Schema of the Categories of Understanding | Critique of Pure Reason

in this and in the next few videos on

this

critique of pure reason playlist i'm

going to be

going through

kant's discussion of

how his

table of the categories of understanding

can be

applied to our

our experience of the world to our

empirical sort of uh

experience of the world

and so i have written here so these are

his system of principles the axioms of

intuition which have to do with quantity

his anticipations of perception have to

do with quality his analogies of

experience which have to do with

relation

and the postulates of empirical thought

in general which have to do with

modality and these i will be getting

into

more in the next few videos in this uh

critique of pure reason playlist

but first i'm going to talk about uh

this idea that he has uh about the

schema or schemata

in plural

and so this is a part that

seems to be kind of uh skipped over a

bit in a lot of people's discussion of

of the critique of pure reason but i

find this interesting and i kind of want

to go through it and so

the schemata are

essentially the way that uh

sort of the connection between

the appearance uh so if we have the

appearance of an object out here so the

object

object appearance

appearance

and we also have concepts

concepts

so kant says that these are two very

different things so

you know the object in appearance is you

know this

uh i guess sort of

i mean it's this experience experiential

thing where a concept is

sort of this more abstract thing you

know the object is concrete and the

concept is

abstract and sort of you know almost lit

just like

like a sort of rule type thing and so

kant

wants to talk about how

the object can be subsumed so

subsumed is his word that he uses

subsumed under the concept

so you know we have that

that x is

p sort of uh proposition here and he

uses the example of

of a plate

plate

is

is circle

so you know like a dinner plate is a

circle and he says that the roundness of

the plate is intuited in

in this concept of circle

and so he wants to know

essentially so he wants to answer the

question

how is a pure concept

in other words the categories of

understanding

applied to appearances

so there must be some third thing

uh between between the appearances and

the concepts that allows this

subsumption to happen

and this will obviously be the

the schema

but that's getting a little bit ahead of

ourselves uh so

he says that this this third thing uh

has to be

uh both pure so the third thing

must

be

pure in other words not

not empirical so it's not something we

learn

so in

empirical it's not something we learn

through experience so it has to be pure

that's what kant means by

pure

and he says it also

must be

both

intellectual

intellectual which is sort of the

the conceptual version of it

and

sensible

and so it it must uh well it must

overlap with both the appearance and

with the concept uh kant says that he

uses the word homogeneous for this he

says that it must be homogeneous with

both

uh sort of the

the object appearance and also with

these sort of

you know

sort of rule-based or abstract concept

so it must be homogeneous with

both of those

so kant goes through this uh so i kind

of put it out in numbered form here it's

not numbered in

in the actual the actual book so he says

that time

is the formal condition of the manifold

of inner sense and connection of all

representations

uh and so that is essentially what we've

talked about before how

how we can be seeing this sort of object

here

so we have this object here that's in

our intuition

but we see it you know at

time t one and at time t2

and at time

t3 and so forth and so

the formal condition of the manifold of

inner sense and connection of

representation so we connect all these

representations and that's what

gives us sort of

the uh sort of the object in general not

just the object as we're perceiving it

at some

one

particular time

and so

thus

time contains a contains the a priori

manifold of intuition

so that's what i was just saying there

so time contains the manifold of

intuition where all these

points in time come together and

uh become sort of the the manifold of

intuition so this in

object and here is the intuition it is

it is a

manifold and that it is sort of all of

these diff representations at different

times coming together into sort of a a

single thing

uh so he says time is

is homogeneous with the categories which

is uh which is one of our our things up

here

that uh must be true of this so it's

homogeneous with

the categories because it is universal

and it is founded on an a

priori

rule

uh and so it's the the rule that uh that

of sort of

well it's the rule of time that time has

this sort of

structure here for us and it's a

structure

and it's a priority it's a priority in

that

humans

that people that a consciousness is what

brings time to bear on reality so time

is uh

not

necessarily how things exist in

themselves but it's an a priory rule

it's a thing that that our consciousness

actually

uh puts on to our experiences in order

