Gottlob Frege - On Sense and Reference

this guy dolab Fraga published this paper Uber Zin un on sense and reference in 1892 and it is the most important paper in the history of the philosophy of language it is very complicated but I'm going to explain it now frager realizes that linguistic terms words have to have two levels of meaning they each have to have a sense and a reference I'm going to explain exactly what those are but first we need to see the puzzle that forces fragga into this position to illustrate this puzzle I'm going to have you watch like a viral

[Music] videoy my name is j what's your name huh Ellen what do you do Ellen did you just do performance I'm on my way to the performance in Brooklyn at the new Brooklyn Arena oh oh JZ okay that was fun the noteworthy thing about this interaction is that the woman her name is Ellen she already knows the meaning of the name Jay-Z so it's not like what happens is that the guy tells her oh there's this name Jay-Z and the name refers to me it's my name that's not what happens no no she's familiar with

the name she knows the meaning of Jay-Z but she still learns something at the end of the video when he tells her that he is Jay-Z so there's like two possibilities she could learn something linguistic about the name or she could learn something empirical empirical just means knowable by observation or experience another term for this is a posteriori and the point of this story is just that what this woman learns at the end of the conversation is not linguistic she's not learning anything about the meaning of the name JayZ she already knew that name she's

learning an empirical fact a fact about the world which is oh this guy that I've been sitting next to he is Jay-Z consider these two sentences Shawn Carter is Shawn Carter and Shawn Carter is Jay-Z that's Jay-Z's uh government name his his regular name Shan Carter that's his name sentences of this type are called identity statements because they say that two things are one thing two things are identical they're the very same thing imagine in the case of Ellen and Jay-Z on the subway imagine that she knew him by the name Shawn Carter like maybe

he got on the train and they introduced themselves to each other and he introduced himself as Shawn Carter that's his name she knows who sha Carter is and she also knows that there's this this musician this rapper named Jay-Z maybe she's seen pictures of him she knows who Jay-Z is but she hasn't yet put it together in her mind that this guy right next to her Shawn Carter is Jay-Z if that's the case then sentence number two can be informative to her it has as Fraga says cognitive value you can really learn something from sentence

number two this woman Ellen can really learn something by discovering or being told that Sean Carter is Jay-Z so I'm writing here that sentence 2 is informative it can teach her something in the way that sentence one never could Shan Carter is Shan Carter yes of course as long as these two names here and here are being used in the same sense to mean the same thing well then one is totally banale and uninformative whereas two can be informative but sentence 2 can also be empirical in the sense that the information that you get from

sentence 2 can be in some cases not about language not about the meanings of the words but it can be something that has to be discovered through going out into the world and existing and and discovering things like namely oh this guy sitting next to me he's a famous rapper that's the point of this example in the middle of the train ride Ellen knows all the linguistic facts she knows what this name Shan Carter means she knows who it refers to it refers to this guy sitting next to me she also is familiar with and

understands the name Jay-Z knows oh that's the name for this famous musician maybe she can name a whole bunch of facts about Jay-Z she can know all the linguistic facts but still there's that moment at the end of the train ride where she learns something like sentence 2 she learns that this guy Shan Carter is Jay-Z and so what she learns can't be linguistic because she already knew the linguistic stuff it has to be some empirical fact about the real world some observable experiential fact now we're ready to State the puzzle how can we have

a theory of language language a theory of names that explains these two features of sentence number two that it can be informative and that more specifically the kind of information that it can give can be empirical information the reason this is a puzzle is that there was this other theory of names published in 1881 by John Stewart Mill and according to Mills Theory the meaning of a proper name like Shawn Carter or Jay-Z the meaning of a name like that is nothing more than the object named and Mill's Theory sounds really good when you read

that paper that he published in 1881 but then you run into cases like this and he can't handle this according to Mill the name Shan Carter and the name Jay-Z mean exactly the same thing and so sentence one and sentence two are no different Mill is unable to explain why a sentence like two can be genuinely Illuminating informative why it can have some cognitive value in a way that a sentence like one doesn't because after all on Mills Theory the meaning of these letters right here is just the dude and the meaning of these letters

right here is the exact same dude so it's just this dude is this dude yeah duh just like in this case this dude is this dude there's no difference now there's an alternative to Mills theory that can explain how sentence two can be Illuminating informative um in a way that sentence one can't and that theory translates sentence 2 as a sentence about language itself on this theory sentence two is really just shorthand for something like sentence two star the name Shan Carter and the name Jay-Z denote the same person if this is what two means

