Full Transcript

Outer Limits of Reason. Chapter 1 --- Introduction

35:15932 summary words · ~5 min readEnglishBy Noson S. YanofskyTranscribed Sep 1, 2026

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Summary

Scientific and technological maturation enables reason to formally discover its own inherent boundaries, primarily through paradoxes, self-referential structures, and reductio ad absurdum.

Understanding what formal systems, mathematics, and logic cannot prove or compute prevents wasted effort on impossible problems and reveals the boundary conditions of rational thought.

Section summaries

Cumulative Progress and the Scope of Reason's Limits

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Yanofsky introduces the course based on his book, emphasizing that traditional education focuses exclusively on what science and mathematics can achieve, whereas this curriculum explores what they structurally cannot do. He contrasts the cumulative, iterative advancement of science and technology—where contemporary artifacts supersede older ones—with the timeless nature of art, literature, and ethics, where ancient works like Shakespeare or the Book of Genesis remain foundational. Because science has advanced significantly, it has reached a mature stage capable of systematically mapping its own boundaries across language, philosophy, computing, and mathematics.

Traditional curricula emphasize scientific capabilities, leaving systematic limitations untaught.
Science accumulates linearly and supersedes past tools, while humanities produce enduring, non-obsolescent insights.
Technological maturation is the catalyst that allows scientific disciplines to formalize their internal constraints.

Establishes the foundational epistemological framework and motivation for the entire course.

Definitions of Paradox and Fallacious Deductions

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The lecture categorizes the term 'paradox' into multiple definitions: seemingly contradictory statements that are factually true (like standing being more fatiguing than walking), assertions contrary to received opinion, and assertions leading to contradictions. Yanofsky demonstrates an invalid deduction by walking through an algebraic proof claiming two equals one using a factored difference of squares. He demonstrates that the apparent paradox stems entirely from an illegal operation—dividing by zero when assuming equal variables—and recounts Bertrand Russell's quip demonstrating that false premises permit proving any absurdity.

Paradoxes fall into distinct categories ranging from counterintuitive truths to deductive fallacies.
Invalid mathematical deductions (such as division by zero) generate pseudo-paradoxes rather than real limits.
From a false premise or an invalid deductive step, any contradictory conclusion can be derived.

Covers basic algebraic fallacy mechanics (dividing by zero) that mathematically literate viewers can skim.

Valid Paradoxes, Self-Reference, and Limit Piggybacking

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Yanofsky isolates the core definition relevant to the course: an assertion that generates a contradiction through rigorous, valid deductive reasoning. This framework serves as a proof by contradiction (reductio ad absurdum) indicating that the starting hypothesis must be rejected. He outlines self-referential paradoxes, such as 'this statement is false', alongside the concept of 'piggybacking' limits, where establishing an impossible lower baseline demonstrates that more complex derivative tasks are equally unattainable.

Formal paradoxes use valid deductive logic to disprove untenable initial assertions.
Self-referential statements are a primary mechanism generating legitimate logical contradictions.
Piggybacking enables proving the impossibility of hard problems by reducing known impossible baselines to them.

Explains the primary logical methodology (reductio ad absurdum and piggybacking) used throughout the series.

Ontological Realism vs. Linguistic Contradiction in Science

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The discussion turns to where contradictions can and cannot exist in reality. The physical universe operates strictly without contradictions, as physical entities cannot simultaneously possess and lack the exact same property. Conversely, the human mind and natural language constantly produce internal contradictions, conflicting desires, and opposing opinions. Science and mathematics represent the specific domain of human language engineered under strict constraints of non-contradiction so they can accurately model the non-contradictory physical world.

Physical reality is strictly non-contradictory in its ontological states.
Human psychological states and natural language tolerate pervasive internal contradictions.
Mathematics and science enforce absolute non-contradiction to maintain fidelity to physical systems.

Provides a crucial philosophical distinction between mental/linguistic constructs and physical reality.

The Mechanics of Humor and Preview of Language Limits

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The lecture concludes by examining the structural kinship between formal paradoxes and humor, noting that jokes, puns, and one-liners rely on establishing a rational premise and abruptly pivoting to a contradictory or self-undermining punchline. Yanofsky illustrates this using jokes from Woody Allen, Steven Wright, and Groucho Marx, emphasizing how Groucho Marx's club membership joke acts as a self-referential paradox. Finally, he previews the upcoming chapter on the foundational limits of human language and challenges viewers to formulate their own definition of reason.