for them to make sense to us

and so time is also

homogeneous with appearance because

time is contained in every empirical

representation of the world

and so

that's that sort of idea that

that we can't understand anything

without time and so time

is in every empirical representation of

the world

we have to understand things as being

things in

time

and so that satisfies this idea that

that time is homogeneous with both the

categories uh and with appearance which

is

uh the thing that that kant says

this third thing this schema that he

will come to call it needs

and so number five hence

application of categories to appearances

becomes possible by the transcendental

determination

of time

and so transcendental

uh determination essentially meaning

that it is

the thing that makes experience possible

so

i think i've talked about before a

transcendental

deduction is essentially saying that

this thing is true

what has to also be true in order for

that thing to be true and so the

transcendental determination of time is

sort of uh uh sort of the the the

faculty in human consciousness that

makes the experience of time

possible

and so he says that the transcendental

determination of time

mediates the subsumption of appearances

under categories

and so that is uh that is what we have

going on up here so

the appearances are subsumed

under the categories

using

time

uh and so we can sort of think about it

if we want to sort of

uh draw this as

uh sort of i guess a schematic for

for lack of a better word

appearances so appearances

appearances

go and they

they affect

the effect so kant uses both the word

affect and

modify

and modify

our sensibility our sense

sensibility

and so that's what sensation is so this

affecting or modifying is

sensation

so sensation so appearances and i guess

we could even say appearances of

of

objects uh so when they affect or modify

our sensibility or

you know our senses you know sight and

touch and things like that that is

sensation

uh and so this actually

gives content to

the categories the

catagories

or pure

concepts

pure concepts so this

idea that the concepts that the

categories of understanding are

pure concepts is important because it

means that they are not

obtained from

uh

from our empirical experience so you

know we can come up with like a concept

of dog for instance so we can come up

with a a dog concept

and that is

not a pure concept because it's a

concept that we get from

experiencing dogs so this is uh this is

uh

not

pure so the categories of understanding

are the pure

concepts

but the sensibility

uh so

gives

content

content

to

the categories of understanding and so

the categories like i said are these uh

much more abstract things and they are a

priori they're

they are they precede experience and so

you can't

sort of

you know picture what these categories

are in your mind

just

by themselves i mean you can't picture

them without the schemata essentially

and so

that's why we need these senses to

actually give content to them

and so the categories

uh also

so kind of going back here so the

the categories the

formal the

formal

pure

the formal pure conditions

conditions

so that's that idea that uh that the

things that we experience must

uh must sort of fit into these

categories they must sort of the

categories are what makes

uh or what makes our our experiences

possible and so the formal or pure

that the categories sort of put onto our

senses

so

this is the formal or pure conditions

under

which

which

the categories which the catagories

are

applied

are applied

this is what he calls the the schema

so these are the schema the formal or

pure conditions under which the

categories are

applied

and so he also

says that

ski

ma

tism

so schematism is the

procedure the procedure

of

application of application

and so

kant also says that the schema because

we

we see here that we have this

sensibility which is where we would have

the image

so the image would be in sensibility

we have the image here

image here kant says that the

the

image

the image

and

schema

and schema

must be distinguished

must

be distinguished

distinguished from each other they're

they're not the same thing uh the a

schema is not

an image so kant uses

the

the illustration so the image so we

could have the image

of

five dots so the image is five

dots so you look at that and you see

five dots

where the

schema

the schema would be sort of like the

concept

the concept of

of five so just like

if i say

five without actually showing five dots

you're not actually looking at something

that

is sort of an instantiation of five then

that would be

the schema

and so

uh the way i kind of uh tried to

try to conceptualize this is that if we

have our x

and i'm going to draw these spaced out

here for a reason x is

p so our proposition

so x would be kind of like the image so

the thing that you're actually looking

at

and p the predicate is our

is our concept and the is is sort of the

the

schema

and so the schema sort of

uh working from

from the concept to the image

sort of makes

makes our

