PREVIEW-Episode 34: Frege on the Logic of Language

0:00 Unknown speaker: This is a Partially Examined Life episode preview. You'll find the full episode available for purchase in the music section of the Itunes store or at partiallyexaminedlife.com store for unlimited access to our back catalog. You can become a pel citizen@partiallyexaminedlife.com membership. Membership also includes access to discussion groups with other listeners, as well as ad free versions of current episodes and a host of other bonus content, all available from a single convenient feed that you can use with a variety of podcast apps.

0:42 Mark: You're listening to the Partially Examined Life, a philosophy podcast by some guys who were at one point set on doing philosophy for a living, but then thought better of it. Our question for episode 34 is something like what makes a sentence true? We'll be discussing three essays by Gottlob Frege on sense and Concept and object, both from 1892 and and the a logical investigation from 1918. We'll also talk a little bit about his introduction to the basic laws of arithmetic from 1904. My name is Mark Linsenmayer and that name is determined both by linguistic conventions and by my own intentions to refer to an entity residing in Madison, Wisconsin.

1:16 Seth: This is the referent of the proper name, Seth Paskin in Austin, Texas.

1:20 Wes: This is Wes in Boston, Massachusetts, in quotation marks.

1:24 Matt: And this is Matt Teichman, failing to distinguish between concept and object in Chicago, Illinois.

1:30 Seth: Welcome, Mat.

1:32 Matt: Thank you. I'm delighted to be here.

1:33 Wes: Good to have you.

1:34 Mark: If you are an avid philosophy podcast listener, you'll recognize Matt's voice and name from his excellent philosophy podcast out of the University of Chicago Elucidations, which is a little different than this. Yeah.

1:45 Matt: So you can check that out. I think if you just Google elucidations these days and it comes up number one or two, which I'm pretty psyched about, that's probably the easiest way to find it. And that's more of an interview format.

1:54 Mark: Yes. Which is dedicated to capturing the brilliant thoughts of the various University of Chicago faculty and visiting faculty. Is that right? Yeah.

2:02 Matt: And also people who are in town to present stuff. Yeah. Whoever happens to be within range of my microphone.

2:07 Mark: Which also means Matt is an actual graduate student at present.

2:11 Matt: Right. I have not yet reached your level of transcending graduate school, but perhaps someday in the future.

2:16 Mark: Perhaps you'll drop out someday in the future.

2:19 Matt: You never know.

2:20 Mark: Maybe we can make it happen tonight.

2:23 Unknown speaker: Yeah.

2:25 Mark: And we're excited about having Matt on here because he's actually had recent contact with folks like Frege. How are we going to pronounce Frege tonight. Is it Frege?

2:34 Wes: Frege, I think. Right.

2:36 Matt: I usually go with Guh, but Frege.

2:38 Mark: But Das is de Frege.

2:40 Matt: Very nice.

2:41 Wes: Right.

2:41 Mark: I think we have to say Frege. You have to do the R. Frege.

2:45 Wes: All right, Mike, you can do that every time.

2:49 Mark: In fact, I'll just do it once and I'll paste it over every time anybody says it at all on the entire podcast and we'll just hear Friggin.

2:57 Matt: Yeah, it'll be like a voicemail, you know, like, please leave a message for Frigate.

3:04 Mark: Let me do the ground rules because I'm interested to get another podcaster's perspective on whether these are helpful and relevant. Okay, here's the first one. We should try not to assume that our audience knows anything about any of this. Is that even possible? Is that a realistic goal?

3:17 Seth: No.

3:19 Matt: I think you can maybe sort of approach it asymptotically. Maybe it's not actually achievable, but it's a. That doesn't mean we shouldn't try for it. Yeah.

3:25 Mark: As long as we use the word asymptotically a lot, we'll assume our audience remembers their high school geometry.