Jokes and puns mimic formal paradoxes by driving rational setups into sudden logical clashes.
Self-referential humor shares the exact formal structure of classical semantic paradoxes.
Defining reason requires establishing clear demarcation lines between rigorous systems and subjective discourse.

Features lighthearted comedic examples and previews upcoming lectures without introducing new formal mechanics.

Key points

Cumulative Knowledge vs. Timeless Humanistic Inquiry — Unlike art, literature, and ethics, where classical expressions remain enduringly relevant without iterative replacement, science, mathematics, and technology build cumulatively on prior breakthroughs until they reach their structural limits.
Valid Deductive Contradiction as a Limit-Detection Tool — The operative definition of a paradox in foundational logic is an assertion that leads inexorably to a contradiction via entirely valid logical deductions, functioning as a formal reductio ad absurdum to prove the initial assertion false.
Ontological Consistency vs. Linguistic Contradiction — The physical universe cannot contain contradictions, whereas human minds and natural languages routinely harbor them; science and mathematics exist as a subset of language constructed under strict non-contradiction rules to accurately model physical reality.
Structural Isomorphism Between Paradoxes and Humor — Jokes and comedic paradoxes operate on the same formal architecture as logical limits: an initial rational premise followed by valid associative reasoning that terminates abruptly in an impossible or self-undermining contradiction.

“science technology has progressed to the point where it's able to see its own limits it's able to see it can do this but it can't do that” — Noson S. Yanofsky

“what a paradox is is kind of like a test to see if an assertion is true or false” — Noson S. Yanofsky

AI-generated from the transcript. May contain errors.

0:02

hello this is nastinowski the class is

0:04

the outer limits of reasoning

0:06

and this is a very interesting classes

0:10

the first tape of this class

0:11

and so i'd like to spend the whole day

0:13

just going through what we'll see in

0:15

this class

0:15

why it's important um the book is the

0:18

outer limits of reason

0:20

what science mathematics and logic

0:21

cannot tell us

0:23

and we're going to um

0:27

we're going to do chapter one today okay

0:31

so let me tell you what this class is

0:33

all about

0:41

the reason why this class is interesting

0:42

is because for your entire

0:44

educational life you've been learning

0:46

what science and math

0:47

and technology can do what this class

0:50

does

0:50

is tells you what science and math and

0:52

technology cannot do

0:54

okay so for that alone it's an

0:57

interesting class

0:58

and worth doing

1:01

when i usually do this class in

1:05

with people i usually do a nice trick

1:07

with a

1:09

with a a chess board

1:13

and i put down some dominoes on a

1:15

chessboard

1:17

i can't do it has to be done with people

1:18

and it has to be you know a challenge

1:20

and we have a lot of fun and we have

1:22

laughter and giggling about it

1:23

but basically you can read about it in

1:26

the beginning of the book

1:27

it's a very nice challenge it's a very

1:28

nice interesting thing and the point is

1:31

that it's something that cannot be done

1:34

okay it's a it's a puzzle it's a

1:36

challenge that

1:38

that there's no solution to it and we

1:40

get a feel for something like that

1:43

okay um

1:48

this is a short introduction to what the

1:49

class is all about

1:51

and the idea is that science technology

1:54

has progressed to the point where it's

1:58

able to see its own limits

2:00

it's able to see it can do this but it

2:02

can't do that

2:03

it can do this but it can't do that and

2:05

so this is a course that

2:06

goes through many different areas of

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science and shows

2:09

what can be done what cannot be done and

2:12

for that

2:13

it's it's rather interesting so we have

2:16

to back up a little and talk a little

2:18

bit about science technology

2:21

and so i want to make this a point

2:24

and it's as follows science

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builds on itself in other words if i

2:30

want to

2:31

make a better cell phone what i should

2:33

do is i should

2:34

look at the previous cell phones and i

2:36

should adjust and make it better and

2:38

fix certain things to make it faster

2:41

more exciting do more features etc etc

2:45

same thing if i wanted to make a better

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train what i do is i'd study all the

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trains that were made

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till now and i would

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build on that i would go further on that