our experience of the image

possible

and then sort of working in the other

direction

it connects

it connects

should be

connects

image

to so the schema connects the image to

the concept but it also

makes the image possible so the schema

is kind of like the is in the x is

p

where you know the concept and image

sort of work in sort of this uh this

mutual recursive

role

and so then kant uh kind of goes through

each of these things

uh in order so looking at the schema of

of quantity the schema of

of quality in the schema of relation in

the schema of

modality and sort of

lays out which what each of these is

uh

sort of more specifically

and so for quantity

for

quantity

he says

that the schema is the

pure image

of

magnitudes

of magnitudes

is

space so

space is sort of the the schema of of

quantity

and he says that the pure image of all

objects of senses in time

uh so he says that it's also the

pure

image of

all

objects

of

senses

in

time

uh and so the pure schema of magnitudes

uh he says

so the pure

schema

of

magnitudes of magnitudes

is

number so number is the

schema here for

magnitudes

and so we can think of it like this we

have the manifold the manifold

the manifold of

intuition

intuition so this is sort of the

the

objects

in

space

in space

uh and we also have the quantity so the

quantity

over here which

is the pure concepts of quantity so pure

concepts

uh and so that would be things like the

the unity in

plurality

and totality

and totality and so these are the

pure concepts of those sort of more

abstract things and so he says that the

schema

is

number

is number and so that is sort of what

connects

you draw these

as double arrows

uh so number is what connects sort of

the

the p the

uh objects in space or the sort of

experience the intuition

uh the the representation with quantity

the pure concepts so that is the pure

schema of

magnitude

so the next one is quality and so kant

uh talks about this so we can have

quality

and so this um

this corresponds

corresponds

to a

sensation a sensation

in

general

and so it indicates

indicates

indicates existence

and so this is sort of

you know

if if this

quantity is telling you how much of

something is there you know in terms of

the shape and size of it in

in the uh in our experience the quantity

is sort of telling us

what is there

and so i like to think of it in terms of

this sort of

uh formula where these sensation

the sensation

of something is equal to

the

reality

the reality minus

negation where reality and negation are

two of the three things under quality

and this we could even say is

the limitation the limitation

which is the third thing under quality

so sensation equals

uh reality

minus negation which means that that

if

if negation

if negation is equal to reality

meaning that the absence of the thing

there is what is actually

real uh then we can say

there

is

nothing that nothing is there because

the reality is a complete negation

uh but

we could all it could also be that the

that the that

we could have

negation

being less than

reality

and that would be sort of

i guess you could say like a smaller

faded existence so if something is

so say we have this sort of

very orange color

that would be like a high reality low

negation then we have

a color that's maybe a little bit less

orange that would be

uh

that would be reality but with a little

bit more negation so here

so here the sensation the sensation of

orange

is stronger than it is here uh and so

the reality minus negation it uh

so i guess we could say

reality minus negation

is uh greater here so we would say

reality one minus negation one in

reality two minus negation two and we

could say that

reality one minus negation one is

greater than reality 2 minus

negation 2. and once again this is you

know just

sort of my way of conceptualizing and

interpreting this

you know

you if you read this you could come up

with your own way of sort of having this

make sense

to yourself but this is uh

the way that

i i sort of interpret this this isn't

something that kant actually talks about

in

the in this chapter in this section of

the critical pure reason

um

and so we could also have the this

reality

uh happen in time

so we can see that this is in space at

this point in space

uh there is a higher sensation of orange

than at this point in space but we could

also

have it be that

say we have

rate here

and say this is time so we have at time

t one

and we have time

t2

and then time

t3 and we'll pretend that those all have

the um

same they take up the same amount of

space

but we could have orange at this time

and then you know we could have no

orange at the other times and so

the this

right here has a negation a negation of

orange negation

of

orange where this has a reality

a reality

of

orange and of course

we could even maybe

uh then put this one as being the sort

of less orange

right here

and so this one has sort of

uh sort of uh

less reality so less

reality

than

at time t2 but still has some reality of

orange and so this

uh this reality of some sensation and it

could be

