof but basically if you allow a contradiction according to the laws of logic >> anything follows from a contradiction >> and this is this is kind of a a good reason to not not get mired in contradictions >> to not allow contradictions which is also why >> if you have uh if you want to disprove an argument if you want to show that something can't be the case one way to do that is to show that it entails a contradiction.

[00:48:12]>> Yeah. So that's kind of a reductio absurdum or I think that I think that other people have called it a reductio per impossibility.

[00:48:20]>> Yeah.

[00:48:20]>> Which I think is like I I think it's just a slightly snazzier term.

[00:48:23]>> Yeah, I think it might be. But whatever whatever you want to call it. If if somebody if somebody holds, you know, two ideas, if they say like um well, I don't know. I I I don't want to give an example because it might get complicated. But if if somebody holds two ideas and you want to show that like they contradict each other, then you have shown that they can't hold both of those ideas. Or if you show that something that they believe necessarily leads to a contradiction, then since we're not allowed contradictions, you know, that's a way of showing that it's it doesn't exist. And it's really interesting how people have kind of Aristotle's um justification for the law of non-contradiction is fascinating. I know that you know you you're very interested in kind of global emotivism or as an idea. Aristotle's um justification for not allowing contradictions is eminently pragmatic.

[00:49:09]It's sort of he sort of goes well I don't know man try and think a contradiction. Try and think in terms of contradictions. You absolutely cannot do it. So, you know, there is a a sense in which um one of the interesting things about about the philosophy of logic is that because you're at this kind of incredibly abstract level where you're almost trying to get a grip on the laws of of thought, um you end up having to say a fair amount is just self-evidently true. The Stoics called their logical rules the industrials for this reason because they basically sort of went well if you think that if P sorry if you think that if P then Q P therefore Q isn't a good argument I don't know what to tell you like I can't I can't show that it's the case I can just I I can just point to it and sort of say it's just there. It's just there. Like come on. It's it's self-evident.

[00:49:59]>> I I don't know how to think apart from using these rules.

[00:50:03]>> But logic also applies. So we've been talking about logical arguments, right?

[00:50:06]So like these rules of inference. If P then Q. P therefore Q. Yeah, that has to be true. But there are also like more atomic logical rules that we accept not as the result of some kind of argument or inference, but they just exist as they are. These are like what often times are called like the foundational laws of logic. So one of the most important of these is the law of non-contradiction.

[00:50:30]>> A proposition can't be true and false at the same time. That's not an inference.

[00:50:34]That's not an argument. That is just a statement. Something like P the the proposition P cannot be true and false in the same way at the same time.

[00:50:43]Like what is what is that? What what is this aim of logic? Is that like do we reason our way into that? Is it is it a prerequisite of reason? Like how do we justify these axioms?

[00:50:53]>> Well, as I said, I think this is one of the the exciting things about the philosophy of logic is that >> if you're trying to ground logic, it's very you can't appeal to logic. you know, if you're trying to ground in something prior to logic, it's that's really really hard. And as I say, an awful lot of ancient logicians and it's surpris, you know, a lot of modern logicians will just kind of say like >> try and present to me a way of thinking that allows me to somebody might just say, okay, well, I'll I'll just I'll imagine that it's yeah, okay, maybe P and P can be true and false at the same time. Cool.

[00:51:23]>> Okay. Right. Let's try that for a second. So, you are accepting that that a proposition can be true and false at the same time, right? So you think it's true that a proposition can be true and false at the same time?

[00:51:34]>> I think it's also false.

[00:51:35]>> Yeah.

[00:51:35]>> So it's false. So it's false that a proposition can be true or false at the same time, which is what I was arguing all along.

[00:51:40]>> And you say, "No, no, no, it can be true or false at the same time." Like, "Yeah, but if it could be true or false at the same time, then that can also be false."

[00:51:46]So it's true and it's false. Another way of of kind of attempting to justify this would be to say something like, "Okay, go out and and kind of live your life >> and never infer from learning something that its opposite could could not be true."

[00:51:59]>> Yeah.

[00:52:00]>> You're just going to run into an awful lot of difficulties. It's like that's just not how the the human brain works.

