Wittgenstein's Tractatus: Understanding Propositions and Logical Pictures

in the previous video we finished the propositions starting with two and so in this video we start with proposition

three the logical picture of the facts is the thought

here we have our first indication that for wittenstein a thinking and language are so closely connected as to be almost

indistinguishable we talked in our previous videos about wittgenstein's picture theory of

language or meaning according to which you know we we say something about the world

by making a picture of the world by giving a an image of the world and for us to do that

what we needed was to have something like a a scale model maybe but it could also just be a sentence

that on the one hand had elements that corresponded to the elements of reality that we wanted to picture

so the sentence maybe contains words that correspond to things in reality or the scale model contains objects that

correspond to other objects in reality so that's the first thing that we need and that the second thing that we need

is a certain variability a certain freedom in putting these different elements together

so that we can picture different possibilities in the world the different ways in which we can set up the scale

model corresponding with different situations in the real traffic or the different ways in which we can

put words together into sentences corresponding with again different situations in the real world

so when i think something

that thought is going to be a logical picture of the facts so that thought 2 is going to have this sort of picturing

relation to reality it contains elements that correspond to things in the world and it has certain degrees of freedom

that correspond to the possibilities of the world now

what wittgenstein says is that the logical picture of the facts is the thought

and so that may prompt the question well what about an illogical picture of the facts right what about a picture that is

not logical well we've already seen that wittgenstein logical form is what

something must have in order to picture reality at all right logical form is what every picture

has without a logical form a picture couldn't be a picture of the facts or a picture of reality

and so the answer uh to any question about well what about illogical pictures is that there are no illogical pictures

right there's no such thing as an illogical picture and if there's no such thing as an

illogical picture and if the logical picture of the facts is the thought then of course there is also no such thing as

an illogical and that in fact is

something that wittgenstein is going to express in the 3.0

so here is um 3.001 a state of affairs is thinkable

what this means is that we can picture it to ourselves so to be thinkable and to be picturable are the same thing

or here 3.02 a thought contains the possibility of the situation of which it is the thought

what is thinkable is possible too so what is thinkable

is possible too what is thinkable is also possible this

that the thinkable or conceivable is the same thing as the possible is a

much contested claim in philosophy so there is some it has some like immediate plausibility

uh here's a way to see an immediate plausibility suppose that somebody asks me to do this somebody says well i want

you to picture the following thing i want you to picture the situation in which it rains

and doesn't rain right i want you to picture the situation in which it rains and doesn't

rain now of course that is a logical contradiction right to claim that it

rains and doesn't rain it's something that that can't happen it's impossible and when i try to picture this situation

i find myself in a bind right should i sort of picture raindrops coming down

well yes and no well it's hard to see how to proceed here so these kinds of cases uh suggest to us

that yeah you know the thinkable and the possible seem to be the same thing

but there are other situations that might bring us to different ideas so here is something that seems eminently

thinkable it seems very thinkable or conceivable that i flap my hands like this and then fly up

into the air right why not i can write a story about that and it would be completely intelligible

i could even claim that i can do this right i could go to people and say i can fly into the air just by flapping

my hands so that seems thinkable and yet of course people won't believe

me and they won't believe me because it's impossible right no one can do that you can't do that it is not possible

so that seems to be a situation where possibility and thinkability are not the same thing

here's another example a famous example from philosophy according to some philosophers it is thinkable

that there are people just like us with bodies just like us and brains just like ours

with the same processes going on in those brains and yet these people are not conscious

they are so called philosophical zombies right they have the same bodies that we have the same brains that we have

but they are not conscious and these philosophers would say well that is thinkable

it's conceivable we can you know it makes it makes sense to describe this and therefore it is possible

and other philosophers say no no the fact that it's thinkable does not mean that it's possible

and so as i said this is a at least a contested claim right the claim that the thinkable and the

possible are the same thing so why is wittenstein saying this here well one way to understand why

wittgenstein is saying this here is that wittgenstein turns out to have a very strict notion of possibility according

to wittgenstein all possibility is logical possibility and so i take it that according to

wittenstein it is possible that i fly up into the air by flapping my hands right that doesn't that that is we can

picture it to ourselves right we can easily picture it to ourselves and so it is possible

if i want to claim that it's impossible i am making a mistake the only possibility and necessity are

logical possibility and necessity but this is a theme that we are going to meet again only at the very end of the

tractatus um when wittenstein is going to among other things criticize the idea of