2:57

okay

2:58

in contrast to science and technology

3:00

and mathematics

3:01

we have other things other areas that we

3:04

study

3:05

and those are like art literature

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ethics philosophy things like that and

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that

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well it builds on it on itself but

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in a more subtle way okay so let's talk

3:19

about let's say literature

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if i was to ask you who was the greatest

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um

3:24

writer of all times you'd say

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shakespeare dante dostievsky or

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something like that

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shakespeare lived 500 years ago

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dante lived i don't know 700 years ago

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uh dostoevsky lived 180

3:37

150 years ago all these people

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were many years ago if i were to ask you

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who the greatest

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painter was so you'd say picasso

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and

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you know this one or that one or

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van gogh or or or whatever but

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the point is they're not necessarily

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contemporary

4:04

and that's a good thing in other words

4:06

when we read shakespeare or when we look

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at rembrandt's paintings

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they're somehow timeless they they go on

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forever and so we don't have to

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constantly update them

4:16

in contrast to art

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literature ethics and things like that

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if i ask you when the best cell phone

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was made

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i can tell you right now it was made

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this year

4:29

okay if i asked you when the best

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automobile made the fastest automobile

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or the fastest train or the

4:36

best rocket ship it was made recently

4:39

okay so we we have this

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difference this major difference between

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art literature philosophy ethics

4:51

okay which is

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in some sense timeless but it doesn't

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really build on itself there are

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different

4:58

things in fact in some sense art and

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literature

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in order to be recognized it has to be

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different than what it was before

5:06

okay it has to be built different as

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opposed to that

5:10

in math science and technology they

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build on previous things if i want to if

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i want to

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write a book on on engineering i have to

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know what was done in previous things

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and i have to

5:22

add to it the latest developments the

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newest developments

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okay now by the way it goes in ethics

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too

5:31

if you read the bible you'll see what

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what's what's you know

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what's going on let's just say the book

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the first

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the book of genesis it's a lot of

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brothers fighting brothers

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it's a lot of people fighting people

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parents worrying about children things

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didn't change that much

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in human nature okay as opposed to that

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things change a lot in science and

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technology

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now if you're an art major or something

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you say no no no

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they do change you know they they do

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build on each other for example

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if you want to become an a portrait

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artist you have to study what was done

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before and then you can you make

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predictions

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but that's more about technique rather

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than art

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beauty or something like that i don't

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want to get into that i don't want to

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argue the point but

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i um and i usually do argue the point

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when i'm in front of students but but i

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don't want to do that now

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so i want to talk about this increasing

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technological advances because of that

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increasing technological advances

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science has advanced and has gotten to

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the point where it can

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where it can see its own boundaries okay

6:46

it can say oh we can do this but we

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can't do that

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oh we can go ahead and do that and we

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can't do this

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et cetera et cetera okay and so that's

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what this class is all about

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because science is advanced in many

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things

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we're going to do that so we're going to

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see this in literature

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in in in language we're going to talk

7:06

about philosophy we're going to talk

7:08

about

7:08

infinity we're going to talk about

7:10

computers a lot we're going to talk

7:12

about

7:12

science we're going to talk about

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mathematics this class covers a lot of

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these different topics and in all of

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them we're showing some type of

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limitation

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okay so i'd like to show you how these

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limitations

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are found that we're going to talk about

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again this is chapter one this is like

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an introduction to the whole book

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so i want to do it basically we're

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trying to show

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limits

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limits of what can be done and what

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cannot be done

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and so we're going to do that now one of

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the primary

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ways of showing limits is what's called

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paradoxes

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and i'd like to go through that

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okay

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a paradox now there are a few different

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definitions of a paradox

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and we're going to go through those

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definitions but we're only going to use

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one of those definitions

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but just for completeness sakes i'd like

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to go through all of them

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and show them what they are

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okay so the word paradox

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dox's thought orthodox heterodox

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taxes thought and paradox means parallel

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a long regular thought it's kind of

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not really irregular so let's go through

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three

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definitions of paradox and again we're

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only going to be interested in one of

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these definitions but it's

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a nice way of looking at this first

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definition

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a seemingly

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contradictory

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statement

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a seemingly contradictory statement

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so a paradox is something that seems to

9:20

be wrong but actually it could be

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right okay let me give you an example it