[00:52:05]So So these these fundamental laws of logic like the law of non-contradiction as it's called seem to be bedrock. they seem to be foundational and and these are the laws of logic with which we use uh w with which we sort of construct arguments and thought and sort of have an ability to to use reason but like I don't know like what are these laws of logic like where do they come from are they psychological concepts do they exist in the universe like do they did they exist before humans existed what what do you think they are so I think that probably the one of the best ways of going about attempting to answer this question is to begin by ruling out the kind of things that they probably can't be. So they can't merely be descriptions of how we in fact do think because we think non-logically an awful lot of the time. In fact um you know I think one of the really interesting um parts of you know Carnean Terski's work in psychology is just to demonstrate that yeah a lot of the time we're not thinking logically. We're thinking heristically we're we're we're drawing from association and emotion. We're not, you know, man is a rational animal in the sense that he can do rationality, but we're not perfectly rational. That's not that's not by any means our dominant mode of thought. So, this was summed up in a sentence by um the the American logician and pragmatist philosopher CS P or Pierce, I quite know which way to pronounce it, um where he said that logic is a normative science, which is to say it's not simply describing how you think, it's describing how you ought to think. and cashing out that ought philosophically is incredibly interesting because you know a lot of people are are very comfortable for example saying something like well you know moral ought they're a bit fishy like you know kind of I'm happy to to be a moral anti-realist I'm happy to be a um a normative anti-realist in that sense but you go take something like logic you say well can you be a normative anti-realist about logic you know that that's strikes me as something that's at least most people are significantly less fond of doing if somebody is like being illogical like literally illogical >> and and you tell them like hey that that that's not logical and they go I know like so what >> you want to say well what do you mean so well you you you should be acting logically and they're like why it's like >> that's just how thinking is supposed to be done that's just what what what it >> and you can't say well that's just what thinking is because they're not thinking logically so so it's not what thinking is but you want to say that they're incorrect >> well to say that they're incorrect effect in the way that they're doing something is to say that there's a way that they should be doing it that they're not.

[00:54:37]>> And you know, you can kind of try and cash this out as as a hypothetical imperative, something like, you know, if you want to preserve truth, then you ought to try and think logically um in this kind of, you know, narrower sense of what logic means. Um, and you know, that does leave it open for somebody to say, I'm not interested in preserving truth.

[00:54:56]>> Or they could say, I'm I'm also interested in preserving truth.

[00:54:59]>> Yes, >> I'm I'm I'm interested in preserving truth and I'm also not interested in preserving truth because I've abandoned the laws of logic.

[00:55:05]>> At which point you at the very least can say well you know clearly not interested in preserving truth you know whatever you say >> you and you want to say to them like you are your thinking is going wrong.

[00:55:13]>> Yes. Yeah. As in your your thinking has become detached from the kind of inferences that preserve truth from a premise to a set of premises to so so there seems to be the sort of normative undertone.

[00:55:23]>> Yes. Yeah. Yeah. Which is you know just you which is I should say normativity is significantly more common place than we often give it credit for. Uh languages.

[00:55:31]What do you mean by normativity?

[00:55:33]>> Norm is oughtness is the kind of way of putting it which I don't by which I don't necessarily mean kind of moral oughtness. My point is that actually normativity >> is a lot more common place than you might think.

[00:55:44]>> And it's not just in the ethical sphere.

[00:55:45]>> It's not just in the ethical sphere. Um language concern um contains within it a sort of element of normativity. Even though you know language tracks how people actually use language, it is also possible to use language incorrectly. So if I was to um say uh you know the the what's that line from the jaboki the the slidy toes do stuff guy and gimble in the wave to sort of mean um uh I fancy a cup of tea then that's I'm using language incorrectly by which you know we're kind of implicitly assuming a function there which is that the purpose of language is to communicate and I'm using language in such a way that I am so unlikely to be understood that I'm essentially going against the assumed function for language and I think we can >> so that's normativity because you should be using language and my point is that it can be sort of very mysterious when we say ought to be thinking like this or or you're kind of using language wrong. Um it can be very it can at first seem very mysterious. I think that that mysteriousness is in some sense a confusion of language.

[00:56:48]>> So the concept of should and should not or ought and ought not can be separated from morality.

[00:56:54]>> Of course. Yeah. And and you know we can partly do this because we can quite naturally define a function for a lot of language and we can quite naturally define a function for logic in a way that um allows you to have this hypothetical part of the imperative. You can say if you want to do this then you ought to do this. If you want to be understood then speak in such a way um such that to the best of your knowledge people will be able to understand you.

[00:57:16]If you want to preserve truth in your reasoning then reason in such a reason according to these logical rules that we have found preserve truth. um that's significantly less to my mind mysterious than the kind of ethical you ought to do this and it doesn't matter any kind of ifs you no ifs buts or may you really ought to do this in the context of logic >> we've said that logic applies to like arguments and sentences and their relations >> but it also obviously involves truth >> like logical validity requires you know if the premises are true the conclusion is true soundness requires premises being true. Logic doesn't seem to apply to expressions like you know huray or go over there. Logic applies to the kinds of statements which have truth value which can be true or false.

[00:58:03]>> So in the context of talking about logic and learning about what logic is what is truth and falsity.

[00:58:11]>> It's complicated and I suppose it depends on again it's probably depends on who you ask. Um one of the the really fascinating findings of um a guy called Alfred Taski um in the 20th century was that you cannot define for for an awful lot of logics you cannot define truth within the scope of the logic you have to appeal to what what's called a meta theory or a meta language uh to define truth within the object language which is the the logic you're talking about.

[00:58:37]So in terms of a kind of more philosophical sense I suppose it collapses to the to the question of what you think truth is in philosophy you know >> do you think that it is a a matter of um correspondence um some people certainly did you know I think Frager has a kind of >> actually I don't probably wouldn't say that but you know um because he also critiqued a lot of correspondence theory so um you know but a lot of a lot of people would say that um that truth is cashed out as correspondence between a set of a proposition and a state of affairs in the world. Um some people would say that it's deflationary. So when I say, you know, snow is white is true, I'm saying nothing more than snow is white.