then it makes sense why two is informative in a way that one isn't one would be translated correspondingly as something like the name Shawn Carter and the name Shawn Carter denote the same person that's obvious but this is not obvious like this is a fact that you might not know and this theory that translates identity statements like this into sort of linguistic statements like this that theory is actually fraga's old Theory from the B Griff shrift which he published in 1879 but 13 years went by between 1879 and 1892 when he published on sense and

reference and during those 13 years Fraga realized that this Theory the theory that translates identity statements into linguistically statements like this that theory wasn't good and the reason is that statements like number two here can be informative not just informative but empirically informative the idea is simply that when Ellen had this moment of realization on the subway she wasn't realizing something about the meanings of these terms she was realizing something about the world around her and Fraga gets this he understands all this stuff about Ellen and Jay-Z and so what he does in on sense

and reference is he tosses out his old Theory and he gives a new theory of sentences like that and and it turns out to be not just a theory of identity statements like this but of all of language very quickly I'm going to illustrate this again with fraga's own example which involves the morning star and the evening star to understand this you're going to need some astronomical background information so here it is if you look at the Sunrise Just Before Sunrise right near where the sun is about to rise you can see a very bright

star sometimes and the name of that star is the morning star and then also just after Sunset right near where the sun just set sometimes you can see this other bright star and that star is called the evening star okay those are stars and people have known about these stars for a long time and they name the stars because we name things but then at some point someone discovered that these two stars were the exact same thing and they're not even Stars it turns out they are the planet Venus so what you've got are sort

of trivial s sentences like the Morning Star is the Morning Star yeah du and then you've got possibly very informative noteworthy sentences like the Morning Star is the evening star so just like in the case of this sentence two this sentence two can be informative and the kind of information that this sentence carries is not linguistic information but empirical astronomical information someone can be in a situation where they know the meaning of this name or this phrase or whatever the Morning Star they know which it is they can even point to it they can even

say that one's the morning star that's the object denoted by the name or the description the morning star and they can do the same thing let's suppose for the evening star they know what this phrase means and they can point to it so they know what is denoted by all of these terms but what they don't know is that these two objects are one object and so when you tell someone the Morning Star is the evening star you can be telling them something that they didn't know already and not something linguistic at all and Mill's

theory of names and fraga's old theory of names that translates identity statements into you know these linguistic statements or whatever neither of those theories can explain these facts about this sentence and this sentence that they are informative and that the kind of information that they can give is often empirical okay so that's the puzzle that's the problem and what frga does is he solves this problem by introducing an additional layer of meaning and that that sort of additional middle layer of the meaning of a term is the sense it is natural now to think of

there being connected with a sign a name combination of words letter besides that to which the sign refers which may be called the reference of the sign also what I would like to call the sense of the sign wherein the mode of presentation is contained okay so frag is talking about three different things the first thing is the name or the sign and then then of course there's the thing that the name picks out or refers to the referent which in this case the referent is the guy the actual person Jay-Z but in addition to

the referent Fraga is saying that there's this other middle level of meaning which he calls the sense and it's really not clear at this point in the paper what the sense of a name or of any expression is but it has something to do with a mode of presentation so I have to explain what that is are you familiar with the concept of a mcmansion that's like a poorly constructed ugly home with too many roof lines or whatever imagine one of these ugly houses and in the front of the house there's like fancy stonework or

bricks or columns or something like that but in the back of the house it's just plastic siding so you can imagine a case where you've seen this house from the front that's one way of viewing the house one literal angle or perspective from which you can view the house you might also Al see the house from the back that's a different perspective a different mode of presentation of the house a different way that the house could be presented to you and you can know the house in both of these ways without actually knowing that they're

the same house and then it might be informative to you to find out oh look at that that's the same one house that's what fra is getting at with this idea of a mode of presentation there are two different ways of knowing Shawn Carter you could know him as The Kid From Brooklyn or whatever or you could know him as Jay-Z the Mogul the billionaire rapper or whatever I don't know if he has a billion dollars but close to a billion or a little more I I think the simplest way although this is a little

contentious to think of the sense or mode of presentation of a name or phrase is to think of it as a description you could describe this guy as a billionaire music mogul or you could describe him as a middle aged man who was born in Brooklyn and still lives most of the time in the greater New York area those are two different ways of presenting or characterizing this guy Shan Carter or Jay-Z fraga's point is this a name or for that matter any other linguistic term a name has not only this level of meaning which