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is more tiring to

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stand than to walk okay

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now that seems to be wrong because

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obviously when you're walking you're

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moving

9:34

more muscles et cetera et cetera but it

9:37

turns out that it's

9:38

actually true you cannot stand for three

9:40

hours straight you can walk for three

9:42

hours straight you have walked for three

9:44

hours straight but you can't stand in

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one place for three hours straight

9:47

okay so that's an interesting statement

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okay a seemingly contradictory statement

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number two

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another definition of the word paradox

9:57

okay

9:58

a statement

10:03

contrary to

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received

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opinion

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in other words if everybody agrees with

10:18

one particular thing

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then if you're saying something that's

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different then

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it's a paradox in some sense okay the

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word is not really used like that

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let me give you an example but again we

10:28

don't talk about politics in this class

10:30

george w bush was a great president okay

10:34

most people many people

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would disagree with that but that's fine

10:41

okay many people would disagree with

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that but that's fine

10:44

but that's an example of a paradox okay

10:48

let's do the third definition

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of the paradox and this is going to be

10:52

closer to what we say

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let's put the third definition into two

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parts

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okay 3a an

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assertion

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that implies

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a contradiction

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through

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and in valid

11:32

deduction

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an assertion that implies a

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contradiction through an invalid

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deduction let's write it out this way

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assertion

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arrow contradiction

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okay but what you get from the assertion

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to the contradiction

11:59

is not a valid way of doing it okay

12:05

now i'd like to give you an example of

12:08

this

12:10

okay and the example is an old trick

12:12

which is actually quite clever if you've

12:14

never seen it before

12:15

once you've seen it and you know the

12:17

trick you find it boring but that's okay

12:19

okay so this is a nice old trick so i'd

12:22

like to prove to you that one is equal

12:24

to two

12:26

okay well we'll do this this is probably

12:28

the most

12:29

math in this class but it's worth seeing

12:32

consider the following

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i'm going to do math this is nothing

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more than 9th grade math you've seen

12:39

this before

12:40

you have variables a and b

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let's assume a is equal to b

12:46

okay we can set any variables equal to

12:49

anything else

12:50

if a is equal to b then a squared is

12:53

equal to

12:54

a times b a squared is equal to a times

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a

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if one of the a's is equal to b we could

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set it a times b

13:02

nothing wrong next a

13:05

squared minus b squared

13:10

okay what's that well

13:16

following this line this becomes a

13:20

b minus b squared

13:27

okay nothing wrong with that now in

13:30

ninth grade

13:31

we know what to call this this is called

13:33

the difference of two squares

13:35

so i'm going to write it as a difference

13:36

of two squares you do this in ninth

13:38

grade

13:39

this is a plus b times

13:43

a minus b equals

13:46

pull out the b i'm going to factor the b

13:49

from this

13:50

i'm left with a minus b let's just

13:53

make sure a times b is a b

13:56

minus b squared that's minus b squared

14:00

a let's do this foil i think it's called

14:02

a times a is a

14:03

squared plus b minus b is minus b

14:06

squared and the other two terms cancel

14:08

each other out

14:10

okay great so again

14:14

i start off with this i show this is

14:16

equal to this

14:17

i rewrite this this way

14:20

i rewrite this this way and now

14:23

i simply divide by a minus b a

14:27

minus b this cancels out with this

14:30

if you do it to one side of the equation

14:32

you got to do it to the other side of

14:33

the equation

14:34

a minus b this cancels out with this i'm

14:37

left with

14:38

a plus b is equal to

14:41

b now remember a is equal to b

14:45

so we have b plus b

14:48

is equal to b another way of saying that

14:51

is

14:51

two b is equal to one b

14:56

and divide both sides by b b

14:59

b cancel out cancel out and i'm left

15:03

with

15:03

two is equal to one

15:10

that's it finished i proved 2

15:13

is equal to 1. okay so i started off

15:17

with an assertion

15:18

and i proved the contradiction by the

15:19

way 2 is not equal to 1. there's no way

15:22

in the world we can do 2 is equal to 1.