3:31 Matt: Right. That's a nice point. Yeah. Actually I violated the rule in the process of phrasing the rule. I'm off to a great start here. This is great.

3:40 Mark: Number two, no fair name dropping. In lieu of making your point, don't say you would understand me if only you had read ou812 A Semiological Analysis of the Works of Van Halen.

3:51 Matt: That book really needs to be written.

3:52 Mark: It actually has had a long fought competition influence with Sammy Hagar's Living With My Disability about why he can't. Why he can't drive 55.

4:02 Matt: But now we're presupposing that our audience is familiar with 1980s arena rock. I know that's fair.

4:07 Seth: Actually, I think we've established that on the blog.

4:11 Mark: Number three. We will be rigorous and exact in all that we say instead of just parroting the disease language of the authors we are reading. That is the new formulation. I'm.

4:21 Seth: Thank you.

4:22 Mark: Does that seem relevant?

4:23 Seth: Yes.

4:25 Mark: Again, it's a goal. The reason we have them is because we are actually likely to violate them.

4:29 Matt: Yeah.

4:30 Seth: Especially Wes.

4:33 Matt: I think Frege is often praised for getting away from this style of writing philosophy where it's kind of unreadable and you have no idea what each sentence even means anymore. But actually, when you go back to Frege, I think it turns out that he does use a fair amount of Jargon that might not be familiar to a newcomer to philosophy.

4:48 Mark: Well, it is the launching point for analytic philosophy. The part of it where every other sentence is in some sort of unreadable symbolic logic that most people will just. Their eyes glaze over.

5:01 Seth: Yeah.

5:02 Matt: Unless they're a computer, in which case they love it.

5:04 Mark: Unless you've tried to translate your document to a Kindle or something readable format. And it doesn't know those quantifier signs and things. And so it's all even more gobbledygook than it is.

5:16 Matt: That sounds pretty horrific.

5:17 Mark: Wasn't that bad here. But anyway. Yes. I found him not terribly unclear. There are things about his theories that. Areas that he doesn't go into that would be nice that if he went into. But he has his little project. Who wants to say what that is? Approximately. Let's put Matt on the spot.

5:32 Matt: Okay.

5:33 Mark: We got Matt because he's actually dealt with this stuff recently. Whereas for the rest of us, this was like a bad dream that we had to get over and. And now we don't pay any attention to it. It was kind of fun for me to revisit it. But anyway, you're still in that land.

5:47 Matt: Yes. I think Frege was sort of simultaneously involved in two different things. Maybe one thing was to put mathematics on firm foundations by coming up with a way of thinking of mathematical truths as logical truths. And maybe another thing that Frege was interested in was thinking very precisely about the way that linguistic meaning works in spoken language, the different ways different languages can mean things.

6:09 Mark: Not that he's doing comparative language. He's not considered interested in German versus English or anything like that.

6:15 Matt: That's right, yeah. Sorry. So he's not doing what kind of linguists today do, which is compare German vs Dutch vs English, but thinking about it kind of more abstractly. If I were to design a language, how would that language work and what are the different things you could design a language to do?

6:29 Mark: And he's specifically concerned with foundations of mathematics. So assertions. Right. Not so much commands or he'll talk about artistic tone and things like that. But that's really just to say this is not what I'm concerned with. I'm concerned with what it is in a sentence that makes it tell me something that makes it state a fact.

6:47 Matt: Right.

6:47 Mark: I shouldn't even use the word fact.

6:49 Seth: But you shouldn't. Right.

6:50 Wes: So I would call that the theory of truth part with the theory of reference and to some extent, meaning along the way.

6:57 Seth: Right.

6:57 Wes: I mean, if the first thing we Think of he's doing the. Trying to found arithmetic in logic. The second thing, at least for what we're discussing tonight, I would see is this theory of truth. And then the third thing is his anti psychologism.

7:11 Mark: Right. Well, it all came with this initial project to come up with a symbolic language to do mathematical proofs in, right?