is the object named but also the way that that object is characterized or presented by the sign by the name Fraga himself actually explains this though with a somewhat abstract mathematical example that might not have been obvious from just reading the text so I'm going to read it and then explain exactly what he means let a b c be the lines connecting the vertices of a triangle with the midpoints of the opposite sides okay so there's no actual diagram in the published paper but I created this diagram you see that inside of this triangle there

are three lines there's the vertical line which is called a and then there's this other line that's line B and then line C is the is the third line going from the lower right to the upper left and the important thing to notice is that all three of these lines intersect they cross each other or meet at the very same point in the middle the point of intersection of A and B is then the same as the point of intersection of B and C so there's just one point here in the middle of this diagram

but fra mentions at least two different ways of describing that exact same point the place where lines a A and B intersect or you could describe the very same point as the place where lines B and C intersect so we have different designations for the same point and these names point of intersection of A and B point of intersection of B and C likewise indicate the mode of presentation so these two different names for the one point the point of intersection of A and B and the point of intersection of c and d these two

names they pick out the same point but they present that point in different ways ways they involve different modes of presentation of that same point and hence the statement contains true knowledge what he means by that is just that because these two different names for that one point have different modes of presentation that sentence the sentence that the point of intersection of A and B is the same as the point of intersection of B and C that sentence like sentence two here can contain real genuine information true knowledge as fragga calls it in our example

accordingly the reference of the Expressions the point of intersection of A and B and the point of intersection of B and C would be the same but not their senses right so these two names have the same reference but different senses different ways of presenting that reference that's exactly what's going on with Shawn Carter and Jay-Z These two names they refer to the same guy they have the same reference but they have different senses they present him in different ways and it's the same way with the example of the morning star and the evening star

the reference of Evening Star would be the same as that of Morning Star but not the sense so those two names the morning star and the evening star they have the same reference which happens to be Venus but they present that reference differently they make reference to Venus via different senses and this Theory this theory that says that for all the linguistic signs there are two levels of meaning the level of sense and the level of reference this Theory can explain both of these facts about identity statements like too it can explain why these sentences

are informative and it can explain why that information can be non-linguistic and empirical it's possible for one to already know the linguistic information one knows the sense of Shawn Carter the meaning and one knows the sense of the term or name Jay-Z but then one can find out oh these two terms that I already know the meaning to they refer to the very same guy that is how fragga solves the puzzle oh but there's more there's like way more the regular connection between a sign its sense and its reference is of such a kind that

to the sign there corresponds a definite sense and to that in turn a definite reference the point frga is making there is just that in the normal case for one name there is one sense and then one reference one to one to one while to a given reference an object there does not belong only a single sign but if instead we start with the object the reference there might be more than one name for that object right there might be Jay-Z and Shan Carter and HOV that's another one I think the same sense has different

expressions in different languages or even in the same language okay this is an additional point but fra thinks that the same sense can be the meaning of different terms it might be I'm sort of playing a little fast and loose here but it might be that Jay-Z and hve HOV I'm pretty sure that's how it's spelled those are two different names but maybe they present him in the same way so they have the same sense two different names same sense same reference that's also possible fraa thinks and then there's the case of what are today

commonly called empty names these are names that are meaningful but they don't refer to anything it may perhaps be granted that every grammatically well-formed expression representing a proper name always has a sense this just means that if a name is Meaningful it has a sense but this is not to say that to the sense there also corresponds a reference but just because a name is Meaningful and has a sense doesn't mean that there really is an object in the world that is referred to by that name uh frag is going to give us an example

right now the words the celestial body most distant from the Earth have a sense but it is very doubtful if they also have a reference the phrase the celestial body most distant from the earth that's a perfectly meaningful label it's a definite description it has a meaning fragga just thinks and I think he's probably right that there is no object in space that is the one object that is the farthest away from the earth maybe because like space curves or I don't know but there's there might not be a thing out in the world that's

referred to in that way but but nonetheless the name can be meaningful here's another thing that's very important to Fraga it's important that the sense of a term is public different people can mean the same thing by a term and so they have to be able to share the sense and for that reason the sense of a term the mode of presentation contained in the name blah blah blah all of that that's not the same as some private mental thing some conception or image in your mind it can't be that because that thing in your

mind is private no one else can see your conception can can have it and so whatever private stuff is going on in there that can't be what Fraga means by sense the reference and sense of a sign are to be distinguished from the associated conception the associated conception is whatever shows up in someone's mind when they hear this name and frga is saying that is not the sense and that's not the reference that's some other thing this constitutes an essential distinction between the conception and the signs's sense which may be the common property of many