15:24

okay that's a contradiction it just

15:26

doesn't make sense if you don't believe

15:28

me let me do your taxes for you

15:30

okay two is equal to one okay now

15:34

what's wrong with this it might be an

15:36

idea to pause the camera for a minute

15:38

and try to figure out what's wrong with

15:39

this

15:40

i you can go this way 2 is equal to 1

15:43

then 2b is equal to 1b

15:45

b is b plus b is equal to b change the a

15:48

to b

15:49

you can get the whole thing the other

15:51

way okay

15:53

look at it for a minute and try to

15:54

figure out what's wrong with it

15:56

okay now i'll tell you what's wrong with

15:59

it

16:01

if a is equal to b then a minus b

16:04

is equal to zero you're dividing by zero

16:07

here

16:08

you're not allowed to divide by zero

16:10

there's no way in the world you're

16:12

allowed to divide by zero it's just

16:14

not it's not legal when you divide by

16:16

zero you get contradictions

16:18

and that's bad things that's why this is

16:20

called an invalid deduction

16:23

invalid deduction not legal it's not

16:26

it's not a legal deduction

16:30

okay so this is an example of an invalid

16:33

deduction

16:34

we did something that was not good in

16:36

mathematics

16:37

not legal and we got a strange

16:39

conclusion

16:41

and that doesn't make a is equal to b

16:43

wrong it just

16:44

we weren't allowed to do that thing okay

16:46

good

16:47

let's go further well before i go

16:50

further i got to tell you a cute joke

16:52

there was a philosopher his name was

16:54

bertrand russell bertrand russell was

16:56

giving

16:56

a talk in front of a lot of people a

16:59

popular talk and he said

17:00

in logic if you start off with a bad

17:02

premise if you start off with a false

17:05

thing you can prove anything

17:08

and somebody said to him you mean if 5

17:11

is equal to 4

17:12

then i can prove i'm the pope

17:15

just out of the thin air he said this

17:18

and bertrand russell said like this

17:20

supposedly he did this instantaneously

17:22

he said five

17:24

is equal to four subtract three from

17:27

both sides

17:29

minus three minus three that's equal to

17:32

five minus three is two four minus three

17:35

is

17:35

equal to one two is equal to one

17:39

two different people you and the pope

17:41

are really the same

17:43

one person

17:52

anyways it's a nice cute joke great

17:55

so this is 3a

17:58

a definition of a paradox okay

18:02

but it's not really the one we're going

18:03

to be interested in we're going to be

18:05

interested in another type of paradox

18:10

i'm going to call it 3b i can do this

18:13

you can't you have to rewrite it it's an

18:15

assertion that implies a contradiction

18:17

through a valid deduction

18:21

okay i'm going to cross out the bad

18:23

arrow

18:24

because that was invalid and i'm going

18:26

to do

18:27

a good arrow and the point is as follows

18:33

this is the type of paradox that we're

18:35

going to deal with for the rest of the

18:36

semester every single day of the rest of

18:38

this month every single class of the

18:39

rest of the semester we're going to deal

18:40

with such a paradox

18:42

the point is as fellows if you make an

18:44

assertion

18:45

and you follow legal rules and you get a

18:48

contradiction

18:49

then you've got something wrong with

18:50

your assertion there's something wrong

18:52

with that assertion

18:54

if you can do that okay so

18:58

by the way we just saw this a second ago

19:00

if you assert

19:01

that five is equal to four you're going

19:03

to get a contradiction

19:04

okay five is not equal to four you're

19:07

going to get a contradiction

19:09

okay so you cannot do that we're going

19:11

to see this over and over again

19:13

um such an example like this over and

19:16

over again

19:17

this is what i mean by a paradox and

19:19

paradoxes

19:20

are going to be our main staple

19:23

in this class okay

19:27

okay let me just say in another way

19:30

what a paradox is is kind of like a test

19:33

to see if an assertion is true or false

19:37

okay so you make an assertion and if you

19:39

get a contradiction

19:41

you know it's false if you don't get a

19:43

contradiction then you know it's okay

19:45

okay now in math they have such things

19:48

it's called the reduction

19:50

uh proof by contradiction and then

19:51

philosophy also reduction of

19:53

sodium it's called okay these are two

19:56

other ways of saying the same thing

19:58

basically these are tests to see if the

20:01

assertion is correct

20:03

we're going to go through many different

20:04

examples i'm going to show assertions