any sensation it could be some smell or

taste or the feeling of of heat or

you know the the

the

loudness of a sound or something like

that and so

uh there is this sort of reality minus

negation which which is the limitation

of the sensation

uh and so that is the schemata of the

uh of the equality so

sensation sensation is the schemata of

quality

and then uh kant also

talks about the

the substance so substance

the

schemata of substance

uh is the permanence the

perma

men's

the permanence of

the

real the real

in

time and so kant has this uh very

aristotelian and scholastic idea

uh

that uh that there is a substance so

some substance and that would be kind of

like the subject in our s

is

p

and so if there is some substance and

then all of the p's all the different

p's we could have s is p one

is p two

is p

three these are all sort of accidents uh

of our subject

and the subject absent any predicates is

the is the

is the substance the subject without any

predicates is the substance and the

substance is what

all accidents are sort of predicated

as

and so

the substance is the thing that persists

so

p1 could be could be true

uh at

at time t1 where p2 could be true at

time t2

and p3 at time

t3 and so

even though this substance is changing

uh

you know

i mean we could think about it in terms

of like an object accelerating so an

object accelerating at t1 has some

velocity but then at t2 has some

different velocity but the object itself

is not changing

only

the things that we are predicating of it

uh are changing and so is the

the uh

the schemata or the schema of substance

is the permanence of

the real in time and so he says the real

in particular so it's the

the actual thing that uh that is there

the actual thing that we are sensing

uh so it's the permanence of the

of the thing that we're sensing we're so

at each point in time so if you see

a car accelerating at time t1 you might

see it at 20 miles per hour then at time

t2 you might see it at 21 miles per hour

you weren't thinking well that's a

different car because this car is moving

at 21 miles per hour or that other car

was moving at 20 miles per hour the same

car

can't be two things

at you know they can't be two things

and so it's the permanence of the reel

in time

and so

the car at t1 is going 20 miles per hour

that's

the reel at time t1

but it is you know all other miles per

hour are sort of negated at time t1 but

then at time t2

the

20 miles per hour is negated now the 21

miles per hour is real but we have this

permanence in time and that is the

substance the car at both t1 and t2 is

the same

car and so that is the permanence of the

reel in time

uh and so

uh

so kant also goes through

um goes through causality so causality

causality so the schema for that is the

succession

the succession

subject

so subject

to

to a

rule

and so succession is once again the sort

of t1 then to t2 then to t3 but uh he

says that this is subject to a rule

because it's

it's uh when some state of affairs at t1

causes

causes some new state of affairs

at t2 and so we can think of you know

there we have two objects here this

one's moving this one's sitting still

and then at

at t one and then at the next point we

have

this object sitting still and now this

one moving at

t two and so the succession

uh from t1 to t2 according to this rule

of causality uh so the succession

uh the succession subject to a rule and

so

i mean we'll go into that quite a bit

more when we get into sort of the

the principles uh but this is the schema

the schema of causality that

one thing happens after another because

of some rule

so that is causality

and then he has what he calls community

community

and so substance causality and community

are all under his uh

his relation so this

uh so i could even uh i guess

write that this is

that this is

relation here this was all under

relation here

and so community is uh

is the simultaneity

the simulator

of objects so if we are looking

uh if we are experiencing something

there is an object here sort of to our

left of field of vision

sort of the upper left and then this one

down here to the bottom right of her

field of vision and we're seeing both of

them at the same time and so they are

simultaneous

and so that is his schema of

community

and so then he has the uh

so we could write for this one the

modality so now we're moving on to one

of the other categories which is

modality and so for this one uh

there is the possibility

possibility

so the schema for possibility is the

agreement

the agreement

of

of

synthesis

of synthesis

of different i'll just write diff here

representations i'll just write rep

in

time

and so that's sort of that thing i was

talking about before where if we have

some object

if we have some object in our intuition

so this representation of an object

we are seeing it at time t one we're

seeing it at time t2 we're seeing it at

time

t

3 and so the agreement of the synthesis

is where we take all of these things

together and sort of synthesize it into

this single object

and so that can also

uh so the reason there's possibility is