[00:59:18]>> Yeah. So for some people to say snow is white is true is to say that that sentence snow is white corresponds with the thing about the world that snow is actually white.

[00:59:26]>> But to say that it's deflationary, >> deflationary means it it actually adds nothing. So there are different ideas of what what truth actually is, right? But also within logic like we need to be able to say that okay whatever your theory of truth is if a premise is true and the second premise is true and the conclusion follows from the premises then the conclusion is true there are some ambiguous cases as to whether to call something true or false right so so the famous example is the sentence like the current king of France is bold >> right now like the current king of France is bold I'm going to ask like is that true or false? And obviously the problem is that France doesn't have a king, >> but I'm like predicating something of this non-existent king that he's bold.

[01:00:13]So it seems like it's false that the king that the current king of France is bold. I want to say that's false.

[01:00:20]>> But it doesn't seem right to say no, no, no, the current king of France isn't bold. Like that's because I'm sort of referring to an object that doesn't exist. So for a statement like that is it true is it false is it is it undefined.

[01:00:34]>> So this is statements like these um that particular one was kind of analyzed quite heavily by virtual his theory of definite descriptions. the specific statement the present king of France is bold as there exists a present king of France there um there exists only one thing the present king of France and that thing the present king of France is bold is kind of very very broadly and nontechnically kind of roughly what the theory of definite descriptions states the general class of statements where it's very difficult to tell whether they're true or false because in some sense they're underspecified or they decompose into other statements um are known exponable statements. And these have been a problem since basically forever in logic. You know, they're kind of one of the classic logical difficulties. They cause a lot of um headache for for some medieval logicians. And um you know, their kind of classic example is stuff like um when did Socrates begin X Y and like actually you know what teenage boys are like absolute masters at coming up with exponentable statements. I think that the classic one uh when I was a teenager was, "Does your mom know you're gay?"

[01:01:42]And and you I don't know if you've seen it. There's this um because this is like this is this is um a fantastic Instagram reel for anyone that's interested about um the kind of logical decomposition of exponable statements. Um which is that there's a guy and he he he says to somebody across the table, um when I click my fingers, you'll forget that you're ever gay. And then he clicks his fingers. And then the guy goes, oh, what are you talking about? I was never gay.

[01:02:05]He goes, "See what?" And and you know, my my my and you know, I I I often I remember thinking about this when I was a teenager a little bit. It's the sort of well, this seems like this has happened to you a lot, did it? Yeah, of course. You know, this look at me. This this is this is exactly the kind of insult that is that is finely tuned to my presentation and manner. Um and this, you know, the the statement like, you know, does your mom know you're gay?

[01:02:30]Does your gay? um effectively decomposes into a you know proposition one you are gay >> and proposition b your mom knows about it. So >> because there's no way to you can't say like yes my mom knows I'm gay. You also can't say no my mom doesn't know I'm gay.

[01:02:47]>> Well that is if if you're not gay. If you're if you're gay then you have a perfect perfectly sent yes to at least one of those. Yeah.

[01:02:53]>> The the idea is that it's got a kind of nested claim within the the broader structure. Um and that's yeah an exponable statement. So you know if if any of you are watching and and people say this at school you can say I'm afraid good sir that's an exponable statement and as a result I will decompose it into it separate propositions and choose to to deny or affirm them individually and I'm sure that the bullying will stop after you say something like that. Um but you know I just kind of use that as as an illustrative example to show that you know this is um explainable statements are very very common place. they're kind of all over the shop and um Russell is dealing with just one of them. And if you want to give a kind of um truth functional analysis where you you maintain your um sharp division between true and false, then you you tend to decompose explanable statements into into >> So wait, so how would how would a logician approach a question like that?

[01:03:48]You know, >> well, they would say there's there's an implicit claim within the present king of France is bold, that there is a present king of France and that he is bold. So would they say it's would they say it's false?

[01:03:58]>> Well, they would say yeah, they would say it's false.

[01:04:00]>> So it's false that the current king of France is gay. And if >> Well, that would also be an exponable statement.

[01:04:05]>> That would be >> that also works cuz the the reason it's false is just because there no present king of France.

[01:04:09]>> Okay. Okay. But then then if I asked you Joe, like does your mom know that the king of France is gay? That would that same logician say yes or no or would they just >> they say it was they would say it was false. They say that one of the claims, well, if they were giving a kind of >> they would say no >> decompositional >> analysis of this, they would say that one of the implicit claims is that the present king of France is gay because really that's false really the phrase would not be like my mom doesn't know the king of this is not the case that my mom knows the king of France is gay.

[01:04:38]>> Yeah. So they they would say that this is a conjunction of two claims. One, the present king of France is is gay or bold or what literally whatever property you want to assign to the present king of France and my mom knows about this. And of course the conjunction of those is false because the left hand of it is is is is false and that you know a conjunction is only true if if both sides are true. So that's how that would be one way of of >> but suppose I said like the current king of France is non-existent.