a sort of law of causation that tells us you know what is possible and what is not possible

okay so the kind of possibility that

wittgenstein seems to be thinking about here is logical possibility and for wittgenstein that is the only kind of

possibility so if you got confused by three point zero two this is the background against which we have to

understand it okay van wittenstein goes on to explain you know that

logic um is sort of the bound of thinking that there's no such thing as an illogical

thought so again here is wittgenstein we cannot think 3.03 we cannot think anything

unlogical for otherwise we should have to think unlogically it used to be said that god could create

everything except what was contrary to the laws of logic the truth is we could not say of an

unlogical world how it would look to present in language anything which contradicts logic

is as impossible as in geometry to present by its coordinates a figure which contradicts the laws of space

or to give the coordinates of a point which does not exist right there is no such thing according

to wittenstein as an illogical thought that is a thought which sort of is a thought

and so pictures reality and at the same time doesn't fit in logical form doesn't have the form

demanded by logic it rains and it doesn't rain is not an illogical thought

because it's not a thought at all um

it's a sentence but it also doesn't express a thought there's no thought expressed by the sentence it rains and

it doesn't rain we cannot think anything illogical because that would be to picture the

unpicturable or to picture that which cannot be pictured or maybe because if i say it's to picture that which cannot be

pictured that seems to claim that there is something that cannot be pictured um

maybe that's not the right way to say it right i mean we're not claiming that there are these

illogical things which unfortunately we cannot think um it's more that you know an illogical thought is a picture that

is not a picture and that just doesn't make any sense all right

let's move on to 3.1 in the proposition the thought is expressed perceptibly through the senses

in a proposition a thought finds an expression that can be perceived by the senses

so here the german word for proposition is and that's could also be translated as

sentence and possibly a translation by sentence makes it easier to understand that wittenstein is here

talking about something that we can hear or see this is in fact what vickinstein tells

us in 3.11 that we use the sensibly perceptible sign

sound or written sign of the proposition as a projection of the possible state of affairs

so what we are what within stan is going to think about now

is language in the sense of signs in the sense of something that you can speak or that you can write

and what he's going to want to understand is what that is right what is this kind of sign

when does a sign become a sign when does it become a sentence those are some of the questions that

wittgenstein wants to ask because obviously not just any you know random string of sounds

uh is a sign or a sentence

and not just any sort of string off of marks on a paper is a sign or a sentence and so we need to know something more we

need to hear what is needed for

a string of sounds or a string of marks on paper to become something that you know could be the sign of a sentence

well let's read 3.11 again we use the perceptible sign of a

proposition as a projection of a possible situation projection that's something i want to

zoom in on but first i want to read on 3.12 and 3.13 the method of projection is to think of

the sense of the proposition i call the sign with which we express a thought a propositional sign

and a proposition is a propositional sign in its projective relation to the world

a proposition includes all that the projection includes but not what is projected

or as ogden says to the proposition belongs everything which belongs to the projection but not what is projected

therefore the possibility of what is projected but not it is itself not what is projected

itself in the proposition therefore its sense is not yet contained but the possibility of expressing it

in the proposition the form of its sense is contained but not its content okay projection uh and then i'll zoom in

on some of these these phrases that i've just read out in order to find out what's going on here and in order to try

to interpret what's going on here projection is basically the kind of relation that i have already been

discussing several times right the kind of relation where we say well these elements of the sentence correspond with

these elements of reality and these different ways of putting the elements together in a sentence

correspond to these different ways that the elements can be in reality right if i if i make those links

well that is the method of projection right that is how we get from the world to the sentence or from the sentence to

the world okay now let's read

3.13 again to the proposition belongs everything which belongs to the projection

but not what is projected what does that mean not what is projected

here's one way to understand i'm going to to talk about two two ways to understand this here's the first way to

understand that the first way to understand it is this it's to say okay for something to be a

proposition for something to be a sentence is of course not just for it to be

a bunch of sounds or a bunch of signs it's something else what we need is

sounds or signs yes sure of course something like that um

but especially we need two things more we need first of all a grammar and a grammar is a set of rules that indicates

how this sentence um well it indicates the rules according to which sentences can be constructed

something and this is a crucial insight of wittgenstein's something can be a sentence only

if it is part of a much larger set of other sentences all of which together are structured by

grammatical rules it is like the scale model a particular position of the scale model

can be a you know a an indication of a situation in reality a picture of a situation in