20:06

are not correct

20:07

okay great let's go on

20:14

okay so i want to go back to my

20:18

chart of how we do things the purpose of

20:22

this class is to talk about

20:23

limits okay and the way we're going to

20:26

get limits

20:27

are many ways we're going to get

20:30

paradoxes okay there are also special

20:34

types of paradoxes

20:36

of a similar type and these are called

20:39

self

20:41

referential

20:46

paradoxes

20:49

self-referential paradoxes these are

20:51

paradoxes we'll see four examples in the

20:53

next section

20:55

of self-referential paradoxes they are

20:57

paradoxes that come with

20:59

things that can deal with themselves for

21:01

example

21:02

this sentence is false that's a sentence

21:06

talking about itself when you have such

21:08

a self-referential paradox

21:10

you have you can get problems you can

21:13

get contradictions

21:15

and so we have to be careful with them

21:17

we'll talk more about those

21:18

in a little bit okay so again we're

21:21

talking about limits in this class

21:23

a lot of the limits come from paradoxes

21:25

there are special types of paradoxes

21:27

called self-referential paradoxes

21:29

there are also other types of limits

21:31

that we're going to get to

21:34

i call these piggyback

21:39

piggyback we can piggyback one limit off

21:43

another let me give you an example

21:45

okay if i'm teaching on the third floor

21:49

if i walk up

21:50

three flights of steps sometimes i'm

21:53

sorry

21:53

if when i walk back sometimes when i

21:56

walk up three fights of steps

21:58

i huff and puff afterwards for a few

22:00

minutes

22:02

then i calm down and i start teaching

22:04

okay

22:05

well if i have a hard time getting to

22:07

the third floor

22:08

when i'm teaching then getting to the

22:10

fourth floor

22:12

would be even harder okay would be even

22:15

harder i would most definitely

22:18

huff and puff if i walk up to the fourth

22:20

and fourth floor

22:22

before teaching okay so what that does

22:25

is it takes the limit that you have

22:27

already and then you try to do something

22:29

even harder

22:30

then for sure it won't be able to do

22:32

we're going to see many different

22:33

examples of that

22:34

especially in chapter five

22:37

okay so those are other ways of finding

22:40

country

22:42

limits okay now we've been talking a lot

22:45

about contradictions

22:46

i want to bring in something about

22:52

contradictions

22:58

okay contradictions can happen in the

23:01

physical world

23:03

okay they can happen in a physical world

23:05

a thing

23:06

an object cannot have a property and not

23:09

have that property that's what a

23:10

contradiction is

23:12

so we can't say that this is white and

23:14

it's not white

23:15

it's either white or it's not white but

23:17

you can't be both

23:19

okay um

23:23

no i can't say that today is tuesday and

23:25

it's not tuesday

23:27

it is either tuesday or it is not

23:29

tuesday one or the other

23:31

right now right here it's either tuesday

23:33

or it's not tuesday

23:34

the physical world doesn't have

23:36

contradictions

23:37

this cannot be water and not water okay

23:40

we know exactly what water is we know

23:43

how to define water

23:44

and i can't make such a there can't be

23:46

such a contradiction

23:48

right so

23:54

the physical world physical universe

24:02

cannot have contradictions in contrast

24:06

in contrast there are contradictions

24:09

where well in your brain

24:13

in your language in your opinions

24:16

you're going to have contradictory

24:18

opinions there's a lot of contradictions

24:20

in politics because people have

24:22

different opinions of what's going on

24:24

and people have different ideas of

24:25

what's going on that's legitimate

24:28

okay that's legal okay but even within

24:32

yourself you have contradictions

24:34

okay for example you want another piece

24:37

of cake

24:38

but you also want to remain thin you

24:41

want to

24:42

not go to school but you also want a

24:44

degree and you want to get a good grade

24:46

can't have both of those you have both

24:48

you want to lie in bed all day

24:50

but you also want to get a good grade

24:52

you can't do that

24:53

that doesn't work okay that's

24:55

contradictory

24:56

because if you don't do the homework or

24:59

you don't study

25:00

you don't read the book you're going to

25:01

fail the course and that's going to be

25:03

bad

25:04

okay so in contrast to the universe

25:09

in mind and what's connected to mind

25:14

language language comes from your mind

25:17

mind and language

25:21