[01:05:07]>> Yes, that's true.

[01:05:08]>> Yeah. But that would be analyzed as there does not exist. And this is where the language of logic becomes really important because you need to be able to translate a statement like that into a form that makes sense. So whereas I said, you know, >> the current king of France is bold and the current king of France does not exist.

[01:05:26]>> That kind of sounds like I'm saying the same kind of thing twice, but I'm not cuz in the first case I'm saying there is a king of France such that he is bold >> and in the other case it's like there is not a king of France.

[01:05:37]>> Yes, exactly. You know, one way of thinking about this, >> but that way you can see they're not the same kind of statement. Yeah, that's to do with how you how you formalize the >> and I think that intuitively, you know, a lot of listeners may have um encountered this when they're looking at the ontological. Famously, one of the responses to the ontological argument is that existence isn't a predicate. And this is just kind of the same sort of thing, saying that, you know, existence isn't isn't a property of the thing.

[01:05:57]When you say the present king of France does not exist, you're not saying that there is a present king of France and he doesn't exist. That's that's absurd.

[01:06:05]You're saying that there is no present king of France. Those statements are equivalent. Mhm.

[01:06:09]>> Um yeah, so that's kind of but these these are another um this does just illustrate another incredibly useful tool for logical analysis which is that you can take statements that at first seem very very confusing and you can break them down into parts and then get a clearer grip on what exactly they mean. alternatives. Um when you because there are logicians that hold that there are there's genuine vagueness in the world or that um there are statements that are genuinely of indeterminate or gradable truth value and these are um these are fuzzy logic >> well they're not fuzzy logicians they >> well they're logicians in fuzzy logic.

[01:06:49]>> Yeah exactly that's a better way of putting it >> and you know or many valued logic.

[01:06:52]>> What is fuzzy logic? What is that?

[01:06:54]>> So fuzzy logic um is a form of many valued logic. So many valued logic very very broadly is just any logic that has more than two truth values. So um there's a Polish logician and I can't pronounce his name but it's spelled like it's pronounced Lucas Cyix and it's definitely not pronounced like that but it's one of the ones I've only seen written down and he came up with um lots and lots of different many valued logics. Um probably the the two most important ones are a three valued logic where you've got true false and half or 01 and half cuz obviously he's kind of assigning in numbers and um an infinite valued logic whereby you have you know 0 0.1 and 0.01 and you've got literally the whole between zero and one zero is false one is true and you've got this >> yeah you've got this this entire continuum um in between the the two >> what do you mean then? So, so take a take a form of logic, a fuzzy logic that says that there are three kinds of truth value. There's 0, one, and 0.5. Like, so 0 means it's false, one means it's true.

[01:07:56]What does 0.5 mean? So, what does that actually mean?

[01:07:58]>> Well, the logic itself um would would not impose an interpretation on that.

[01:08:03]You know, it's just a series of rules.

[01:08:05]Um, but, you know, you might think of that as depending on what interpretation you're you're you're using, you might think of that as indeterminate. Uh, you might think of it as vague. Um you might you know I'm sure that there are some interpretations but it's just like I I don't know. Um there are you know the infinitely many valued ones you know you might think that um uh you might use that to if you were to embed that in something like a a doxastic or epistemic logic you might want to use gradability to represent confidence or something like that. Um there are types of fuzzy logic that mesh quite well with probability theory. So some people want to use them in that in that way. the the the interesting thing about fuzzy logic doesn't denote a single logical system or even a single definition for logical connectors. It denotes more of a kind of general uh vibe I suppose. It's any logic that has this kind of continuous um truth values between zero and one. Um and the actual definitions of the of the connectives like and or or or implication or by implication will be different. they they they will they will cash those out in slightly different ways and as a result they'll end up with slightly different values for for their sentences. But um >> yeah, it's it's it's a logic that is is quite often used to deal with vagueness um or uncertainty or something like that. Um >> you just mentioned epistemic logic.

[01:09:24]What's that?

[01:09:25]>> So epistemic logic is um well let's start with modal logic because epistemic logic uses a lot of the same tools as modal logic. Again I'm keeping things very very nontechnical. Um, modal logic is a logic that is aimed to study necessity and possibility.

[01:09:42]>> So, you know, we talk about this kind of thing in philosophy a lot. You know, you might say, well, um, is X necessarily true? Is it merely possibly true? Is it is it is it true in this world? And and modal logic allows you to talk about this kind of stuff. So, >> you know, the logic we've been talking about so far is like a statement is either true or false.

[01:09:59]>> Yes, that's classical logic, but a statement can be true. Like it's it's it's true that two and two is five.

[01:10:05]>> It's also true that this chair is brown.

[01:10:07]>> Yes.

[01:10:07]>> But it seems it's not necessarily true that the chair is brown. It could have been blue, but it seems necessarily true that two and two is five. Uh two and two is four. So there seems to be this different kind of truth. There's necessary truth and there's possible truth. And so modal logic is attempting to take that into consideration.