and therefore is not part or a mode of the individual mind fraga's point there is simply that the sense of a term is common property it's something that multiple people can share and you can see why fra thinks this the sense is the meaning of the name and he wants two different people to mean the exact same thing if the meaning of a name was some private thing inside your own mind then you could never mean the exact same thing by a term as someone else this wasn't in the part of this paper that I've

assigned but fra also thinks that the sense of a name or a term determines the reference that is why is this reference the reference of this name right why is Jay-Z the name of this guy oh well it's because there's some description there's some characterization there's some mode of presentation of this guy that's associated with the name and he meets that description he fits that mode of presentation Fraga thinks something like that also there's this famous telescope analogy that explains how all of these things are related and I'm going to use this in my picture

of that uh that's a pretty good drawing let's read the quote and figure out what fra is saying somebody observes the moon through a telescope I compare the moon itself to the reference it is the object of the observation mediated by the real image image projected by the object glass in the interior of the telescope and by the retinal image of the Observer the former I compare to the sense the latter to the conception or experience okay so there's a person who's looking through a telescope and they see the moon and there's three things involved

here there's the moon there's the image of the moon on the piece of glass inside the telescope and then there's the image on the inside of the person's eye on their retina that's like the back of the eye or something there's the image that is reflected inside their eyeball the Moon is analogous to the referent it's the object out there in the world the image on the inside of the telescope is analogous to the sense right because a sense is a public thing and different people could come and look through the telescope and they would

see the very same image on the glass inside the telescope it's not the object out there but it's still something public that different people can interact with it's common property and then there's the image on a person's retina that is analogous to the conception the mental conception that's a totally private thing only you can see the images on the back of your retina no one else can come and look at those the purpose of this analogy is just to explain how all of these things the reference the sense and the conception are related to one

another Fraga actually doesn't care about mental stuff like your Associated mental conception or experience or whatever this this is irrelevant really when he's talking about the meanings of terms he's just talking about the sense and the reference but he has to mention all of this stuff about conception just so that his readers don't accidentally or mistakenly think that when he talks about sense he's talking about some private mental thing he's clarifying that that's not what he's talking about okay now things get real up to this point we've only been talking about names or maybe subject

Expressions whatever we weren't talking about whole sentences now fra is going to start talking about the sense and the reference of whole sentences like sha Carter is Rich or Jay-Z is Rich the thing you have to absolutely understand in order to understand what happens in this part of the paper is the idea of compositionality I have a whole other video explaining compositionality and if you haven't watched that you got to go watch it Link in the description but very briefly the idea is this the meaning of a whole sentence is composed of or built up

out of the meanings of the individual parts so the meaning of this sentence JayZ is rich is made up out of the meaning of Jay-Z the meaning of is and the meaning of Rich you put those together there's some rules for that and you get the meaning of the whole sentence this is a fact about language and Fraga takes it very seriously he thinks that compositionality is operating at both the level of sense and reference if terms if linguistic terms have sort of two levels of meaning they have the level of sense and the level

of reference then those the sense bits are all going to add up together to give you the sense of a whole sentence and also all the references are going to add up together to give you the reference of a whole sentence so what he's trying to do in this part of the paper the middle of the paper is he's trying to figure out okay I've already basically said what the sense and reference of like a name is what's the sense and reference of a whole sentence and he's constrained in his answer to that question by

compositionality the only thing that could be the sense of a sentence is something that could be made up out of the senses of those individual words or terms and the only thing that could be the reference of a whole sentence is something that could be made up out of the references of all the individual words or terms the first thing that Fraga considers as a possible sense or reference of a whole declarative sentence is what today we call a proposition frga doesn't call it a proposition he calls it a thought now that's confusing because normally

when you think of thought you think of a private mental thing and that's not what FR is talking about here when he says thought he means the the publicly available meaning of a sentence is this thought now to be regarded as its sense or its referent so the question is is the proposition or the thought associated with a sentence is is that the sense of the sentence or the reference of the sentence let us assume for the time being that the sentence has a reference if we now replace one word of the sentence by another

having the same reference but a different sense this can have no influence upon the reference of the sentence ah so Fraga has found a little test to tell whether the proposition or the thought or whatever is the sense of the sentence or the reference he realizes that there are these terms Shan Carter and Jay-Z which have different senses is but the same reference and so if you switch between the two if you swap out this this name Shawn Carter and you put in this name Jay-Z into the same sentence that's the difference between three and