7:18 Matt: Yeah.

7:19 Mark: So that means that every sentence has to be precise and you know, it has to be founded as an axiomatic system, right?

7:25 Matt: Yeah. So I mean like a regular mathematical proof, you know, it's sort of written in half prose, half technical language and like basically people have to check it. But the dream, I think, behind this project of Frege's was to be able to write mathematical proofs in this really strict, really rigorous as formal language that could be checked by a mechanical procedure and thereby putting the mathematical proof on firmer foundations. We could be more certain about a proof if a computer could check it, rather than having to rely on people who are fallible and something kind of like that. Right.

7:53 Mark: That they found that even these very well established proofs, you know, some of them were corrected over time or they relied on some kind of intuitive leap or there just wasn't a lot of uniformity in the methods overall used for them. So that was the point in coming up with this. You know, if you're trying to prove a true sentence, there are specific ways to relate that to other sentences and that has to do with the structures of the terms involved. All right, so that's where he's coming from. And then if you try to apply that to ordinary language, then you initially. Can I just give the sense and reference thing quick, or is this jumping ahead?

8:25 Matt: Go for it.

8:26 Mark: It's running into the idea that it seems like if we could have a one to one correspondence between these terms in this pseudo mathematical language and everyday language terms, then if I say something about an individual, and then I say another thing about that individual using a different name for that individual, then it should be true. Right. So if you say Mark is sitting in this room and you say Mr. Linsenmayer is sitting in this room, those both refer to the same person, so they're both true. But what if you put them in these contexts of talking about somebody's belief?

So let's just say Wes thinks Mark is sitting in this room. Well, Wes thinks Mr. Linsenmayer is sitting in this room. Do those mean the same thing? Well, what if he doesn't know my last name? So he thinks Mark is sitting in this room, but he doesn't know. Think Mr. Linsenmayer is sitting in this room. So that shows right there. Okay. There's something imperfect about ordinary language that, like, if we're going to really make it purely symbolic, we have to get rid of all those sort of ambiguities. But, well, we want to give some kind of account of, you know, what can Wes conclude from his beliefs.

So he came up with this distinction between the referent of a term, which is me in both these cases, and the sense of the term which in these case. Each of these names for me, has a different sense. We've talked about his example a bunch of times of the morning star and the evening star. And it was actually a scientific discovery that those both were the planet Venus or another favorite is the I can have beliefs about Clark Kent without having beliefs about Superman, and vice versa. So those are very intuitively obvious examples.

9:50 Wes: Yeah. So for us to discover that the morning star is in fact the evening star, and for that to be something that's informative, it has to be the case that the identity that we're asserting there is not simply a definitional identity like A equals A. There have to be two things that are different. We know the referents are the same Venus. So the question is, what's different there that makes that proposition informative in the way that it is? And what's different, Frege will say, must be the sense. And those are the different descriptions under which we've come to understand the reference.

You know, we've experienced one description, the star rising in the morning and the other in the evening. Those are two different ways of experiencing the same thing. So those different ways are what Frege will call sense. And he sees that as a solution to something which otherwise would be a very difficult paradox to get around.

10:41 Matt: Yeah, I mean, maybe another way to say that would be, well, it's just sort of repeating the same example. But nonetheless, if I told you Elvis Costello is Elvis Costello, you'd be like, great, duh. But if I told you Elvis Costello is Declan McManus, maybe you didn't know that there was the opportunity for you to learn something there, because it's not just an empty statement, Right?

10:58 Mark: And before we dive too far into that, maybe we can just sketch where the rest of this goes, that once you introduce that, then what are these things? Now, we've said that there are these referents, but then there are these senses. So what are the ontological implications of this? Do we have to say, you know, if the referent is presumably in most cases, in the cases we've talked about a physical thing out in the world. Well, you know, is that the case throughout? You know, if we talk about mathematical objects, are those somehow objective things or those in the mind?