[01:10:28]>> Yes. And um so it's the logic of possibility and necessity. Yes, exactly.

[01:10:32]And so the way that this is cached out on a kind of model system um the kind of the the yeah the model theory for um modal logic is uses something called criy modeling um which I assume was invented by sort cry. I actually don't know um but it's called cry modeling so you kind of hope so.

[01:10:49]>> Um and the idea is that you have a world where you intuitively live at. So you've got a a world where Alex lives and then you've got a bunch of possible worlds around you and some of those and the the what's what is necessary is the stuff that is true in all of the worlds that are accessible to your world. So this allows you to define different notions of possibility. So say you wanted to restrict your notion of possibility to or your restrict your notion of accessible worlds to only those worlds that share the same physical laws as your world. Well, then you've got a very very neat very systematic definition of physical possibility. Say you wanted to um examine possibility but keep a few different propositions fixed. Then you would effectively say right well you know let's only be let's only have those worlds um be accessible to our current world where these few propositions are fixed. You can kind of kind of play around with the modeling a bit like that. There are different um restrictions on how the relationship of accessibility works which gives you slightly different modal logics but again I don't you know So starting simply like we're we're we're using these ideas of other worlds. We're not talking about like a multiverse like you know universe existing. It's just a way of thinking right. So like there's a >> that there's another possible world that that could have existed where you know like that table doesn't exist. So we just sort of conceptually think of it as like there is this possible world that is the same as this one except that table doesn't exist.

[01:12:14]>> Yes. We can think of them as as well for the purpose of discussion here anyway we can think of them as just sets of propositions. Yeah. So I mean think of them as you know you've got a a series of propositions >> set of propositions.

[01:12:24]>> Yes. Well depending on who you ask there are there are people that do impossible world semantics where in order to model you know impossibilities they will they will allow for certain worlds to have inconsistent sentences.

[01:12:36]>> There are also um modal realists >> who believe that actually David Lewis who think that you know these possible worlds are actually real worlds. They actually like truly exist. That's a little bit fringe, but it's it's usually just a way of thinking about the world.

[01:12:51]So So if I want to say like one way of me saying it's it's possible that you know I I could have not existed that that was possible. I can rephrase that as there is a possible world in which I do not exist. Yes. And that would be that would allow you to treat that sentence in a modal logic rigorously and comfortably. This same framework ends up being really really handy for a whole bunch of other things. So um you know classic question what do you mean by believe >> is comes up a lot at the moment >> and a a doxastic or epistemic logician uh would look at that question say I know exactly what I mean by believe by believe I mean it's true at every possible world that is accessible to me >> um which is effectively saying imagine that you're an agent living at world one >> and you've got a series of of of worlds that you're considering let's say to give it a kind of psych psychological interpretation Well, then everything that's true in every world that you're considering is effectively what you believe is the kind of reasoning that an epistmic or doxic logician might use to justify their kind of their their usage of this um framework of necessity to deal with things like belief and knowledge.

[01:14:02]They're not saying that, you know, they're they're using the same logical apparatus, but they're giving a different interpretation to the symbols.

[01:14:09]And this is I think again something that really illustrates just how handy logic can be is that sometimes you design something that's to be used for something totally different to to a new usage and then suddenly you find that actually this kind of broad idea of necessity if you kind of relativize the interpretation to an agent and you don't think of possible worlds as possibilities but instead as worlds that this agent could be considering then actually you have a very neat formal system for dealing with belief and knowledge.

[01:14:33]>> Take that Jordan Peterson.

[01:14:35]>> Well and that's just one way of dealing with belief. you know, you could you could you could talk about it, you know, a whole series of other ways, but I I think that this is a >> this is at the very least a very good way of formally treating belief.

[01:14:47]>> Um, so we've got kind of and this is back to what we said at the beginning.

[01:14:51]It's beginning to sound like we've got different logics or different kinds of logic depending on what our task is. If we're interested in epistemology, we might use epistemological logic. If we're interested in possibility, we might use modal logic. If we're interested in sentence construction, we might use predicate logic. And so when we spoke earlier and you were talking about how there might be like different kinds of logic for different kinds of circumstances, might have sounded like, wait, what are you talking about? Surely there's logic and there's non-logic. But I hope people can begin to see how >> the way we construct a logical system can be very different. I mean the whole conversation we had about P's and Q's and if that and that and logical fallacies didn't even consider or incorporate the the concept of possibility versus necessity for example and so you need this >> sort of other way of thinking about logic modal logic in order to incorporate that.

[01:15:40]>> Yes. and and um and in some sense you can still have these different logics even if you are a logical monist and you think that ultimately there is one true way of thought you could still say oh you know these are still very useful tools but ultimately there is a there is a logic theory of everything >> is yes exactly um and different people opposed different um kind of logics to fill this role I think that Owen Griffith and um Alexander Pazo's one was an first order infinitary logic which is very interesting but I I I can't remember how exactly the functions But I remember enjoying it at the time. Um, and you know, as I say, there can be different candidates for this ultimate monist logic, but you know, you don't you don't have to if you if you find all these tools useful, that doesn't philosophically commit you to logical pluralism.