reality only because it lives so to speak in a much larger space of other possible ways that

the scale model could be put together right it's only because we can change the positions of these little cars and

buildings and people and so on and so forth that any of the ways that we can put

them together can be a picture of a particular reality and this is true with sentences in

general right the cat is on the mat to take this standard example of a of a sentence

often used in philosophy and linguistics the cat is on the mat is a sentence only because it lives

in a realm of of sentence parts and grammatical rules that indicate that you know in this case for instance the cat

can be taken out and replaced by other kinds of nouns like the dog is on the mat the baby is on the mat

also that the mat can be taken out and replaced by other nouns the baby is on the cat the cat is

on the baby the mat is on the dog um is on or maybe even is and on separately have their own grammar and

can be replaced by certain other things and so on and so forth right it is only because the sentence the cat is on the

mat lives in this realm of variations that it can in fact

picture a realm of possibilities or a particular possibility in reality namely a cat

sitting on a mat which is one among many possibilities right something else being on the mat the cat being somewhere else

and so on and so forth so that's one thing that we need we need a grammar which basically gives us a

realm of variation which corresponds to

the realm of possibilities that we are trying to uh to picture and then the second thing that we need

is this piece-by-piece relationship right where elements of the sentence correspond to

particular things in the world that we want to picture right we have to make sure that the cat actually

um points to that cat out there in the world that this this phrase actually corresponds to a particular thing in the

world so those are the two things and one way to read

now the claim that to the proposition belongs everything which belongs to the projection but not what is projected is

this it is to say well the projection is all the stuff i've just been talking about it's the grammar

and the relations of elements of the language to things in the world

and what doesn't belong to the proposition is what is projected and those are just the things in the world

right the cat doesn't belong to the proposition the mat doesn't belong to the proposition and so on and so forth

so that's one way to read this but it's maybe not the best way to read it and to see that let's look again at

the last sentence of 3.4 13. in the proposition the form of its sense is contained but not its content

well it certainly seems that if i have the cat is on the mat and i have its grammar

and i have the relation of all the elements of the sentence two things in the world to the cat and the mat and so

on then i have not only its form but also its content right there doesn't seem to be anything

formal about this grasp of the sentence i grasp the full content and so maybe wittgenstein is saying

something else and i think that indeed wittgenstein is saying something else my preferred interpretation of what

wittenstein is doing here is to say that what belongs to the projection is and so what belongs to the

proposition as such right what makes it a proposition at all is just the grammar and not the

relations to particular things in the world so in order to recognize something as a

proposition at all we need to see it as something that belongs to this realm of grammatical

possibilities and then we can see that this realm of grammatical possibilities

has the right structure to picture this realm of possibilities in the world and that is why we can say that in the

proposition its sense is not yet contained but the possibility of expressing it

so this grammar because it fits this realm of possibility in the world can express this realm of possibility in the

world it shows the possibility of expressing it but it doesn't yet contain its sense

and so something is a proposition if it has this grammatical structure of which it is a part

um but of course it only becomes really meaningful if we do something in

addition which is linking the elements of the sentence to things in the world okay so that's i think the best way to

understand why ruthenstein is saying what he does here it is maybe not the most important thing

because most of the time in fact almost all of the time when we are interested in certain

sentences or propositions we are going to be interested in senses of propositions where the identification

or or the link with specific things in the world has already been made so usually we have of course both a

grammar and a link to certain things in the world but okay maybe there are certain cases

where it makes sense to separate the two and uh in fact there are maybe a few points later on in the trichtardus where

it's going to be helpful to understand that there are these two things that maybe wittgenstein talks about sentences

and propositions already if we just have the grammatical structure and maybe in a sense still have to make

the connection to particular elements of the world let's move on to

3.14 what constitutes a propositional sign is that in it its elements the words

stand in a determinate relation to one another a propositional sign is a fact a proposition is not a blend or a

mixture of words a propositional sign is a fact what does that mean well what with constraints

pointing out is that only a fact can picture a fact it is the fact that

the cat is on the mat the fact that these elements

are put together in this way right the fact that these elements are put together in this way

pictures that the cat is on the mat it is the fact that the elements are

put together in a certain way that pictures that the corresponding things in reality

are put together in a certain way it's only because

a sentence is a fact because it's not just a bunch of things thrown together but it's a

bunch of things put together in a particular in an articulate way that makes it able to picture a um

effect in reality so the propositional sign is a fact in fact wittenstein tells us a little