So there's that question. Even if we admit that all the referents are somehow objective things that we're referring to, what about these senses? I mean, are these just things in my individual mind? Okay, so that's an issue. And then he uses this analysis again. He's interested, just like in the mathematical case, in being able to give valid principles of deduction, just like Aristotle was doing back, you know, when he founded logic in the first place. But now by introducing not only the sense reference distinction, but earlier in creating his mathematics, I guess his big innovation was the introduction of the fact that you can have two quantifiers.

Is that right? So you could have sentences like everybody loves somebody.

11:59 Matt: Right.

12:00 Mark: Whereas Aristotle could deal with like, all men are mortal. Socrates is a man. Therefore Socrates is mortal. So the all men, that's one quantifier for all men. But the everybody loves somebody, that is for everybody, there is somebody who he loves. So the all and the there is some, those are both quantifiers and they have special symbols. And just the fact that you could put those together like that was a big deal. Right. This is what Frege basically invented this notation, and this is what enabled him to deal with mathematics.

12:28 Wes: Yeah. So he invented mathematical logic or symbolic logic, the kind of thing that we all learn in introductory logic. Course, that's Frege. He did that for the purpose of founding arithmetic in logic. But it's had huge consequences otherwise. And really it's a revolution in logic, which logic really hadn't changed since Aristotle's time. And Aristotle didn't really make a distinction, say the particular in the syllogism. Socrates is a man and all men are mortal. The quantifiers are all hidden there. There's no real distinction, which for Frege will be critical between the all men is mortal being a subject and Socrates being a subject.

Well, in fact, the all men is not really a subject in the same way that Socrates is. You really have to parse the structure, the true structure of that, I think, Mark, which you already mentioned, is that for all X, if X is a man, then X is mortal. It's really a hypothetical proposition that's hidden. That seems to be a statement on the same level as Socrates being a subject.

13:27 Seth: I feel like you guys might have jumped in to the deep end of the pool a Little bit. So let's dial it back just a little bit. Frege had to do some conceptual work in order to articulate the system and for it to work properly. And I think the key critical move that he made was sort of focusing on articulating the concept of the subject and a predicate. And he talks a lot in the writings that we read about that way that functions in natural language. But he has in mind the logical structure of what he calls subjects and predicates. So if you start with that concept, the idea of a subject and the idea of a predicate, you can think of the subject as a thing and the predicate as kind of a quality or a property of that thing. So in the sentence Seth is in Austin.

14:15 Wes: Oh, no, don't do that.

14:16 Seth: Don't do that one. Okay, the grass is green. How's that? Okay, so in the sentence the grass is green, the subject of that sentence is grass or the grass. And the predicate is green and is. The word is functions to connect the subject and the predicate in that sentence. So you can say of the grass that it has the property of being green or that you. It has the quality of being green or it is green. And that basic structure of subject and predicate is sort of the anchor for his entire system. Because basically, what the formalization does is the formalization allows you to ascribe predicates to objects. So if you've ever done formal logic and you see something that says like capital F small A or capital G small B, what you're basically seeing there is a very simple subject object predication

15:18 Wes: notation essentially developed by Frege. It was modified because Frege's original notation was hard to print.

15:23 Seth: Yes.

15:24 Mark: Predicate calculus.

15:25 Seth: Predicate calculus. What's important is that the subjects, for Frege, are ultimately what you might call. I hate to use this word, but I don't really know how else to say it right now. They're sort of singular or irreducible. And predicates are typically something that can be applied to multiple subjects, and they're what he calls concepts. So you have sort of objects and concepts, and those are associated with subjects and predicates. And that's the conceptual work that he had to do in order for this whole mathematical system to make sense.

15:58 Wes: So the subject, or proper name, let's say, will refer to an object, and the predicate will refer to the concept under Frege's scheme.

16:07 Mark: Yep.