[01:16:24]>> Um, >> yes. Uh, sorry. Oh, yes. To logical fallacies. Sorry, I just wanted to point out as well that there also a huge there's there's a huge camp of things that we call logical fallacies that resist formal treatment quite well. Uh, so something like a no true Scotsman fallacy. So, you know, I say something like no true philosopher would fear death and you point to me a bunch of philosophers that did fear death and I say, "Oh, well, you know, that's that's there's not really philosophers." We tend to say, "Okay, that's there's something wrong with that." And people have have used the no true Scotsman fallacy to >> um to label this. And I think, you know, we all agree that's dodgy in some way.

[01:17:06]And actually it's dodgy in a way that's quite difficult to treat formally because >> logic doesn't prescribe definition because you could you could construct an argument that says like if somebody is a real philosopher then they don't feel fear death. This person does fear death therefore they're not a real philosophic to dictate definitions either because it would be it would you would have a a logic then that was not topic neutral at all. It's dictating an entire language.

[01:17:30]The whole point about logic is that you can have the P's and it's like algebra >> like you have P's if P's and Q's and all this kind and the idea is that like you can substitute in any sentences and it will still work. if if it's like well if P has this definition then it works but if P has this definition it doesn't work you haven't got a universal system of logic and this is where um some fallacies uh or kind of other bits of faulty reasoning >> are more readily treated in a field called informal logic which is you know which a lot of people would just say isn't logic and I kind of sympathize with that but I like it as a >> informal logic is >> looking at arguments as they actually occur in the world and extending their scope slightly beyond formalism to sort of more broadly ask the question what is a what is a good argument what is good logical reasoning even in taking into account extra formal criteria so >> an informal logician >> might look at that the kind of not true Scotsman fallacy and say something like right okay well we're not just considering formal constraints what is a logical argument for that as in a logical discussion for or reasonable discussion for so kind of get out of out of our formal heads.

[01:18:43]It is for the communication of ideas um under the assumption that the ideas with the greatest support uh will be accepted. The ideas with less support will be rejected etc etc etc. And you can you know informal logicians and philosophers will define certain rules that that that dictate um uh the kind of things that go on in a in a in a idealized reasonable discussion. We could almost think of this as a language game if you wanted. You know, there are, you know, one of them might be that um you can't >> uh if you you you can't dismiss an opponent's point without giving a formal argument as to why it's not true. That's not a that's a a rule of discussion in a reasonable discussion, but it's not it's not a rule of law. It's not it's not it's not an axiom.

[01:19:29]>> Um there's no kind of logician that's going to kind of go around your house and beat you up if you don't follow it.

[01:19:34]But but you're departing from the conventions of um of a reasonable discussion.

[01:19:40]>> Yeah.

[01:19:40]>> Another one might be, you know, you've got to ensure that your opponent um and you are using similar terminology. Or you might say you've got to ensure that you you and your opponent are you are making your points clear to your opponent in terms that they will understand. And you could say, well, the no true Scotsman fallacy, if you if you want to accept this as a rule of of conversation, um a reasonable conversation, you could say, well, the no true Scotsman fallacy is in contradiction to this, you know, it's it's not that it's logically I mean, you haven't committed a logical contradiction by going, well, they're not really philosophers.

[01:20:12]>> There's no logical contradiction, but it feels like we want to be able to incorporate the wrongness of doing something like that. And that's where you get these >> informal logical fallacies.

[01:20:21]>> Another one is like Bailey. So, Um in fact I think the majority of logical fallacies that people have heard of are probably informal logical fallacies.

[01:20:30]>> Yes. Because a lot of logical fallacies will depend on context.

[01:20:33]>> Men Bailey.

[01:20:34]>> Well, Men Bailey um fallacy is where you have two versions of argument. One of which is modest and very defensible which is the Mot. Um and another which is more ambitious but significantly um harder to defend. So say I am a you know say say I'm a particular kind of of of um theist. Uh I don't you know I I again I don't want to kind of rag on anyone here but like you know this is a kind of a type of of argument you might have encountered is where someone says something like okay um there is you know there must be an origin of a per se causal chain um therefore there we we have a ground level metaphysical point and we call that point God. And if if one challenges them on uh any theistic matter, it's very tempting to retreat to that. And then the Bailey might be something like the God of the Bible is true, significantly more ambitious, significantly harder to defend. And you know, Aquinus has arguments as to why these are these, you know, I'm not accusing Aquinus of this.

[01:21:34]>> The idea is you you put forward an argument like, you know, the God of the Bible exists and someone says, well, are you sure about that? And they start interrogating them and that person starts retreating back towards Oh, well, you know, I think there's a first cause of the universe.

[01:21:44]>> Exactly. And it's sort of like, okay, but you've just retreated into a much simpler. So you're now defending kind of a different more like modest version of the argument.

[01:21:52]>> That's the Mton Bailey fallacy.

[01:21:55]>> But again, you haven't, at least strictly speaking, you haven't done anything like illogical.