later on in what i think is a pretty wonderful note 3.14 that we may be it may be easier for us

to understand this fact nature of sentences we don't think of it in terms of words

but if we think of it in terms of objects so there he tells us that the essence of a propositional sign is very

clearly seen if we imagine one composed of spatial objects such as tables chairs and books instead of written signs

then the spatial arrangement of these things will express the sense of the proposition

so for instance there is absolutely nothing that can stop me from saying that this thing this pen corresponds to

the cat and this thing my telephone corresponds to the mat

and that the spatial relation of the pan to the telephone corresponds to the basically same spatial relation of the

cat to the mat and then what i have here is the propositional sign

that expresses the thought that the cat is on the mat right this this

situation this state of affairs this fact this fact that the pen is on the telephone

expresses that the cat is on the mat and this this fact that the telephone is on the

pen expresses the fact that the mat is on the cat and so on and so forth so that's

a way to think about that it's a way to see that that propositions themselves are facts are already structured right

they are put together in a specific way and they could have been put together in another way and these other ways

correspond to different ways that the world could have been and therefore wittgenstein can say in

3.1432 and this may be confusing at first but it's basically a way of repeating what i

just said that we should not say the complex sign arb

says a stands in relation r to b right as if the sign

says something where the fact nature of that sign is completely obscured right we cannot read from this the

complex sign blah blah says blah blah we can't see that the sign is a is a fact instead we should emphasize this fact

nature and say well that a

the sine a right that the sine a stands in a certain relation to the sine b says that

arb that the sign the cat stands to a certain relation to the sign the mat says that the cat is on the map

that the sign my pen stands in a certain relation to the sign my telephone says that

the cat is on the map that's basically what wittenstein is abstractly saying in 3.1432

okay let's check out the 3.2s for a while in propositions thought can be so

expressed that to the objects of the thoughts correspond to the elements of the propositional sign

or in a proposition a thought can be expressed in such a way that the elements of the propositional sign

correspond to the objects of the thought well basically the same thing the objects of the thought are the

things that the things in the world that my thought is about right the things in the world that my

thought is about in a proposition thoughts can be so expressed that 2d objects of the

thoughts correspond the elements of the propositional sign so my sign has elements it has parts and those parts

correspond to the things in the world that i'm thinking about yeah okay that's exactly what we've

already been talking about several times right when i say the cat is on the mat

or when i think the cat is on the mat um you know i'm thinking about the cat and

i'm thinking about the mat and in my sentence there are elements the cat and the mat that correspond to these things

that i'm thinking about so much is clear the one thing that might give us pause

here in 3.2 is wittgenstein's use of the word can in propositions thoughts can be so

expressed why can doesn't it always have to be this way no wittgenstein would say

usually in fact maybe even always in our normal uses of language there are no

elements of the propositional sign that really express the objects of the thought

and that is because the real objects of the thought the things that my thought fundamentally

is about are the simple objects the simple things that form the substance of the world

that we learned to think about in the propositions too the cat and the mat are certainly not

among the simple things in the world and so the signs that or the parts of my sign the cat and the mat certainly do

not correspond to simple things in the world but wittgenstein says at least in

principle it ought to be possible to analyze any sentence

to the point where we are talking about the simple things in the world and then in our sentences

those simple things would have to be expressed right there would have to be signs parts of the sentence

corresponding to the simple things that i'm talking about and that is why wittgenstein can say in

3.201 these elements i call simple signs and a proposition completely analyzed

so whitney says here thinking through something that has to be possible according to him it has to be possible

to take any sentence including something like the cat is on the mat to analyze it completely until it talks only about

simple things and then that analyzed sentence is going to have paths

that correspond or stand for those simple things and those parts are simple signs

and what is the nature of those simple signs well 3.202 tells us the simple signs employed in propositions are

called names right because what do they do well the

only thing that those simple signs do is they correspond to a particular thing a particular object and of course that is

precisely what a name does a name corresponds to a particular object

in naming an object we give it a sign that corresponds to it so

according to wittgenstein any meaningful sentence can be analyzed until you get to the simple signs which are the names

of the simple objects that form the substance of the world here's something that wittgenstein says