16:07 Matt: So the grass refers to an object, a bunch of grass, and the predicate green refers to, well, the concept green. And we haven't really said what that is yet, but maybe for now we can think of that as something like the property of being green, with the proviso that will say more about that later.

16:20 Mark: That's exactly what the whole difficulty is here. That, you know, it sounds like we are analyzing the parts of a sentence, but really it's not a matter of the parts of a sentence because we're interested in the. You know, again, if everybody knows that Mark and Mr. Linsenmayer refer to the same thing, if that's already established by definition or something like that, then the fact that we're using one of those words and not the other doesn't matter. Or if we're using a word in German versus a word in English that doesn't matter, that is not supposed to be reflected in the analysis.

So what we're concerned with is not those words themselves. We're concerned with the meaning. And so the question is, well, what is that meaning? Is that an object in the world somehow? Is that just something that's in my individual mind? Is it subjective? That's where this whole anti psychologism thing that you mentioned, Wes, comes in.

17:04 Seth: Yeah, right.

17:05 Unknown speaker: The reason why this stuff is important

17:07 Wes: is because he's trying to account for the logic of sentences. They behave in certain counter intuitive ways in some circumstances. Which is one of the reasons he erects this ontology that some people might see as strange. And one of those examples in the onsense and reference paper is that if you have a sentence that says, say this patch of grass is green and that's true, and you take that in what's called an intentional context or indirect discourse, and you say that Seth believes that the grass is green, you dramatically change the way the truth value of the particular sentence the grass is green relates to the truth value of the sentence as a whole.

And that's what Frege, as a logician and as a mathematician, he was concerned about how does the truth value of a whole relate to the truth value of a part? In some cases it's very simple. If you take one true sentence and put an and next to it, and then another true sentence, the result is going to be true or a true sentence and a false sentence and the result for the whole will be false. But in certain contexts, those sort of easy rules simply don't work. You guys have already mentioned examples like this. But it's not the case that if I believe that Mark Twain wrote Huckleberry Finn, that I also believe that Samuel Clemens wrote Huckleberry Finn, even though Mark Twain and Samuel Clemens refer to the same referent.

And it seems like I should be able to do a sort of substitution which might work in other circumstances.

18:30 Mark: Yeah. In math, in algebra, if you take any equivalent. Right. If you have any term. So if I have the number eight, I can just put in four plus four. At any point, the number eight shows up and any equations that I had that in, they'll still be true. And so it seems like. So that's what this whole. Why we're calling it a truth value, as should have been obvious from what Wes was saying, that just means, is the sentence true or not? Does it have the truth value true or does it have the truth value false? And we call it that just kind of on analogy to math that you should be able to substitute in.

If you're concerned with the truth of a complex sentence. And it's. Let's just say A and B and C, where A is a whole sentence that is true, B is a whole sentence that is true, and C is a whole sentence that is true, then A and B and C is also true. That's just the definition of the logical operator.

19:14 Seth: And. Right.

19:15 Matt: Yeah. You know, you can figure out whether the big sentence A and B and C is true without even really knowing what A and B and C mean necessarily. All you'd have to know is that they're all true. And then you can figure out that the whole big thing is true.

19:27 Wes: Yep.

19:28 Mark: We probably don't want to go too much more into the basics of symbolic logic, because we could spend the whole time talking about that. So, yeah, if you're really confused right now, stop, open Wikipedia or something like that and look up symbolic logic. But we should say something about. Once we've got these analogies set up, and we know he's trying to use math as the prototype here, then we can talk about. He said, well, he talks about truth values, but he also talks about truth functionality, which is something. A term we threw around on the Wittgenstein episode.

And people were like, what is truth functionality? Well, we just gave an example of that. Right. A function is just. You apply some operator to one or more individuals and you get some result. And you can in fact look at any predicate. One of Frege's big arguments was that you could look at any predicate as a function. So is green maps the domain of everything. So in other words, I can ask, is Wes green? Is this grass green? Is my computer green? You could apply it to anything, and then it maps it to A bunch of truth values. So if I say, is the computer green?