[01:21:59]>> Yes. Because you you've switched if you were to analyze that in terms of propositions. Nothing has, you know, you've not made any kind of invalid >> Yeah. point.

[01:22:06]>> And another another helpful example might be like the ad homonym fallacy, right? If I say, you know, like Joe, like I just think you're stupid and therefore I I I don't agree with you.

[01:22:16]Someone say, well, that's the adminant fallacy. I haven't committed a logical fallacy there. I've just said, you know, Joe is stupid. Uh, therefore, he's wrong.

[01:22:24]>> Which like and you know, you can you can render that as a formal fallacy if you like. And there there are there are a number of arguments whereby um it's the line between a facious usage of something and a non-fellacious usage of something is is surprisingly.

[01:22:37]>> Yeah. So, you could formalize it. You could say something like, you know, um, premise one, Joe thinks the sky is blue.

[01:22:44]Uh, premise two, Joe is stupid.

[01:22:47]Conclusion, therefore the sky is not blue.

[01:22:50]And that would be a logical fallacy. But that would, as you say, like all genuine logical fallacies kind of just collapse into the nonsequittor. The nonsequittor is a fallacy. The nonsequit fallacy is committed when a conclusion doesn't follow from the premises.

[01:23:04]>> Yes. Exactly. And and all >> if it's raining outside, then I'll get wet.

[01:23:08]uh it is raining outside, therefore my raincoat is red.

[01:23:12]>> That's a nonsequittor. The conclusion just doesn't follow from the premises.

[01:23:15]And so a logical fallacy, a formal logical fallacy will involve some kind of problem with the structure. Whereas an informal logical fallacy will be harder to pin down and >> logical and you can say and some things that people call logical fallacies are arguments where one of the premises is unound on its face. So some ad homonym fallacies might be rendered like this.

[01:23:35]You know, you say something like this person is stupid. Um, uh, premise to, uh, everything that stupid people say is false. Conclusion, anything this stupid person says is false. And you say, well, that's, you know, structurally fine. Is it valid?

[01:23:50]>> Um, >> soundnesswise, most people kind of go, well, premise too, that's obviously not true. So, you know, you can kind of you can that's the ad homonym fallacy, but you have to be careful to >> remember that that's if like I don't think we should call them logical fallacies uh when they're like as you say informal logical. They're just like fallacies of a different kind. You know, they're they're they're unound, but there's nothing wrong with the logical structure. So, I think people I this is actually one of the problems is when when you're having an online debate and someone says, "Oh, that that's an ad hominum fallacy or that's a modern Bailey or that's a this or that's no true Scotsman." They often throw those out as if they have the same force as proving to someone that their argument is literally logically invalid.

[01:24:31]>> Yes, it's not. I mean, it's still bad to do that and that might show that their argument is faulty, but it doesn't have the same like this is absolutely like demonstrably invalid in the way that a formal logical fallacy does. And of course, in either case, um your uh just proving that an argument is facious isn't sufficient to show that the conclusion is false. That's important to specify. Yeah, a huge number of um very very bad arguments for true conclusions.

[01:24:57]>> Yeah. So like the fallacy of composition is an important one. Like you know you might say like so some people say like everything in the universe has a cause therefore the universe has a cause. See that commits the fallacy of composition.

[01:25:07]It's like saying every brick in a wall is small therefore the wall is small.

[01:25:12]That doesn't follow. But sometimes you can use that facious argument that where the conclusion doesn't follow from the premises but the conclusion is true. you know, all the bricks in a wall are red, therefore the wall is red.

[01:25:23]>> That is actually true, >> but it's still sort of committing this fallacy. But fallacies don't always mean the conclusion is false. It just means that the inference of that conclusion from those premises is like illegitimate.

[01:25:36]>> Yes. And also, you know, for the for the wall example, you could you could analyze that as having an implicit premise in it, right? which is, you know, say you wanted to add premise number three, you could say that, well, a hidden premise in an argument is that redness is the kind of property that transfers from parts to holes.

[01:25:54]>> And then, you know, you kind of you can cash out the fallacy of composition the other side saying, well, smallness is the kind of property that transfers from parts to holes. You can say, "No, that's that's not true. That's false, which is why that one's invalid and this one is."

[01:26:04]>> Yeah. So that there is a fair amount of of freedom in how you take natural language arguments and choose to treat them >> um kind of using kind of propositional form and stuff like that. I think that um often times uh one you know criterion oh sorry a criteria for how you might want to go about this often times it's it's it's kind of generally to go with like informativity like how >> um how much does it tell you about the other person's argument um is a pretty good uh metric for in practice how it's going to be most helpful to formalize that argument. So, >> you know, one of the one of the dangers of of formalizing every ad homonym fallacy, for example, as um simply this person's stupid, therefore what they say is wrong, is that although, you know, that that that gets to the representation that that argument is is invalid and and therefore a bad argument, it might you might discover that uh your interlocutor um the hidden premises supporting your interlocutor's ad homonym fallacy might tell you something about their wider views or or the other kind of moving parts of their philosophical framework and that can be very handy.