3.221 objects i can only name signs represent them i can only speak of

them i cannot assert them a proposition can only say how a thing is not what it is

propositions can only say how things are not what they are

well why does he say that here's the pan right and it seems that i can certainly say what it is

it's a pen aha wittgenstein would say well that is already enough to prove that what you

are holding is not a simple object

right because what are you saying when you're saying that this is a pen well you're saying you're describing it

by explaining what kind of complex it is right a pen is something that is built up out of certain constituents

in a certain way and so to say that something is a pen is to describe it as a complex of a certain

kind and of course a complex is something that is built up of objects that are

simpler than it is itself furthermore a complex is always contingent it is always something that

also could have not existed right it is possible

for the constituents of my pen to form a different complex or maybe to form no complex at all and be scattered

through the world and then this pen will no longer exist right so yes of course you can say what

something is if that thing is a complex but you can't say what something is if that thing is a simple object simple

objects you can only name that is the meaning of 3.221

and then we come to an incredibly important claim 3.23 which sort of condenses an entire

argument that we get sort of stitched together out of different parts of the tractatus but here it is condensed into

one little sentence with with almost no explanation but we need to understand it in order to understand what whiskey

design is doing here the requirement that simple science be possible is the requirement that sense be determinate

the requirement that simple science be possible is the requirement that sense be determinate wittgenstein is obviously

thinking about a an objection here right he has said that every sentence can be analyzed until you get the simple signs

that name simple objects why would we believe him why would we believe him right i mean he

can't give us the analysis he can't give us even any examples why would we believe this

here is wittenstein's argument extremely compressed well he says why do i require that

simple size be possible why do i claim that it must be possible to analyze all sentences into simple signs

because only if you require that is sense determinate okay what does he mean

well he means this any sentence any meaningful sentence which is any sentence

um pictures a possibility right it's a picture of a possible state of affairs

okay it's a picture of a possible state of affairs but

whether a state of affairs is possible cannot depend on what is actually the case

right whether something is possible doesn't depend on what is actually true and so whether a sentence is meaningful

whether it really pictures a possibility cannot depend on whether anything else is true

right whether something is meaningful can't depend on what is true

but names are only meaningful or maybe i should say sentences which contains names are only meaningful if those names

actually correspond to something like the claim that

kabul lives in amsterdam well if shaq kabubl is not the name of anything and i'm

assuming that it's not the name of anything then this sentence

is not a picture of reality it it i do not paint any picture of reality by telling you that shaq kabubl

which is a name with no referent lives in amsterdam so in order for a sentence to be

meaningful a sentence with names those names actually have to refer to something

and so if whether a sentence is meaningful cannot depend on any truths well then it had better be the case that

whether a name refers to something cannot depend on any truths but names of complexes

only refer to something if certain other things are true suppose that i take this pen and i name

this pen and i name this pen richard

hi richard any sentence about richard is meaningful only

if richard exists that's how names work but richard only exists

if it's true that certain constituents of richard form a particular kind of complex

right it could easily have been the case that richard did not exist and so whether any sentences about

richard are meaningful depends on

whether certain things are true and that's not allowed when we are talking about sort of the real names

and so the real names that we need in order for our language to sort of really be about the world to really connect to

the world must be a different kind of name it must be a kind of name that is not

the name of a complex which might also not exist these must be the names of the

elementary things the simple things which exist no matter what right which form the substance of the world

and so here in 3.23 we have extremely compressed this argument that

it must be possible to analyze sentences into the names of simple things because we need names for language to connect to

the world we need meaning to be independent of truth

and we can only have names that are meaningful independent of truth if they are the names of simple things

and so the very nature of language and the nature of the language world relationship requires it to be possible

that language is analyzed into simple signs that are the names of simple things that form the substance of the

world okay 3.24 is actually a bit of explanation of

that even though it might not be obvious if you don't already have the argument sort of before you

because that's where where wittenstein tells us something about complexes right a complex can be given only by its

description which will be right or wrong i can describe the pen but i can't name it

that wouldn't really be a name a proposition that matches a complex will not be nonsensical if the complex

doesn't exist but simply falls if i talk about this complex if i talk about this pen and it doesn't exist i

will simply have set something false if i say my pen is black um and in the meantime somebody has

destroyed my pen that will be simply false because what i'm really saying is these and these are these

simple things are in this in this complex and the complex is black but they're not in that complex and what i

say is not nonsensical but simply false okay so vikkistan makes a few further claims

he tells us that a proposition has one and only one complete analysis

he tells us that names cannot be analyzed further that they are primitive signs um and i think we can sort of see

how all of that fits into the story that i've been telling you so

so much for the 3.2s in the next video i will go on at 3.3 and look at the rest of the threes with

you