No, that is mapped to false. Is grass green? Yes, that is mapped to true, etc. Etc.

20:34 Wes: And just to give you the mathematical background of that mapping, since we can assume everyone's had high school algebra, if we think of a typical equation like Y equals X squared, and that equation is on a certain domain, where the domain really is just let's think of as things that are going to get plugged in and then the result's going to come out on the other side. So we map, let's say 1 to 1 and then 2 to 4, because we're squaring everything. And then what the map looks like algebraically is a parabola if we graph it out and assume that x's are on a horizontal axis and y's are on a vertical axis. So Frege is extending that idea of function to where here the function is the equals X squared part.

21:20 Matt: So instead of mapping numbers to numbers, Y equals X squared takes one bunch of numbers and maps it to another set of numbers. It maps 1 to 1, maps 2 to 4, 3 to 9, etc. Etc. Minus 1 to 1, negative 2 to 4. A concept, as Frege is thinking of it, it's not going to map numbers to numbers, but it's going to map things to truth values. And that would be like the examples that Mark just gave. So the concept is green will be a function that maps the shirt in my closet to true and my computer to false. And anything that's green, it'll map to true. Anything that's not gre, it'll map to false.

21:52 Wes: Yeah, so the is green is analogous to the Y squared.

21:56 Matt: Yes.

21:56 Mark: And why the hell would he want to do this?

21:58 Wes: And there we should say mapping the truth values. Just to fill in the ontology there, Frege, you know, as we see in Onsense and Reference and elsewhere, he's going to say that statements refer to truth values as a whole. So we already talked about, say a particular name is referring to an object, but also having a sense, and then that having a predicate, which refers to a concept. Where a concept is a type of function. Well, the whole thing taken altogether, refers to a truth value for Frege. And then the sense of the whole thing is what he calls a thought. So you can speak of reference and sense, whether you're looking at, say, an individual object or a predicate, or the combination of the two into a sentence. I think that's important before we, as confusing as it's going to be to listeners, just to put that on the table.

22:46 Mark: Well, that's one of the crazy things about Frege that it makes sense like, oh, the name grass refers to that stuff that is out there in the world. And maybe the term green refers to a property or the fact that a bunch of things like the grass have something in common. It refers to whatever that is so that we understand we should stick to

23:04 Wes: proper names, by the way, for examples of naming objects. That just makes it easier. Grass is a tricky case, I think.

23:10 Seth: Yeah.

23:11 Mark: For everything. If it is grass. So is grass could be interpreted as a predicate.

23:15 Seth: Yeah.

23:16 Mark: A concept. But then to say also reference. Oh, this whole sentence, my shirt is green. Because that's true. The sentence as a whole refers to the true. Like that just seems that breaks away from what we think refer to means in ordinary language.

23:31 Wes: Yeah. To give listeners a. You know, like we've talked about competing theories like the logical atomism of Russell and Wittgenstein, which were a version of the correspondence theory of truth, where what those at least atomic sentences, not necessarily complex sentences, but at least in a simple atomic sentence will refer to a fact, not to T. Right.

23:53 Mark: T meaning true. Yeah.

23:54 Wes: Yeah. So it is a very, very strange result that Frege is giving us.

23:59 Matt: Yeah, it's very strange and counterintuitive at first. And you know, he has very particular reasons for thinking this strange and counterintuitive thing. And I definitely agree. Yeah. The more intuitive thing to say would be that a name stands for a thing like Matt stands for me. And maybe a predicate stands for a property. So is happy stands for the property of being happy. But then you'd think that probably the sentence Matt is happy stands for the situation of Matt being happy or the state of affairs that Matt is happy or something like that rather than a truth value.