because that object could change in time

and so at time t one

the object uh is

for t1 is actual at t1 in some way but

then at t2 it could be actual in some

other way and so at t1

the object at time t2 was the possible

object and so

not the object as it actually is but the

possible object and so that brings us to

actuality to actuality

to actuality and the

schema for that is the existence

the existence

at

a

determinant

a d

d

terminate time and so that's what i

meant where he said at t at time t 1

there is some representation of the

object that is actual

but at time t 1 the representation of

the object at time t 2 is

a possible

representation and so the existence of

it at time t1 when it's actual is the

existence at the determinant time where

t1 is the

determinant time

then there is also

necessity necessity which

is uh the

existence the existence

the

existence at

all

time and so an unnecessary existence

would be

essentially you know it would be

something like like

two plus two equals

five this is sort of this timeless

five i got my

my 1984 on the mind apparently two plus

two equals four

uh is is something that is true at all

times so

this is just a a sort of necessary truth

that uh just by definition this is true

uh and so

that is uh the existence at all time

so i wanted to conclude this video with

this sort of uh quote at length from

this section of the critique of pure

reason

because i think this sums up what uh

what kant was trying to do in this

part of the book

so he says we have thus seen the

schematism of the understanding by means

of a transcendental synthesis of

imagination

and so imagination remember is

uh that sort of faculty that he talks

about that sort of uh

can call up all of the different

representations and bring it together

into

uh a unified concept

amounts to nothing else than the unity

of the manifold of intuition

in inner sense and therefore

indirectly the unity of a perception as

a function

corresponding to inner sense

and then down here so

this is the next paragraph

these schemata of the pure concepts of

the understanding therefore

are the true and only conditions

under which these concepts can gain a

reference to objects

that is a significance

and thus the categories are in the end

of no other but a possible empirical

use

for as the grounds of an a priori

necessary unity because of the necessary

union of all consciousness in one

original app perception

they serve only to subject appearances

to general rules of synthesis

and thus to render them capable of

thoroughgoing connection to experience

so this

is that idea that

we need the the categories of

understanding in order to

have experience the the categories of

understanding are what make experience

possible

so all our knowledge is contained within

this whole

of all possible experience

and transcendental truth which precedes

all empirical truth and renders it

possible

consists in a universal reference to

that possible experience

and so all our knowledge contained

within this whole a possible

experience and so

uh that's he's talking about how the the

categories of understanding make

experience possible here

the transcendental truth

the transcendental truth which is uh the

categories of understanding

which precedes all empirical truth and

renders it possible

so the categories of understanding uh

he's saying is a priori it's it's their

before experience

and renders experience possible

consists in a universal reference

to that possible experience the

universal reference are the the schema

that we've been talking about

and so that is uh

yeah that is kant's idea here of the

the schema which is the way

sort of the the this mediating

this mediating third thing he calls it

that subsumes

uh the objects of appearance so

so our our experience here under these

concepts

and so in the the next

probably few videos i i'll probably do

the axioms of intuition and the

anticipations of perception

in a single video

then the analogies of experience will

probably take at least one its own video

probably

possibly two or even more uh because

this is sort of the the thing that kant

is really interested in because it has

to do with things like causality and

so forth which is you know kind of a big

thing in in metaphysics and

and epistemology and stuff and it's it's

very important to kant's project here

but anyway

uh i will get into these um

these principles of the understanding

which is

sort of

uh

how the concepts are applied

uh i guess you could say via the scheme

this this schemata so how they are

applied so the the schemata is actually

sort of the

the i guess faculty of applying the

uh the categories of understanding of

applying the pure concepts and so the

principles

is sort of i guess you could say the

the formula for actually

applying these uh these concepts these

pure concepts or categories of

understanding to our experience and so

that is what i will be talking about in

the next few videos

i hope you found this video

helpful and interesting

in your

in your quest to better understand kant

and i will see you in the next video

you