four if you swap them out because these two names have the same reference then switching between these two sentences should not change the reference of the whole sentence but it should change at least sometimes the sense of these sentences we're just switching out two terms we're going from a term with one sense to a term with a different sense so these two sentences should have different senses but because these two names have the same reference these two sentences should have the same reference frag is trying to figure out whether or not the proposition or the

thought expressed by a sentence is the sense or the reference well there's this constraint these two sentences will have different senses but the same reference yet we can see that in such a case the thought changes Fagan notices that these two sentences Express different propositions they express different thoughts so the thought cannot be the reference of a name because the thought changes between these two but the reference can't change because this this name has the same reference as this name this has the same reference as this these are referentially the same so if something changes

if the thought changes then the thought has to be the sense not the reference the thought of accordingly cannot be the referent of the sentence but must rather be considered as the sense okay so having figured out what the sense of a whole sentence is it's the proposition expressed by that sentence the next question is well what's the reference what is the reference of a declarative sentence like like this or like this sha Carter is Rich Jay-Z is Rich we know what these names refer to they refer to the guy what do the whole sentences

refer to and once again when figuring this out frga is constrained by compositionality whatever this thing the reference is it's going to have to somehow be built up out of the references of all the individual parts and this gives Fraga an argument for why the reference of a declarative sentence like this is that sentence's truth value the truth value of a declarative sentence is just whether or not the sentence is true or false there's two possible truth values true is one of them false is the other you know this sentence Jay-Z is Rich that's true

its truth value is true so fragga thinks that this whole sentence refers to truth or the true that's what it refers to okay weird but he has an argument for why he thinks this has to be the case the reference of a whole declarative sentence has to be composed up out of the references of the individual Parts therefore any change in the reference of any of the individual Parts must result in a change in the reference of the whole sentence and whenever there is not a change in the reference of the individual parts like when

switching between three and four the references of all of these parts this name this this this name this this the references of all this stays the same when you switch from 3 to four so the reference of these whole sentences has to stay the same therefore whatever the references of these declarative sentences are they have to be the same these two sentences have to have the same reference because all of their parts have the same reference because Shawn Carter and Jay-Z are two different names with the same reference these two names are what's called co-referring

terms co-referring terms co-referring terms they refer to the same thing and so this test that frga has come up with is oh well if you swap out one term for another term that's co-referring right if you go from sentence three to sentence four if you do this swap you have to always preserve the reference of the whole sentence so then the question for Fraga is very simple what is something about these sentences that always stays the same whenever you swap out co-referring terms whenever you go from a sentence like three to a sentence like four

what stays the same every time well it's not the thought it's not the cognitive value the thought changes that's the sense and that changes it's the truth value whenever you swap in a different name for this guy the resulting sentence will always have the same truth value as these two and there it is hve hve is Rich that's true as well this is true this is true and this is true you're never going to be able to get a sentence that just switches in a co-referring term here and all of a sudden that sentence is

false whereas all of these remain true you're never going to get that because the truth value always stays the same when you swap in co-referring terms and that is fr's argument for why the truth value of a declarative sentence is the reference of that sentence and the same would hold if these sentences were false right if instead of saying sha Carter is Rich this sentence said sha Carter is enshrined in the Country Music Hall of Fame well then three would be false but then the same sentence where you swap in Jay-Z that would also be

false hve would also be false any sentence that is false of Shawn Carter is also false of Jay-Z is also false of hve swapping out these names with different senses but the same reference changes the thought or proposition but never changes the truth value at least that's true in the case of simple sentences like this more complex sentences with like quotations and things like that this won't work but we're not going to worry about that now let's just read fraga's argument for this conclusion if our supposition that the reference of a sentence is its truth

value is correct the latter that is the truth value must remain unchanged when a part of the sentence is replaced by an expression having the same reference and this is in fact the case right cool that's just what we were saying liit explains adbi Muto substitut P Salva veritate that's my best shot pronouncing the Latin it means equal are those which for each other mutually substituted can be saving the truth and what that means in comprehensible English is just that what it is to say that two things are the same thing is that every sentence

that's true of one is true of the other what else but the truth value could be found that belongs quite generally to every sentence concerned with the reference of its components and remains unchanged by substitutions of the kind in question frga is asking what could it that stays the same when you keep doing this substituting other than the truth value and the implied answer to this question though he doesn't say it in the paper the implied answer is nothing there's nothing other than the truth value that that fits this role and therefore the truth value

of a declarative sentence has to be its reference okay those are all the major claims in the paper there's a whole bunch of other weird grammatical stuff in the second half of the paper but no one ever talks about that and I'm not assigning that to my students so this video is done