[01:27:06]>> Yeah. And it's important to note that like it kind of depends exactly what's being meant because like there are times when the so-called ad hominant fallacy might kind of be appropriate which is to say like you know uh if somebody says I believe this proposition and I say well why do you believe that? Yeah, I believe the earth is flat. Well, why do you believe that? Well, because Mark told me.

[01:27:25]>> I'm like well you know Mark is a complete idiot and I wouldn't trust what he says. Well there you go. You could go that's the ad hominant fallacy. But maybe the argument could be formally cashed out as like you know >> uh if somebody is stupid then what they say is less likely to be true. You know that's and so this is a statement that this person said therefore this statement is less likely to be true.

[01:27:46]>> Yeah. So if we were going to formalize that yeah we'd say something like um >> if someone is stupid then their statements are less likely to be true.

[01:27:55]um which is like plausible. It's plausible in the sense that actually I don't quite know what we would mean by stupid if if we didn't if it didn't entail that um you know Mark is stupid uh therefore um the things that Mark says are less likely to be true where you know we're saying less likely than the average person I suppose would be something um kind of a way that we could we could extrapify that and then you've got a you've got an argument that at the very least isn't obviously unsound its face. Well, I think the the the context in which this particular problem comes up the most is the appeal to authority fallacy.

[01:28:26]>> So there's this fallacy that says that if you say, well, I believe this is true because this authoritative figure says or or the appeal to popularity. I believe this is because loads of people believe it. Yeah, that's kind of a fallacy. Sure. But there are some contexts in which it it is actually sensible to trust authorities. You know, like I I like I don't know, you might believe in climate change because of scientific consensus even though I'm not a scientist and I have absolutely no idea how to interpret, you know, CO2 data. Got no idea what's going on there.

[01:28:54]Like it still might be reasonable to believe in climate change if the popular consensus of authoritative figures say that. Somebody could say that's an appeal to authority. And in some context, you kind of want to be like, yeah, it is. But, you know, that's that's kind of fine.

[01:29:08]>> Well, I all of the um all the the idea of something being logically facious would mean um here is that um it doesn't guarantee the truth of the conclusion.

[01:29:17]So, so um it you know say if you were to to chunk that down into propositional form, you kind of have the flip side of the argument we just gave about this hypothetical mark. I'm so sorry if anyone in the audience is called Mark.

[01:29:26]Um here you'd say something like okay if something is um first premise if there's expert consensus on something it is more likely to be true. Second premise there's expert consensus on climate change or any other proposition you want to stick in there. um conclusion um therefore um that's more likely true and you know so I think that's a very um a nice way of breaking it down partly because it actually immediately exposes the fault lines of a debate that you would have with somebody who doesn't agree because most of the time >> if somebody is questioning expert consensus they normally are questioning that first premise they're normally saying no I think that even when um there is expert consensus on something that doesn't make make it more likely to be true. So again, you can kind of see how breaking things down into propositional form in this way can do a lot to clarify the contours of a debate where what the substantive disagreements between you and your interlocutor might be.

[01:30:22]>> Yes, everybody learn logic. Where should they learn logic? What what can you recommend that they read if someone's no introduction to this?

[01:30:28]>> Well, so the open logic project is um a website with free logic textbooks. I wish I was involved. I'm not. Um then they they they're there. Download them for free. Very very readable. Um what you know to give you a an idea of how um readable and kind of uh useful they are um the the for all x free logic textbook was literally the the the textbook for the first undergraduate Cambridge logic course that was >> yeah when I did logic in first year at university it was Vular Halbach's logic manual >> which I thought was actually quite a good introduction that's where I would point people to but I've done a lot less reading on logic than you have so that sounds like a really cool project That's the And there are there's there's ones on set theory, there's ones on category theory. I don't understand category theory at all. Um I wish I did, but I don't. Um there there ones on probability theory. It's it's a fantastic resource. Uh, another one, if you're >> more mathematically minded, um, the book, I can't remember who it's by, it's called a friendly introduction to mathematical logic, and that will take you right the way from, you know, formalizing statements, uh, through propositional logic, predicate logic, and uh, all the way through to girdles incompleteness theorem, which is a a tricky old proof. So, by the time you've got there, you're you're doing pretty well. Cool. Um, well, there you have it, ladies and gentlemen, and good luck to you, Joe.

[01:31:50]Oh, thanks. This has been fun. You know, I say that at the end of a lot of podcasts, like this has been fun. And it always is, but I think that >> I like podcasts that are that are quite a lot of time sort of discuss all over the place, but it's nice to have a particular task, intro to logic, what's it all about. I think we've covered most of the important bases, at least to give people a basic idea, resources in the description. Hopefully, they agree that we've done a relatively good job here.

[01:32:12]And thank you for the time.

[01:32:14]>> Oh, thanks for having me. If you enjoyed that conversation, you might like one of my previous episodes with Joe, which you can watch by clicking the link that's on your screen. To support my work and get early adree access to episodes, subscribe to my Substack at alexoconor.com.

[01:32:27]Thanks for watching.