mind and language has contradictions

25:24

again

25:25

you can say the statement i want to lie

25:27

in bed all day and i don't want to go to

25:28

school

25:29

but i want a good grade that's a

25:31

contradictory statement

25:33

can't happen so you can have

25:36

contradictions

25:37

here you can't have contradiction there

25:41

are no contradictions here

25:42

but in the human mind is not a perfect a

25:45

perfect

25:46

thing and so there are contradictory

25:48

contradictions in your mind

25:49

there are contradictions in your

25:51

language you have contradictions in your

25:53

language

25:54

however there is a part

25:58

of this a mind and language

26:02

where we don't allow contradictions okay

26:05

we do not allow contradictions it's a

26:08

part of language and a part of mind

26:10

it's called science

26:13

and math

26:17

science and math is a way part of

26:20

science and math

26:20

is a way to describe the physical

26:22

universe you

26:24

better make sure that science and math

26:26

doesn't have a contradiction

26:28

because otherwise it's not going to

26:29

describe the physical universe

26:31

you have to be able to make that

26:33

distinction you say look

26:35

this can have contradictions therefore

26:39

this science and math which is part of

26:41

mind and language

26:42

science is made up by human minds if the

26:45

language is expressed by human minds

26:47

but it can have contradictions because

26:50

it's going to be predicting that

26:52

we saw this 10 minutes ago when we

26:54

talked about dividing zero

26:56

you can divide you can divide any two

26:58

numbers whatsoever

27:00

except for one you can divide numbers by

27:02

14 you can divide numbers by 14.3

27:05

you can divide numbers by negative

27:08

4.13872

27:10

i don't care what number but there's

27:11

only one number that you can't divide by

27:13

what zero why why can't you divide by

27:17

zero

27:17

because if you divide by zero you will

27:19

get contradictions

27:21

let me just show you zero times

27:24

four is equal to zero times five

27:28

that's a true statement zero times four

27:31

is equal to zero times five

27:33

they're both equal to 0. so that's a

27:34

true statement now if i was able to

27:36

divide by 0

27:40

i'd get 4 is equal to 5. that's a

27:43

contradiction

27:44

you can't have a contradiction okay

27:48

four apples is not equal to five apples

27:50

so you can't do that

27:52

so when you're in third grade they teach

27:55

you already

27:56

look you don't want contradictions in

27:58

your math you don't want contradictions

28:00

in your science

28:01

you can't say water is h2o and h3o

28:05

that's not true okay those are two

28:07

different things

28:08

okay water is h2o that's a fact that's

28:12

part of science

28:13

e equals m c squared that's einstein i

28:16

don't know what it means

28:17

but it's part of science it's either

28:20

true or not true

28:21

but it's definitely not contradictory

28:24

okay so you cannot have contradictions

28:28

here you cannot have contradictions here

28:31

you can have contradictions here

28:34

and we're going to see more of this when

28:36

we go further up

28:39

okay great

28:53

okay just want to say one more

28:57

thing at the end of the chapter i bring

29:00

in

29:01

that one should try to define reason

29:04

okay this book is called the outer

29:06

limits of reason

29:08

okay and the class is called out of

29:10

minutes

29:11

our limits of reasoning so it would be

29:13

light not

29:15

it would be very nice to have a

29:16

definition of what

29:18

reason is okay now i can tell you what

29:22

is in reason and what is out of reason

29:24

okay science

29:25

math physics biology chemistry all those

29:28

are reason okay things that have

29:32

opinions

29:33

i'm not sure about politics is

29:35

definitely not reason

29:36

okay um but it would be

29:40

poetry art is not reason

29:43

there are other things there are other

29:44

important things that human beings do

29:46

but it would be nice to come up with a

29:48

definition of reason

29:50

now i come back to that in chapter 10

29:53

but i want you to keep that question in

29:55

your mind throughout the class

29:57

because we're gonna try to come up with

29:59

a good definition of what reason means

30:02

okay now i'd like to discuss one last

30:05

thing before i let you go

30:07

and that is this concept of

30:11

you have an assertion and you get a

30:12

contradiction that's very very simple

30:15

that's very very similar to something

30:17

else that we commonly know

30:19

if you ever read a joke you always see

30:22