24:26 Mark: So yeah, it's definitely weird you mentioned Russell. Maybe we should give the quick biography to make it clear how since I think we've given a good overview of the system, at least some of the dangling pieces.

24:38 Wes: The Stanford article on Frege, which of course I looked at the biography part is just like four or five bullet points, you know, born and at such and such university dies, blah, blah, blah. You know, it's like Frege had no life is what the.

24:53 Mark: I certainly never learned about it when we learned him. What we heard since you mentioned Russell is that this was a guy who was in Germany at the the same university, his academic life and didn't publish that much. And a lot of it was in this very Specialized mathematical logic area. And the only reason that anybody's heard of him is because Bertrand Russell, who is already famous, discovered his work and wrote a lot about it and in fact, contradicted a lot of it.

25:21 Wes: Ruined it.

25:22 Mark: Yes. The mathematical logic in particular. We don't have to go into the specifics, but there was some key part of the overall theory about classes that Russell showed that there was some paradox in it and pointed this out to Frege. And the rest of it made him miserable.

25:36 Wes: He got really depressed about it.

25:39 Mark: Yeah. The rest of Frege's career was like seeing what could be salvaged. Well, now that sort of the overall system was blown, and he tried to revise it a few times, I guess, but he really didn't participate in the next few rounds of scholars revising this project, which Russell went with it with the Principia Mathematica. It was a very famous book, which, of course, has itself been. When Godel came along very quickly.

26:01 Wes: Yeah.

26:02 Mark: So the specifics of the mathematical logic are sort of interesting for history.

26:05 Wes: You say the quest to found arithmetic in logic failed, although it failed in its ultimate intention of being a founding. But the relationships are.

26:14 Seth: You know, it's because founding anything always fails.

26:19 Matt: Reasonable conclusion to draw. It's maybe also worth saying that Wittgenstein was a big promoter of Frege and indicated that Frege was the philosopher to whom he was most indebted. And Wittgenstein, of course, has been a huge deal ever since his first and only book. Right.

26:32 Mark: And that book was influenced by Russell. Russell actually worked with him to get it published and wrote the intro to it. If you listen to our Tractatus episode, you'll hear all about that. So there's this very direct chain from Frege to Russell to Wittgenstein. And the other piece that we talked about in the Husserl episode was that Husserl started also trying to write on the philosophical foundations of arithmetic and wrote about it in a very different way, in this more psychologistic way. And this. If you listen to that episode, you'll see he's.

Husserl is all about analyzing experience. So it's kind of giving an empirical account of math was where he started. And it was interesting that I ran across, you know, I've on this podcast, used a number of times, the argument that I think we can give an account for the origin of our ideas of number just through abstraction. Which is the kind of thing that Hume would say.

27:14 Wes: Right.

27:15 Mark: I see three kittens, I see three gloves, I see three this, three that. Eventually I can abstract from all that and come up with the number three. And Frege came up with, or at least was a popularizer. I don't know of a pretty definitive argument against that that at least convinced Husserl that that didn't work. Which is, well, what does that abstraction process look like? Like, if you take away. Okay, so I've got three gloves, take away everything about them that makes them gloves, there's nothing left. If you take away all the pieces and then you take away all the pieces of these three CDs and these three pencils, there's nothing left to compare. The only way you'd be able to imagine that you could abstract in this way is because you already have the number three in the first place.

27:51 Matt: Right.

27:52 Mark: That this pretense of abstracting is pure bullshit, that we must be getting our numbers ideas from somewhere else.

27:58 Seth: Yeah.

27:58 Matt: Another point that Frege makes too, is that you can count abstract things, like number of ways to beat somebody in chess. There are three ways to beat my friend in chess. And, well, what's going on with that? You know? Yeah, that can't work in the same way as abstracting the number three away from three hats or whatever.

28:10 Mark: Exactly.

28:11 Wes: Yeah. That idea, which is one element of psychologism, it's not. The whole story comes from John Stuart Mill. This idea that in fact there aren't simply necessary logical truths as opposed to empirical truths, that in fact logical and arithmetic truths are also derived from experience. And that was subsequently widely rejected. Frege railed against that for years. He railed against psychologism and various authors, including Mill. And he wasn't listened to until he criticized one of Husserl's early works, which was psychologistic. And then Husserl responded positively and became an immediate convert. And the rest of his philosophical career argued against psychologism as well.

28:49 Matt: Right. It also might be interesting to mention that Mill anticipated a lot of Frege's ideas. For example, he anticipated the sense reference distinction and a similar distinction he drew between what he called denotations and connotations. A lot of very interesting back and forth.

29:01 Wes: Yeah. And Mill is actually complicated because he's both psychologistic in some ways and anti psychologistic in others. Yeah.

29:07 Mark: This is the same guy that we talked about in our utilitarianism episode, if you look back to that, but we didn't talk about any of that aspect of him. But you could see his ethical idea that you have to talk about ethics in terms of happiness. You have to talk about concrete things. You know, it's all a very empirical bent.

29:20 Wes: We did have two readers of our blog, like, debate this for more than 60 comments. One of them wanted to ground arithmetic and empirically, and the other.

29:32 Seth: Anyway, hey, I'm just curious. Did we read an article called On Thought?

29:36 Wes: Yes, the one you did at PowerPoint.

29:38 Seth: Yeah, I'm just curious. I was just checking in, making sure I wasn't in the wrong podcast.

29:44 Wes: Yeah, Seth wants us to get back on topic. Yeah, before we do that, we want to make sure we have the sense and reference ontology down and all that.

29:53 Seth: Well, I think it's important for us to at least talk about sense reference and what he means when he says the thought, the sense of a sentence, because that all ties into the concept of truth value, which gets you to all the weirdness that you talked about.

30:09 Matt: Okay, sure.

30:09 Mark: Let's get concrete.

30:10 Seth: Okay, how about if I do a quick. A quick little summary and you guys can let me know what you think. So Frege, in the article, the thought, he says, look, we have this idea. We want to say that we have ideas and that our ideas correspond to reality in some way. And that's what truth means. That's really kind of like what's implied and what's sort of assumed is this correspondence theory of truth. So I have an idea or a picture in my head of something in the world, and if it maps in some appropriate way and it's an accurate representation or an accurate it corresponds to it some way that then my idea is true.

And what Frege says is, well, that's not really the case. It's not that ideas are true. It's that sentences that express ideas can be true or false. So he says true. When you think about it, correspondence is a relational thing. You have to have an idea, and you have to have a thing or a reality or an object or something to which it can correspond. But when you think about the meaning of the word true, it's not really a relation word like correspond. X corresponds to Y. You don't say X trues Y. What you say is X is true or X is false. And so he says, there's something weird about this.

Truth is not really about correspondence in this sense. And he says the reason why is that anytime you talk about truth, what you end up talking about is a sentence. Specifically, he mentions a spoken sentence, but I think this applies to written sentences as well. So you're not saying my idea of something is true. What you're saying is this sentence that I'm saying right now, my idea corresponds to the object. What you're saying is that sentence itself is true, not that the idea is true, but that the sentence which expresses the relationship between the two things is true.

So what he says is really, when we talk about truth, what we're talking about is truth of the sentence and not truth of an idea or truth of an object. In fact, objects can't have truth. You can't say the chair is true. That doesn't make sense. You can't say my idea is true because it's an object. It just doesn't make sense to say that. All you can do is say some declarative sentence expresses something that is true or false.

32:30 Matt: Yeah, expresses a thought. I mean, one of the weird things in Frege's philosophy is that he draws this sort of technical distinction between thought and idea. And normally we think of those two words as meaning the same thing. So what he calls a thought is much closer to what we would call a proposition.

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