the joke starts off very very typical

30:25

very

30:25

sane very normal the punch line of a

30:29

joke

30:29

is always that boom that point that's

30:33

a contradiction that's strange that's

30:34

weird okay

30:36

and i do three jokes in the book

30:39

but you could do this with almost any

30:41

joke a joke always starts off

30:44

saying rational but then you take it

30:47

you follow the reasoning and you come to

30:49

a crazy conclusion

30:50

so here's a nice joke woody allen he's a

30:53

director

30:54

or an actor cheated on his metaphysics

30:57

exam

30:58

okay cheated on his metaphysics so woody

31:01

allen went to school he went to nyu

31:04

he this is a joke whatever but he

31:06

cheated on his exam how do you cheat on

31:08

exam

31:09

you look into your friends your

31:12

neighbor's

31:12

paper but it was a metaphysics exam an

31:15

exam that dealt with heavy

31:17

you know death life soul etc etc

31:21

so woody allen cheated on his

31:24

metaphysics exam

31:25

by looking into the soul of the boy

31:27

sitting next to him

31:30

okay so again it starts off with a

31:32

typical thing it's terrible to

31:34

analyze a joke i agree but we have to do

31:37

it because we want to show

31:38

that this is very similar to what we

31:40

call the paradox

31:41

start off very similar very nice he

31:43

cheated on his exam had it each year on

31:45

an exam

31:45

well he looked into something what did

31:48

he look into

31:49

the soul of the boy sitting next to him

31:51

okay

31:52

obviously he didn't okay stephen bright

31:56

stephen wright is a comedian he says

31:59

he would kill to get a certain price

32:02

he would kill for the nobel peace prize

32:05

okay again

32:07

saying oh i'd kill to win the new york

32:09

city marathon that's a funny joke

32:11

whatever

32:12

or oh i'd kill to win that medal et

32:14

cetera et cetera that's typical

32:16

but here he's he would kill to win the

32:19

nobel peace prize

32:20

that's a prize made specifically for

32:22

people so who

32:23

do noble things don't you know save

32:26

people from dying

32:27

but again that's the joke but again it

32:29

starts off normal

32:31

and then it goes follows the reasoning

32:34

and then it gets to a crazy conclusion

32:36

groucho marx didn't care to belong to

32:38

any club

32:40

that what type of club wouldn't groucho

32:43

marx want to belong

32:44

any club that would have him as a member

32:47

now that's

32:48

cute okay i wouldn't belong to that club

32:50

that's a typical thing

32:51

said but groucho marx said i wouldn't

32:53

belong to any club that would have

32:55

me as a member by the way that's not

32:57

only a joke that's a self-referential

32:59

joke

33:00

that's a joke that groucho marx says and

33:03

it affects himself the very fact that

33:05

they will let him into the club

33:07

means that he will not be in the club

33:10

okay it's another thing also puns are

33:13

the same way

33:14

a pun is a joke that comes from

33:18

using one word in two different ways you

33:20

ready have you heard about the guy whose

33:22

whole left side was cut off

33:26

he's all right now

33:29

he's all right now okay

33:33

so a person's left side is cut off

33:36

not very funny but whatever okay and

33:39

then we're using the word

33:40

right in two different ways right as in

33:42

the right side of his body is all right

33:44

he's all right

33:45

or he's okay obviously he's not okay but

33:49

it's a cute little line but again it

33:51

starts off

33:52

his whole body is fine it starts off

33:54

telling an interesting thing

33:56

and then it goes and it goes crazy okay

33:59

he's all right now

34:01

okay i'm reading a book about

34:03

anti-gravity

34:04

it's impossible to put down okay

34:07

this is a typical thing you say oh i'm

34:09

reading this book about this and this

34:11

okay it's impossible to put down that's

34:13

very cute

34:14

but anti-gravity that means you can't

34:16

keep it down okay next

34:18

did you hear about the paradox

34:21

dr shapiro and dr miller pair

34:25

of doctors paradox

34:28

again a pun that's used

34:32

to make a the the

34:36

the the end of the joke

34:39

is funny because it's it's a

34:41

contradiction

34:42

in some sense it's it's a funny

34:44

contradiction anyways

34:46

so that's the beginning of the book

34:50

okay and in the next tape

34:53

we're gonna we're gonna in the next tape

34:56

we're gonna

34:57

go on and um start

35:01

talking about language paradoxes and

35:04

what we learn about the limitations of

35:05

language

35:06

okay have a wonderful day

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